Common Core Math

Leave a comment

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

Consider these 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 idiotic 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.

“Any NCO with the FM”

Leave a comment

From Mike Lewis

Here’s the problem as I see it. The primary role of the NCO is training Soldiers, yet NCOs in general are lacking. This isn’t their fault because one can’t effectively teach what one was never taught. I didn’t get to attend MMTC before retiring and it was still a pilot then, but 200 NCOs a year doesn’t get the Army healthy.

Drill Sergeants come from all over the Army. They get marksmanship in DS school, but at what level and from whom? How much time out of those few weeks is dedicated to learning things never previously learned in any formal training environment before coaching and diagnosing problem shooters, or is it just the bare basics? I say this because a vast number in the formation never got any formal instruction in weapons employment after BCT and much of the stuff floating around is “I learned this from my buddy in Group or Regiment” while not giving context and/or getting it wrong.

This leads to what we see here. It won’t get fixed until the Army takes small arms training seriously and quits collectively lying with green blocks on Command and Staff slides then never progressing beyond baseline skills for qual.

I’m a Responsible Gun Owner? Seriously?

4 Comments

The description given in the article below is not uncommon and it often applies to military, law enforcement, and hunters as well.

While living in San Antonio, I was a TCOLE (formerly TCLEOSE) certified instructor and worked part-time at the Alamo Area Regional Law Enforcement Academy. As a Texas resident, I took the TxDPS – License to Carry course described below. While living in Wisconsin, I was certified by the state Department of Natural Resources as a Wisconsin Hunter Education instructor and taught classes. I’ve been in the U.S. Army in various capacities for a quarter century and with the US Army Reserve Marksmanship Training and Competitive Program since 2004.

I’ve been fortunate to have been involved with many skilled people in all of these experiences but that was largely due to my seeking them out and knowing what to look for. I already had higher-level shooting experience via organized competition and held Classifications from national-level organizations before doing any of this. The then-director of the DNR Hunter’s Ed program attended HunterShooter events I held. I applied for that Academy after having a fellow Shooting Team member speak well of the training director and his program. My Texas LTC course was taught by a fellow instructor and USAR Shooting Team member. I specifically took the class from him to avoid the clown show described below.

Gun owners are often their own worst enemy. The level of incompetence described here is not uncommon. Military, law enforcement, hunters, and concealed carry people are often at novice levels. Mandatory qualification levels are only useful if they’re difficult enough to assess useful skill. That means people incapable of displaying minimal useful skill must be failed. The other approach is for the program to intend to pass everyone. This means standards are adjusted down until everyone can. This article describes the results of that.
More

Yale Police Protest Over Firearms Test

2 Comments

Yale Police Protest Over Firearms Test
http://www.wsj.com/articles/yale-police-protest-over-firearms-tests-1478474266
More than 70 police officers at Yale University are protesting a new policy that allows them to be fired if they don’t pass a firearms test in 30 working days after having failed it twice.

How difficult is this test, really? The article doesn’t mention, but it’s almost certainly the rudimentary levels found throughout law enforcement. In one formal study, it was found there is a tiny 13% difference in skill between complete novices that had never fired a handgun and academy-trained police officers. Academy-trained police officers are still novices, and these police officers at Yale University are protesting being held accountable for this 13% improvement because they can’t do it, or the academy that graduated them couldn’t teach them to do so, or both.

“Training” at this level is just an introduction to concepts. Passing such a qualification is merely routine hygiene that introductory concepts have been retained at a level 13% above complete novices, not training.
https://firearmusernetwork.com/fitness-is-hygiene/

Note for all instructors: This is why maintaining reasonable but challenging standards coupled with semi-regular competition is important. It prevents underskilled “instructors” from working with recruits by revealing with numbers how unskilled they actually are. It puts a performance goal that indicates when low performance is happening and identifies those that are doing better and best. Encouraging and hosting competitive events creates a culture that reinforces skill development for recognizing and rewarding those that do well, which identifies potential candidates to help teach the others.

These police officers at Yale University are protesting for the “right” to remain underskilled and to never find better qualified firearms instruction at their academy.

Qualified to teach Tactical Training: NRA CCW

2 Comments

The following video is a promotional and demonstration video of a small arms instructor. The NRA and the state of South Carolina recognizes this instructor with certifying paperwork, which is more official documentation than some military and police small arms instructors may have.

Some maintain that only taking formal instruction is valid training while competition should be avoided as it is not training (ignoring how dictionaries actually define the word training) and that it leads to bad habits/ training scars. So you should only take a class from a certified instructor to avoid bad habits.

Only Police and Military are Qualified to Carry Guns

1 Comment

This one from John Tate.

Polícia Militar are a type of preventive state police in every state of Brazil. The Military Police units, which have their own formations, rules and uniforms depending on the state, are responsible for maintaining public order across the country including the Federal District and its capital, Brasília. Deployed solely to act as a deterrent against the commission of crime, units do not conduct criminal investigations. Detective work, forensics and prosecutions are undertaken by a state’s Civil Police.

In Brazil, all firearms are required to be registered with the minimum age for gun ownership being 25. It is illegal to carry a gun outside a residence, and a special permit is granted to certain groups, such as law enforcement officers. To legally own a gun, an owner must hold a gun license, which costs BRL R$1000, and the owner must pay a fee every three years to register the gun, currently at BRL R$85.

– Wikipedia

Here’s a video segment of Polícia Militar, one of those special-permit groups, on the range. You’ll need to be signed in to a Facebook account to see this.

https://www.facebook.com/932312266810490/videos/1047727638602285/

Good thing this officer never attended competition shooting events. Wouldn’t want to develop any bad habits or training scars!

Qualified to Teach Tactical Training: SEALs

Leave a comment

All good instructors and coaches must be serious students of their craft and this requires demonstrated performance at higher than novice levels. Sadly, within the firearms world this higher level performance is rarely required or found outside of organized competitive shooting. Regardless of the instructor or coaches background (claimed or real), this is reason enough to demand some sort of reasonable level of success in something like competitive shooting, if only to demonstrate the person is capable of doing more than merely qualify.

If you’re foolish enough to believe a military or police service record is enough, watch this video. Skilled people will note his demonstrated gun handling and shooting and realize he wasn’t worth considering, regardless of the claimed experience.

Older Entries

%d bloggers like this: