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Sat Apr 10, 2021, 09:27 PM

4th/5th Grade Math Advice Needed

I agreed to help a friend's 4th grader with math.
She is doing okay, her parents want to be in the advanced program.

Met with her teacher - he thinks she is where she should be.

Working on angles and number patterns now.
Any advice or interesting exercises?

I taught college for eight years and 20 years of teaching engineers and network folks - very different audience.

Thanks in Advance,
Dale

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Arrow 10 replies Author Time Post
Reply 4th/5th Grade Math Advice Needed (Original post)
PBC_Democrat Apr 10 OP
SheltieLover Apr 10 #1
madaboutharry Apr 10 #2
PoindexterOglethorpe Apr 10 #3
Karadeniz Apr 10 #5
BigmanPigman Apr 10 #4
Buckeye_Democrat Apr 10 #6
soothsayer Apr 10 #7
eppur_se_muova Apr 10 #8
Tetrachloride Apr 10 #9
Lucky Luciano Apr 10 #10

Response to PBC_Democrat (Original post)

Sat Apr 10, 2021, 09:30 PM

1. Khan Academy

👍

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Response to PBC_Democrat (Original post)

Sat Apr 10, 2021, 09:34 PM

2. Why do her parents want her in the advanced program?

Donít they understand they are setting her up for failure, which is the worst thing to do to a child?
From what you say she is doing ďok.Ē She would struggle to keep up with the other kids.

I donít get that kind of parenting.

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Response to PBC_Democrat (Original post)

Sat Apr 10, 2021, 10:05 PM

3. I know this is 4th/5th grade, but let me share this. (Warning, long post)

When I was in high school in the 1960s I was in a wonderful math program, UICSM, which stands for the University of Illinois Committee on School Mathematics. It was a "new" math. I'm yet to meet someone who didn't go to my high school who ever heard of it. Anyway, one of the reasons it was wonderful was that it taught us to think, and we proved EVERYTHING. It was incredibly rigorous, and afterwards, some 30 years after taking my last high school math class, I was able to test into algebra 2. And when I was in that class, memories of what I'd learned all those years ago came bubbling up, and were very helpful.

Here's what's important, even though it's beyond the grade level you're dealing with. In the third year of UICSM, the last year I took it, we were well into calculus. I'd gotten A's in the geometry part, B's in the rest, but when we hit calculus, I could not understand it and just barely passed the final semester. So 30 plus years later I need to take math through college algebra. Ok. I take algebra 2, get a B, college algebra, get an A. I decided to take statistics because I thought it would be useful. Then, because I really was having a good time with math, I decided to take calculus. I was 47 years old. And I got it. I loved the class, what I was learning. My final grade was a B, mainly because I managed to make some dumb mistakes on the final, but I learned an A's worth. During the semester I kept on grabbing math teachers I knew at the community college I was attending and asking them how was it I was doing so well at my advanced age, when back when I was 16 I could not get it at all? To a person they said, "Oh, Poindexter. People don't understand that math is developmental." They'd go on to say that other than the real math prodigies, most high school students at 17 or 18 really aren't quite ready for calculus. Give them a year or two and they'd be fine. These teachers also felt that the local very good public schools were pushing a lot of kids a bit too fast and hard in the math, and needed to ease up.

I have shared that over and over with high school students and with their parents. They are often quite relieved to hear that. I saw this developmental thing with my younger son, who in the excellent private school he attended, was always at the upper edge of what he was ready for in math. I encouraged him not to take calculus, because he was struggling enough that it made no sense. He was very relieved, probably fearing that I would say to him, "Your older brother took calculus and did just fine so of course you will take it too."

So anyway, if the teacher thinks this girl is where she should be, please try to convince the parents to trust the teacher. It may be that in another year or two this girl will blossom in math and be able to get into the advanced program. If not, it's not the end of the world nor the end of her being able to do well in math in the future.

One frustrating problem with conventional schools is that of necessity they have to teach kids in groups, and everyone is expected to learn the same thing at the same time. I was up against that when my older son was having trouble learning to read, but was ahead of the other kids in math. Eventually everything settled, but it made me very understanding of why some people choose to home school.

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Response to PoindexterOglethorpe (Reply #3)

Sat Apr 10, 2021, 10:09 PM

5. Yes, yes, yes...

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Response to PBC_Democrat (Original post)

Sat Apr 10, 2021, 10:09 PM

4. I taught K-6th(GATE).

Gifted And Talented Education(GATE) for 20 years.

With math use tons of visuals and manipulatives. Too bad they can't work in pairs or groups. Angles and number patterns are usually fun for my students due to the hands on manipulatives and the visual "games" they discovered (like puzzles). I incorporated art into most subjects. Kids love to draw. Visual learners and those who have a difficult time grasping some concepts "get it" through the use of visuals. I learned in my teacher classes that gifted kids are part of the "special" group of kids. Those who have a physical learning disability, those who are slow learners, and those who are high achievers all are "special" education.

