mathematical competence thesis

ORIGINAL RESEARCH article

Comparison between performance levels for mathematical competence: results for the sex variable.

$\r\nRamn García Perales*$

Department of Pedagogy, Faculty of Education of Albacete, Castilla-La Mancha University, Albacete, Spain

Schools promote all-round education for each of their students. This requires teachers to work on all of the possibilities offered by a subject, including mathematical ability. This process of adjustment and individualization is essential for students who have excellent performance or aptitudes. This study uses an ex post facto, descriptive and quantitative research methodology to examine the results of giving the online version of the Evaluation Battery for Mathematical Ability (BECOMA On) to 3795 5th-year primary school students. The sample was selected from 147 Spanish schools from 16 autonomous regions and 2 autonomous municipalities. Three levels of performance were identified, 3 being the highest, and different statistical indices were calculated for each of them. The results were also analyzed according to sex, with statistically significant differences in the highest performance level. In addition, the study highlighted a diagnostic gap in the identification of higher capacity students, a pending challenge for education systems for the educational inclusion of all students.

Introduction

Educational processes nowadays are characterized by homogeneity and multidimensionality, which makes it difficult to deal with the diverse potentials, needs, and interests in the classroom. Occasionally, there may also be a lack of diagnostics that would allow for the modified, individualized educational responses which are common for students who are highly capable and have high aptitudes ( García-Perales and Almeida, 2019 ). Discovering and working on talent should be a basic objective in an advanced society, and generalizing the detection process and targeting it at the entire school population would be an interesting way of achieving that aim. This study presents an example of that in the field of mathematics. The process allows various situations to be addressed flexibly based on specific student characteristics in order to encourage each student’s cognitive abilities to the highest level.

Mathematics is important because it is applicable in daily life and in solving various types of problems ( Cázares et al., 2020 ), as well as having interdisciplinary connections to other parts of the curriculum ( Gilat and Amit, 2013 ). This generalization to routine everyday contexts is a fundamental aspect of being included as a key skill in education ( Méndez et al., 2015 ). In the case of mathematics, it is included in maths competency and basic competencies in science and technology. Maths competency is defined as “students’ ability to formulate, apply, and interpret mathematics in various contexts. It includes mathematical reasoning and using mathematical concepts, procedures, facts, and tools to describe, explain, and predict various kinds of phenomena” ( Ministerio de Educación y Formación Profesional, 2019 , p. 17). This definition provides a key aspect of maths evaluation, the measurement of mathematical ability in a broad range of contexts, with a view to highlighting the importance of generalizing what has been learned to a wide variety of situations, familiar or otherwise. The search for constructive, committed, reflective citizenship is a fundamental premise of educational processes, aspects which maths teaching has a strong influence over ( Organization for Economic Cooperation, and Development, 2019b ). Maths competence has been evaluated in all six editions of the Program for International Student Assessment (PISA) every three years from 2000 to 2018.

The PISA assessments are a fundamental reference for evaluation. The fact that there is a large, worldwide sample for the PISA tests means that the conclusions are extremely important in the development of education policy. Its conceptual framework has been used in many studies ( García-Perales, 2014 ; Ferreira et al., 2017 ; Rodríguez-Mantilla et al., 2018 ; Fuentes and Renobell, 2019 ; Sason et al., 2020 ). The distinctive characteristics of PISA include ( Ministerio de Educación y Formación Profesional, 2019 ): seeking to guide educational policies, integration of the concept of competence in assessment, the important role of autonomous and lifelong learning, regular deployment, and sensitive international coverage. When interpreting results for each item, PISA uses Item Response Theory (IRT). In this regard, children’s answers are considered according to the child’s level of ability in mathematical competence, in other words, estimates of student performance focus on the type of mathematical tasks that they can solve correctly ( Ministerio de Educación y Formación Profesional, 2019 ). This means performance levels can be identified that allow each child to be placed on a continuous scale of competence for the measured construct ( Roderer and Roebers, 2013 ), showing the percentage of subjects in each level together with their distinctive characteristics, in this case for mathematical competence. This methodology was used with the BECOMA On, the instrument in the present study, in which three performance levels were set based on the scores.

Among the many conclusions from PISA relating to mathematics, reports have stressed that students’ interest in and enjoyment of this area is low, and even noted the presence of personal issues such as anxiety and lack of confidence, especially in girls ( Organization for Economic Cooperation, and Development , 2013; Mizala et al., 2015 ; Organization for Economic Cooperation and Development, 2019d ). Throughout the PISA assessments, boys have always had better results than girls in mathematical competence ( Ministerio de Educación y Formación Profesional, 2019 ), with sex being a predictor variable of mathematical performance ( Farfán and Simón, 2017 ; Fuentes and Renobell, 2019 ; Palomares-Ruiz and García-Perales, 2020 ). Biological and social factors may act in an interrelated way ( Chamorro-Premuzic et al., 2009 ; Muelas, 2014 ), including intellectual capacity ( Schillinger et al., 2018 ), complex mathematical reasoning ( Desco et al., 2011 ) and other factors of an individual nature with an impact on the mathematical learning process ( Song et al., 2010 ; Marsh and Martin, 2011 ; Rodríguez and Guzmán, 2018 ), school ( Carey et al., 2016 ; Dowker et al., 2016 ; Schillinger et al., 2018 ), and family ( Pelegrina et al., 2002 ; Ferreira et al., 2017 ; Rodríguez-Mantilla et al., 2018 ). Analyzing students’ mathematical performance according to sex is one objective of the present study.

The results for mathematics performance in the 2012 PISA tests—the most recent that evaluated mathematics preferentially—and the 2018 tests—the most recent evaluation—are summarized briefly below. In PISA, student results are ranked in seven performance levels: below level 1, 1, 2, 3, 4, 5, and 6. In PISA 2012, Spanish boys scored an average of 492 points and Spanish girls averaged 476 points ( Ministerio de Educación, Cultura y Deporte, 2014a ). In PISA 2018, Spanish boys averaged 485, while the girls averaged 478. In both cases, the differences between sexes were statistically significant ( Ministerio de Educación y Formación Profesional, 2019 ). Examining these differences more closely, the results for the highest levels 5 and 6 stand out; in PISA 2018, 8% of boys and 5.50% of girls were in one of these two levels. Other studies have also indicated these differences between the sexes in performance and higher ability ( Llor et al., 2012 ; García-Perales and Almeida, 2019 ; Ministerio de Educación y Formación Profesional, 2020 ; Palomares-Ruiz and García-Perales, 2020 ). In contrast, 24.60% of boys and 24.80% of girls were in the lowest levels—1 and below 1—with no statistical significance between the sexes ( Ministerio de Educación y Formación Profesional, 2019 ). As Figure 1 shows, at the higher performance levels the differences between the sexes begin to be more significant, with more boys than girls in those higher levels of mathematics performance (something which is also seen in the OECD average). This is an issue that raises concerns about the potential consequences for future academic and professional choices.

Figure 1. Performance levels and gender in PISA 2018 for Spain and the OECD. Source: Ministerio de Educación y Formación Profesional (2019), p. 89.

Continuing to look at children with excellent performance in mathematics, in PISA 2012, 8% of Spanish students exhibited excellent performance (6.70% and 1.30% in the two top performing groups), similar figures to previous editions of PISA for mathematics skills, whereas the OECD average was 9.30% and 3.30% in the top two groups ( Instituto Nacional de Evaluación Educativa, 2013 ). In PISA 2018, 6% and 1% of Spanish students were in the top two groups, whereas the OECD mean was 9% and 2% respectively ( Ministerio de Educación y Formación Profesional, 2019 ; Organization for Economic Cooperation, and Development , 2019a , b , c ). This raises a fundamental question. In Spain do we not have high performing students? or is our own system not capable of identifying and cultivating them?

What makes a student highly capable at mathematics? PISA 2018, the most recent version, set out the following characteristics for achievement level 6 or higher for maths skills ( Ministerio de Educación y Formación Profesional, 2019 , p. 64):

“They know how to formulate concepts, generalize and use information based on their research and model complex problems, and they can use their knowledge in relatively atypical contexts. They can simultaneously relate different sources of information and representations, and switch between them flexibly. Students at this level have a high level of mathematical thinking and reasoning. These students can apply this comprehension, as well as their mastery of mathematical operations and symbolic, formal relationships to develop new approaches and strategies to address new situations. Students at this level can consider their actions, and precisely formulate and communicate their actions and thinking about their discoveries, interpretations, arguments, and adaptation to novel situations.”

Other research also influences the conceptualization of the most mathematically capable children ( Geary and Brown, 1991 ; Greenes, 1997 ; Sriraman, 2003 ; Rotigel and Fello, 2004 ; Almeida et al., 2008 ; Desco et al., 2011 ; Jaime and Gutiérrez, 2017 ; Kurnaz, 2018 ; Ramírez and Cañadas, 2018 ). Within the field of higher abilities, it is worth paying particular attention to the female population. For example, in Spain, the percentages diagnosed as highly able in school year 2018/19 varied considerably by sex, 65.06% of those identified were boys and 34.94% were girls ( Ministerio de Educación y Formación Profesional, 2020 ). Girls are a higher risk group among the highly able, the identification processes are more detrimental to them ( Kerr, 2000 ; Landau, 2003 ; Jiménez, 2014 ) and stereotypes abound ( Bian et al., 2017 ). In addition, even nowadays there are still inequalities in the socialization processes between the sexes ( Hadjar et al., 2014 ; Ministerio de Educación y Formación Profesional, 2019 ), and girls’ potentials are occasionally undervalued ( Pomar et al., 2009 ). UNESCO (2019, p.72) stated that “the disadvantaging of girls is not based on cognitive ability, but rather on the processes of socialization and learning they grow up with, which shape their identities, beliefs, behaviors, and life choices.”

There is research into maths competency indicating that boys tend to get better results ( Preckel et al., 2008 ; Llor et al., 2012 ; Instituto Nacional de Evaluación Educativa, 2013 ; Ministerio de Educación y Formación Profesional, 2019 ) despite both sexes receiving similar mathematics teaching from the beginning of schooling. Perceptions of and attitudes toward mathematics are particularly important ( González-Pienda et al., 2012 ; Mato et al., 2014 ; Ministerio de Educación, Cultura y Deporte, 2014b ; Preckel et al., 2008 ; Ministerio de Educación y Formación Profesional, 2019 ; Cueli et al., 2020 ; Palomares-Ruiz and García-Perales, 2020 ), girls can exhibit anxiety and lack confidence in this area ( Instituto Nacional de Evaluación Educativa, 2013 ; Rodríguez-Mantilla et al., 2018 ). It is essential to consider girls’ levels of attention or execution rates in approaching mathematical tasks ( Boaler, 2016 ; Farfán and Simón, 2017 ; Hattie et al., 2017 ; Rodríguez and Guzmán, 2018 ; Cueli et al., 2020 ), as well as other motivational and emotional factors ( Else-Quest et al., 2010 ; Rodríguez-Mantilla et al., 2018 ). Teacher training and practice must consider these discrepancies between aptitude and attitude toward mathematics ( Nortes and Nortes, 2013 ; Rico et al., 2014 ; Ursini and Ramírez-Mercado, 2017 ). This variable is a key determiner of educational success in any academic discipline. The more interested students are and the more they believe learning mathematics to be a useful source of knowledge, the better their performance will be ( Figueiredo and Guimarães, 2019 ). This becomes even more important when changing educational stages in the face of deteriorating attitudes toward learning ( Mato et al., 2014 ). Self-efficacy also influences educational development and is a key variable to consider in students’ individual adjustment in the area of mathematics ( Ruiz, 2005 ; Zalazar et al., 2011 ; Rosário et al., 2012 ). Better and deeper understanding of these attitudinal and motivational aspects is an essential challenge for mathematics teaching.

