My Problem With How Math is Taught in K-12

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brockrwood

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My math teachers in 6-12 grades, while good people, taught marh in the abstract. It was just learn this concept, run the equation, get the result. Maybe plot it on graph paper.

There was never any “why are we doing this”? What real world problem can we solve by doing this math?

So I struggled with math in school. Most of my math skills I learned, on my own, as an adult.

Model rocketry gives a kid a reason to learn the math. Usually a fun reason. Which rocket went higher, yours or mine? Well, if we knew a little basic trigonometry, we could find out!

That gives the math a purpose and a fun reason to learn it. If math had been taught to me that way, I would have enjoyed it more and gotten better grades in it.

I can’t be the only person who feels this way. Is there an organization or movement I can join to promote teaching math this way?

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You are correct, but parically.

I remember doing the same thing thru high school.. rote exercises.. repetitive solving for 'X'.. We did have the odd problem where the problem was applied to "real life" issues, but that was about it. Again, more letters, more functions more derivatives, etc..

But (this is the partial part) This was supposed to be tied with the science classes you were taking. You learned the math in math class [the why, the expansion, how it comes together, etc..], but you learned how to apply it in physics and / or chemistry class. that's where the problem solving came in.. That is, assuming you a) were offered the class & took it, and b) understood how you were applying it / how they both tied into each other....

And that I feel, is what is missing.. In my day, and likely today... There lies a certain disconnect between the two.. No real / collective attempt to ensure that what is being taught in math class can easily be applied to the science class & visa versa.. (It's pointless to learn how to plot a parabola when gravity & forces won't be taught for another few months..) Now, as well, we no longer really have any "Home economics" classes (no, not only how to cook an egg or sew a button) but home economics: how to balance a check book, how "compound interest" works on a loan / mortgage, how taxes work & what to expect when you are in a 22% tax bracket..
 
that's exactly why college calculus is such a weed out. separate from physics, it is just arbitrary, meaningless. forced memorization (integrals) just as a hazing. and, not all majors really need it.

much more appropriate to teach probability and statistics, linear algebra, discrete math, and other everyday practical stuff like basic accounting and itnerest.

that said, I can think of a half dozen kids that got the hook in to math, coming from their rocketry experience and passion.
 
You are correct, but parically.

I remember doing the same thing thru high school.. rote exercises.. repetitive solving for 'X'.. We did have the odd problem where the problem was applied to "real life" issues, but that was about it. Again, more letters, more functions more derivatives, etc..

But (this is the partial part) This was supposed to be tied with the science classes you were taking. You learned the math in math class [the why, the expansion, how it comes together, etc..], but you learned how to apply it in physics and / or chemistry class. that's where the problem solving came in.. That is, assuming you a) were offered the class & took it, and b) understood how you were applying it / how they both tied into each other....

And that I feel, is what is missing.. In my day, and likely today... There lies a certain disconnect between the two.. No real / collective attempt to ensure that what is being taught in math class can easily be applied to the science class & visa versa.. (It's pointless to learn how to plot a parabola when gravity & forces won't be taught for another few months..) Now, as well, we no longer really have any "Home economics" classes (no, not only how to cook an egg or sew a button) but home economics: how to balance a check book, how "compound interest" works on a loan / mortgage, how taxes work & what to expect when you are in a 22% tax bracket..
Based on what you said, the math and science classes should be combined. Teach the science and introduce the math that explains it as you go along.

That sounds like a great idea! Has it been tried in middle school and high school?

You are right. Nobody just invents math for fun. They invent it because they need it to explain something. Newton needed calculus to explain his new physics. (Leibniz invented the same calculus in a more convenient form, with easier notation and syntax, so we use his instead.)

The ancient Greeks needed geometry to build temples.
 
In parrticular, I struggle with one of my other favorite hobbies, AC analog electronics, because you need to understand vector math, integration, and differentiation to truly master it.

My math teachers should have said, hey, let’s build a class AB transistor audio amplifer, with bootstrapping. When we are done you can crank Thin Lizzy with it in your bedroom. We need to learn a bunch of advanced math to understand it, but you will be able to really annoy your parents with it when we are done.

I would have aced that class.
 
Based on what you said, the math and science classes should be combined. Teach the science and introduce the math that explains it as you go along.

That sounds like a great idea! Has it been tried in middle school and high school?

You are right. Nobody just invents math for fun. They invent it because they need it to explain something. Newton needed calculus to explain his new physics. (Leibniz invented the same calculus in a more convenient form, with easier notation and syntax, so we use his instead.)

The ancient Greeks needed geometry to build temples.

Based on what you said, the math and science classes should be combined. Teach the science and introduce the math that explains it as you go along.

That sounds like a great idea! Has it been tried in middle school and high school?

You are right. Nobody just invents math for fun. They invent it because they need it to explain something. Newton needed calculus to explain his new physics. (Leibniz invented the same calculus in a more convenient form, with easier notation and syntax, so we use his instead.)

