I was sent a copy of the book "Balancing the Equation" for the purpose of review. An affiliate link has also been included in this post.
Thank you for joining in the “Balancing the Equation” book study. I am joining in a group of dedicated math bloggers to take a closer look at this text. My opinion? You want a copy for yourself. I consider myself to be quite well versed in understanding math education, where it falls relative to the current political arena (and yes, math education is very tied up in politics!) but this book has given me a more robust understanding of the very specific twists and turns that have taken place that bring us to the space in math education that we occupy today.
If you are just joining in the book study, you may want to go back (links at the bottom of this post) to begin the study from the beginning. Each day a new blogger has added their chapter to the conversation so, depending on the date you are joining us, you may want to grab a coffee (or your beverage of choice), sit back, and hop on through. Alright, enough chit chat, on to Chapter 2!
Throughout the text the authors continue to revisit the pendulum swinging between developing conceptual understanding and developing procedural skills. Chapter 2 of Balancing the Equation seeks to examine the historical context behind these pendulum swings.
Upon first glance, it seems like there is a simple answer and that balance needs to be struck between conceptual understanding and procedural skills.
Major spoiler: Yes, balance is the answer.
In fact, it’s the name of the book J And yet, that is not how math education is handled in all districts, buildings and classrooms. So the question then becomes why?
The answer, my friends, lies in a historical context that is littered with political tension and decisions being informed by groups of people who have little to no background in child development. Not shocked by this answer? Neither was I. And yet I found this chapter to be wildly interesting to read in terms of understanding how entire generations could be effected so profoundly by a pendulum swing in one direction or another.
Kanhold and Larson argue that, initially, math education was not a mandate in our country in terms of childhood education. As a need arose for citizens to know basic math, basic math skills were introduced in classrooms. And these skills were taught rotely. This makes sense. Students needed to know how to “do specific things” with numbers and they were taught how to perform those specific skills, provided with examples and then allowed to practice those skills.
As time went on and as the scope of mathematical skills broadened, theories on more effective math teaching practices began to emerge. A man by the name of Warren Colburn introduced the idea that perhaps if students were given math tasks which allowed them to develop an understanding of math concepts that they may be able to more easily and effectively understand mathematics and apply their understandings.
It was only 4 short years before Colburn’s theories received significant backlash. The reasoning? Parents would rather that math be taught the “old fashioned way”.
Parent preference is not grounded in research on how students learn best and yet the tides turned back to the “old fashioned” approach. To be fair here, Larson and Kanhold do point out that the preference of parents is often grounded in their perception of the current math teaching approach and that perception is often derived from what is seen in curriculum or how curriculum is interpreted and implemented by individual teachers. This constant tug between educational theory and
implementation is another common theme throughout the history of math education.
This same pattern continued in turn with the pendulum swinging back and forth every few decades (the text goes into detail here outlining a number of shifts and the forces at work). Sometimes the swing happened at the hand of research as it did in the 1950s and 1960 when “New Math” was introduced. Sometimes, the swing occurred as a result of parents or legislators. Legislation introducing state testing for students at a variety of grade levels was the cause of one such swing. Despite a 2008 study commissioned by the national government that stated that math education must include a balance of conceptual understanding and procedural fluency, a drive towards procedural skills occurred when NCLB (No Child Left Behind) was introduced. High stakes testing quickly drove education at the classroom level to focus on a more narrow set of standards that would be tested at a given grade level.
CCLS (Common Core Learning Standards) have now been introduced and embedded within the standards themselves you will find very specific language that aims to convey the balance required for highly effective math instruction. But, if we have learned anything in chapter 2 of this book, we know that an attempt to shift the landscape of math education will surely be met with backlash and a pull back to what is traditional. Continue on the blog hop to continue the book study with a review of chapter 3 to see how the most current shift is playing out.
If you would like to keep up with this blog hop... and why wouldn't you :) Check out the line up below!