“How did you get that answer?”

 

This is what I call the how question: the phrase that I have used the most throughout the six years of my experience as a math tutor.

 

Students’ responses vary. Sometimes they try their best to explain their reasoning. Other times they would tell me they used the formula (Because that’s just how it works! they would exclaim). They also may confess that they had guessed or that they do not know. Among these remarks, the most notable and personally surprising response is when they show their troubled faces asking, “Am I wrong?”

 

This agitated response is especially common when I first meet students. Most of them are in middle or high school, and they feel uncomfortable demonstrating their ideas. Perhaps, the only time they are asked about their thoughts is when their answers are incorrect. Or, they may have blindly followed the memorized procedures, so they are unsure of their solutions. Either way, I am heartbroken every time I encounter such a reaction. Inability to respond to the how question reveals the absence of student reasoning in their past math learning experience.

 

As students’ critical thinking develops, they 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 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 the 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 interpretation 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, their ways of promoting student math proficiency have “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 of such questions arise in my twenty-five-year-old brain. Questions relating to the goal 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. But still, they have yielded disappointing outcomes. How come? What is a better way of ameliorating math education then? Answering these questions will shape my educational path towards designing successful student-responsive curricula and policies where students could proficiently utilize the how question when engaging with mathematics.

 

In this blog, I hope to exhibit my thoughts – any of my “klueless” thoughts – that emerge from this journey. ∎

 

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¹  National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors.

²  Boaler, J. (2015). What’s math got to do with it?: How teachers and parents can transform mathematics learning and inspire success (pp. 57-83). New York, NY: Penguin Books.

³  National Center for Education Statistics. (2013, 2015, 2017, 2019). National Assessment of Educational Progress: An overview of NAEP. Washington, D.C.: National Center for Education Statistics, Institute of Education Sciences, U.S. Dept. of Education. Retrieved 2020, from https://www.nationsreportcard.gov/ndecore/xplore/NDE

⁴  Organisation for Economic Co-operation and Development (2009, 2012, 2015, 2018), Program for International Student Assessment; Reading, Mathematics and Science. Retrieved 17 December 2020, from https://pisadataexplorer.oecd.org/ide/idepisa/report.aspx

⁵  Loveless, T. (2020, November 30). Common Core Has Not Worked. Retrieved 2020, from https://www.educationnext.org/common-core-has-not-worked-forum-decade-on-has-common-core-failed/

⁶ Park, H., & NoWorryEdu (2015, July 22). 수학교육과정 개정을 위한 학교 수학교육 관련 설문조사 결과보도 [Survey Report Regarding Mathematics Education for Mathematics Educational Reform]. Korea: 사교육걱정없는세상 정책대안연구소 [NoWorryEdu Policy Reform Research Facility]

⁷ Korean Ministry of Education. (2009, 2015). National Curriculum Information Center. Retrieved 2020, from http://ncic.go.kr/mobile.kri.org4.inventoryList.do;jsessionid=C195DF22B97D97123E149704E192EAE1?degreeCode=1012

⁸ Organisation for Economic Co-operation and Development (2009, 2012, 2015, 2018), Program for International Student Assessment; Reading, Mathematics and Science. Retrieved 17 December 2020, from https://pisadataexplorer.oecd.org/ide/idepisa/report.aspx