Is high school-level math really important?

amother

Wed, Oct 30 2019, 5:00 am

DrMom wrote:

Looking into the Common Core method of teaching math, I can see why students get lost.

It's a cute exercise, but I hope they also teach the quick way of subtracting.

They don't, and that's part of the problem.

But the students I have didn't learn Common Core all the way from first grade. It was first rolled out in the curriculum in 2014. These students were in 5th or 6th grade then.

It's not as outrageous at the high school level. We teach students to solve equations, evaluate graphs, etc. pretty much the same ways we used to. It's just that the questions have become so convoluted and difficult.

amother

Vermilion

Wed, Oct 30 2019, 5:22 am

amother [ OP ] wrote:

I'm a hs math teacher and probably not going to be for too much longer. One of the many reasons is that I just cannot justify to myself why it's important that my students know the material that I'm teaching.

Trust me, I know that it's supposed to teach logical reasoning. But a) there are plenty of people who are pretty good at logical reasoning but are terrible at math, b) many people get through life just fine without strong logical reasoning skills-and those are often the people who didn't do well in math in high school, and c) math is really hard for most people, so they're not learning the reasoning skills that it's supposed to teach, anyway.

Even great math teaching is usually either just teaching to a test, which doesn't really teach math, or attempts to teach students reasoning skills that are way above most of their heads.

So, as a math teacher who loves math, convince me: why is it important to teach high school level math? Why is it considered such an essential part of the curriculum?

(Note: I'm not talking about percentages, arithmetic, fractions, or the like. I'm talking about Algebra, Geometry, Trigonometry, Pre-Calculus, and Calculus.)

This question could be asked of essentially any subject. Many students favorite subject is math and its skills are essential to everything in life. Students who know the success of completing a difficult math problem or the reasoning skills behind it are better human beings and more reasonable people than those who don't. Period. I can usually tell if someone did well in mathematics just by seeing how they approach problems in life.

amother

Wed, Oct 30 2019, 5:26 am

amother [ Vermilion ] wrote:

"Many students'" favorite subject is math? Really? Go take a poll in any classroom. At least 80% of the class will tell you that they despise math. I'm pretty sure this is universal, based on the amount of negative feedback I've gotten about math in every place I've been.

To say that people who know the success of completing a difficult math problem are better human beings than those who don't is asinine.

You can usually tell if someone did well in mathematics just by seeing how they approach problems in life- but I maintain that most of those people who are good at it, are good at it naturally. Also, that's not universally the case, since as I said, there are many highly intelligent people who struggled mightily with math. It doesn't mean that they cannot reason or problem solve.

nchr

Wed, Oct 30 2019, 5:29 am

nchr wrote:

Got you. I agree with that. Students should be able to discern it by themselves anyways or, if not, let it just be part of one of those sections of the text book about trying another method etc.

Something else to note is that adults, including those on this site, have expressed sentiments of common core being difficult. This shows a lack of mathematical understanding or reasoning skills because it is extremely simple and easy to understand. Someone who had even a basic understanding of math should be able to intuitively use common core math. Maybe that is the different between those who excel at math and those who do not.

amother

Wed, Oct 30 2019, 6:19 am

nchr wrote:

That is 100% false. I was in the 99th percentile in the country in math and scored 100 on my Regents. I can understand Common Core math and still acknowledge that it is convoluted, difficult, and unnecessary.

It is a curriculum meant for advanced math students, not for the mainstream.

cbsp

Wed, Oct 30 2019, 7:26 am

nchr wrote:

I'm a math /computer science major.

Common core is convoluted.

My DD in 3rd grade would glance at a problem, whisper the correct answer to herself, and then get stuck when she tried to solve it the way she was taught to solve it (and show her work).

She now gets special Ed services for math.
It makes no sense.

Hashem_Yaazor

Wed, Oct 30 2019, 8:02 am

I'm also in Computer Science. My husband and I both excelled at math (let's leave it at that). We know math cold. We have spent more time on homework with our kids' math with CC curriculum than we ever needed to before (and we're getting some things wrong). My math whiz son (who scores 100% on state math tests) had poor grades in some 3rd grade math because on any given day the assignment would be to do math on method 1 vs method 2 or 3 and he just knew the answer and might mix up which method to use.

(And he just got a C on a classword assignment, after acing his test...why? Because he didn't show his work. Not because it was wrong. But he might have used the wrong method, CHV.
In the meantime, he's all of 12.5 and he's teaching his 11 yo sister her math because he does understand it better than his parents after having to go through it. And she's smart in her own right and doing beautifully in school. But her brother is a better teacher than the teacher who didn't learn math via this curriculum himself. I don't know what will happen when we send him off to yeshiva. We appreciate his help while we can get it Smile

)

JoyInTheMorning

Wed, Oct 30 2019, 8:08 am

If I were designing lower and middle school curriculums, I'd focus on getting the kids to do good estimations. That's the kind of numeracy I'd want them to have. If you're a third or fourth grader multiplying 353 by 43, you should be able to do a quick estimate by realizing that 353 by 43 will not be too far from 350 by 40, then do 350 x 4 x 10 = 3500 x 4, which means doubling 3500 twice, which means around 14000. So that's a very rough start. Then, they should be do the standard method to get 15,179. This gives them some reassurance that they're basically in the ballpark. Even better if you also check 350 by 50, which, repeating most of the steps but modifying the last, gives you 17,500. So your result of 15,179 sits nicely between the two estimates, and is closer to the lower one, which makes sense.

