Stop the Math Pendulum Swings - Why can't we meet in the middle?
Written by John Seelke
Image by Shubham Sharan
A couple of months ago, Facebook’s algorithm posted an article from The Economist that caused me to pause and read it. The article, posted online November 6, 2021, and entitled “America’s Math Wars,” discussed how, as with many components of education or society, math pedagogy had become a political point of discussion.
From the article’s perspective, conservatives prefer a more traditional style of mathematics, focused on skills such as memorization of times tables and learning algorithms to churn out computations quickly and correctly. On the opposite end, progressives have advocated for a deeper conceptual understanding of the why behind the algorithm. Such changes in math education have occurred for decades. This 2016 article in Wired Magazine notes math education began to drastically change around the 1960s (when the Space Race led to a larger focus on STEM in general).
There was a greater focus on word problems as opposed to repetitive arithmetic. Even with these changes, in the late 1980s and early 1990s, when I was a middle and high school student, many math books had similar characteristics. They had examples that showed how to do the problem. They had A, B, and C level problems, which gradually moved from easier to more complex (with the word problems always coming towards the end).
And homework assignments read something like this: p265 (1 - 31 odd) - if the teacher allowed you to check answers in the back of the book, or p324 (2 - 34 even) - if the teacher didn’t want you checking answers.
As a parent of twin seventh graders who began kindergarten after the creation of the Common Core State Standards, I have seen firsthand the changes in math instruction for my daughters. Solving two-digit addition problems was no longer done with “carrying the one,” but rather was done by decomposing numbers and then re-composing them into groups of 10. Similarly, multiplying was demonstrated using concepts such as area models.
The lack of memorization was completely different from my own memorization of math facts. I vividly remember in 4th grade having timed tests for addition, subtraction, multiplication, and division (the latter up through 12). Such an exercise would be considered a travesty to Stanford scholar Jo Boelar, who famously encouraged schools to stop forcing students to memorize math facts.
A similar debate has occurred around pedagogical practices in general - direct instruction versus student-centered instruction. Some scholars have touted that despite the negative connotations around direct instruction, studies have consistently shown it has been successful in students' learning (perhaps as demonstrated by standardized tests, but that’s a conversation for another post).
Even with this evidence, one only needs to walk into a student-centered classroom, where conversations are focused on understanding mathematics, to see students enjoying the class more than sitting in rows, listening to a teacher lecture on and on. One could argue that there is plenty of anecdotal evidence that students enjoy student-centered learning more than direct instruction. And some articles have demonstrated that student centered learning can result in improved metrics. But, is enjoying learning good enough if it doesn’t result in improved metrics?
Both of my daughters are considered on somewhat advanced tracks in mathematics. One daughter is in a science and math magnet program at her school, taking an Advanced version of Algebra 1. The other took Math 6 last year but did well enough that she is in a combined 7th-grade/8th-grade math class that will enable her to take Algebra 1 in 8th grade.
When faced with a problem such as 54 divided by 12, one or the other is often stuck on the best way to find a solution. No calculator around? Just ask Alexa - she can find the answer! Every time they call out “Alexa, what is 8 times 7?” I cringe and worry that their generation of students will rely on calculators or not be able to compute basic math facts.
In his 2000 article on ever-changing math pedagogy, Northwestern professor James Spillane noted that district leaders understood math reforms as being different from their current pedagogical practices, leaders “tended to focus on piecemeal changes that often missed the disciplinary particulars of the reform” but another way, leaders were reaching for quick fixes to low math scores as opposed to understanding the reasons behind the changes. And second, leaders often don’t consider the negative repercussions of potentially positive changes.
A good example of this is the push to digital learning and digital instruction. Yes, most traditional math books weigh A LOT and combined with other heavy textbooks turned students into hunched over terrapins.
Digital Learning
The COVID-19 pandemic and subsequent virtual learning showed the power of digital curriculum - no textbooks, just teacher shared materials, student activities, and a workbook for students to follow along and answer problems.
So many districts have moved to digital learning. And some parents in those districts are asking, “Where is my child’s textbook?”
While textbooks helped me survive many math classes, both high school and college, by referring to worked out examples, the larger issue related to digital versus on paper learning is whether the change in format impacts how powerful the material is in supporting learning. RAND corporation has done numerous studies on the value of high quality instructional materials (HQIM). And companies such as Ed Reports have focused on measuring the quality of multiple instructional materials, some of which are based online.
Could some curricular tools be better than others if they were provided in a different format? Another question that needs to be asked is the role of high quality materials in student centered classrooms. Some articles have noted that the success of student-centered classrooms rely heavily on the teacher. Yet this does not necessarily mean that such classrooms can succeed without high quality instructional materials. Both are vital to supporting student achievement.
All decisions in education, including changes related to pedagogy or even things like digital textbooks, impact student learning and student achievement. Along the lines of our political rhetoric, conversations around education decisions have devolved into finger-pointing and seeing someone with a different point of view as wrong. All involved in education share a common goal - they want students to find academic success. Let’s focus more on what we have in common and ways to compromise and collaborate rather than pointing fingers.
The episode is a presidential debate, and prior to the main event, the staff of the incumbent, President Jeb Barlett, was seen trying to find the right 10-word answer that could be given in the debate. They were looking for the soundbite that voters would remember.
Later in the episode, Bartlett’s opponent gives a ten-word response. Bartlett’s comeback to his opponents ten-word answer: “Here’s my question: What are the next 10 words of your answer” Bartlett later notes that most decisions in leading the United States are quite complex and nuanced, and they can’t be solved with just ten words.
The same can be said with education reform. As I stated earlier, I know plenty of students who benefited from DC-CAP; however, I also know that the program did not break the cycle of poverty. How do I know that? Because I still keep in touch with many of my former students, many of whom did begin college, but for various reasons, were unable to finish their degrees.
Some of these students are struggling financially, living paycheck to paycheck. Others are working 60 hour a week jobs as government contractors just to make ends meet. Many students are working extra hard to pay off student loans that unfortunately did not end up with a degree. In some cases, the debt prevents those students from even gaining access to their transcript if and when they decided they wanted to return to college and either finish a degree or use some of the credits they earned towards a new degree.
John Seelke is currently an Instructional Specialist in Secondary Mathematics in Montgomery County, MD. Over his 20 year career in education, John has taught at the K-12 level, at the university level and has worked in two district offices. In 2007, he was honored with the Presidential Award for Excellence in Math and Science Teaching (PAEMST), representing Washington, D.C.
