problem solving process code org

Pilot - U1L02 - The Problem Solving Process

I am including the slide deck I used to help deliver the lesson

I prepared the lesson as recommended by the plans but very shortly into the lesson I changed gears and modified it because it was clear that I was losing student interest.

Modifications: Students seemed unmotivated by the information because it was something that they were familiar with because it is late in the year)… I decided to instead ask them to compare the model for problem solving being presented with any other system they could find and document.

Students were asked to present an artifact comparing them and create hypothesis of why there were differences between them.

Here is a sample project https://goo.gl/Q2Tq1f

The discussions were very insightful particularly when students were discussing the value of simple models vs. more complete or complex models.

Notes: Even though the lesson did not go well as originally planed I am aware of how important it is and I am sure that when I do it again at the beginning of the year it will run much better.

I am teaching six classes, three seventh grade and three eighth grade. The classes are one hour in length and meet every other day. They have had computer classes every year since first grade, but they have not done any computer science other than “hour of code” type activities. Each student has a computer to use during class. They are keeping journals, grade seven on line, grade eight on paper. I am doing this to see which method gets more meaningful results. I followed this lesson pretty closely using a slide presentation as a guide. User “spear” posted a very helpful slide show on this forum.

I think the lesson went well, but it took longer than I thought. I had the students answer a journal prompt at the beginning. Prompt: We use the term “problem” to refer to lots of different situations. I could say I have a problem for homework, a problem with my brother, and a problem with my car, and all three mean very different things. In your journal, I want you to brainstorm as many different kinds of problems as you can and be ready to share with the class. Next they shared examples and I wrote them on the board and we created categories and placed the problems into the created categories. This led to the idea of having a strategy and the activity guide. We did all activities in the guide and shared some responses. In the next class instead of making posters. I gave each group 8 sticky notes and wrote the four steps on the board. I then asked them to write two strategies for each step and post them in the appropriate place on the board. We read what was written and I consolidated the responses in a document. I will post this in the classroom. Strategies I think this lesson went well. It was straightforward. Students seem to understand the four steps and the importance of having a strategy to solve problems. I think the journal entry helped them brainstorm problem types.

Once again thanks everyone for the awesome feedback and sharing your resources! Its great to see that some people are using the resources others have shared!

I teach at a high school in SLC, Utah. My class is very diverse in that we have multiple languages in the class, English is not the native language of 95% of my students, I have pretty close to 50/50 boy, girl ratio and the class is a good representation of students from the entire school ranging from grades 9-12. Our class period is 90 minutes every other day.

Things that went well: The activity guide did a great job of helping students organize their thoughts with the 4 steps. It also gave students the chance to see that the process can work forwards and backwards.

Things to reflect on: It took some brain storming for students to come up with things they are good at. Perhaps have them think about the prompt the previous day so they can talk with a friend or family member about it.

I was gone the 2nd half of the lesson where the were to find a classmate to solve a problem with, so this part of the activity was a little tricky because the students are new to the course and haven’t built strong relationships yet to feel completely safe sharing what they are/are not good at.

Related Topics

How it works

For Business

Join Mind Tools

Article • 4 min read

The Problem-Solving Process

Looking at the basic problem-solving process to help keep you on the right track.

By the Mind Tools Content Team

Problem-solving is an important part of planning and decision-making. The process has much in common with the decision-making process, and in the case of complex decisions, can form part of the process itself.

We face and solve problems every day, in a variety of guises and of differing complexity. Some, such as the resolution of a serious complaint, require a significant amount of time, thought and investigation. Others, such as a printer running out of paper, are so quickly resolved they barely register as a problem at all.

Despite the everyday occurrence of problems, many people lack confidence when it comes to solving them, and as a result may chose to stay with the status quo rather than tackle the issue. Broken down into steps, however, the problem-solving process is very simple. While there are many tools and techniques available to help us solve problems, the outline process remains the same.

