Reading Dr. Gerofsky’s article on the history of mathematics education made me realize that many questions I am asking as a mathematics teacher have been debated for over a century. Understanding, memorization, inquiry, and technology are all part of this complicated history. What surprised me was how often similar conflicts returned, even as society changed. Three moments made me pause and reconsider both my own learning experiences and the classroom I want to create.
My first stop was Table M.1, which compares conservative and progressive stances in mathematics education. I recognized many connections between the progressive column and what I have been learning about BC’s curriculum: inquiry, flexible problem-solving, communication, and understanding. These are qualities I want my students to develop. However, the table also made me wonder whether our assessments always support these goals. If we encourage students to explore different approaches but mainly reward speed and correct answers, what are we really telling them matters?
This tension feels familiar from my teaching experience. Although exams can assess understanding, preparing for them can easily become practising recognizable question types and remembering the expected steps. I initially found myself thinking that BC’s approach seemed more supportive of learning than the emphasis I associate with exams such as the SAT and AP. However, I cannot judge an entire education system through particular exams. What attracts me most is the possibility of using ongoing formative assessment to understand students’ thinking and help them improve. When exam preparation does not dominate every lesson, teachers have more space to follow students’ questions and invite different solutions.
The more I teach mathematics, and the more I learn in this program, the less satisfied I am with describing it as simply a right-or-wrong subject. Answers and reasoning still need to be mathematically valid, but there can be several meaningful ways to solve a problem. The quickest method is not always the one that helps a particular student understand best. The discussion of Dewey’s emphasis on inquiry helped me recognize that this concern is far from new. Why, after so many years, is it still difficult to give exploration enough space in mathematics classrooms?
My second stop was the discussion of mathematics anxiety among elementary teachers and their reliance on memorized procedures. Although this passage describes teachers in North America, I immediately thought about my own education in China. From middle school onward, I often learned mathematics by remembering the steps. Sometimes I did not understand why a method worked, but my memory was good enough to help me answer questions successfully. This gave me the impression that I was good at mathematics and that learning it was fairly easy.
During my final two years of high school, mathematics became much harder. Looking back, I wonder how many earlier ideas I had never fully understood. This pattern continued into university, where I could sometimes use formulas without understanding the concepts behind them. It was only when I began teaching that certain ideas became much clearer. I found myself thinking, “So this is what a derivative describes,” or “Now I understand what integration is doing.” Preparing to explain mathematics to someone else made me revisit gaps that good grades had allowed me to overlook.
This is one reason my classroom feels different from the classrooms I experienced as a student. Sometimes I feel as though I ask a hundred questions in one lesson. I want to know what students think a concept means, why a method works, and where the idea might be useful. They may not immediately solve every problem independently, but I want them to have some sense of what they are studying. This reading also reminds me that asking questions is not enough by itself: I need to listen carefully and give students time to think.
It also brought back an online discussion I had encountered about whether anyone could learn calculus. After these first few weeks in the BEd program, I am more willing to question assumptions about who is capable of learning advanced mathematics. However, believing in students’ potential does not mean expecting everyone to learn at the same pace. Prior knowledge, time, teaching approaches, and support all matter. My own understanding developed much later than my ability to reproduce procedures. That makes me hesitant to treat a student’s current difficulty as evidence of a fixed limit.
My third stop was the description of reforms that emphasized flexible problem-solving, multiple representations, technology, and mathematical communication. I was struck by how familiar these goals sounded. Ideas that feel current in my teacher education were already central to earlier reforms.
With today’s calculation and visualization tools, I can see why students might spend less time performing lengthy calculations and more time interpreting relationships. However, I also feel uncertain. A strong foundation in arithmetic and algebra can make later learning much more accessible. If students rely on a calculator whenever it is available, they may miss opportunities to develop fluency or recognize an unreasonable answer. Students may not yet know which skills they need to practise independently and which tasks can usefully be supported by technology.
I found the reminder that these reforms still valued computational fluency especially helpful in thinking through this tension. Technology and basic skills do not have to compete. As a teacher, I need to be clear about the purpose of a task: are students practising a procedure, exploring a relationship, or interpreting a result? Sometimes working without a calculator will support that purpose; sometimes a graphing tool will reveal something that calculations alone would obscure. What I am still learning is how to make those choices thoughtfully, so that tools extend students’ mathematical thinking while they continue developing the foundations they need.
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