Purpose

Fortunately, as they get more used to the how question, students become more willing to engage in mathematical conversations and frequently immerse themselves in their thoughts. On such occasions, my job is not to teach them anymore – it is to introduce conceptual tools and empirical definitions, ask the how question, follow their course of thoughts, and discuss any flawed logic. With such guidance, students often approach the solution, ensuing increased confidence and interest in math. Even when they are wrong, many of their ideas develop into valuable ways of understanding concepts. So I believe that math classrooms should incorporate student reasoning.

 

Seemingly, many state leaders and policymakers in the United States had similar beliefs as me. The Common Core State Standards (CCSS) were implemented in most states approximately ten years ago, emphasizing critical thinking and in-class discussions. Advocates of the CCSS expected significant improvement in students’ problem-solving abilities, abstract and quantitative reasoning, and constructing mathematical arguments.¹ Indeed, many traditional, memorization-based math classrooms have hitherto transformed into reasoning-oriented, communicative ones, which could enhance students’ engagement, math achievement, and real-life applicable problem-solving abilities.²

 

As I learned more about the Common Core, however, I began to wonder – if the CCSS have been truly successful, why do many of my students, all of whom experienced the standards throughout their primary and secondary education, still have trouble answering the how question? In fact, the CCSS have engendered controversy, as student math competence has slightly decreased since its implementation.^3,4

 

Experts have expressed different opinions about this outcome – some believe that the standardized tests cannot reflect the effects of the Common Core, some criticize each school and district’s inadequate implementation of the standards, and others condemn the entirety of the CCSS. In any case, although there has been little empirical research that shows the failure of the CCSS, its way of promoting student math proficiency has “not translated into higher student achievement.”⁵

 

The case of the CCSS reminds me of the reform endeavors in South Korea. The country is known for its high student math competence, but many Korean students experience heavy academic stress and pressure from their environments, as they are forced to memorize numerous formulas to solve challenging questions. Seemingly, those who have failed to overcome such a strain develop fear and anxiety against mathematics. A statistic from 2015 reported that nearly 46% of middle school students and 60% of high school students in Korea consider themselves to have given up on math.⁶ The Korean Ministry of Education has attempted to remedy students’ anxiety by reducing the topics covered in secondary mathematics classrooms,⁷ but generally decreased student performance has hitherto ensued.⁸ Such disheartening facts led me to wonder: Are there more effective ways to cope with students’ math anxiety?

 

Many similar questions arise – questions relating to the purpose of math classrooms (Improving student math proficiency? Reducing math anxiety?). Karl Weierstrass, the father of modern analysis, states that “a mathematician who is not somewhat of a poet will never be a complete mathematician.” I believe that this element of mathematics, the one so explorative and creative that it is even comparable to poetry, must be the core of each math classroom, whatever their goal may be.

 

But implementing this idea is much more complicated than simply designing good policies and curricula. Both nations mentioned above render meaningful progress in education: The CCSS in the United States have initiated the transform towards incorporating student reasoning in math classes, and Korea has become mindful of student math anxiety and endeavors to remedy it. Their reforms are the products of contemplations of renowned scholars. Still, disappointing outcomes have emerged. How so? Is there a better way to ameliorate math education?

 

These questions entail numerous thoughts and ideas that shape my educational path. In this blog, I hope to exhibit such thoughts and ideas – any of my “klueless” thoughts – that emerge from this journey.∎