When kids get to fractions and decimals, they can use similar techniques.

The point of all this is first, to make sure that kids can work with numbers and get answers that are in the ballpark. This is crucial for everyday life, e.g., when you're budgeting or buying a house. Second, for school, it gives them a way of checking and gaining confidence that their answers aren't totally off.

Along the way, kids might discover some of the Common Core methods on their own, as they are figuring out how to produce tighter estimates of their problems.

But this is all irrelevant to the OP's concern. As important as it is to be able to do decent estimations, you need to learn the quick methods, because without being able to do addition, subtraction, multiplication, and division of whole numbers, fractions, and percents, you are not going to succeed at pre-algebra (e.g., exponent arithmetic, square roots), algebra, trigonometry, and geometry. You can't understand or use the quadratic equation unless you're very familiar with these arithmetic operations. Note that solutions to equations aren't necessarily whole numbers, even in the relatively easy world of Regents exams, so its crucial to be able to manipulate fractions, percents, roots, etc.

And all of this doesn't even begin to address the much more difficult issue of solving word problems, which is the real skill that kids need for using math in other areas like chemistry or physics.

#BestBubby

Wed, Oct 30 2019, 8:13 am

Government claims common core math is to make students understand math better but I believe it is the opposite. Government has a history of implementing NEW methods which all fail - the most glaring example is Whole Word method and abandonment of phonics. Even after numerous studies showing that whole word is creating semi-illiterates, government refuses to abandon Whole Word and just renames it "balanced literacy" - claiming to include phonics - but really doesn't.

Ever since Federal Government started funding - and running - education, scores in math and reading have plummeted. This is DELIBERATE. It is much easier to enslave an uneducated semi-literate population than an educated population that can read and understand numbers.

DrMom

Wed, Oct 30 2019, 8:15 am

nchr wrote:

I actually think common core math is common sense. If someone asks you to multiple 22 by 18 and you don't have a piece of paper wouldn't you naturally do something like 18 x 10 x 2 plus 18 x 2 as mental math? When you subtract 48 from 353 wouldn't you do something like 350 - 48 + 3 in your head?

Yes I would. But I also think it's useful to teach kids the more "conventional" ways of doing arithmetic.

Examining mathematics from various angles (no pun intended) can impart deeper understanding. It also increases the probability that at least one of the methods you teach will make sense to the student. Kids who might not "get it" when taught one method may "see the light" when taught using another method.

And if, despite all the effort, they don't understand the fancy explanations, at least they'll know the conventional method so they can balance a checkbook. Although I guess nobody does that anymore...

cbsp

Wed, Oct 30 2019, 8:18 am

DrMom wrote:

Looking into the Common Core method of teaching math, I can see why students get lost.

It's a cute exercise, but I hope they also teach the quick way of subtracting.

Ok, somehow I missed this so I'm going back to comment.

I guess according to the condescending narrator I'm disqualified to comment since I've been brainwashed by the old method.

But I'm commenting anyway.

As a math major I agree 100% that the kids should learn that there is a "why" behind the recipe.

But you know what? That cutesy narrator has a really proficient adult hand and brain quickly filling in the answers to all the extra steps.

That same adult also can figure out the best alternative method to use when figuring out a problem.

Take the kids just starting to write, just starting to learn - each digit they need to write is a labor of love, now they are confused because yesterday's method is so different than today's method and which do I choose? Maybe I need to do all 3? or 4? And even those steps that seem to fill themselves out magically still require the child's thought process.

So now it's 45 minutes later and 2 out of 10 or so problems have been completed. And no math has been achieved at all. Lots of frustration, though.

It's like they forgot there's supposed to be a forest but wow, we really like this one tree, look at the pretty leaves.

Mommyg8

Wed, Oct 30 2019, 8:22 am

nchr wrote:

Not necessarily.

I just checked my son's homework and I don't think he's being taught common core, so I'm not really familiar with the whole method; I'm responding only to the above example.

There can be many ways to solve any given math problem. That's actually one of the things that I really like about math, and that I really find so cool, that you can solve a problem in a few different ways and still come up with the same answer Smile

.

From what I'm understanding from this thread, they are trying to get the students to understand the logic behind the math they are doing. I'm wondering if they have geared their curriculum to be age appropriate, as from what I understand, higher level thinking/logic/abstract skills may not develop until a child is older. Forcing them to use non-existent skills to solve problems would be very, very frustrating, I would imagine.

The way math has always been taught, was that children were taught basic arithmetic by rote and drill, and it was only when they got older that they were taught higher level math such as algebra and trigonometry. In fact, when my parents were young there were two tracks in high school, and only one track took higher level math. This, to me, seems to be more aligned with common sense.

Personally, I think the best way to teach logical thinking is to have really bad math teachers. Then the kids will have to figure things out completely themselves, and wouldn't that certainly hone their thinking skills? Good math teachers, in my experience, break down the math so that almost anyone can do it, as long as they are capable of following instructions (which means pretty much anyone). You don't even need to understand the concepts behind the math at all in order to do ok on tests. So I guess this is going back to teaching math badly - develop your thinking skills and don't rely on the teacher!!!

amother

Wed, Oct 30 2019, 8:27 am

JoyInTheMorning wrote:

What you are describing is number sense, which is the single most important skill that elementary and early middle school math classes are supposed to develop. Understanding the interplay of numbers. Place value. Decimals. Fractions. Estimation. Properties of integers. Properties of operations (commutative, associative, identity, distributive properties...) This is what so many students are lacking and the biggest reason that they struggle with high school math.