The main stages of problem-solving are outlined below, though not all are required for every problem that needs to be solved.

1. Define the Problem

Clarify the problem before trying to solve it. A common mistake with problem-solving is to react to what the problem appears to be, rather than what it actually is. Write down a simple statement of the problem, and then underline the key words. Be certain there are no hidden assumptions in the key words you have underlined. One way of doing this is to use a synonym to replace the key words. For example, ‘We need to encourage higher productivity ’ might become ‘We need to promote superior output ’ which has a different meaning.

2. Analyze the Problem

Ask yourself, and others, the following questions.

• Where is the problem occurring?
• When is it occurring?
• Why is it happening?

Be careful not to jump to ‘who is causing the problem?’. When stressed and faced with a problem it is all too easy to assign blame. This, however, can cause negative feeling and does not help to solve the problem. As an example, if an employee is underperforming, the root of the problem might lie in a number of areas, such as lack of training, workplace bullying or management style. To assign immediate blame to the employee would not therefore resolve the underlying issue.

Once the answers to the where, when and why have been determined, the following questions should also be asked:

• Where can further information be found?
• Is this information correct, up-to-date and unbiased?
• What does this information mean in terms of the available options?

3. Generate Potential Solutions

When generating potential solutions it can be a good idea to have a mixture of ‘right brain’ and ‘left brain’ thinkers. In other words, some people who think laterally and some who think logically. This provides a balance in terms of generating the widest possible variety of solutions while also being realistic about what can be achieved. There are many tools and techniques which can help produce solutions, including thinking about the problem from a number of different perspectives, and brainstorming, where a team or individual write as many possibilities as they can think of to encourage lateral thinking and generate a broad range of potential solutions.

4. Select Best Solution

When selecting the best solution, consider:

• Is this a long-term solution, or a ‘quick fix’?
• Is the solution achievable in terms of available resources and time?
• Are there any risks associated with the chosen solution?
• Could the solution, in itself, lead to other problems?

This stage in particular demonstrates why problem-solving and decision-making are so closely related.

5. Take Action

In order to implement the chosen solution effectively, consider the following:

• What will the situation look like when the problem is resolved?
• What needs to be done to implement the solution? Are there systems or processes that need to be adjusted?
• What will be the success indicators?
• What are the timescales for the implementation? Does the scale of the problem/implementation require a project plan?
• Who is responsible?

Once the answers to all the above questions are written down, they can form the basis of an action plan.

6. Monitor and Review

One of the most important factors in successful problem-solving is continual observation and feedback. Use the success indicators in the action plan to monitor progress on a regular basis. Is everything as expected? Is everything on schedule? Keep an eye on priorities and timelines to prevent them from slipping.

If the indicators are not being met, or if timescales are slipping, consider what can be done. Was the plan realistic? If so, are sufficient resources being made available? Are these resources targeting the correct part of the plan? Or does the plan need to be amended? Regular review and discussion of the action plan is important so small adjustments can be made on a regular basis to help keep everything on track.

Once all the indicators have been met and the problem has been resolved, consider what steps can now be taken to prevent this type of problem recurring? It may be that the chosen solution already prevents a recurrence, however if an interim or partial solution has been chosen it is important not to lose momentum.

Problems, by their very nature, will not always fit neatly into a structured problem-solving process. This process, therefore, is designed as a framework which can be adapted to individual needs and nature.

Join Mind Tools and get access to exclusive content.

This resource is only available to Mind Tools members.

Already a member? Please Login here

Get 30% off your first year of Mind Tools

Great teams begin with empowered leaders. Our tools and resources offer the support to let you flourish into leadership. Join today!

Sign-up to our newsletter

Subscribing to the Mind Tools newsletter will keep you up-to-date with our latest updates and newest resources.

Subscribe now

Business Skills

Personal Development

Leadership and Management

Member Extras

Most Popular

Newest Releases

7 Reasons Why Change Fails

Why Change Can Fail

Mind Tools Store

About Mind Tools Content

Discover something new today

Top tips for tackling problem behavior.