The parents always wanted their kids to be challenged, even though not ready. One student came back to visit while in high school and he said I gave them harder work than they got in middle school. I told him he can thank his parents for that...it was their idea. But when it came time for their little rocket scientists to do a test or a project, let alone nightly homework, the parents usually realized they would end up doing half the homework and they themselves and eventually they backed off.

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Response to PBC_Democrat (Original post)

Sat Apr 10, 2021, 10:24 PM

6. Maybe think of some fun math puzzles?

I eventually majored in math, and I was mostly motivated early-on by math problems with solutions that surprised me, going against my intuition at the time.

My father often gave me those kinds of problems, like this one:
https://www.slader.com/discussion/question/in-a-classic-math-problem-a-king-wants-to-reward-a-knight-who-has-rescued-him-from-an-attack-the-k-2/

Obviously, it would need to be done with whatever the child is currently learning.

My Dad even gave me the "Three Utilities Problem" when I was a little kid, but that didn't seem very mathematical to me back then.
https://en.m.wikipedia.org/wiki/Three_utilities_problem

All that I knew was that it seemed to be impossible, after repeated tries, so I gave up. Yet that puzzle stuck with me, and I recalled it while taking a "Graph Theory" class in college. Then I used that new knowledge to PROVE it was impossible, which was about an 8-page proof for me I think. I did that just for "fun" back in those days.

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Response to PBC_Democrat (Original post)

Sat Apr 10, 2021, 10:28 PM

7. I like simple things like this

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Response to PBC_Democrat (Original post)

Sat Apr 10, 2021, 10:41 PM

8. You know how the parents feel. You know how the teacher feels. How does the student feel ?

She might be reluctant to say, particularly if she disagrees w/her parents, but it's worth a try.

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Response to PBC_Democrat (Original post)

Sat Apr 10, 2021, 10:56 PM

9. Education Design, especially Gifted and Talented is what I did for years, especially regarding math.

If any parent or teacher has a wish, I can design something.

Pick your topic: language, math, sciences, humanities, the arts. The list is never ending.

Describe the abilities and interests. and that's a nice start.

Plenty of low-stress stuff to start with.

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Response to PBC_Democrat (Original post)

Sat Apr 10, 2021, 11:22 PM

10. Hah...I feel bad for my eight year old son. It's not good to have a dad who is a math PhD.

I tell him that I hope he is better at math than I am. No pressure of course! LOL

The way I get him to tolerate my crap is by letting him use the Oculus only if he does math with me.

Heís not bad, but definitely no Terence Tao or 1% of Tao.

I was able to get him to understand why summing from 1 to n is n(n+1)/2.
If S is that sum then:

S = 1 + 2 + 3+...+ (n-1) + n
and in reverse order
S = n+(n-1) +...+ 2 + 1

Adding both rows, you get each column adding to n+1 on the right and there are n of those.

2S = (n+1) + ... + (n+1) = n(n+1) and dividing by 2 gives us
S = n(n+1)/2.

The story for the above is that 8 year old Karl Friedrich Gaussí class got into trouble and was given the rote exercise of adding the numbers from 1 to 100. He had the answer in less than a minute because he came up with the above proof and gave the correct answer of 5050. She recognized that Gauss was gifted at that point (geez ya think?!).

They didnít do that in class, but I thought it could be understood (I wanted to teach him mathematical induction which I havenít gotten to, because he gets annoyed. This would be a good easy example to use induction on for an alternative proof. It wouldnít be as constructive by induction though because you need to know the result a priori).


They just started fractions in school, but they are taking a month to do what I explained in an hour. I really donít know why. The reason I wanted to do induction was so I could prove the prime factorization theorem to him which is almost trivial by induction. That would be useful for understanding reducing fractions by canceling common primes in the numerator and denominator.

I was able to teach him about getting common denominators and I explained least common multiples, but not how to get the least common multiple efficiently. Prime factorization helps a lot there actually. He knows how to add fractions now by getting common denominators, but I havenít done reducing fractions yet.

He gets most of the concepts, but doesnít really love math, so I definitely need to back off a lot or heíll hate me! In school he doesnít always ace the math tests (usually gets one question wrong, but he always tells my wife, ďdonít tell daddy!Ē). It is almost always due to the fact that his language comprehension is atrocious and the problem was too wordy and not just straight pure math.

Maybe this can jog your mind for a few ideas.

I canít wait until my son finally gets to more interesting math so I can really show him good stuff. I think calculus is a bit overrated. I think they should do linear algebra in high school instead. That is huge for statistics and modern applied math often used for data scientists and machine learning practitioners that are more and more in demand every day. Being good at multivariable calculus absolutely requires strong linear algebra. I wish that was emphasized to me before grad school! It would have saved me from some hassles! Got Carried away obviously...

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