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Let’s talk about new math

by admin

I see the hate for “new math” in a lot of different places. Instagram posts, my Facebook newsfeed, even the local news. I know that social media is a bubble, often giving less than accurate portrayals on the general public’s opinion, but it seems like there is a large number of people out there who aren’t fans of Common Core math instruction.

Now, I should acknowledge, I am not a math teacher. As my posts evidence, I teach language arts and am quite passionate about it. But prior to my content area switch, I was. I did all of my field experiences, clinicals, and student teaching in math classrooms. I took enough credit hours of math classes during my undergrad to have a minor in it. And I 100% subscribed to and continue to subscribe to the method of instruction being so lovingly referred to as “new math”.

The first thing I want to say is this: A large number of people publicly shaming mathematics being taught differently are not educational professionals. In fact, many of them do not have any background with instructional strategies and are not familiar with the philosophy behind this change. And, to be fair, they shouldn’t. They do not work in this field and are not responsible for the mathematical skill-building that educators are. Many are parents who are wholly and rightfully invested in their child’s education, and to them and any others who would like to understand further, I’d like to offer some background.

Common Core mathematics standards began their development 10 years ago, in 2009. They began because each state had their own, wholly separate standards of proficiency for what students should learn and be able to do in each grade level. The idea behind them is essentially that all students in a given grade level in all states should, ideally, be learning the same concepts or skills. As an educator, this makes sense to me. Many students go out of state for college, many families move across state lines throughout their child’s schooling, and the notion that our educational systems could vary widely depending on each state’s individual standards doesn’t support those moves. The idea that kindergarteners in different states could have differing educational experiences does not seem logical. Not to mention the fact that having states write and ratify their own unique standards could perpetuate the achievement gaps that exist between wealthier and lower income areas or even states. The adoption of these common standards also creates a sense of collaboration among content area teachers, regardless of their geographical location, which as social media gained in popularity, is a hugely beneficial resource. The Common Core standards were adopted quite quickly, many states reviewing and ratifying them as early as 2011. My own state, Illinois, planned for full implementation of the language arts and math standards by the 2013-14 school year. Beyond the content area standards, standards for college and career readiness were also written.

A major difference in how these standards, specifically the content-specific ones, were drafted was that teachers and educational organizations played a huge role. Many policy decisions regarding education are created by politicians or lobbyists who have little to no background in K-12 education. The Common Core standard committees did not follow this precedent, instead involving classroom teachers and organizations like the National Council of Teachers of Mathematics directly in the process and post-adoption feedback procedures.

So it is clear that these “new math” standards were not only written by those with a foundational knowledge of mathematics instruction, but they were also adopted and revised as necessary by the stakeholders directly involved with them.

The instructional changes for math specifically were designed to help students have a deeper and clearer understanding of mathematics as a whole. Traditionally, even in my own time as a student, math class was mostly about memorizing formulas and applying them to different numbers or the dreaded word problem. Often, we weren’t given a lot of background on the formulas themselves or what the numbers were actually doing or, importantly, why they worked the way they did. We were taught a2+b2=c2, we filled the numbers in from the right triangle to solve for the missing variable, and we knew the theorem was named after Pythagoras.

It wasn’t until college when I took a class called Number Theory that I realized there was a whole lot more to math than I had originally realized. As an undergraduate elementary education major, I decided to specialize in math because I thought it would help me get a job. This was a time when horror stories of 300+ applicants for 1 teaching job were shared with me every single time I told someone I wanted to be a teacher, and I was scared. I had mounting student loans and knew I needed a job after graduation to pay for them. I’d always been a decent math student, picked up on the concepts pretty quickly and earned solid grades, so I figured why not?

I walked into Number Theory on the first day, confident enough in my mathematical background. I was a second-semester sophomore and had already taken calculus (still scarred from that experience), so this class had to be easier than that one. Boy, was I wrong. The concepts we discussed in this class were foundational, but we were expected to actually understanding the mathematical thinking behind them. Numbers would interact and we had to explain why the function or theorem would react the way it did. The day we changed our number system from base-10 to base-6 I nearly lost my mind. But that’s when it dawned on me that mathematics is far greater than memorization and regurgitation. It’s infinitely more artistic and much deeper than plugging in numbers to solve for x.

This was my mathematical awakening. After Number Theory, I went on to take Analytical Geometry, a similar class except with geometric functions instead of algebraic. We began to manipulate shapes and coordinates, learning how and why they were influenced by seemingly simple changes in an equation. In other words, we began to see further than just the solution to the problem on the test.

The Common Core standards for mathematics seek to do this much earlier than sophomore year of college. Instead of taking an elective mathematics course (because so many people choose those), our students are being taught math in a way that helps them better understand numbers, equations, and formulas. When students are taught multiplication by separating the place values, it is absolutely not to waste their time or create busywork. It is so they begin to see the place values as hundreds, tens, and ones instead of just applying the method their teacher told them. It is so they can understand why that method works. When they get to the stacked method we all are familiar with, they have a background knowledge on multiplication and numbers themselves that helps them see how and why that model works. When they are taught division by the partial quotient model, breaking down the dividend into place values and seeking multiples of the divisor, we are encouraging them to see why long division works the way it does. We are giving them the foundational understanding of numbers that will aid them in writing proofs and justifying their answers in the future. Beyond that, they see what early mathematicians saw when they created these theorems and solution models. They see beyond the solution. They see math.

In addition to the skill-based standards, the Common Core also ratified the Standards for Mathematical Practice. These 8 skills are ones that apply to mathematical thinkers, but they also apply to any student in any discipline. They include things like making sense of problems and persevere in solving them, constructing viable arguments and critique the reasoning of others, and attend to precision. [A full list can be found here, along with reasoning behind the inclusion of each practice standard.] These practice standards are designed to encourage a deeper, more analytical understanding of the mathematics discipline as students move through their schooling. They are meant to work with the content standards to produce students who can engage with mathematics in an authentic, legitimate way. Through them, teachers are bolstered in their ability to focus on helping students understand rather than memorize. Because, as the Common Core website states, “…a lack of understanding effectively prevents a student from engaging in the mathematical practices.”

In our nation, it’s vital that we are encouraging students to think analytically. It’s necessary that we are teaching our children to understand rather than to mindlessly follow what they are told. In my math class, students were required to not only supply the correct answer to problems, but to justify (ahem, write a proof) for why their answer was correct. No justification? Wrong answer. We spent time breaking down new formulas or theorems, drawing connections to our prior knowledge and figuring out why they worked. We were able to do these things because my students had instruction that supported it, both in my classroom and in the years prior. We were able to reason through what was happening because the standards I was held to required that my students learn to think about math instead of memorize it long enough to pass the test. It may have taken longer and may have been infinitely different from the way I learned mathematics, but the actual understanding that came from it was so worth it. The learning that transpired was authentic and applicable.

I ask all those who wish to voice their disagreement with “the new math” to consider all this before they decide to hit share or speak out loudly against it. I ask that you take a step back and review your expertise and ability to comment knowledgeably prior to doing so. I ask that you contemplate the many professionals and authorities on the topic of mathematical education who worked tirelessly to ensure that students actually learned math rather than learned to memorize. I ask that you take a beat and try to understand that just because we all, myself included, learned math one way doesn’t mean that it was the right way. Change is uncomfortable and can be frightening, but when it’s been approached with such care, it can hardly be considered detrimental. And if that’s not enough, try to prove why multiplication works—beyond just showing me how quickly you can solve the equation you saw on tv.

Resources: Preparing America’s students for success. (2019). Retrieved from http://www.corestandards.org/.

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