Students Doing Math

Teaching Students How to Study Math

When it came to me, it was the beginning of my first year of college. When I found out that I had received a grade of C on my calculus midterm, I felt defeated. It wasn’t the letter C that bothered me in the least. Simply put, I wanted the grade to reflect how well I understood the material, but unfortunately, I believe that it does not. Although I was familiar with all of the ideas that were being tested, I ended up making a lot of mistakes that weren’t discovered until after the test was given back to me.

When I first started teaching, I noticed that many of my students were having trouble with the same things. They would have a day to review and prepare for the tests before I would give them. My students were acting out of control during one of those sessions when they were supposed to be studying instead. During our debriefing and reflection on the difficulties we encountered that day, I paused for a moment and asked the class in a direct manner, “How do you study math?” At that precise instant, I had a realisation:

The vast majority of my students had no idea what to do when they were presented with such a query.
Their misbehaviour occurred because they were not provided with any structure or direction regarding how to proceed with their day.
Students ought to be instructed in effective methods of studying math, and I ought to be the one to impart such knowledge to them.
Now, at the beginning of each new school year—before I present my students with any content—I instruct them in the proper way to study mathematics. This gives them the opportunity to see the purposeful intent behind how everything we do in class throughout the year will contribute to their education.


According to Professor Rochelle Gutierrez, “Mathematics is not a noun but a verb.” [Citation needed] It is not something we are aware of; rather, it is an action that we carry out. Math is a skill that can be acquired through practise. Students frequently fall victim to the common misconception that studying mathematics merely entails going over old notes or assignments. Because of this, the harmful misconception that mathematics is solely something that needs to be memorised is kept alive. It is impossible to commit to memory every possible path to a solution for the infinite mathematical concepts that can be represented in different ways. (However, the chess grand master Magnus Carlsen is in the running.)

When they are studying, rather than focusing on memorization, I tell my students to try to replicate the mode of assessment that will be administered to them. In the best case scenario, students would practise on their own if they were getting ready for a test that was designed specifically for them. In the event that it is a presentation of learning, they could get valuable experience by presenting and demonstrating their work to their classmates, members of their family, or other close friends and acquaintances. Before taking their exam, students would have time to evaluate their work and make any necessary adjustments thanks to this opportunity.

We all make mistakes. Students need to be able to recognise and fix their own errors before anyone else can judge the quality of their work. This is the purpose of the studying process. When they are studying, they want to make mistakes in the same way that they might make mistakes on the test, so that they can learn from those mistakes. As a result, they might be able to practise for the assessment by simulating a mistake they know they’ll make and practising how to fix it.


When students are preparing for their individual exams, they can study by doing practise tests that come with answer keys or by working through problems that they have already solved (not looking at the work or answer as they rewrite the original task on a separate sheet of paper and work to complete it).

In order to get my students ready for this, I tell them, “It’s okay to mess up; the important thing is to learn from them.” After all, errors serve as valuable learning opportunities because they highlight areas in which improvement is necessary.


In the event that students are unable to complete the activity that they are learning, there is a scaffolded regression that they can complete to determine their zone of proximal development in order to better prepare for the evaluation.

1. Students could finish the task, look back at a previous problem that was similar to the one they are currently working on to determine what steps they may have skipped, and then move on to another problem. This occurrence lends credence to the old adage that “practise does not make perfect; perfect practise makes perfect.” If they are not successful in getting the correct answer, it does not matter how many practise problems they complete. When working with my students, one of the most common pieces of advice I give is, “Don’t practise until we get it right; practise until we can’t get it wrong.” When they enter an evaluation, I want my students to have the attitude that they have already completed the task at hand and are prepared to demonstrate what they have learned.

2. Students were permitted to refer to their own notes. At this point, taking accurate notes is absolutely necessary. When performing the tasks, it becomes a way for students to support themselves with rationale behind the concepts that they are expected to know.

3. If a student needs support, they can seek it from either another student or from the teacher.

When we instruct our students in the proper way to study, they gain an understanding of how the foundation is being laid for them to achieve the results of their efforts. They are aware of the connections that exist between all of the academic resources that they will come across over the course of the year and how those resources will provide them with the opportunity to not only learn but also accurately demonstrate what they have learned.