Who wants a bell curve? Strong case for learning mastery in mathematics

Sarah never laughed in my class. At least not with her eyes. Holding her breath, she spoke. Whispers of words I usually can’t hear. She is one of the many students I remember because despite my best efforts, I have not been able to help her see herself as a mathematical thinker or build her curiosity and math skills.

For most of my teaching career, I taught math to eighth graders who needed extra support. My co-teachers and I were tasked with making sure that students included all first-year algebra curriculum components. Most students already hated math and believed they were bad at it and would never improve. They had gotten bad grades in the past, they thought math was boring and that was what was expected of us.

How can I blame them? Many students found the math difficult, dry and difficult. There was constant confusion and frustration in the math class. These students were polite and kind. They did not tell me these things. But Tina goes for a drink whenever she can near the water fountain, the way Joe was sitting with his shoulders bowed and the way Samantha tested her, her head was on her hands, silent tears were sliding down her cheeks, I could see it.

We started with a review of fractional operations each year. The students shouted. My heart sank. Understanding Fraction is a high predictor of success In high level math. They weren’t sure if 1/20 was bigger or smaller than 2/5. I tried to increase the conversation and curiosity. How big is the 20th? What if you made 100 pieces of something? 1000 pieces? Will those pieces be small or big? We moved on. The majority of the students, who did not understand the last unit and were now placed in a new class, always had to move on with the course. I knew that if a student didn’t understand fractions in September, they wouldn’t understand negative exponents in March (Spoiler alert: fractions again!). This type of education is a house of cards. We have set them up.

In May, our students took a standardized test of algebra and we always had a bell ringing. Teachers are often praised for ringing the bell. I never understood that. I didn’t want the bell curve. I wanted everyone to master literature. This I felt was essential. Nothing else crept into my stomach and felt immoral. How can I make the majority of my students face high school without elementary marks and lose confidence?

What is mastery?

To develop Dominance, Students should acquire basic skills, practice using them together and know when to apply what they have learned.

Learning is contextual. The generalization of learning in new contexts (called education researcher transfer) requires facilitation. Many years later I was told that dominance was unrealistic. There will always be students who did not get an A. “But don’t we think they should master high school math?” I will answer. “Don’t you really believe that all these students are able to understand fractions?”

My favorite rebuttal was that not every student has Honors Mathematics. “If they all had an A,” the thought continued, “how do we know who can really work at the next level?”

As mentioned by Sanjay Sarma in his bookGrip“The American education system has long been” conquering “people who are considered eligible for academic investment and those who are not. This is nowhere near as clear as mathematics education. Is classified. Expect long-term success of students. From elementary school to high school and college, these tracks often become “.Traps“Which reinforces systemic inequality in our society. We are witnessing” target displacement “; the categorization of students, basically helping to provide better education, has now become the ultimate goal.”

Another popular defense of the situation was that students needed to learn some “lessons” from poor grades, such as how to take good notes, study more effectively, or work faster on tests. This argument was some version of “hard love”, where we were helping students experience the consequences of their actions. We seldom took the time to clearly teach or discuss those skills. If we don’t teach them, how will they know how to succeed next time? Another popular answer was that we didn’t have time. Yet the pace of our teaching means that students have surface-level perceptions, concepts are kept poor, and need to be re-taught over and over again.

My experience of teaching mathematics took place in academically strong independent schools with a lot of resources. In this context, if you cannot ensure the mastery of students’ quantitative literacy, where and when is it possible?

Creating a system that gives all students the opportunity to master basic mathematical concepts and believe in their own mathematical reasoning is not easy, but you should try.

The current system forces everyone on the same schedule to reach proficiency. It ignores individual differences as well as cognitive science research of the last several decades. Our current model of teaching mathematics misses the opportunity to elevate generations of students with the joy and power of statistics.

Teaching is a very difficult and complex task. However, we know a lot about human education that can help us imagine a better system.

We can begin with the shared high expectation that all students in our class have the ability to master basic mathematical skills and mental habits. We can make proficiency a result of learning and not the time given in class. We can adjust our classrooms and assessments so that students can move beyond content at the pace that suits them best and master the skills they can use for the rest of their lives.

Some individuals and organizations are already making these changes. For example Modern classroom projects Provides professional development for teachers on mastery-based classroom teaching models and Mastery Transcript Consortium There is a network of schools that redesign high school transcripts.

We must accelerate this change before the second generation of smart students is reduced and the majority is sidelined.

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