Tips to tackle instances of problem behavior effectively

Defeat Procrastination for Good

Saying "goodbye" to procrastination

How Emotionally Intelligent Are You?

Boosting Your People Skills

Self-Assessment

What's Your Leadership Style?

Learn About the Strengths and Weaknesses of the Way You Like to Lead

Recommended for you

How to manage defensive people.

Lowering Defenses by Building Trust

Business Operations and Process Management

Strategy Tools

Customer Service

Business Ethics and Values

Handling Information and Data

Project Management

Knowledge Management

Self-Development and Goal Setting

Time Management

Presentation Skills

Learning Skills

Career Skills

Communication Skills

Negotiation, Persuasion and Influence

Working With Others

Difficult Conversations

Creativity Tools

Self-Management

Work-Life Balance

Stress Management and Wellbeing

Coaching and Mentoring

Change Management

Team Management

Managing Conflict

Delegation and Empowerment

Performance Management

Leadership Skills

Developing Your Team

Talent Management

Problem Solving

Decision Making

Member Podcast

How to Know When You've Learned Everything You Can From a Programming Problem

The answer may seem obvious: you’re done with a problem once you’ve solved it.

That’s how I approached problem-solving when I began learning to code. I was on a problem-solving treadmill: solving as many problems as quickly as possible.

And why not? There’s no shortage of problems to solve. Besides, don’t you get better by solving more problems? More to the point: what else can you do once you have the answer? As it turns out, quite a bit. The fallacy of my approach soon surfaced.

Although I solved the problem, I didn’t learn much from it. That’s because a few days or weeks later when I tried to re-solve the problem or when I came across a related one, I got really stuck . Mistakes were made. Concepts were confused. Progress was stalled.

I now realize that getting the solution is only part of the problem-solving process. Then, in the words of a mathematician named George Pólya, it’s time to “look back.”

Looking Back

Pólya writes about the problem-solving process in his book, How to Solve It , through the lens of mathematical problem-solving. But his ideas are applicable to programming. What’s particularly interesting to me is his fourth phase: looking back.

“By looking back at the completed solution, by reconsidering and reexamining the result and the path that led to it, [students] could consolidate their knowledge and develop their ability to solve problems,” Pólya writes.

In some ways, solving a problem is like creating a piece of art. There’s always something more we could do. “We could improve any solution, and, in any case, we can always improve our understanding of the solution,” explains Pólya.

For me, “looking back” is a practice of self-improvement and learning . The aim is to:

• Learn from my successes: understand what you wrote and why.
• Solidify my learning of new concepts.
• See patterns and understand the context for using a particular data structure or algorithm.

Consider a basketball player who takes 1,000 shots each day. That sounds admirable. But as he rushes to get the 1,000 shots in, his form gets sloppy. He uses the wrong technique.

He’d benefit more from taking a few hundred shots, then evaluating his performance: watching a video recording of his form, seeing the flaws, and correcting them. Then, he'd hit the court again.

Now he’ll be more informed, since he looked back and evaluated his performance. He’ll practice better.

The same is true with solving problems. The idea isn’t to check a box so you can claim you solved “x” number of problems. Instead it’s doing your best work each time and learning as much as possible along the way.

There are three reasons why looking back matters.

Reason #1: See the Patterns and Understand the Context

You’ll see similar patterns over and over again in the problems you solve.

Understand how to use a particular algorithm, like binary search. Train your eye so you know when and how to apply it. So when you encounter a related problem in the future, you’ll be ready. Doing so will save time (and frustration) in the long run.

Reason #2: Solidify Your Learning

Say you used something that’s new to you to solve a problem, like a stack or queue.

Do you really know how to use it again? Do you feel comfortable using a stack in a related problem? Take the time to understand anything new you used so you can use it again in the future.

Reason #3: Learn from Your Successes

Mathematician Richard Hamming gets to the heart of the matter with this quote from his book, The Art of Doing Science and Engineering.