Understanding the dimensions that can have an impact on men’s and women’s educational paths is key and affects future academic and professional choices ( Hadjar et al., 2014 ; UNESCO, 2019 ; García-Perales et al., 2021 ). It is essential to try to extrapolate from research to answer the question; why is there a difference in the choice of scientific and technical careers between men and women? This study focuses on mathematics, although the same challenge applies to other disciplines such as Science, Technology and Engineering. The goal is to achieve an equal, equitable educational system that allows all students to meet the changing demands of the globalized 21st century society ( Ryu et al., 2021 ), regardless of gender, because there is currently a gender gap in these disciplines ( Kijima and Sun, 2020 ).

The objective of this study was to analyze the results in the BECOMA On from students in the three levels of mathematics achievement. In order to understand and conceptualize these levels of performance, the results were examined in relation to the participants’ sex.

Materials and Methods

The study used an ex post facto, descriptive, quantitative research methodology with the aim of describing the relationships that exist between groups of quantitative data from a series of modulating variables.

Participants

The study sample was made up of 3795 5th year primary school students, aged around 10-11 years old, from 16 regions in Spain. Each regional education authority selected the schools to participate voluntarily in the study, depending on the schools’ availability to participate and them having suitable technological tools for performing the study. Instruments were applied to class groups in their usual classrooms using online devices. The distribution of the sample by sex was 2002 boys (52.75%) and 1793 girls (47.25%).

The sample was grouped by levels of performance. Based on the results, 3 similarly sized hierarchical levels were set, with 1 being the lowest and 3 being the highest performance. The levels for the BECOMA On are shown in Table 1 .

Table 1. Performance levels in BECOMA On.

The mean level was 1.97 ( SD = 0.82), with asymmetry of.05, the distribution of the levels followed a symmetric curve, with kurtosis of -1.50, platykurtic distribution with negative excess kurtosis.

Mathematics competence was the main variable in this study. It was measured using the BECOMA On. As mentioned above, mathematics has a key role in educational processes, particularly because of its generalization to subjects’ daily lives, a fundamental aspect for effective, autonomous development in society. The other variable used was the participants’ sex, male (M) or female (F).

The BECOMA On is a battery that evaluates mathematical skills in 5th year primary schoolchildren online. It is made up of 30 items spread over 7 evaluation tests: Mathematical interpretation (Items 1-5; Statistics and Probability Dimension), Mental arithmetic (Items 6-11; Arithmetic Dimension), Geometrical properties (Items 12 and 13; Geometry Dimension), Logical numerical series (Items 14-19; Arithmetic Dimension), Discovering algorithms (Items 20 and 21; Arithmetic Dimension), Conventional units (Items 22-27; Magnitudes and Proportionality Dimension), and Logical series of figures (Items 28-30; Geometry Dimension). In establishing the content and evaluation indicators for the items in each dimension, Royal Decree 126/2014, of February 28, which establishes the basic curriculum for Primary Education, was used as a reference ( Ministerio de Educación, Cultura y Deporte, 2014c ). The instrument is structured as in Table 2 .

Table 2. Instrument structure.

Each item has a possible score of 0 (wrong), 1 (partially correct), or 2 (correct), giving a possible overall minimum score of 0 and a possible overall maximum score of 60. It takes 41 minutes to do the test. In terms of statistical validity ( Palomares-Ruiz and García-Perales, 2020 ), the instrument had a reliability index of 0.83 using Cronbach’s Alpha, and validity indices between.78 and.86 (content and construct). The Difficulty Index (DI) for each item was as follows:

As Table 3 shows, the battery had a moderate difficulty index (DI = 0.45) and appeared reactive to various levels of difficulty. Item 28 was the most difficult (DI = 0.09) while item 13 was the easiest (DI = 0.75). Item selection was judged by a group of 51 professionals in mathematics from various educational stages, giving an overall validity index for the instrument of 0.81 and a Kappa statistic of 0.82.

Table 3. Difficulty Index for items in the BECOMA On.

A month before the data collection period, staff at each of the participating schools were given a training course covering the differential characteristics of the battery, and what they had to consider when applying it, with instructions and monitoring times. Data was collected throughout February 2019 through the online application of the instrument.

Consent was obtained from each participating student’s parents or guardians for them to take part in the study, requested on the researchers’ behalf by the director in each school. Subsequently, a list of children with family authorization was kept by the educational administration in each Spanish region.

Before presenting the results according to the study objectives, the descriptive statistics are presented for each item in the instrument: mean, standard deviation, frequencies and percentages.

As Table 4 indicates, the level of difficulty can be analyzed according to the average results from each item. The easiest items were Items 4 ( M = 1.49, SD = 0.75), 5 ( M = 1.54, SD = 0.71), 7 ( M = 1.58, SD = 0.67), 13 ( M = 1.61, SD = 0.72), and 14 ( M = 1.63, SD = 0.65), and the most difficult items were 11 ( M = 0.74, SD = 0.84), 16 ( M = 0.81, SD = 0.77), 17 ( M = 0.80, SD = 0.76), 21 ( M = 0.82, SD = 0.89), and 28 ( M = 0.56, SD = 0.65). The mean for the battery set was 34.83 ( SD = 9.69). Figure 2 shows the item with the lowest difficulty level—number 14—and Figure 3 shows the item with the highest difficulty—number 28.

Table 4. Descriptive statistics of the items of the BECOMA On.

Figure 2. Item 14, the easiest item in the instrument in this study. Authors’ own work (2020).

Figure 3. Item 28, the most difficult item in the instrument in this study. Authors’ own work (2020).

In terms of asymmetry, negative scores predominated—21 of the 30 items—, in other words more values appeared to the left of the mean. In terms of kurtosis, almost all the values—27 of the 30 items and the total score—were negative, a platykurtic distribution with a lower concentration of results around the mean, an interesting aspect when analyzing different levels of performance according to the results.

The results are presented based on the study objectives, first the results in the BECOMA On for the three performance levels and then the descriptive statistics. Following that, each level is examined in relation to sex.

Table 5 shows the results in the BECOMA On for the three performance levels. The frequency and percentages for each performance level are given. There were 1319 students (34.76%) in level 1, 1263 (33.28%) in level 2 and 1213 (31.96%) in level 3.

Table 5. Frequencies and percentages for the performance levels for each item response.

Table 5 gives the totals for each level and response option. In the mean results for all items, 15.45% of the students were in level 1 and scored 0, 10.25% were in level 1 and scored 1, and 9.06% were in level 1 and scored 2; 9.09% of students were in level 2 and scored 0, 9.63% were in level 2 and scored 1, and 14.56% were in level 2 and scored 2; 3.99% of the students were in level 3 and scored 0, 6.97% were in level 3 and scored 1, and 21.01% were in level 3 and scored 2. Level 1 and 2 student responses were more erratic and reflected a clear difference between levels. To determine statistically significant differences, Table 6 shows the means, standard deviations and the results of the ANOVA test.

Table 6. ANOVA Test comparing performance levels.

The students in level 1 had a mean score of 24.49 ( SD = 4.67), in level 2 the mean score was 34.93 ( SD = 2.58), and in level 3 it was 45.97 ( SD = 4.76). The students in level 3 had higher mean scores in all items. Furthermore, the differences between levels were statistically significant in all items, p < 0.001, with the level 3 students scoring higher. To complete the characterization of these three groups of students, another variable, students’ sex, was used for comparison between levels.

The sex distribution of the original sample of 3795 students was 2002 boys (52.75%) and 1793 girls (47.25%). The mean score in the instrument for boys was 35.18 ( SD = 10.08) and for girls it was 34.44 ( SD = 9.22), with a p -Value < 0.05. To more closely examine the significance of the differences between the sexes, the results were analyzed according to each level of performance. The frequencies and percentages for each sex in each of the three levels are given below.

At level 1 performance, there was little difference in the proportions for each score ( Table 7 ): 23.12% of the responses were boys scoring 0, 15.68% were boys scoring 1, and 13.21% were boys scoring 2; 21.33% of the responses were girls scoring 0, 13.80% were girls scoring 1, and 12.86% were girls scoring 2. Looking at the frequencies of scores of 2 for both sexes, there were differences. There were more boys scoring 2 in items 15 (boys 5.69% and girls 3.26%), 20 (boys 17.44% and girls 14.94%), 22 (boys 25.78% and girls 22.52%), and 27 (boys 17.66% and girls 13.34%). More girls scored 2 in items 1 (boys 20.55% and girls 22.21%), 7 (boys 20.70% and girls 23.28%), 8 (boys 12.66% and girls 14.25%), and 12 (boys 23.43% and girls 25.02%).

Table 7. Frequencies and percentages by sex from students with level 1 performance.

For the level 2 students, the frequencies and percentages for each response option were as follows ( Table 8 ):

Table 8. Frequencies and percentages by sex from students with level 2 performance.

At level 2 the results were similar to level 1 in terms of sex, with small differences between boys and girls. 13.53% of responses were boys scoring 0, 14.98% were boys scoring 1, and 21.84% were boys scoring 2; 13.78% were girls scoring 0, 13.95% were girls scoring 1, and 21.91% were girls scoring 3. Looking at the frequencies of scores of 2 for each item, there were also differences between the sexes. More boys scored 2 in items 15 (boys 16.94% and girls 9.74%), 17 (boys 8.71% and girls 5.38%), 18 (boys 16.31% and girls 12.67%), and 19 (boys 15.04% and girls 11.80%). More girls scored 2 in items 7 (boys 35.79% and girls 39.75%), 8 (boys 26.68% and girls 30.64%), 23 (boys 21.06% and girls 25.65%), and 30 (boys 22.33% and girls 27.40%).

For the level 3 students, the frequencies and percentages for each response option were as follows ( Table 9 ):

Table 9. Frequencies and percentages by sex from students with level 3 performance.

