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Math for seven-year-olds

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Re: Math for seven-year-olds

#41

Post by oldbuzzard »

lifeofanalysis wrote: post #32

Interesting co-incidence. Just last week, I sent out an email to my friends, saying that I want to teach mathematics to their kids by a math-by-email service, kinda like the chess-by-email of the old days. The idea is quite simple: I will send out a daily email with a grade appropriate set of math questions and/or games. Your child provides the answers back by email. I check the answers, provide corrections/feedback.…

or like math in the old days [1].

Israel Gelfand's stuff is model for enrichment at an upper level. Alexander Zvonkin's "Math from 3 to 7" book published by MSRI could be a model for younger kids.

I think the "new math"materials for the '60s and '70s and the Eastern European materials from a similar period provide a model for education. Unfortunately, they require mathy folks to present and interpret the material.

PS. I'm not criticizing public school teachers. I also feel inadequate. In order to teach DS7, I feel like I should probably work through Herstein's Abstract Algebra. I'll put it on the list... Currently I'm working through Euclid... Next Fall our homeschool will have a geometric focus... after that... who knows.

[1] See http://gcpm.rutgers.edu/books.html ... this was a pale imitation of what Soviet era math circles would offer but is still way beyond anything extant.

Re: Math for seven-year-olds

#42

Post by lifeofanalysis »

oldbuzzard wrote: post #41
lifeofanalysis wrote: post #32

Interesting co-incidence. Just last week, I sent out an email to my friends, saying that I want to teach mathematics to their kids by a math-by-email service, kinda like the chess-by-email of the old days. The idea is quite simple: I will send out a daily email with a grade appropriate set of math questions and/or games. Your child provides the answers back by email. I check the answers, provide corrections/feedback.…

or like math in the old days [1]. Israel Gelfand's stuff is model for enrichment at an upper level. Alexander Zvonkin's "Math from 3 to 7" book published by MSRI could be a model for younger kids. I think the "new math"materials for the '60s and '70s and the Eastern European materials from a similar period provide a model for education. Unfortunately, they require mathy folks to present and interpret the material. PS…

Your URL is broken -- has extra dots at the end.

Re: Math for seven-year-olds

#43

Post by oldbuzzard »

ColinWright wrote: post #8
crasshopper wrote: post #7

Earlier quoted context omitted.

For graph colouring I think the right WP link is Ramsey theory. Also not sure graphs are a "branch" of mathematics, that would be like saying polygons are a "branch" of mathematics. (Branches would be like CA, AT, DG, ... as in http://arxiv.org/list/math/recent. ) I see graphs as just a common object that relates to a variety of mathematical areas.

> For graph colouring I think the right WP link > is Ramsey theory. That turns out not to be the case: Ramsey theory is an area of Graph Theory that overlaps with, but neither subsumes, nor is subsumed by, questions related to coloring graphs. > Also not sure graphs are a "branch" of mathematics, ... It may be the case that you are unsure, but my PhD is in Graph Theory, specifically, and I can assume you that it is a…

Hmmm... Sets, Groups, Topology, Algebraic Structures... Sounds alot like the Bourbaki "Mother Structure's".

Sets and Algebra, I can teach as a homeschool dad. Group theory, topology, and abstract algebra are to difficult for me.

I don't think this is intrinsic. Lots of Rosen is hard for me.I suspect Smaullyan's math logic book coming out this Summer will be transparent(Euler diagrams alone make it clearer). Likewise, lots of Stewarts Calc is obscure. Yet, strangely Spivak's Calc is clear and simple. I suspect there are similar resources for abstract algebra and topology.. I assume that I will have worked through baby Rudin before DS finishes highschool... however, there must be a more direct, less abstract path.

Re: Math for seven-year-olds

#44

Post by oldbuzzard »

lifeofanalysis wrote: post #42
oldbuzzard wrote: post #41

Earlier quoted context omitted.

or like math in the old days [1]. Israel Gelfand's stuff is model for enrichment at an upper level. Alexander Zvonkin's "Math from 3 to 7" book published by MSRI could be a model for younger kids. I think the "new math"materials for the '60s and '70s and the Eastern European materials from a similar period provide a model for education. Unfortunately, they require mathy folks to present and interpret the material. PS…

Your URL is broken -- has extra dots at the end.

