Too often, students have viewed struggle in math as an indication of failure or as an indication the student is not a “math person.” We believe all students can be successful in math. We want our students to know that successful people struggle quite often - in fact, as problem-solvers, mathematicians and really any other creative person, spend most of their time struggling with problems - and they enjoy the challenge. They view mistakes as feedback, not failure. If one approach doesn’t work, then their response is to figure out why and try another. We encourage our students to view struggle and mistakes as part of the learning process - and as an indication that they are challenging themselves. We want them to respond by trying again and we want to give them strategies for stronger resilience and perseverance. We believe in giving students multiple opportunities in the learning cycle to master a concept, with the teacher providing guidance and feedback along the way. The development of a growth mindset towards struggle will only become more important as students advance toward college and career, where success will depend on a desire to take on new challenges and a willingness to struggle with them.
Fundamentally, we want students to be making sense of the math from the start of freshman year. Procedural fluency is important, but it should come through sense-making. Asking students to present and explain their thought process not only helps to verify understanding but also helps to show students that there is often more than one way to solve a problem. Sense-making discussion helps students understand why procedures work, which helps students apply them more adeptly and more flexibly.
Math is problem-solving, not recipe-following. And as students move on in math and in life, they will increasingly face problems they initially won’t know how to solve. From the start of freshman year, we want to help students develop important skills which will empower them as they move through the math curriculum. Defining objectives, applying previous math knowledge, and forming strategies for effectively utilizing all available resources are all essential problem-solving skills. These skills are important not only for success in our upper division courses, but also for success in college and career.
Our department teachers use a variety of instruction methods, but we believe students particularly benefit when they are problem-solving in groups under the active guidance of an instructor. We strive to give them discussion-worthy problems which are open in nature, and which support both accessible entry points and high ceilings, to accommodate a full range of learning. Teachers engage with students through direct instruction and guidance, but also by encouraging discussion and debate within teams that prompts students to share different ways to think about a problem for deeper learning. This not only leads to deeper understanding, but in the process, students also learn valuable teamwork and collaboration skills that will serve them in college and beyond.