At level 3 there were greater differences between the sexes, with boys scoring higher than girls. 6.78% of responses were boys scoring 0, 11.89% were boys scoring 1, and 37.38% were boys scoring 2; 5.70% of responses were girls scoring 0, 9.91% were girls scoring 1, and 28.33% were girls scoring 2. Looking at the scores of 2 for each item, there were large differences between the sexes. This was notable in items 15 (boys 39.57% and girls 20.86%), 19 (boys 34.05% and girls 20.61%), 22 (boys 53.01% and girls 39.32%) and 27 (boys 44.44% and girls 31.90%). At this level, the differences were smaller in items 3 (boys 34.46% and girls 29.51%), 26 (boys 23.99% and girls 18.14%), 28 (boys 7.67% and girls 6.92%), 29 (boys 25.47% and girls 23.50%) and 30 (boys 39.24% and girls 35.37%). There were no items in which more girls scored 2 than boys.

Once the frequencies were established for each level by sex, a t -test was performed to determine whether there were statistically significant differences according to sex. The results are given in Table 10 .

Table 10. t -Test by sex between performance levels 1, 2, and 3.

As Table 10 shows, there were statistically significant differences at p < 0.05. This significance was due to an unequal frequency between the sexes at performance level 3, where there were 680 boys (17.92%) and 533 girls (14.04%). In the other two levels, 1 and 2, the results were more similar, level 1 included 686 (18.08%) boys and 633 (16.68%) girls, while level 2 included 636 boys (16.76%) and 627 girls (16.52%). According to statistics from the Ministry for Education ( Ministerio de Educación y Formación Profesional, 2020 ) for non-university education in school year 2018/19 (the most recent available data), of the 35494 students identified as highly capable, 23092 were boys (65.06%), and 12402 were girls (34.94%). This reflects a continuing disparity between the sexes in the identification of highly capable students, with the diagnostic process being detrimental to girls. This indicates an inequality in education and the need to examine causal factors more deeply.

Society’s scientific and technological progress requires highly qualified professionals ( Frey and Osborne, 2017 ) as there are constant innovations and shifting requirements ( Macià and Garreta, 2018 ). Schools are fundamental in developing students’ talents ( Mandelman et al., 2010 ). The most recent Spanish education laws address educational needs, and addressing and adapting to students’ needs from the very beginnings of schooling is fundamental. Equality and innovation promote quality and social development ( Organization for Economic Cooperation, and Development, 2019a ), and evaluation and research help monitor them in order to establish educational policies ( Schleicher, 2018 ; Harju-Luukkainen et al., 2020 ).

This study focused on the analysis of mathematics skills in the three groups of students identified by performance following the application of the BECOMA On, an instrument with high indices of reliability and validity. Understanding the potential of the students in these three levels is of significant social and educational interest and understanding the complexity of the mathematical approaches and strategies they use in problem solving is fundamental ( Jaime and Gutiérrez, 2017 ). Initially, the results were as expected, students in the highest level—3—demonstrated better results and assessments than students in levels 1 and 2. What is interesting is the presence of various statistically significant differences.

Just over a third, 1319 students (34.76%), were identified as belonging to performance level 1, 1263 (33.28%) to level 2 and 1213 (31.96%) to level 3. Comparing the results of these three groups, statistically significant differences were found, p < 0.001; level 3 students had higher scores in all of the items in the instrument. Level 3 students were the most capable in mathematics. It is important to consider the processes for identifying these highly capable students. From time to time, unfortunately, their potentials, needs, and interests seem to be neglected in the learning and teaching process, and occasionally there are various serious adaptation problems ( Pomar et al., 2009 ; García-Perales and Almeida, 2019 ).

To complete the characterization of these three groups of students, the levels were compared in relation to students’ sex. In the study, 52.75% of the participating sample were boys and 47.25% girls. In performance levels 1 and 2, there were few discrepancies in performance between the sexes, with varying differences in favor of one sex or the other. However, at level 3, there were greater differences, and it was the boys who had the highest scores in all items. Boys in level 3 had 6.78% of responses scoring 0, 11.89% scoring 1, and 37.38% scoring 2. For the girls in level 3, the percentages were 5.70%, 9.91% and 28.33% for scores of 0, 1, and 2 respectively. This resulted in statistically significant differences, p < 0.05, since at performance level 3 or higher, there were 680 boys (17.92%) compared to 533 girls (14.04%). This reflects a continuing disparity between the sexes in the higher achievement levels for Mathematics, also seen in other research ( Baye and Monseur, 2016 ; Hyde, 2016 ; Ministerio de Educación y Formación Profesional, 2019 ), demonstrating an inequality in education and the need to examine causal factors in depth ( Calvo, 2018 ).

In short, the instrument used is functional and original because it establishes a relationship between assessment and mathematical and digital skills. Its close connection with the Spanish school curriculum for the 5th grade of primary education gives it a valuable practical component for use in developing educational practices. The detection of learning needs and potentials, in this case for mathematics using online evaluation, is key because of mathematics’ instrumental and interdisciplinary nature, and it opens up an interesting path for the generalization and application of such instruments.

Schools must develop educational practices that allow inclusive, quality education for all ( Franco et al., 2017 ; Arnaiz-Sánchez et al., 2018 , 2020 ). Educational administrations must ensure all students achieve functional and meaningful learning, making it a priority to support the existence of equitable, democratic schooling adjusted to each student’s needs and characteristics. Educational policies must be directed toward achieving this end. In this regard, it is essential to consider all the variables that influence the teaching and learning processes, including student sex ( Hadjar et al., 2014 ; Farfán and Simón, 2017 ; Palomares-Ruiz and García-Perales, 2020 ), with a view to rethinking actions to foster improvement in academic performance and to promote innovation in education.

As noted in the introduction, biological factors, such as intelligence or certain personality traits, and contextual factors, such as stereotypes and the family itself, may explain differences between the sexes in mathematical performance, especially at higher performance levels. In this regard, analyzing the contexts in which boys and girls socialize is fundamental for studying these differences between the sexes ( Hadjar et al., 2014 ; Mizala et al., 2015 ; Palomares-Ruiz and García-Perales, 2020 ), an issue that should be approached from various perspectives ( Del Río et al., 2016 ). In addition, the differences between the sexes highlight the need to rethink educational practices from the perspective of equality and innovation, trying to prevent mathematical learning from leading to academic and professional segregation ( Cantoral et al., 2014 ). In this regard, working on STEAM skills (Science, Technology, Engineering, Arts and Mathematics) may be a useful approach for promoting coeducation and gender equality in education ( UNESCO, 2019 ; Ryu et al., 2021 ), including non-formal education ( Juvera and Hernández-López, 2021 ), and may be generalizable to highly capable mathematics students ( García-Perales and Almeida, 2019 ). Teacher training in teaching mathematics is especially important ( Monroy and Marroquín, 2020 ) and is a key aspect for teaching and learning in the other STEAM fields ( Román-Graván et al., 2020 ; Hernández-Barco et al., 2021 ; Ortiz-Revilla and Greca, 2021 ), in which women are underrepresented ( Lehman et al., 2017 ; Botella et al., 2019 ; McCullough, 2020 ).

The large sample participating in this study underlines the importance of using ability tests for diagnostic processes, in this case for Mathematics. The generalization of specific activities for any schoolchild, whatever their abilities, means starting a process of educational adaptation and individualization ( Díez and Jiménez, 2018 ; Torres, 2018 ). Currently, educational processes are characterized by their complexity and multidimensionality, with multiple factors that can have an impact on teaching and learning as part of mathematics teaching ( Palomares-Ruiz and García-Perales, 2020 ). For this reason, it would be advisable to expand the variables of analysis in future studies with BECOMA On, and include variables such as academic performance, teachers’ and students’ perceptions of students’ interest in and motivation for mathematics, and whether highly capable students are detected. In addition, future studies will seek to generalize the application of this instrument to other educational levels, the sex of the students will be a fundamental variable. Generalizing studies for this variable to other educational levels would add weight to the results from this study. In addition, attempts will be made to perform repeated-measure replication study designs, similar to those used in other studies, using the written version of this instrument ( García-Perales et al., 2020 , 2021 ). Identifying any student’s potential for mathematics helps to offer an individualized educational response, which is a priority of inclusive, high-quality education.

Data Availability Statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.

Ethics Statement

Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. Before the study began, written informed consent to participate in this study was provided by the regional administration of each school. These educational institutions did require written informed consent from the parents. We ensured the anonymity of the responses and the confidentiality of all data collected, with published results not containing any school identifying information.

Author Contributions

RG designed the study, collected and analyzed the data, and wrote the manuscript. AP contributed to the interpretation of the data and wrote, revised, and refined the manuscript. RG and AP have participated in sending the article to the journal. Both authors contributed to the article and approved the submitted version.

The study was supported economically by the Castilla-La Mancha Regional Government (JCCM) and the European Regional Development Fund (FEDER) [Project Reference/Code SBPLY/19/180501/000149]. It has also had the support of the National Institute of Educational Technologies and Teacher Training (INTEF), the National University of Distance Education (UNED), and the University of Castilla-La Mancha (UCLM).

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Almeida, L. S., Guisande, M. A., Primi, R., and Lemos, G. C. (2008). Contribuciones del factor general y de los factores específicos en la relación entre inteligencia y rendimiento escolar. Eur. J. Educ. Psychol. 1, 5–16. doi: 10.30552/ejep.v1i3.13

CrossRef Full Text | Google Scholar

Arnaiz-Sánchez, P., De Haro, R., Alcaraz, S., and Mirete-Ruiz, A. B. (2020). Schools that promote the improvement of academic performance and the success of all students. Front. Psychol. 10:2920. doi: 10.3389/fpsyg.2019.02920

PubMed Abstract | CrossRef Full Text | Google Scholar

Arnaiz-Sánchez, P., De Haro, R., and Mirete, A. B. (2018). “Procesos de mejora e inclusión educativa en centros educativos de la Región de Murcia [Educational improvement and inclusion processes in educational centers in the Region of Murcia],” in Inclusión y Mejora Educativa [Inclusion and Educational Improvement] , eds J. C. Torrego, L. Rayón, Y. Muñoz, and P. Gómez (Alcalá de Henares: Servicio Publicaciones Universidad), 271–281.

Google Scholar

Baye, A., and Monseur, C. (2016). Gender differences in variability and extreme scores in an international context. Large Scale Assess. Educ. 4, 1–16. doi: 10.1186/s40536-015-0015-x

Bian, L., Leslie, S. J., and Cimpian, A. (2017). Gender stereotypes about intellectual ability emerge early and influence children’s interests. Science 355, 389–391. doi: 10.1126/science.aah6524

Boaler, J. (2016). Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching. San Francisco, CA: Jossey-Bass.

Botella, C., Rueda, S., López-Iñesta, E., and Marzal, P. (2019). Gender diversity in STEM disciplines: a multiple factor problem. Entropy 21, 1–17. doi: 10.3390/e21010030

Calvo, G. (2018). Las identidades de género según las y los adolescentes. Percepciones, desigualdades y necesidades educativas. Contextos Educ. Rev. Educ. 21, 169–184. doi: 10.18172/con.3311

Cantoral, R., Reyes-Gasperini, D., and Montiel, G. (2014). Socioepistemología, Matemáticas y Realidad. Rev. Latinoamericana Etnomatemática 7, 91–116.

