By Amos Tarfa
We have decades of research, curricula, technologies, interventions, and instructional approaches. So why are so many students still struggling to actually do mathematics?
More technology does not always mean greater excellence in mathematics. Despite the progress we have made technologically and in many other areas, many students still dislike mathematics, and some struggle to do it well. One reason worth exploring is that some students simply do not care as much as we would like them to. We have not given them a reason to care.
Could there be a connection between a student’s lack of interest and willingness to learn and poor mathematical performance? No matter what we try, if the student is not invested in the learning process, is there a limit to how much progress we can make?
These are questions worth considering as we examine the challenges facing mathematics education today.
The Importance of Mastery
One of the problems with the modern education system is that students are often allowed to move on to the next class without mastering the fundamentals taught in the previous one.
Mathematics builds upon itself. When students move forward without understanding foundational concepts, they may struggle to grasp the more advanced ideas that depend on them. Over time, these gaps can make mathematics increasingly difficult.
What, then, does mastery look like?
One way to recognize mastery is when a student can teach what they have learned to someone else. When students can explain a concept in their own words and demonstrate their understanding to another person, they show that they have gone beyond simply repeating information.
We need to ask ourselves whether moving students through the curriculum is enough if they have not mastered the knowledge they are expected to learn. Progress should mean more than advancing to the next class. Students need a solid foundation upon which to build their mathematical understanding.
Giving Students a Reason to Care About Mathematics
The problem today is not necessarily that we need to increase the supply of materials available for mathematics education. Instead, we need to consider how we can help students develop a greater interest in and appreciation for mathematics.
One way to do this is by teaching students the context that gave rise to mathematical concepts, as we discussed in the previous blog post.
Mathematics did not simply appear as a collection of formulas and procedures that students must memorize. The concepts we teach today emerged from questions, problems, and the work of people seeking to understand the world around them. Exploring that context can help students see why mathematical ideas matter and how they connect to one another.
When students are taught concepts without understanding the context that gave rise to them, they may become apathetic toward the subject. Mathematics can begin to feel like a collection of arbitrary rules rather than a body of knowledge worth understanding.
Think about it: Would you want someone to tell you to learn something without helping you understand why it matters?
Students deserve the opportunity to understand not only how to do mathematics but also why mathematical ideas exist and what makes them meaningful. Giving them that context may help foster the interest and appreciation that make learning more engaging.
Rethinking Mathematics Education
We have invested decades in developing curricula, technologies, interventions, and instructional approaches. Yet many students continue to struggle with mathematics.
Perhaps we need to look beyond the materials themselves and consider whether students are mastering the fundamentals and whether we are giving them compelling reasons to care about what they are learning.
Students need a strong foundation in mathematics. They also need opportunities to understand the ideas behind the concepts they study. When we prioritize mastery and help students appreciate the context in which mathematical knowledge developed, we can take meaningful steps toward improving their experience of learning mathematics.
The question is not simply how much material we can provide or how quickly students can move through it. It is whether they are developing the knowledge and understanding necessary to do mathematics well—and whether they can see why that knowledge is worth acquiring.
If we want students to succeed in mathematics, these are questions we cannot afford to ignore.
About the Author
Amos Tarfa is a medical physicist and mathematics and science curriculum writer who seeks to help every child reach their full potential in mathematics and in life. His goal is to raise the next generation of mathematicians, scientists, and thinkers who also understand the history and philosophy of science, logic, and theology.
He is the creator of Counting to Calculus, a curriculum designed to take learners from basic mathematics to calculus in one year. Amos also teaches a summer MIT Outreach Math Class in Wyoming. He lives in Cheyenne, Wyoming, with his wife, Stephanie, and their seven children.
Learn more about Amos’s work:
