I was recently talking with a high school student about math, and she said something that really resonated with me. She had some homework problems that she did not know how to do. The teacher had shown examples in class, but the homework problems were slightly different. She explained, “It’s like all of my math knowledge could be represented by separate chains, and each of my chains has a broken link. I listen while the teacher describes how to do the problem, but usually there seems to be a part that they skip or that I don’t understand. Suddenly they have the answer written down, and I don’t know how they got from what I understood last to that answer.”
This student had concluded that her struggle to understand math meant that she was just not good at math. We need to stop conveying to students that their struggle to understand ideas fully and to process and reason through math concepts means that they are not good at math. Actually, it might mean the opposite—that they possess the critical thinking skills necessary to become an excellent math student.
What If Our Approach to Teaching Math Is Wrong?
Studies at the Mangels Lab of Cognitive Neuroscience of Memory and Attention at Baruch College at the City University of New York found that when math is taught in a stressful and high-pressure atmosphere where students do not feel successful, this can lead to significant math anxiety which inhibits math performance. This math anxiety tends to affect our most promising high-achieving students.
Often, when this happens, teachers and parents are told to address it with strategies to calm and refocus the student, but what if the real problem is the way we’re teaching math? It’s as if we’re trying to teach students to navigate by showing them one random set of directions or by putting one starting point and destination in Google Maps and then going over each of the resulting turns.This makes math knowledge like chains where students must remember each step or link in order to successfully navigate the problem. It also results in the student not understanding how a new piece of math knowledge relates to what they’ve learned previously.
Instead, we should be showing them the map, and having them use it to figure out all the possible routes to get from point A to point B. As teachers, we should be emphasizing math problem-solving and math thinking instead of quick performance and correct answers.
What Would This Look Like, and How Would It Work?
To use this method, teachers would act as facilitators. They would present the class with the problem, then in small groups or as a whole class, students would describe what they notice. The teacher would summarize and list these observations while asking questions and providing information that would lead students in their problem-solving. Students would then work as a group to brainstorm methods to arrive at a solution. The teacher would summarize and list each method with the group and lead the class toward deciding which method was most effective.
Students would have to describe how this method worked and why it was the easiest and most effective method.This could work at any level, and it may look different at the early elementary level from what we see at the late elementary/middle school level.
What Are the Advantages of Teaching Math This Way?
1. Critical thinking is enhanced because students are engaged: Students discuss what they notice, explain their thinking, and are actively involved in finding solutions to the problem. This is very different from the traditional math classroom, especially in middle and high school, where students sit quietly taking in information, writing down examples, and working on practice problems independently.
2. It builds math confidence: This method shows students that they’re capable of solving problems on their own or by working together. Having students take an active role in their learning builds confidence and makes them less reliant on the teacher to be the provider of solutions. It empowers them to figure out even difficult problems by doing the complex and often difficult work of thinking through the problem themselves.
3. It teaches students a growth mindset: When students see math as a performance subject rather than a subject where learning is emphasized, they’re more likely to fear math. When teachers shift the focus from right or wrong answer to an emphasis on mathematical thinking, they help students to understand that their math ability can grow. Instead of thinking that if they don’t understand something right away, it means they’re bad at math, they know that if they don’t understand something, they have the ability to work on it and figure it out.
4. Math performance is improved: When students see math as a set of ideas they can explore and figure out, they have no reason to fear math, and their performance in math will improve. Speed and time pressure block working memory, preventing students from showing what they know. However, Stanford expert Jo Boaler found that students who learn through strategies rather than simply memorizing facts achieve superior performance because they understand the relationships between numbers.
5. This method is more applicable to how math is used in adulthood: If students get a job where they use math, they will probably need to know how to apply their knowledge of math to solve complex and unique problems. They’ll have to use problem-solving to work through to a solution, and they’ll have the opportunity to brainstorm with others. Even students who do not grow up to pursue a career where they use math will have to use math to solve everyday problems. These real-world problems also require that a student think critically about which math skill to apply based on the current situation.
At first, requiring students to use critical thinking to solve problems will be frustrating to students who have always been immediately provided with a method to find the correct answer. However, if you stick with it, in the long run it will make students into problem-solvers who are capable of asking their own questions and finding their own solutions.
This piece was originally submitted to our community forums by a reader. Due to audience interest, we've preserved it. The opinions expressed here are the writer's own.