Carey, E., Hill, F., Devine, A., and Szücs, D. (2016). The chicken or the egg? The direction of the relationship between mathematics anxiety and mathematics performance. Front. Psychol. 6:1987. doi: 10.3389/fpsyg.2015.01987

Cázares, M. J., Páez, D. A., and Pérez, M. G. (2020). Discusión teórica sobre las prácticas docentes como mediadoras para potencializar estrategias metacognitivas en la solución de tareas matemáticas. Educ. Matemática 32, 221–240. doi: 10.24844/EM3201.10

Chamorro-Premuzic, T., Quiroga, M. A., and Colom, R. (2009). Intellectual competence and academic performance: a spanish study. Learn. Individ. Diff. 19, 486–491. doi: 10.1016/j.lindif.2009.05.002

Cueli, M., Areces, D., García, T., Alves, R. A., and González-Castro, P. (2020). Attention, inhibitory control and early mathematical skills in preschool students. Psicothema 32, 237–244. doi: 10.7334/psicothema2019.225

Del Río, M. F., Strasser, K., and Susperreguy, M. I. (2016). ¿Son las habilidades matemáticas un asunto de Género? Los estereotipos de género acerca de las matemáticas en niños y niñas de Kínder, sus familias y educadoras. Calidad Educación 45, 20–53. doi: 10.4067/S0718-45652016000200002

Desco, M., Navas-Sánchez, F. J., Sánchez-González, J., Reig, S., Robles, O., Franco, C., et al. (2011). Mathematically gifted adolescents use more extensive and more bilateral areas of the fronto-parietal network than controls during executive functioning and fluid reasoning tasks. NeuroImage 57, 281–292. doi: 10.1016/j.neuroimage.2011.03.063

Díez, L. P., and Jiménez, C. J. (2018). Influencia de la organización escolar en la educación de los alumnos de altas capacidades. Enseñanza Teach. 36, 151–178. doi: 10.14201/et2018361151178

Dowker, A., Sarkar, A., and Yen Looi, C. (2016). Mathematics anxiety: ¿what have we learned in 60 years?”. Front. Psychol. 7:508. doi: 10.3389/fpsyg.2016.00508

Else-Quest, N. M., Hyde, J. S., and Linn, M. C. (2010). Cross-national patterns of gender differences in mathematics: a meta-analysis. Psychol. Bull. 136, 103–127. doi: 10.1037/a0018053

Farfán, R. M., and Simón, G. (2017). Género y matemáticas: una investigación con niñas y niños talento. Acta Sci. 19, 427–446.

Ferreira, A. S., Flores, I., and Casas-Novas, T. (2017). Introdução ao Estudo, Porque Melhoraram os Resultados PISA em Portugal?: Estudo Longitudinal e Comparado (2000-2015). Lisboa: Fundação Francisco Manuel dos Santos.

Figueiredo, M., and Guimarães, H. M. (2019). A relevância dos fatores motivacionais nos estilos de aprendizagem da Matemaìtica no iniìcio do ensino secundaìrio. Quadrante 28, 79–99.

Franco, V., Melo, M., Santos, G., Apolónio, A., and Amaral, L. (2017). A national early intervention system as a strategy to promote inclusion and academic achievement in Portugal. Front. Psychol. 8:1137. doi: 10.3389/fpsyg.2017.01137

Frey, C., and Osborne, M. (2017). The future of employment: how susceptible are jobs to computerization? Technol. Forecast. Soc. Change 114, 254–280. doi: 10.1016/j.techfore.2016.08.019

Fuentes, S., and Renobell, V. (2019). La influencia del género en el aprendizaje matemático en España. Evidencias desde PISA. Rev. Sociol. Educ. RASE 13, 63–80. doi: 10.7203/RASE.13.1.16042

García-Perales, R. (2014). Diseño y Validación de Un Instrumento de Evaluación de la Competencia Matemática. Rendimiento Matemático de los Alumnos Más Capaces. dissertation/master’s thesis. Madrid: Universidad Nacional de Educación a Distancia (UNED).

García-Perales, R., and Almeida, L. S. (2019). Programa de enriquecimiento para alumnado con alta capacidad: efectos positivos para el currículum. Comunicar 60, 39–48. doi: 10.3916/C60-2019-04

García-Perales, R., Jiménez-Fernández, C., and Palomares-Ruiz, A. (2020). Seguimiento de un grupo de alumnos y alumnas con alta capacidad matemática. Rev. Investig. Educ. 38, 415–434. doi: 10.6018/rie.366541

García-Perales, R., Jiménez-Fernández, C., and Palomares-Ruiz, A. (2021). Elecciones académicas e interés vocacional en alumnado con alta capacidad matemática. Ensaio Avaliação e Políticas Públicas em Educação 29, 160–182. doi: 10.1590/S0104-40362020002802539

Geary, D. C., and Brown, S. C. (1991). Cognitive addition: strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children. Dev. Psychol. 27, 398–406. doi: 10.1037/0012-1649.27.3.398

Gilat, T., and Amit, M. (2013). Exploring young students creativity: the effect of model eliciting activities. PNA 8, 51–59.

González-Pienda, J. A., Fernández, M. S., Suárez, N., Fernández, M. E., Tuero, E., García, T., et al. (2012). Diferencias de género en actitudes hacia las matemáticas en la enseñanza obligatoria. Rev. Iberoamericana Psicol. Salud 3, 55–73.

Greenes, C. (1997). Honing the abilities of the mathematically promising. Math. Teach. 90, 582–586.

Hadjar, A., Krolak-Schwerdt, S., Priem, K., and Glock, S. (2014). Gender and educational achievement. Educ. Res. 56, 117–125. doi: 10.1080/00131881.2014.898908

Harju-Luukkainen, H., McElvany, N., and Stang, J. (eds) (2020). Monitoring Student Achievement in the 21st Century. European Policy Perspectives and Assessment Strategies. Berlin: Springer International Publishing.

Hattie, J., Fisher, D., and Frey, N. (2017). Visible Learning for Mathematics: What Works Best to Optimize Student Learning. Thousand Oaks, CA: Corwin.

Hernández-Barco, M., Cañada-Cañada, F., Corbacho-Cuello, I., and Sánchez-Martín, J. (2021). An exploratory study interrelating emotion, self-efficacy and multiple intelligence of prospective science teachers. Front. Educ. 6:604791. doi: 10.3389/feduc.2021.604791

Hyde, J. S. (2016). Sex and cognition: gender and cognitive functions. Curr. Opin. Neurobiol. 38, 53–56. doi: 10.1016/j.conb.2016.02.007

Instituto Nacional de Evaluación Educativa (2013). PISA 2012: Informe Español. Volumen I: Resultados y contexto. Madrid: Ministerio de Educación, Cultura y Deporte.

Jaime, A., and Gutiérrez, A. (2017). “Investigacioìn sobre estudiantes con alta capacidad matemaìtica,” in Investigacioìn en Educacioìn Matemaìtica XXI , eds J. M. Munoz-Escolano, A. Arnal-Bailera, P. Beltraìn-Pellicer, M. L. Callejo, and J. Carrillo (Zaragoza: SEIEM), 71–89.

Jiménez, C. (2014). El Desarrollo Del Talento: Educación y Alta Capacidad. Lección Inaugural del Curso Académico 2014-2015 de la UNED. Madrid: UNED.

Juvera, J., and Hernández-López, S. (2021). Steam in childhood and the gender gap: a proposal for non-formal education. EDU REVIEW. Int. Educ. Learn. Rev. 9, 9–25. doi: 10.37467/gka-revedu.v9.2712

Kerr, B. (2000). “Guiding gifted girls and young women,” in International Handbook of Giftedness and Talent , eds K. M. Heller, F. J. Mönks, R. J. Sternberg, and R. F. Subotnik (Oxford, UK: Pergamon Press), 649–657.

Kijima, R., and Sun, K. L. (2020). ‘Females don’t need to be reluctant’: employing design thinking to harness creative confidence and interest in STEAM. Int. J. Art Design Educ. 40, 66–81. doi: 10.1111/jade.12307

Kurnaz, A. (2018). Examining effects of mathematical problem-solving, mathematical reasoning and spatial abilities on gifted students’ mathematics achievement. World Sci. Res . 5, 37–43. doi: 10.20448/journal.510.2018.51.37.43

Landau, E. (2003). El valor de ser superdotado. Madrid: Consejería de Educación.

Lehman, K. J., Sax, L. J., and Zimmerman, H. B. (2017). Women planning to major in computer science: who are they and what makes them unique? J. Comput. Sci. Educ. 26, 277–298. doi: 10.1080/08993408.2016.1271536

Llor, L., Ferrando, M., Ferrandiz, C., Hernández, D., Sainz, M., Prieto, M. D., et al. (2012). Inteligencias Múltiples y Alta Habilidad. Aula Abierta 40, 27–38.

Macià, M., and Garreta, J. (2018). Accesibilidad y alfabetización digital: barreras para la integración de las TIC en la comunicación familia/escuela. Rev. Investig. Educ. 36, 239–257. doi: 10.6018/rie.36.1.290111

Mandelman, S. D., Tan, M., Aljughaiman, A. M., and Grigorenko, E. L. (2010). Intelectual gifteness: economic, political, cultural and psychological considerations. Learn. Individ. Diff. 20, 286–297.

Marsh, H. W., and Martin, A. J. (2011). Academic self-concept and academic achievement: relations and causal ordering. Br. J. Educ. Psychol. 81, 59–77. doi: 10.1348/000709910X503501

Mato, M. D., Espiñeira, E., and Chao, R. (2014). Dimensión afectiva hacia la matemática: resultados de un análisis en educación primaria. Rev. Investig. Educ. 32, 57–72. doi: 10.6018/rie.32.1.164921

McCullough, L. (2020). Proportions of Women in STEM Leadership in the Academy in the USA. Educ. Sci. 10, 1–13. doi: 10.3390/educsci10010001

Méndez, D., Méndez, A., and Fernández-Río, F. (2015). Análisis y valoración del proceso de incorporación de las Competencias Básicas en Educación Primaria. Rev. Investig. Educ. 33, 233–246. doi: 10.6018/rie.33.1.183841

Ministerio de Educación, Cultura y Deporte (2014a). Marco General de la evaluación de 3er curso de Educación Primaria. Madrid: Ministerio de Educación, Cultura y Deporte.

Ministerio de Educación, Cultura y Deporte (2014b). PISA 2012 Informe español. Resultados y contexto. Madrid: Ministerio de Educación, Cultura y Deporte.

Ministerio de Educación, Cultura y Deporte (2014c). Real Decreto 126/2014, de 28 de febrero, por el que se establece el currículo básico de la Educación Primaria. Boletín Oficial del Estado 52, 1–58.

Ministerio de Educación y Formación Profesional (2019). PISA 2018. Programa para la Evaluación Internacional de los Estudiantes. Informe Español. Available online at: https://cutt.ly/zr3uTgk (accessed September 25, 2020).