The ancient Greeks needed geometry to build temples.
That would be brilliant! I can think of dozens of demos that would be fun and interactive, with the math as a follow on or even a precursor to demonstrate on paper what you can watch evolve in the physical world. Chemistry and physics by dint, can be exciting to witness, but not so much math. Having said that, realize most teacher's have their hands tied, ground down by institutionalized and authoritative school boards dictating progress thru a chosen text book. Rote memorization, call and response, and apathetic parents all conspire to remove any "Aha" moments as supplies and even teachers for the teachers fall under budget and time constraints. Testing is used as a value judgement for teacher's reviews for adequate curriculum progress. In-the-box methodology stifles any creativity in both students and staff, often conceived by those who do not "teach" but merely supervise said progress thru a single sourced text and yet the sciences are cross-pollinating and interactive. I wanted to be a teacher until I found out how much they didn't make and the burn-out rates. I always think of this one professor, a brilliant man with sterling accomplishments who could utilize the engineering concepts he tried to teach, but stood with his back to the class, pipe in hand or mouth, and mutter to the blackboard, expecting us to keep up with the calcs. Absolutely no spark.
 
So much agreement here. So much to say. Also, a little good news and a little bad.

In 5th grade the way you learned multiplication tables in my school was rote memorization. I'm a visual learner, I can't memorize numbers, even to this day. Doing simple invoicing, etc., moving between documents I love my two monitors because I don't have to memorize the numbers if even for a few moments - it's like a kind of short-term memory number dyslexia. It was a shame because I LOVE science and technology - I can grasp complex concepts easily, but the numbers and formulas might as well be Egyptian hieroglyphics...

My 5th grade teacher didn't sympathize. He dragged me to the office and into a walk-in, windowless storage room you had to enter through the Principals office. (And Principals in the mid-60's weren't like today's principals in polo shirts high-fiving kids in the hall. We all feared them and for good reason). I was sat at a desk under a single light bulb with a stack of legal pads and pens and ordered to write the times tables (even the ones that repeated) several hundred times each. I had to take lunch and recess with kindergarten through 2nd graders. It took me two weeks. It was humiliating and so traumatizing I still have near panic attacks at tax time, I loathe & fear numbers that much, still.

I had a video gig for three years shooting math lessons taught in elementary classrooms all over the Tacoma, Wa. school district several years ago. It was an experimental math teaching program using innovative teaching techniques and was part of a long-term study by a University in Oregon, like some of the techniques discussed above, and we followed the same students for three years as they learned and put into use the techniques they were taught. For example, visual learners - like me - were taught to use visual aids like graphing, shapes, making arrays of dots to demonstrate the relationships between numbers. (I used this technique when I was a kid but would get in trouble if teachers saw rows of dots on the margins of my papers - I was supposed to memorize those numbers!). For verbal learners kids the kids would form small work groups where kids who understood the concept would communicate it, teach math to their peers at a language level that their peers understood. And it all not only worked, but worked very, very well - It was amazing! I'm not ashamed to admit I learned math concepts in those third and fourth-grade classrooms.

The bad news is that the parents didn't understand it. They weren't there in the classroom, so they were confused. "Just teach them math! What's all this making arrays of numbers and dots on the paper! Make them memorize the numbers like I had to - it worked fine for me!" When they found out these new techniques were part of the 'Core Curriculum' it gave them all the more reason to hate it and go to school board meetings to demand a return to 100-year old techniques.

I spent 20 to 30-hours a week in those classrooms video taping maybe thousands of hours of classroom teaching and seeing first-hand these kids who would have been written off as not being 'math people' getting excited about math & numbers and thinking that - possibly, just maybe, they could be aeronautical engineers or design buildings, software or rockets...only to find their ignorant parents throwing fits and demanding they revert to what was proven not to work only because they couldn't understand third grade math...
 
There was a post on FB with an argument..

This kid got the questions wrong. Right result, but wrong understanding.

"What is 5 x 3 = ? "

he put down 5+5+5=15 . this was marked as wrong.

what he was supposed to put 3+3+3+3+3=15

And this is where the argument was.. yes, they both =15.. it's how you get there that matters..
 
I worked with a person from Belarus years ago and when he immigrated to the US (real citizen, not fake or green card, full citizen) one of the things that made his jaw hit the floor was that his child, educated up to what we consider 5th-grade-ish was doing calculus, not multiplication. There were apparently issues where the teachers wrote him up for 'not doing it right, even though he got the right answer'. I don't know if this is at all true, but it is what he said and his son is an aerospace engineer now and basically was able to pass his high-school math classes with what he learned in elementary school.