“I regard the study of successes as being basically more important than the study of failures...there are so many ways of being wrong and so few of being right, studying successes is more efficient.”

As programmers, we deal with our fair share of errors. And then (many tries later) we run the program and it works. Now is a great time to put Hamming’s words to practice and study your success.

Do you understand how your program works? Do you understand what you wrote and why you wrote it?

By looking back⁠—when the information is still fresh in your mind⁠—you’re preparing your future self. It’ll help you bridge your understanding and solidify your mental models. It’ll help you improve and prevent repeating the same mistakes over again. In short, it’ll help you get better.

Four Ways to Look Back

There are a few ways that I “look back” at problems. Give them a try.

Teach Yourself

A fantastic way to help solidify your mental models is to teach yourself. After you complete a program or problem, go through your code and explain it line by line. It’s one of the best ways of “looking back” when you’re learning something new.

I’ve found this process invaluable while learning web development. After I complete a project, I copy my code into a Google Doc. Starting at the top, I make comments throughout to teach myself about important concepts.

Here’s an example of some code and some of the comments I wrote.

• Use props to access data passed down from the parent component.
• Add state hook. The hook takes a default, which is an object that contains everything I need for the form: name, email, role.

This method of “looking back” is about understanding. In this example, I was learning about state, props, and forms in React.

Writing out comments to explain your code will help you solidify concepts in your mind. If you can’t type a short explanation of it on the spot, then revisit the topic.

This method is equally useful for future problems and projects. I regularly pull up old problems and programs I’ve notated. I use them as a reference when writing related programs or solving related problems. Doing so reinforces key ideas, and to Hamming’s point, it helps me remember my successes: what to keep doing.

Study Solutions of Great Programmers

It’s not only useful to study your own code, but also the code of others who have solved the same problem. There are a lot of great programmers out there and we can learn from them.

After I solve a problem, I apply a learning technique that Ben Franklin used to become a better writer. His process involved trying to reproduce an article from a publication he admired after he’d forgotten the details of it.

I follow a similar process to become a better programmer.

Here’s how it works:

• Solve a problem .
• Find a programmer who’s better than you and who’s solved the same problem.
• Study their solution : read each line of code and type a comment in your editor to explain it.
• Re-solve the program after some time has passed. Use the comments you typed out as hints to guide you along the way.
• Compare your program to the one you studied.

To be clear, this practice isn’t about memorizing or copying someone else’s code—far from it. Rather, it’s about learning: get practice reading code; see another way to solve the same problem; experiment with new parts of a language; and get practice teaching yourself. It’s also about applying what you’ve learned by putting it into your own style.

Add a Constraint

See how different techniques apply to the same problem when you add a constraint. For example, you solved the problem using a hash table. Now try solving it using an array.

The idea is to gain another perspective, and adding a constraint can do just that. It’ll get you out of your comfort zone, forcing you to think creatively.

As a result, you may find a slicker approach and cut the length of your program in half. Or may realize what data structure not to use, which is equally important.

Here’s the point: you’ll have another approach at your ready when you’re faced with a related problem in the future.

Solve a Related Problem

The programming website LeetCode is great for many reasons. One is providing similar questions for problems that you solve.

In one problem on LeetCode you are given an array of integers and a target number. The aim is to find two numbers that add up to the target and return their indices.

You solve the problem.

Now solve a related one, which LeetCode provides. This time you’re given an array of integers that’s sorted in ascending order, along with a few additional constraints to differentiate this problem from the previous one.

Solving a related problem is a great way to get practice using a similar technique, data structure, or algorithm in a different context.

Looking back focuses on the process , instead of the end result. And revisiting the process matters. It’s getting out of your comfort zone, trying something new whether that’s a data structure or algorithm. It’s realizing there are different ways to solve the same problem. It’s understanding how to write better code. It’s about learning.  

Yes, it takes some time to look back. But it’s time well spent: it’s how we get better.