Ministerio de Educación y Formación Profesional (2020). Datos Estadísticos Para Enseñanzas No Universitarias. Available online at: https://cutt.ly/GgeQCdi (Accessed October 6, 2020).

Mizala, A., Martínez, F., and Martínez, S. (2015). Pre-service elementary school teachers’ expectations about student performance: how their beliefs are affected by their mathematics anxiety and Student’s gender. Teach. Teach. Educ. 50, 70–78. doi: 10.1016/j.tate.2015.04.006

Monroy, D., and Marroquín, B. (2020). Didáctica de la Matemática y su importancia en los profesores en formación. Rev. Guatemalteca Educ. Superior 3, 47–59. doi: 10.46954/revistages.v1i1.4

Muelas, A. (2014). Influencia de la variable de personalidad en el rendimiento académico de los estudiantes cuando finalizan la Educación Secundaria Obligatoria (ESO) y comienzan Bachillerato. Hist. Comun. Soc. 18, 115–126. doi: 10.5209/rev_HICS.2013.v18.44230

Nortes, A., and Nortes, R. (2013). Formación inicial de maestros: un estudio en el dominio de las Matemáticas. Prof. Rev. Curríc. Form. Prof. 17, 185–200.

Organization for Economic Cooperation, and Development (2013). PISA 2012 Assessment and Analytical Framework: Mathematics, Reading, Science, Problem Solving and Financial Literacy. Paris: OECD Publishing.

Organization for Economic Cooperation, and Development (2019a). Balancing School Choice and Equity: An International Perspective Based on PISA. Paris: OECD Publishing.

Organization for Economic Cooperation, and Development (2019b). PISA 2018 Assessment and Analytical Framework. Paris: OECD Publishing.

Organization for Economic Cooperation, and Development (2019c). PISA 2018 Results (Volume I): What Students Know and Can Do. Paris: OECD Publishing.

Organization for Economic Cooperation and Development (2019d). PISA 2018 Results (Volume II): Where All Students Can Succeed. Paris: OECD Publishing.

Ortiz-Revilla, J., and Greca, I. M. (2021). “Intentions Towards Following Science and Engineering Studies Among Primary Education Pupils Participating in Integrated STEAM Activities,” in The 11th International Conference on European Transnational Educational (ICEUTE 2020). Advances in Intelligent Systems and Computing , eds A. Herrero, C. Cambra, D. Urda, J. Sedano, H. Quintián, and E. Corchado (Cham: Springer).

Palomares-Ruiz, A., and García-Perales, R. (2020). Math performance and sex: the predictive capacity of self-efficacy, interest and motivation for learning mathematics. Front. Psychol. 11:1879. doi: 10.3389/fpsyg.2020.01879

Pelegrina, S., García, M. C., and Casanova, P. F. (2002). Los estilos educativos de los padres y la competencia académica de los adolescentes. Infancia Aprendizaje 25, 147–168. doi: 10.1174/021037002317417796

Pomar, C., Díaz, O., Sánchez, T., and Fernández, M. (2009). Habilidades matemáticas y verbales: diferencias de género en una muestra de 6ş de Primaria y 1ş de ESO. Rev. Int. Faisca de Altas Capacidades 14, 14–26.

Preckel, F., Goetz, T., Pekrun, R., and Kleine, M. (2008). Gender differences in gifted and average-ability students: comparing girls’ and boys’ achievement, self-concept, interest, and motivation in mathematic. Gift. Child Q. 52, 146–159. doi: 10.1177/0016986208315834

Ramírez, R., and Cañadas, M. C. (2018). Nominación y atención del talento matemático por parte del docente. UNO Rev. Didáctica de las Matemáticas 79, 23–30.

Rico, L., Gómez, P., and Cañadas, M. (2014). Formación inicial en educación matemática de los maestros de Primaria en España, 1991-2010. Rev. Educ. 363, 35–59. doi: 10.4438/1988-592X-RE-2012-363-169

Roderer, T., and Roebers, C. M. (2013). Children’s performance estimation in mathematics and science tests over a school year: a pilot study. Electron. J. Res. Educ. Psychol. 11, 5–24. doi: 10.25115/ejrep.v11i29.1555

Rodríguez, D., and Guzmán, R. (2018). Relación entre perfil motivacional y rendimiento académico en educación secundaria obligatoria. Estudios Sobre Educación 34, 199–217. doi: 10.15581/004.34.199-217

Rodríguez-Mantilla, J. M., Fernández-Díaz, M. J., and Jover, G. (2018). PISA 2015: predictores del rendimiento en Ciencias en España. Rev. Educ. 38, 75–102. doi: 10.4438/1988-592X-RE-2017-380-373

Román-Graván, P., Hervás-Gómez, C., Martín-Padilla, A. H., and Fernández-Márquez, E. (2020). Perceptions about the use of educational robotics in the initial training of future teachers: a study on STEAM sustainability among female teachers. Sustainability 12:4154. doi: 10.3390/su12104154

Rosário, P., Lourenço, A., Paiva, O., Rodrigues, A., Valle, A., and Tuero-Herrero, E. (2012). Predicción del rendimiento en matemáticas: efecto de variables personales, socioeducativas y del contexto escolar. Psicothema 24, 289–295.

Rotigel, J. V., and Fello, S. (2004). Mathematically gifted students: how can we meet their needs. Gift. Child Today 27, 46–51. doi: 10.4219/gct-2004-150

Ruiz, F. (2005). Influencia de la autoeficacia en el ámbito académico. Docencia Univ. 1, 1–16. doi: 10.19083/ridu.1.33

Ryu, J., Lee, Y., Kim, Y., Goundar, P., Lee, J., and Jung, J. Y. (2021). “STEAM in Gifted Education in Korea,” in Handbook of Giftedness and Talent Development in the Asia-Pacific , ed. S. R. Smith (Singapore: Springer).

Sason, H., Michalsky, T., and Mevarech, Z. (2020). Promoting middle school students’ science text comprehension via two self-generated “linking” questioning methods. Front. Psychol. 11:595745. doi: 10.3389/fpsyg.2020.595745

Schillinger, F. L., Vogel, S. E., Diedrich, J., and Grabner, R. H. (2018). Math anxiety, intelligence, and performance in mathematics: insights from the german adaptation of the Abbreviated Math Anxiety Scale (AMAS-G). Learn. Individ. Diff. 61, 109–119. doi: 10.1016/j.lindif.2017.11.014

Schleicher, A. (2018). World Class: How to Build a 21st-Century School System, Strong Performers and Successful Reformers in Education. Paris: OECD Publishing.

Song, L. J., Huang, G., Peng, Z., Law, K., Wong, C., and Chen, Z. (2010). The differential effects of general mental ability and emotional intelligence on academic performance and social interactions. Intelligence 38, 137–143. doi: 10.1016/j.intell.2009.09.003

Sriraman, B. (2003). Mathematical giftedness, problem solving, and the ability to formulate generalizations: the problem-solving experiences of four gifted students. J. Second. Gift. Educ. 14, 151–165. doi: 10.4219/jsge-2003-425

Torres, L. L. (2018). Culturas de escola e excelência: entre a integração de todos e a distinção dos melhores. Rev. Sociol. Educ. 11, 167–185. doi: 10.7203/RASE.10.1.9135

UNESCO (2019). Descifrar el Código: La Educación De Las Niñas en Ciencias, Tecnología, Ingeniería Y Matemáticas (STEM). Francia: UNESCO.

Ursini, S., and Ramírez-Mercado, M. P. (2017). Equidad, género y matemáticas en la escuela mexicana. Rev. Colomb. Educ. 73, 213–234. doi: 10.17227/01203916.73rce211.232

Zalazar, M. F., Aparicio, M. M. D., Ramírez, C. M., and Garrido, S. J. (2011). Estudios Preliminares de Adaptación de la Escala de Fuentes de Autoeficacia para Matemáticas. Rev. Argentina Ciencias Comportamiento 3, 1–6.

Keywords : math performance, assessment instrument, primary education, educational inclusion, sex

Citation: García Perales R and Palomares Ruiz A (2021) Comparison Between Performance Levels for Mathematical Competence: Results for the Sex Variable. Front. Psychol. 12:663202. doi: 10.3389/fpsyg.2021.663202

Received: 02 February 2021; Accepted: 19 May 2021; Published: 17 June 2021.

Reviewed by:

Copyright © 2021 García Perales and Palomares Ruiz. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Ramón García Perales, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

The Mathematical Competencies Framework and Digital Technologies

First Online: 21 February 2023

Cite this chapter

Eirini Geraniou ORCID: orcid.org/0000-0002-6360-0316 20 &
Morten Misfeldt ORCID: orcid.org/0000-0002-6481-4121 21

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 20))

529 Accesses

4 Citations

This chapter discusses the influence of the increased use of digital technologies for mathematical teaching and learning and their relevance to the Danish mathematical competencies framework (KOM) (Niss & Højgaard, 2011 , 2019 ), and how the different types of digital technologies may influence different components of the KOM framework. Inspired by the notion of mathematical digital competency (MDC) (Geraniou & Jankvist, 2019 ), we address the influence and potential of digital technologies in relation to the KOM framework’s three components of (1) the eight mathematical competencies (for students of mathematics); (2) the three second order competencies, known as types of overview and judgement; and (3) the framework’s description of the six competencies for mathematical teaching. Using carefully chosen examples, we facilitate our discussions on how these different components of KOM may be perceived in the digital age. We conclude by discussing how mathematical competencies are “affected” by digital technologies and argue for revisiting the KOM mathematical competencies and extending the MDC framework.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Available as PDF
Read on any device
Instant download
Own it forever
Available as EPUB and PDF
Compact, lightweight edition
Dispatched in 3 to 5 business days
Free shipping worldwide - see info
Durable hardcover edition

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Towards a definition of “mathematical digital competency”

Towards a definition of “mathematical digital competency for teaching”

The Use of Digital Technologies in Teaching and Assessment

Appel, K., & Haken, W. (1977). Every planar map is four colorable. Part 1: Discharging. Illinois Journal of Mathematics, 21(3) , 429–490.

Google Scholar

Appel, K., Haken, W., & Koch, J. (1977). Every planar map is four colorable. Part II: Reducibility. Illinois Journal of Mathematics, 21(3) , 491–567.

Artigue, M. (2010). The future of teaching and learning mathematics with digital technologies. In C. Hoyles & J. -B. Lagrange (Eds.), Mathematics education and technology—Rethinking the terrain . The 17th ICMI study (pp. 463–475). Springer.

Blomhøj, M., & Højgaard Jensen, T. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and Its Applications, 22 (3), 123–139.

Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 222–231). Horwood.

Chapter Google Scholar

Bocconi, S., Chioccariello, A., Dettori, G., Ferrari, A., & Engelhardt, K. (2016). Developing computational thinking in compulsory education—Implications for policy and practice . EUR 28295 EN. https://doi.org/10.2791/792158

Bozkurt, G., & Ruthven, K. (2017). Classroom-based professional expertise: A mathematics teacher’s practice with technology. Educational Studies in Mathematics, 94 (3), 309–328.

