Mathematical Problem Solving
MATH 626
Overall Course Reflection
Problem Solving in Mathematics focused on developing strategies for approaching challenging and non-routine mathematical problems. In this course, we explored a wide range of problem types drawn from areas such as algebra, geometry, number theory, combinatorics, and probability. Rather than relying on standard procedures, we were encouraged to think creatively and flexibly. We discussed heuristics such as working backwards, finding patterns, drawing diagrams, or breaking a problem into simpler parts. We also looked at how we could incorporate these ideas into our mathematics classroom.
This class pushed me to become a more resilient problem solver and helped me build confidence in tackling unfamiliar problems. It helped me to rethink how I engage with mathematics. Being “stuck” is often where the most meaningful learning happens, and I became more comfortable sitting with difficult problems without immediately knowing the solution. This is something that I want to pass along to my students, to help them deepen their respect for mathematics.
Course Artifacts
Problem Assignment Video
This video is a presentation showing my take on how to embed a problem-solving task in my classroom. For this project, I designed and crafted a task for an Intermediate Algebra class, covering systems of equations. I begin the task by having a bag full of coins and slowly reveal information about the coins. Students need to work with groups to determine the quantities that match the information provided.
(Creation time: 2 hours)
Problem Solving Video
This video is a presentation on my demonstration of using Polya’s four step problem solving framework to solve a problem on exponential decay. In the video, I work through each step of the process, understanding the problem, devising a plan, carrying out the plan, and looking back to check and interpret the solution. This is a process and a problem that I used with my students in Algebra 1 this year. I also demonstrate some ways that teachers could extend and generalize this problem for their students.
(Creation time: 2.5 hours)
Final Project
This artifact is my final project, for which I designed problem-solving activities for an Intermediate Algebra course. The project focuses on embedding tasks that support student thinking, address misconceptions, and build reasoning skills across three key objectives: setting up equations from context, interpreting graphs, and solving quadratic equations through factoring. Students engage in activities such as matching equations to scenarios, identifying and correcting errors, constructing and interpreting graphs collaboratively, and working backward from solutions to build quadratic equations. These tasks help students connect concepts, communicate their thinking, and develop persistence. I also incorporated reflection, metacognitive journaling, and error analysis to promote deeper learning.
(Creation time: 12 hours)
Group Work Exercises
These are group problem-solving exercises that I completed collaboratively with three other math educators. In these exercises, we worked together to solve challenging, open-ended problems. One involved combinations on a lock, and the other focused on analyzing knight’s tours on various chessboard sizes. This demonstrates how I engage in mathematical problem solving as part of a team, through contributing ideas, refining strategies, and learning from others’ reasoning. It also reflects my understanding of the value of group work in developing deeper insights, resilience, and mathematical communication skills.
(Creation time: 5 hours per exercise)
Problem Solving Assignments
These problem-solving assignments showcase my work on challenging homework problems that required individual problem solving. These assignments gave me the opportunity to apply problem-solving strategies to a variety of open-ended and tricky mathematical problems. They required me to think creatively, explore different approaches, and justify my reasoning clearly and thoroughly.
(Creation time: 5-7 hours per assignment)