I write about the programming skills you need to master and the concepts you need to learn, and the best ways to learn them ( amymhaddad.com ).

Programmer and writer | howtolearneffectively.com | dailyskillplanner.com

If you read this far, thank the author to show them you care. Say Thanks

Learn to code for free. freeCodeCamp's open source curriculum has helped more than 40,000 people get jobs as developers. Get started

Your browser is not supported. Please upgrade your browser to one of our supported browsers . You can try viewing the page, but expect functionality to be broken.

CS in Algebra curriculum and content is being deprecated. Within the next few months, this lab will no longer be available. Please check out Bootstrap: Algebra instead. Learn More .

Undergraduate students’ analogical reasoning in solving HOTS statistical methods problem

[email protected]

[email protected]

[email protected]

• Split-Screen
• Article contents
• Figures & tables
• Supplementary Data
• Peer Review
• Open the PDF for in another window
• Reprints and Permissions
• Cite Icon Cite
• Search Site

Amalia Silwana , Cholis Sa’dijah , Sukoriyanto , Hendro Permadi; Undergraduate students’ analogical reasoning in solving HOTS statistical methods problem. AIP Conf. Proc. 29 April 2024; 2622 (1): 080003. https://doi.org/10.1063/5.0134036

Download citation file:

• Ris (Zotero)
• Reference Manager

Analogical reasoning is a process of concluding identical relationships or problem-solving structure similarities of the source problem to be applied in solving the target problem. The aim of this research is to describe analogical reasoning of first semester undergraduate students in solving higher order thinking skill (HOTS) statistical methods problem. This research is descriptive qualitative research. The research subjects are six undergraduate students: two high-ability undergraduate students, two medium-ability undergraduate students, and two low-ability undergraduate students. Research data obtained from the result of HOTS analogical statistical methods problem test and interviews. The research results showed that high-ability undergraduate students could pass through the encoding, inferring, and mapping stages well in solving HOTS analogical statistical methods problem. But not all of the high-ability undergraduate students could pass through the applying stage, since some of them make a little error calculation due to lack of accuracy. While medium-ability undergraduate students could only pass through the encoding stage, and low-ability undergraduate students couldn’t pass through all of the analogical reasoning stages.

Citing articles via

Publish with us - request a quote.

Sign up for alerts

• Online ISSN 1551-7616
• Print ISSN 0094-243X
• For Researchers
• For Librarians
• For Advertisers
• Our Publishing Partners  
• Physics Today
• Conference Proceedings
• Special Topics

pubs.aip.org

• Privacy Policy
• Terms of Use

Connect with AIP Publishing

This feature is available to subscribers only.

Sign In or Create an Account

Help | Advanced Search

Computer Science > Artificial Intelligence

Title: gold: geometry problem solver with natural language description.

Abstract: Addressing the challenge of automated geometry math problem-solving in artificial intelligence (AI) involves understanding multi-modal information and mathematics. Current methods struggle with accurately interpreting geometry diagrams, which hinders effective problem-solving. To tackle this issue, we present the Geometry problem sOlver with natural Language Description (GOLD) model. GOLD enhances the extraction of geometric relations by separately processing symbols and geometric primitives within the diagram. Subsequently, it converts the extracted relations into natural language descriptions, efficiently utilizing large language models to solve geometry math problems. Experiments show that the GOLD model outperforms the Geoformer model, the previous best method on the UniGeo dataset, by achieving accuracy improvements of 12.7% and 42.1% in calculation and proving subsets. Additionally, it surpasses the former best model on the PGPS9K and Geometry3K datasets, PGPSNet, by obtaining accuracy enhancements of 1.8% and 3.2%, respectively.

Submission history

Access paper:.

• Other Formats

References & Citations

• Google Scholar
• Semantic Scholar

BibTeX formatted citation

Bibliographic and Citation Tools

Code, data and media associated with this article, recommenders and search tools.

• Institution

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .