Firearm User Network

Many people have strong opinions about what is commonly known as Common Core Math. As with many things, the general, popular opinion of laypersons is often wrong.

This has a number of parallels to small arms instruction. Personnel with minimal experience (which describes most military and law enforcement) assume their limited exposure is The Way and anything that deviates from that must be wrong because they’ve never bothered to consider it.

It’s also similar to anti-gun arguments. Non-shooters with little-to-no formal firearm education that know little-to-nothing about guns and unwilling to study the matter beyond looking at memes are only too happy to spew their opinions about it and demand their way into public policy. Similarly, non-mathematicians with little-to-no formal math education that know little-to-nothing about what the common core approach is intended to teach and unwilling to study the matter beyond looking at memes are only too happy to spew their opinions about it and demand their way into public policy.

As a non-mathematician, my initial, layperson, knee-jerk reaction was similar to the common, negative response: “What is this? That’s not how I learned it!” Then, I took the path less traveled. Within minutes, I was able to Google up writings and videos from the mathematicians that created it (including the video by Dr. Jo Boaler below) and quickly reversed my opinion. Part of the approach is learning how to learn. I quickly found similarities with this teaching approach to what is needed to understand theories in computer science. A few examples:

https://www.ece.ucsb.edu/~parhami/pubs_folder/parh02-arith-encycl-infosys.pdf

https://plato.stanford.edu/entries/lambda-calculus/
https://en.wikipedia.org/wiki/Lambda_calculus

https://en.wikipedia.org/wiki/Relational_algebra

https://en.wikipedia.org/wiki/Big_O_notation

For a given program’s computation, a programmer may not need math knowledge beyond simple arithmetic, however, that doesn’t teach the theory behind how a computer works. Understanding the how and why behind the scenes requires a level of knowledge beyond working a simple algorithm.

Doing math “like they used to teach it” is mechanically working a single, basic algorithm without true understanding. Some people can successfully intuit a number sense without being deliberately taught it but many do not. Showing how to solve the same problem in different ways, demonstrating “backwards and forwards, inside and out” requires a full command of the knowledge. It’s not about which way is faster (use a calculator, or a spreadsheet program, or MATLAB if you just want to compute the answer fast), it’s about developing a deeper understanding.

The worst part about it is that it breaks one of the most important things in education: Parent involvement. Multiple studies have shown that the most important thing to educate kids is parental involvement. And parents look at this, don’t understand it, and then tune out of their kid’s education.

What the “new” approach labeled as “common core” is supposed to be is alternative ways of doing problems. It’s supposed to simplify things and help students use the same “math tricks” that a lot of people learn to do in their heads. Learning math in a variety of ways to gain a full understanding. But it fails.

1. Parents aren’t given any guidance on how to help their kids use these methods.
2. Methods are often instructed using small numbers where “the juice isn’t worth the squeeze” to apply these methods, and where such methods appear to be nonsense.
3. The teachers themselves seem to not really understand what they are teaching, and just read it blindly from a book.
4. The books themselves all too often have errors.
5. Just as “the old way” doesn’t work for all students, the “new way” doesn’t work for all students either. Forcing students to learn all the ways and be equally proficient with them is dumb.
6. Frankly, good math teachers are as rare as hen’s teeth. Good math students go and do things like be developers for Google and get to be millionaires by 30. They don’t go and get paid $45K a year to teach in public schools. Entirely too many math teachers don’t get these concepts themselves and stand virtually no chance of teaching it.

Consider the following explanations of the rationale of this education approach by some of the mathematicians that created it. This will take longer and require more deep thinking than blindly sharing and/or liking memes on social media. Perhaps that’s the cause of the real problem.

You’re wrong about Common Core math: Sorry, parents, but it makes more sense than you think

8 Common Core Math Standards, Explained

From Michael Goldenberg The mistake here is pretending that there is any such animal as “Common Core Math.” There is not. There is a set of content standards; there is a set of standards of practice for both students and teachers (which is very similar to the Process Standards from NCTM going back more than a decade).  And then there are a bunch of curricular packages (mostly textbook series for various grade bands, but also some online material, most notably (and horridly) ENGAGE-NY, which has been forced on all public schools in NY State and Louisiana). Those materials are not “the Common Core” but merely various implementations that CLAIM to be aligned to the standards. Period. So anyone who uses the term “Common Core Math” other than to refer to the standards is in error. And that goes for Dr. Boaler, much as I respect her and her work. It’s just silly and misleading and dangerous to pretend that there is some monolithic entity that is isomorphic to COMMON CORE MATH. There isn’t. And likely won’t be. 

Those who know the history of math education in the US know about “The” New Math, c. late 1950s into the early 1970s. But again, no such animal ever existed. There were a bunch of separate projects funded by the federal government to design new approaches to math. Some produced textbooks, but few of those got published and distributed past the pilot schools/district with which each individual project worked. One series, however, did get widely published and used: the Dolciani series. Some people, including people who generally hate what NCTM was pushing in the ’90s and henceforth and also hate “Common Core Math” to the extent that it is similar to those ’90s reform math texts, really LOVE Dolciani. Others despise it. I have mixed feeling about the series. It is VERY formalistic, much more like college math books than anything that appeared in the US prior to the ’60s for K-12.

As someone who now knows a lot of math, they’re okay. But as a kid, I probably would have found them dry and off-putting. And my dad, who had to try to help my younger brothers with homework out of those books, was at a loss, despite having studied math through calculus in school. It was too far from his own experience.  What we see now is people who are reacting against Common Core math books similarly to how my father reacted in the ’60s to Dolciani, but he didn’t blame everything on Obama. He didn’t blame it on Eisenhower or JFK, either. He just knew that he was out of his depth.  

Note, I’m NOT claiming that all the materials being hawked by publishers as “Common Core Math” are any good. Maybe NONE of them are. But that’s not really the issue. Most of what people are screaming about and finding a host of conspiracies behind (see all the crazy videos and many of the nastier comments against Common Core) is just ideas about teaching math better that have been around for decades.

The math isn’t new, and neither, really, is most of the pedagogy. Most of it makes perfect sense if done intelligently, but of course is confusing if it’s presented badly (seriously, folks: what ISN’T confusing in math if presented badly?) or if you’ve never seen it before and are so angry that you won’t even stop to think about how it might be sensible either because you’re embarrassed to say to your child that you simply don’t get it.

Bottom line: calm the fudge down, folks. When the smoke clears and the Common Core is gone, most professionals in math education will still want your kids to learn how to approach math more deeply and thoughtfully than you were presented with. That’s the nature of people who actually care about more than a small elite learning math. I’m one of them. Jo Boaler is one of them. There are thousands of us out there. We’re (mostly) pretty smart folks who spend our lives studying math, kids, learning, and teaching.

You may certainly disagree with anything or everything we think and say, but that doesn’t make it communism or corporate capitalism, either. You can fight it, but you’re not really helping your kids when you do so blindly and with great prejudice, when you swallow every horror story your read and hear, when you react out of fear and ignorance (and tell yourself it’s really out of deep knowledge of mathematics and its teaching, when few Americans really know mathematics deeply or are at all familiar with research on teaching and learning the subject at various levels), and kick and scream that you know more about all this than any college professor or K-12 teacher (you might be right to some extent about any given teacher, of course).

I wait patiently for parents who take the time to actually think rather than just react emotionally. Those who do the former often find that there’s a good deal to like out there, no matter what label is put on it, and the anti-Communist lunatics who post videos here are for the most part out of their minds. But of course, if you need to believe that progressive math (before or after the Common Core label got placed on it) is really about “dumbing down” kids, be my guest. Your loss, and, sadly, your kids’ loss. 

From Rufus Driscoll
It looks weird because you’re seeing it from the other side of the wall. I used to think it looked stupid and over the top until I became a Maths tutor.

When teaching a child maths before they truly understand what numbers are and how they relate to each other, telling them to simply put numbers on top of each other and follow the steps to make a new number gives them very little understanding. Some kids will see the relations without all the added breakdowns but you’d be surprised at how many will simply chug along doing the usual steps and never really get the process of what they’re doing.

The issue with this is that once you forget just one of the steps involved in getting from a to b, you will be completely unable to solve the problem. If someone is taught to understand how numbers form and work together, it doesn’t matter if they forget the one way they were taught to solve a particular problem; they will be able to reach the correct solution even if it does take longer than using the perfected method.

From Violet Crawley
The gag is, all the countries who score at the top of the PISA actually do teach their kids the “number sense” way. It works.

The problem is that American teachers are woefully underqualified, so they confuse the kids because they themselves aren’t good at math.