Personally, I feel that if you're lucky enough to get a teacher that actually understands the subject and the impact of that subject, you can be educated extremely well. If your teacher barely understands how to teach the subject, you're screwed. I also personally feel that it would be smarter to teach the concepts of geometry based calculus/math before telling people that 3 apples plus 2 oranges = 5 pieces of fruit. . . I believe my friend indicated this is how math was taught in the former Soviet Union (i.e. calculus, not fruit). In college, every single one of my math professors were born and educated in the Soviet Union. In general, the people from that generation and that region are considered by many to be extremely math profficient. Obviously I don't agree with lots of other stuff from that time period, but I think that is one area where the rest of the world should look to understand why they did things so well in math education.
 
Guys, the issue wasn't that the kid got "15" as the answer, but that he understood that the question asking for 3 fives vs. 5 threes..

yes, either way you get '15' but what happens when you get an algebra type question that has a few variables, and all multiplied.. you need to know the order and how that derives the answer..
 
Guys, the issue wasn't that the kid got "15" as the answer, but that he understood that the question asking for 3 fives vs. 5 threes..

5 x 3 could equally be:
five groups of 3, or
Five, three times.

There's nothing in simply "5x3=?" to tell you it should be one vs the other.



When our son was being "taught" how to subtract, the teachers had some weird series of steps to follow. Our son didn't understand, and the teachers quickly got frustrated and insisted that if he would just memorize those steps and follow them and he would get the right answer. He was getting discouraged and asked me about it. So I showed him a number line, explained how negative numbers worked and that subtracting is the same as adding a negative number. He understood that right away, and though the teachers didn't quite get it, they allowed him to do it his own way.

He's an applied math major now, a sophomore, and was recently invited by the dept. head to take a senior-level math research class next semester.
 
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Here's the deal. Commutation only applies in scalar arithmetic. Complex numbers, quaternions, octonions? Nope. Order dependent.

In fact, the 3 laws of arithmetic that you learned disappear one by one moving up in higher dimensions. Commutation, association, distribution...

Linear algebra says matrices are specified by rows x columns (x more dimensions, etc).

So the kids learn 5x3 is organized one way. That's what the test was about.

It confounds adults who learned a rule, but never learned that rule doesn't always apply for all algebras.

Is this concept appropriate for young kids? Debatable.

Kinda like introducing set theory in "new math". Confounds adults! But opens the door to a much larger universe. Relevant? Appropriate for everyone? Debatable.

The same stuck on a rule thing happened with Pluto. It is a planet! I learned that 50 years ago! Except it isn't in some ways, except it actually is, radioactive core, subsurface liquid ocean, 5 moons.. yeah.
 
Linear algebra says matrices are specified by rows x columns (x more dimensions, etc).

So the kids learn 5x3 is organized one way. That's what the test was about.

If this test was teaching linear algebra principles, I'll agree. If it was simply over learning multiplication, I can't.
 
In fact, the 3 laws of arithmetic that you learned disappear one by one moving up in higher dimensions. Commutation, association, distribution...

The same stuck on a rule thing happened with Pluto. It is a planet! I learned that 50 years ago! Except it isn't in some ways, except it actually is, radioactive core, subsurface liquid ocean, 5 moons.. yeah.
The question looked like scalar mulitplication. No vectors or matrices involved. Why bring extra dimensions and where the laws don't apply into the discussion. Unnecessary complication.
 
The question looked like scalar mulitplication. No vectors or matrices involved. Why bring extra dimensions and where the laws don't apply into the discussion. Unnecessary complication.
yes the question looked like that.

I completely agree, no need to introduce extra ideas at that basic level.

I remember the original news article, and there was more to it than the commonsense readin ritin rithmetic indignation. my google-fu fails right now so I can't find a link, sorry. anyway, my GF worked on common core, training teachers in it, and apparently yes 5x3 and 3x5 are treated differently. even though everyone knows the product is the same, the concept was that layout is important.

do you have 5 bags of 3 apples, or 3 boxes of 5 apples? yes those are different.


bottom line: I couldn't help my kids much with high school algebra 2, because the methods are different now. sure, I could get right answers, but not the way the teacher wanted. and I realized they were learning underlying concepts in a better way than I did, last century...

Imagine my indignation (not) now imagine the outrage felt by regular folks, after being told what they thought was solid forever just ain't always. yeah, gonna get a reaction.
 
oh and BTW, other posters mentioned traumatic experience learning arithmetic by rote memorization... I agree, happened to me too. definitely the wrong way to teach it.

we know enough about childhood education to completely redo it, make it easy, fun, and effective. biggest pushback comes from the parents! and, wrongheaded ideas like NCLB. (which many believe was intended to destroy public education...)
 
Reading through this exemplifies that there are many ways to approach math concepts. I hope that the people that have participated in this discussion support helping students identy and explore the style that works for them.

We simply cannot have a functioning society in the high technology future if only 10-15% of our population is comfortable with anything beyond basic arithmetic. We need to reach those for whom the traditional methods have failed.
 
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