Article Google Scholar

Dreyfus, T. (1999). Why Johnny can’t prove. Educational Studies in Mathematics, 38 (1–3), 85–109.

Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2) , 213–234.

Ferrari, A. (2012). Digital competence in practice: An analysis of frameworks. A technical report by the Joint Research Centre of the European Commission . European Union.

Fitzpatrick, R. (2008). Euclid’s elements of geometry . ( http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf ) [The Greek text of J. L. Heiberg (1883–1885) from Euclidis Elementa, edidit et Latine interpretatus est I. L. Heiberg, in aedibus B. G. Teubneri, 1883–1885 edited, and provided with a modern English translation, by Richard Fitzpatrick.]

Geraniou, E., & Jankvist, U. T. (2019). Towards a definition of “mathematical digital competency.” Educational Studies in Mathematics, 102 , 29–45. https://doi.org/10.1007/s10649-019-09893-8

Gravemeijer, K., Stephan, M., Julie, C., Lin, F. L., & Ohtani, M. (2017). What mathematics education may prepare students for the society of the future? International Journal of Science and Mathematics Education, 15 (1), 105–123.

Hatlevik, O. E., & Christophersen, K.-A. (2013). Digital competence at the beginning of upper secondary school: Identifying factors explaining digital inclusion. Computers and Education, 63 , 240–247.

Jankvist, U. T., & Geraniou, E. (2021). “Whiteboxing” the content of a formal mathematical text in a dynamic geometry environment. Digital Experience in Mathematics Education . https://doi.org/10.1007/s40751-021-00088-6

Jankvist, U. T., & Misfeldt, M. (2015). CAS-induced difficulties in learning mathematics? For the Learning of Mathematics, 35 (1), 15–20.

Johansen, M. W., & Misfeldt, M. (2017). Computers as a source of a posteriori knowledge in mathematics. International Studies in the Philosophy of Science, 30 (2), 111–127. https://doi.org/10.1080/02698595.2016.1265862

Kallia, M., van Borkulo, S., Drijvers, P., Barendsen, E., & Tolboom, J. (2021). Characterising computational thinking in mathematics education: A literature-informed Delphi study. Research in Mathematics Education . https://doi.org/10.1080/14794802.2020.1852104

Kunter, M., Klusmann, U., Baumert, J., Richter, D., Voss, T., & Hachfeld, A. (2013). Professional competence of teacher: Effects on instructional quality and student development. Journal of Educational Psychology, 105 (3), 805–820.

Mariotti, M. (2006). Proof and proving in mathematics education. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 173–204). Sense Publishers.

Mason, J. (1991). Questions about geometry. In D. Pimm & E. Love (Eds.), Teaching and learning school mathematics: A reader (pp. 77–90). Hodder and Stoughton.

McEvoy, M. (2008). The epistemological status of computer-assisted proofs. Philosophia Mathematica, 16 , 374–387.

McEvoy, M. (2013). Experimental mathematics, computers and the a priori. Synthese, 190 , 397–412.

Misfeldt, M., & Jankvist, U. T. (2020). Teknokritisk matematikundervisning: at åbne den skjulte matematik i demokratiets tjeneste. [Technocritical mathematics education: Opening the hidden mathematics in the service of democracy.] I C. Haas, & C. Mathiessen (red.), Fagdidaktik og demokrati (pp. 331–348). Samfundslitteratur.

Misfeldt, M., Szabo, A., & Helenius, O. (2019). Surveying teachers’ conception of programming as a mathematics topic following the implementation of a new mathematics curriculum. In The eleventh congress of the European Society for research in mathematics education (No. 13) . Freudenthal Group; Freudenthal Institute; ERME.

Niss, M. (2010). Modelling a crucial aspect of students’ mathematical modeling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 43–59). Springer.

Niss, M. A. (2016). Mathematics standards and curricula under the influence of digital affordances: Different notions, meanings and roles in different parts of the world. In M. Bates & Z. Usiskin (Eds.), Digital curricula in school mathematics (pp. 239–250). Information Age Publishing.

Niss, M. & Højgaard, T. (2011). Competencies and mathematical learning—Ideas and inspiration for the development of mathematics teaching and learning in Denmark (No. 485). IMFUFA, Roskilde University. English translation of part I-VI of Niss and Jensen (2002). Retrieved from: http://milne.ruc.dk/imfufatekster/pdf/485web_b.pdf

Niss, M., & Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102 , 9–28. https://doi.org/10.1007/s10649-019-09903-9

Niss, M., & Jensen, T. H. (2002). Kompetencer og matematiklæring—Ideer og inspiration til udvikling af matematikundervisning i Danmark [Competencies and mathematical learning—Ideas and inspiration for the development of mathematics teaching and learning in Denmark]. The Ministry of Education.

Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings learning cultures and computers . Dordrecht Kluwer.

Ruthven, K. (2011). Constituting digital tools and materials as classroom resources: The example of dynamic geometry. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to ‘lived’ resources: Mathematics curriculum materials and teacher development (pp. 83–103). Springer.

Tymoczko, T. (1979). The Four-color problem and its philosophical significance. Journal of Philosophy, 76 (2), 57–83.

Young, J. (2017). Technology-enhanced mathematics instruction: A second-order meta-analysis of 30 years of research. Educational Research Review, 22 , 19–33.

Download references

Author information

Authors and affiliations.

UCL Institute of Education, London, UK

Eirini Geraniou

University of Copenhagen, Copenhagen, Denmark

Morten Misfeldt

You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eirini Geraniou .

Editor information

Editors and affiliations.

Danish School of Education, Aarhus University, Copenhagen, Denmark

Uffe Thomas Jankvist

Curriculum, Pedagogy and Assessment, UCL Institute of Education, London, UK

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Geraniou, E., Misfeldt, M. (2022). The Mathematical Competencies Framework and Digital Technologies. In: Jankvist, U.T., Geraniou, E. (eds) Mathematical Competencies in the Digital Era. Mathematics Education in the Digital Era, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-031-10141-0_3

Download citation

DOI : https://doi.org/10.1007/978-3-031-10141-0_3

Published : 21 February 2023

Publisher Name : Springer, Cham

Print ISBN : 978-3-031-10140-3

Online ISBN : 978-3-031-10141-0

eBook Packages : Education Education (R0)

Share this chapter

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Publish with us

Policies and ethics

Find a journal
Track your research

Home
Faculty of Science / Naturvetenskapliga fakulteten
Department of Mathematical Sciences / Institutionen för matematiska vetenskaper
Doctoral Theses / Doktorsavhandlingar Institutionen för matematiska vetenskaper

Exercising Mathematical Competence: Practising Representation Theory and Representing Mathematical Practice

Parts of work, institution, disputation, date of defence, collections.

Doctoral Theses from University of Gothenburg / Doktorsavhandlingar från Göteborgs universitet

Publication type

Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser .

Enter the email address you signed up with and we'll email you a reset link.

We're Hiring!
Help Center

PROBLEMS AND DIFFICULTIES ENCOUNTERED BY STUDENTS TOWARDS MASTERING LEARNING COMPETENCIES IN MATHEMATICS

Related Papers

Necdet Guner

The aim of this study is to identify whether high school students encounter any difficulties in mathematics and reveal the reasons for such difficulties. The participants of the study, which was a descriptive case study based on qualitative understanding, were a total of 164 students, including 85 students from Anatolian High Schools and 79 students from Science High Schools. Approximately 11% of the participants said they had no difficulties in math, whereas 99% of the students from Anatolian High Schools and 78% of the students from Science High Schools said they had difficulties in mathematic. Their thoughts about the reasons for such difficulties were analyzed by content analysis method considering the type of high school they attended. The findings obtained revealed that the difficulties encountered by the participants in mathematics were teacher-, contentand studentbased. Anatolian High School students stated that they intensely faced teacher-based difficulties, whereas Scienc...

Denniel Gallos

Poshan Niraula

With the rapid development of science and mathematics, many works of the people have become understandable. Despite the development of various technologies, people need mathematical knowledge in everyday tasks. Students are exposed to various problems while teaching mathematics. Themes are explored for why students are experiencing those problems, what may be the solution to those problems, and more. The problems encountered by students during their geometry, arithmetic and algebra learning are presented in a systematic way. Due to inadequate practical content in the curriculum, students have difficulty in learning. Therefore, the curriculum should include practical content.

Zenodo (CERN European Organization for Nuclear Research)

Yuri Gonzaga

Psychology and Education: A Multidisciplinary Journal

Psychology and Education , jeremias E Obina , Danilo E. Derio Jr. , Annie Rose D. Rosa , Jonna Fe Gorit , Jolai G. Bolaños

Mathematics is one of the subjects that is taught in all Schools and Universities. It is usually viewed by students as difficult subject. This study aimed to determine the factors that affect the Mathematics performance of Mathematics major students and the extent of each factor. Further, it sought to determine the challenges encountered by the respondents in learning Mathematics. The study has three research questions and it made used of the explanatory-sequential research design. Relevant literatures were reviewed on theories and findings that emerged from different authors. There were 57 respondents involved in the study, 47 from 1 st year to 3 rd year Mathematics major student and 10 from 4 th year students at Notre Dame of Midsayap College. Data collection was done by using questionnaires. The findings showed that factors that affect Mathematics performance are the sources of the challenges in learning Mathematics. It also indicated that learning Mathematics is affected by numerous factors such as needs, interest, and seriousness of the subject matter, teachers' practices and methodologies, teachers' personality, parental support and home environment. The respondents have encountered challenges in learning Mathematics such as unfavorable teaching practices, lack of time management, lack of motivation, poor internet connectivity, and difficulty to get rapid feedback, lack of knowledge and regulation skills, and limited quotas.

International Journal of Educational Research Review

Omoniyi Oginni

Educational Research and Reviews

Mithat TAKUNYACI

Adriel Roman

Mathematics in the Modern World (MITMW) is one of the general education subjects taught in the new college curriculum in the Philippines. In this study, the self-assessment of students on their acquisition of the competencies set in the MITMW are being described as well as the extent of difficulties and performance. Using descriptive correlational research design, this study hypothesized that the perceived extent of acquisition of the first year college students on the competencies intended for Mathematics in the Modern World and their extent of difficulties experienced provide significant relationship to their performance. Two hundred seventy-one (271) first year college students were surveyed using validated questionnaires. Results revealed that the first year college students have higher extent of acquisitions on the competencies set in the MITMW (knowledge, values, and skills). Students experienced slight difficulties on the different topics of MITMW with satisfactory performanc...

IJESRT Journal

The study was conducted to determine the learning difficulties in Mathematics of the senior students of Cathedral School of La Naval, Naval, Biliran. This utilized a descriptive method of research. Different statistical tools were used in the analysis of data: frequency and percentage for the profiles, number of mistakes and performance. Mean and t-test with alpha level of significance was set at 0.05 to determine the correlation. The findings of the study showed that there is significant difference between the performance and age while there is no difference between performance and sex and parents'/guardians' highest educational attainment with very high correlation. A very high correlation was also found out in terms of performance and learning difficulties, where both variables were significant. The item which incurred the greatest number of mistakes was on Perfect Square Binomial. Mentors should give focus or remediation on topics were students' low performance was identified and further establish friendly ambiance so that they could fill-in the learning gap of the learners with the use of various teaching strategies and materials.

Francesca Gregorio

The huge difficulties related to the transition from secondary to tertiary mathematics are documented by several official data. The analysis of these difficulties is a main issue in educational research at undergraduate level. It is of particular interest the case of the students who choose mathematics as a major. In fact, for the most part, they are students considered excellent in mathematics during secondary school, they seem to have the cognitive resources to succeed, but, in many cases, they encounter several difficulties during their university experience. Therefore, it appears particularly interesting to study also the affective sources and consequences of these difficulties. With this aim, we developed a qualitative and narrative study focused on students’ reflections about their mathematical difficulties in the university experience.

Registrar's Office

Graduate Academic Programs >
Engineering >
Biomedical Engineering >
MS in Medical Physics
General University Information
Undergraduate Academic Programs
Architecture
Arts and Sciences
Communication
Education and Human Development
BS/MS Five-Year Program in Biomedical Engineering
BS/MS in Neural Engineering
Certificate Program in Medical Physics
MS in Biomedical Engineering
MS in Neural Engineering
PhD in Biomedical Engineering
PhD in Medical Physics
Chemical, Environmental and Materials Engineering
Civil and Architectural Engineering
Electrical and Computer Engineering
Industrial and Systems Engineering
Mechanical and Aerospace Engineering
Ocean Engineering
Marine, Atmospheric, and Earth Science
Nursing and Health Studies
Law Academic Programs
Graduate Student Handbook for UOnline Students
Special Programs
Program Index
Course Listing
Previous Bulletin Archives

The medical physics graduate program is accredited by the Commission on Accreditation of Medical Physics Education Programs, Inc. ( CAMPEP ). The program, serving both MS and PhD degrees, ensures that the students receive adequate didactic and clinical training to continue in education and research, enter clinical physics residencies or begin working as medical physicists in radiation therapy and diagnostic radiology departments. MS students are trained with an emphasis on developing skills necessary for clinical medical physicists,

In addition to the requirement of physics minor-equivalent undergraduate coursework, the qualifications and documentation required for admission to the MS program in Medical Physics are the same as for the College of Engineering.

In general, the following four types of students are typically admitted to the MS program in Medical Physics:

Students with undergraduate degrees in biomedical engineering and other engineering disciplines who seek advanced professional training or specialization in a particular area of medical physics
Professional engineers with degrees in other engineering disciplines who plan to enter the field of medical physics
Students with an undergraduate degree in Physics, Mathematics, Computer Science, Chemistry, Biology or other fields of natural or health science who seek to diversify their career opportunities by acquiring a medical physics degree
Students who are preparing for admission to advanced health-related or other professional programs such as medical school

Students may be given conditional admission and required to take additional undergraduate courses in engineering, physics, and/or mathematics depending on their previous course work, as specified in the admission letter. The requisite courses will be prescribed by the Department Chair or Graduate Program Director during the first advising session.

The objective of the Medical Physics program is to provide advanced knowledge in the field of medical physics with an emphasis on therapeutic medical physics, and to provide the training required for students to become licensed medical physicists. This program is coordinated by the Department of Biomedical Engineering and the Department of Radiation Oncology at the School of Medicine.

The program is opened to students enrolled in the regular MS program, as well as the dual degree (BS/MS) program. Candidates are required to have completed the physics minor equivalent coursework that must include Modern Physics ( PHY 360 or equivalent), before they start their coursework in the Medical Physics program.

Students in the Medical Physics program must complete Human Physiology for Engineers ( BME 602 ) and one of the remaining two courses from the human physiology ( BME 601 or BME 603 ) course series, and 23-credits in the core curriculum in the area of medical physics.

The topic of the non-thesis MS project ( BME 707 / BME 708 ), or MS thesis must be related to medical physics. In general, the project is co-supervised by Faculty from the Department of Biomedical Engineering and the Department of Radiation Oncology

Required Core Courses

All students enrolled in the MS program are required to complete the following core graduate courses:

Two human physiology courses ( BME 602 , and BME 601 or BME 603 )
23 credits in medical physics

The Human Physiology Courses ( BME 601 / BME 602 / BME 603 , 3 credits each) are designed to provide a basic understanding of organ-level physiology and anatomy, neurophysiology, and cellular and molecular biology. Students with an MD from a medical school accredited by the World Health Organization are exempted from taking these courses. Students holding advanced degrees in the life sciences, or equivalent experience in the field, may also be exempt. Each such exception requires the approval of the Department Chairperson and Faculty member responsible for the course of concern. Students who receive an exemption, must replace the exempted course(s) with another 3-credit graduate course(s) that meets the degree requirements.

Curriculum Requirements

Ms in medical physics - nonthesis option.

The MS non-thesis option is intended for students with an undergraduate degree in biomedical engineering or related disciplines who seek advanced training or specialization in a specific area of biomedical engineering; for professional engineers with undergraduate degrees in other disciplines who want to enter the field of biomedical engineering; and for students who want to prepare for admission to advanced health-related or other professional programs.

Non-Thesis MS Project

General description.

All students enrolled in the MS non-thesis program must complete a two-semester 3 credit Master's project ( BME 707 and BME 708 ), under the supervision of a project mentor and departmental project coordinator. The project must demonstrate the candidate’s ability to solve complex scientific or technical problems at the interface of engineering and medical physics.

The MS project can be a research or design project. The project must include a significant research or design component contributed by the M.S. student, including, but not limited to, the design of an experiment or process; the development of a device, instrument, or system; the development of a computer program; the analysis of experimental data. Projects cannot be limited solely to the review of literature, the development of research or design proposals, or the collection of experimental data.

At the completion of their project, students must submit a written project report and complete a public oral defense of their project.

Project Mentor

Students who select the MS non-thesis track must identify a project mentor and select a project before they register for their second semester of full-time study. The project mentor is generally a primary faculty member from the Medical Physics Graduate Program. The role of the project mentor is to help the student identify a suitable project, to monitor the progress of the student, to provide guidance and training in the relevant topics, and to review the final report and presentation.

Students may complete their project under the supervision of a faculty member from another Department at the University of Miami, or from the local biomedical industry, or from a local clinic, under the following conditions:

The student must receive the approval of the Department Chairman and Graduate Program Director.
The student must identify a co-mentor who must be a primary faculty member from the Medical Physics Graduate Program. The co-mentor must be familiar with the topic of the proposed project. The role of the co-mentor will be to monitor the student progress and ensure that the Master's project report and presentation satisfy all of the relevant requirements.

Project Coordinator

The project coordinator is a member of the primary faculty of the Department of Biomedical Engineering who is responsible for teaching the BME 707 / BME 708 course. The role of the project coordinator is to:

Help students identify a project and mentor.
Ensure that the projects satisfy the program objectives.
Provide general guidance and graduate scholarship training.
Ensure that the students are making suitable progress towards the project goals.

Project Abstract

Non-Thesis MS students must submit a one-page project abstract to the Department Chairman or Graduate Program Director and to the MS Project Coordinator at the time when they register for BME 707 / BME 708 . The abstract must include the name of the project mentor (and co-mentor, if any), the title of the proposed project, and a brief description of the goals of the project and proposed methods. The abstract must be approved by the mentor, MS Project Coordinator, and Department Chairman or Graduate Program Director before the student can start work on the project. ( Project Abstract Template )

Project Report

Non-thesis MS students must submit a detailed report describing the work completed during the project. The report must describe the objectives and significance of the work, and summarize the activities completed by the student as part of the MS project. The report must demonstrate that the work performed by the student satisfies the general project criteria. The typical length of non-thesis M.S. project reports is 20 to 30 pages. If the project resulted in the submission of a full-length peer-reviewed scientific article, the article can be submitted in lieu of a report, as long as the following conditions are satisfied:

The student must be the first author of the article.
The article must reflect the work performed by the student as part of the project.
The article must be submitted for publication in a peer-reviewed journal or conference proceedings volume.
A one to two page introduction must be submitted to summarize the project goals and main outcomes.

The report must be reviewed and approved by the project mentor (and co-mentor, if any). Once the report is approved by the mentor(s), one printed copy and one electronic version in PDF format must be submitted to the Project Coordinator by the specified deadline. The final report must be approved and signed by the Project Mentor(s), Project Coordinator and Graduate Program Director or Department Chairman. ( Signature Page Template )

Project presentation

Non-thesis MS students must give an oral presentation of their project. The oral presentation is generally scheduled during the scheduled final examination time of BME 707 / BME 708 in the semester of graduation.

Project grade

The final grade for the project is given by the Project Coordinator. The final grade is a combination of a grade submitted by the Project Mentor(s) assessing the overall performance of the student on the project, and a grade given by the Project Coordinator assessing the quality of the oral presentation and report.

Curriculum Requirements:

Ms in medical physics - thesis option.

The thesis option is typically selected by students who are oriented towards a career in academic or industrial research and development, or students who want to acquire an initial independent biomedical research experience before seeking admission to doctoral programs.

Thesis Option

General description.

The Master's thesis is a research monograph which describes the significance of the research and summarizes the research activities completed as part of the MS degree requirements. The objective of the thesis is to evaluate the candidate’s competence in the area of the MS research. The thesis must demonstrate that the research is original and that the candidate has the ability to solve complex scientific and/or technical problems at the interface of engineering and medicine or biology.

Thesis Mentor

Students who select the MS thesis track must identify a thesis mentor before they register for their second semester of full-time study. The thesis mentor must hold a primary or secondary faculty appointment in the Department of Biomedical Engineering. Exceptions can be made only with approval of the Graduate Program Director and Department Chairman.

The thesis mentor supervises the research work of the student and provides training and guidance in the relevant research topics, including design of experiments, experimental techniques, and scholarship activities. The mentor helps the student select a thesis topic and develop a plan, and chairs or co-chairs the thesis committee. The mentor works closely with the student to ensure that there is satisfactory progress towards the thesis goals.

Thesis Committee

The thesis must be approved by a thesis committee. The duties of the thesis committee are:

to consult with and to advise students on their research;
to meet, at intervals, to review progress and expected results;
to read and comment upon the draft thesis;
to meet, when the thesis is completed, to conduct the final oral examination and to satisfy itself that the thesis work is original; that it demonstrates the candidate's ability to solve complex scientific and/or technical problems at the interface of engineering and medicine or biology; that it is written in lucid and correct English; and that it is submitted in approved format.

The thesis committee will consist of not less than three members, with the following requirements:

The committee chair shall be a Primary Faculty member of the Department of Biomedical Engineering, as well as a regular member of the Graduate Faculty. The Committee Chair is generally also the thesis mentor.
A thesis mentor who is not a member of the Primary Faculty of the Department of Biomedical Engineering, can serve as Co-Chair of the Thesis Committee, together with a second Co-Chair who shall be a member of the primary faculty of the Department of Biomedical Engineering.
It is an additional requirement of the Department of Biomedical Engineering that at least two committee members should be primary Faculty members from the Department.
One committee member must be from outside the Department. Outside members of the thesis committee can include part-time faculty that teach within the Department.
At least one committee member must be a regular member of the Graduate Faculty of the University of Miami.

The committee is nominated by the Graduate Program Director. Usually, the student consults with his/her research mentor and with the Chairperson or Graduate Program Director to select the Committee members.

Thesis Format and Deadlines

It is the duty of the student to ensure that the thesis defense is scheduled and that a final version of the thesis approved by the Dissertation Editor is submitted to the Dissertation Editor by the required deadlines set by the Graduate School. All information pertaining to the formatting and electronic guidelines for electronic thesis submission can be found on the Graduate School website .

Each thesis must be accompanied by a Certificate of Defense Approval for Master’s Thesis signed by all members of the Committee. Forms can be downloaded from the Graduate School website.

Evaluation Forms

The student is responsible for distributing dissertation evaluation forms to the members of the Thesis Committee for the final oral examination. The evaluation forms are used to assess the overall quality of the graduate program at the Department, College, and University level. The evaluation forms are available on the Graduate School and Department of Biomedical Engineering websites. The completed forms must be collected by the Thesis Mentor and forwarded to the Office Manager at the Department of Biomedical Engineering.

Transfer to MS Non-Thesis Program

Students enrolled in the MS thesis program who do not wish to complete their thesis can transfer to the MS non-thesis program and graduate from the MS program under the following conditions:

The transfer must be approved by the Department Chair or Graduate Program Director.
All requirements of the MS non-thesis option must be satisfied, including completion of a two-semester 3 credit Master's project ( BME 707 and BME 708 ), submission of a project report, and oral defense of project. Completed thesis credits may count towards the three credit MS project requirement.

Sample Plan of Study

Ms program in medical physics.

Typical curricula for each option of the MS program in Medical Physics are shown in the following tables. The course sequence and timeline can be adjusted based on individual needs. The minimum residence requirement for the MS degree is two semesters in full-time study or the equivalent in part-time work. Students can also complete the BS/MS program in Medical Physics.

MS without Thesis

Ms with thesis*.

*Students who are not able to complete their thesis during the 3rd semester and have completed all 30 required credits of graduate work, must enroll in 0 credits of Research in Residence ( BME 820 ) to maintain full-time student status.

The goal of the Medical Physics Graduate Program at the University of Miami is to train students to develop the necessary academic framework as well as a thorough practical understanding in medical physics, including areas of diagnostic radiologic physics, health physics, nuclear medicine, and a designated focus on radiation therapy.

Student Learning Outcomes

Students will be able to apply knowledge of mathematics, science and engineering to formulate and solve relevant medical physics problems.
Students will be able to communicate scientific and technical research effectively in writing and oral presentations.
Students will be able to work with physicians and technicians in conducting diagnostic radiology or radiation therapy.

Office of the University Registrar

1306 Stanford Drive
The University Center Room 1230
Coral Gables, FL 33146
[email protected]
Parking & Transportation

Print Options

Print this page.

The PDF will include all information unique to this page.

PDF of the entire 2022-2023 Academic Catalog.

IMAGES

The components of mathematical competence and their relationship
(PDF) Mathematical Competence and Performance in Geometry of High
(PDF) An evaluation of the selected mathematical competence of the
Formation of Professional-Mathematical Competence of Students in the
Mathematical Competence and Competency. Picture inspired by (Niss
(PDF) Developing students' mathematical competence through equipping

VIDEO

3-Minute Thesis Competition 2023
Three minute Thesis Competition 2018: Chiara Marzi
Write mathematical equation using LaTex software
The Role of Mathematics in Philosophy
Models of Thinking Using Math
MATH KANGAROO LEVEL 3-4 PART 2 || WITH ANSWERS

COMMENTS

The impact of mathematics teachers' professional competence on instructional quality and students' mathematics learning outcomes
Very recently, Blömeke et al. [56••] investigated the relationship between cognitive aspects of mathematics teachers' competence, such as MCK and MPCK, and situated aspects of these teachers' competence, such as perception, interpretation, and decision-making, instructional quality (measured by classroom observations), and students ...
PDF Effectiveness of Mathematical Word Problem Solving Interventions for
Mathematical competence in school uniquely predicts student success in both higher education and future employment (Cavanagh, 2007; National Mathematics Advisory Panel [NMAP], 2008). Specifically, successful completion of higher-level mathematics courses (e.g., algebra) is associated with higher standardized test scores
PDF MATHEMATICAL COMPETENCIES AND THE LEARNING OF MATHEMATICS ...
This paper presents the Danish KOM project (KOM: Competencies and the Learn-ing of Mathematics), initiated by the Ministry of Education and other official bod-ies in order to create a platform for in-depth reform of Danish mathematics educa-tion, from school to university. The author of the paper was appointed as the di-rector of the project.
(PDF) Mathematical Competence, Teaching, and Learning
Mathematical Competence, T eaching, and Learning. Reflections on 'Challenges in Mathematical Cognition' by Alcock et al. (2016) Kerry Lee*. [a] National Institute of Education, Nanyang ...
A systematic literature review of the current discussion on ...
Modelling and applications are essential components of mathematics, and applying mathematical knowledge in the real world is a core competence of mathematical literacy; thus, fostering students' competence in solving real-world problems is a widely accepted goal of mathematics education, and mathematical modelling is included in many curricula across the world.
PDF MATHEMATICAL COMPETENCIES IN A ROLE-PLAY ACTIVITY
Table 1: Cluster related to cognitive mathematical competencies Mathematical thinking competency includes understanding and handling of scope and limitations of a given concept; posing questions that are characteristic of mathematics and knowing the kinds of answers that mathematics may offer; extending the scope of
Comparison Between Performance Levels for Mathematical Competence
The mean level was 1.97 (SD = 0.82), with asymmetry of.05, the distribution of the levels followed a symmetric curve, with kurtosis of -1.50, platykurtic distribution with negative excess kurtosis.Variables. Mathematics competence was the main variable in this study. It was measured using the BECOMA On. As mentioned above, mathematics has a key role in educational processes, particularly ...
Mathematical Proficiency as the Basis for Assessment: A ...
Mathematics teaching and learning goes beyond computations and procedures; it rather includes complex problem-solving and critical thinking. Kilpatrick, Swafford, and Findell (2001) identify five mathematical competencies that are present in mathematics learning: conceptual understanding, procedural fluency, adaptive reasoning, strategic competence, and productive disposition.
Mathematical Competencies Framework Meets Problem-Solving ...
In this chapter, it is argued that the mathematical competencies framework (Niss & Højgaard, 2011, 2019) is a suitable tool to study mathematical problem solving supported by the use of digital tools, and that its analytical power is strengthened by coordinating it with theoretical notions from research on mathematical problem solving.The chapter illustrates the potential of such networking ...
Self-perceived and actual competencies of senior high school students
Self-perceived and actual competency in General Mathematics. The descriptive statistics of the self-perceived competence of the students in General Mathematics are presented in Table 1. Results indicate that the overall self-perceived competency was satisfac-tory (M = 2.73, SD = 0.66).
The Mathematical Competencies Framework and Digital Technologies
Inspired by the notion of mathematical digital competency (MDC) (Geraniou & Jankvist, 2019 ), we address the influence and potential of digital technologies in relation to the KOM framework's three components of (1) the eight mathematical competencies (for students of mathematics); (2) the three second order competencies, known as types of ...
(PDF) An Analysis of Students' Mathematical Competencies: The
Abstract. This study aimed to investigate students' mathematical competence in learning relationships between units according to the students' performance in a SUKEN test of Level 6. A total ...
PDF Journal of Sciences Mathematical Competence and ...
Mathematical Competence Level. Table 5.0 reflects the mathematical competence level of the respondents in terms of mathematical concepts and problem solving skills. As revealed, the level of ...
PDF High school mathematics teachers' competence on the contents of a
Only Grade 8 students of School A have high level of performance in mathematics. (14.8%) Generally, a grade 8 student of School A performs high in mathematics. (43.5%) Grade 8 students in school A are high in mathematics. (20.4%) The performance of all grade 8 students is high in mathematics. (21.3%) Figure 8.
Dissertations.se: MATHEMATICAL COMPETENCE
Search for dissertations about: "mathematical competence" Showing result 1 - 5 of 15 swedish dissertations containing the words mathematical competence. 1. Assessing mathematical creativity : comparing national and teacher-made tests, explaining differences and examining impact ... Abstract : This doctoral thesis details the introduction of the ...
Learning Competency and Styles of Senior High School Students in
This finding implies that mathematical competency is not dependent on the gender of the respondents. Furthermore, this result reveals a similar situation of male and female students in terms of mathematical competency. The senior high school track and competency test having a p-value of 0.002 and r of -0.220, have a significant relationship.
Exercising Mathematical Competence: Practising Representation Theory
Combined, the two studies show that the framework have explanatory power for various mathematical practices. In light of this framework, this thesis exercises both aspects of mathematical competence: the productive aspect in representation theory and the analytic aspect in the development of the framework.
ACER Research Repository
ACER Research Repository is a digital archive of research papers and reports produced by the Australian Council for Educational Research. Learn about mathematical competencies and more.
PROBLEMS AND DIFFICULTIES ENCOUNTERED BY STUDENTS ...
Mathematical competence has been identified as one of the competencies essential for personal fulfilment, active and productive citizenship, social belongingness and employability in the modern society. ... Competencies in Mathematics. Unpublished Master's Thesis. Bataan Polytechnic State College, Bataan, Philippines. [14] Limjap, A. A. (2002 ...
PDF Teachers' Competence and Students' Academic Performance in Mathematics
Math teachers, the competence along instruction, research and extension and performance of students as well as the relationships of the said variables. The respondents were Mathematics teachers in the College of Education in the DMMMSU-NLUC for the first semester of SY 2016-2017. ...
PDF Mathematical Competencies and Character Traits Teachers in Relation to
The overall rating for the teachers' character traits was of 3.15 described as proficient. For Personal traits, teachers had a rating of 2.91 as Proficient level, 3.32 for Social Growth described as Proficient level, and 3.21 for Professional described as Proficient level. The overall rating for the pupils' academic performance in the final ...
PDF Analysis of Digital and Technological Competencies of University ...
basic skills in mathematics and science" (Garzón-Artacho et al., 2021). According to Skov (2016), digital competence should be understood as the ability to combine knowledge, skills and attitudes appropriate to the context. Digital competence is therefore divided into the following areas: (1)
MS in Medical Physics < University of Miami
Non-Thesis MS Project General description. All students enrolled in the MS non-thesis program must complete a two-semester 3 credit Master's project (BME 707 and BME 708), under the supervision of a project mentor and departmental project coordinator.The project must demonstrate the candidate's ability to solve complex scientific or technical problems at the interface of engineering and ...