Fixed

Re: Math for seven-year-olds

#45

Post by gohrt »

slackpad wrote: post #28

This is the kind of experience would never be allowed with the Common Core type approach. I can't imagine people spending a classroom day on something like this (even though it's awesome and super valuable), but alas it's not content that will appear on the standardized tests.

That's an incorrect slag on Common Core.

It is true that standardized tests would put pressure to ignore this sort of "enrichment" material, but that's a (Pearson) test problem and a (unfairly constrainted) teacher problem, not a Common Core problem.

Put another way:

If a student is exceeding the test standards, there is time to branch out to enrichment topics.

If a student is not passing the basic arithmetic standards of the standardized tests, it's open for debate how to reach a passing level, or if it is appropriate to engage in a major alternative curriculum.

Re: Math for seven-year-olds

#46

Post by oldbuzzard »

If this sort of thing interests you, then either the modern Moebius Noodles[1] material or the vintage Young Math[2] materials like "Maps, Tracks, and the Bridges of Konigsberg: A Book about Networks by Michael Holt" would also.

[1] http://http://www.moebiusnoodles.com/ [2] http://www.valerieslivinglibrary.com/math.htm

Re: Math for seven-year-olds

#47

Post by gohrt »

j2kun wrote: post #35
kaitai wrote: post #29

Earlier quoted context omitted.

Why wouldn't this be allowed with the Common Core? The Common Core is a set of standards for what students should have learned by the end of a year, and for fourth grade, for instance, the Core consists of things like "Use the four operations with whole numbers to solve problems," "Understand decimal notation for fractions, and compare decimal fractions, " and "Generate and analyze patterns." One can fault the Common…

At a high level you're right, Common Core philosophy does encourage this sort of lesson. The unfortunate part is that Common Core still is largely a list of facts that students need to know, and when they need to know them. This is why graph theory is not "compatible" with the standards, because in the huge list of topics they pretend these things don't exist. And since the Common Core is really a document for non-te…

There are so many hours in the day.

Either you argue that graph theory is more important than the other topics (which?) or you acknowledge that graph theory is an enrichment topic for some students who learn the core material faster or devote more time to math study.

It is true that Common Core lacks "enrichment" -- by defining a minimum standard, it doesn't specify what to do with student with more capacity to learn. But that's left to individual students, teachers, and schools, not incompatible.

If a teacher can teach their students 7G math standards in 6 months of the year, the teacher has plenty of class time for other topics.

Re: Math for seven-year-olds

#48

Post by bsilvereagle »

gohrt wrote: post #45
slackpad wrote: post #28

This is the kind of experience would never be allowed with the Common Core type approach. I can't imagine people spending a classroom day on something like this (even though it's awesome and super valuable), but alas it's not content that will appear on the standardized tests.

That's an incorrect slag on Common Core. It is true that standardized tests would put pressure to ignore this sort of "enrichment" material, but that's a (Pearson) test problem and a (unfairly constrainted) teacher problem, not a Common Core problem. Put another way: If a student is exceeding the test standards, there is time to branch out to enrichment topics. If a student is not passing the basic arithmetic standar…

> If a student

I think the problem is that in a vast majority of schools the classes are taught to the lowest common denominator. Sure, one , or two, or ten students could be exceeding the standards but if one or two other students are not passing the standards, I think teachers are very unlikely to introduce these enrichment topics.

Re: Math for seven-year-olds

#49

Post by pbhjpbhj »

j2kun wrote: post #34
pbhjpbhj wrote: post #26

Earlier quoted context omitted.

That's great, an enjoyable and inspiring read. Can you - or another reader - recommend a resource that's perhaps just a little more advanced though, please? What's the next step after formalising the language used, understanding connectivity and path traversal ... perhaps, what would the subheadings of a follow up lesson to this be? I'm not asking to be spoonfed, really!, there are just so many resources on the web a…

I think a good answer is going to depend heavily on your goals (applied or theoretical). Maybe you could elaborate on that?

Um ... bit of both. My goal is personal enjoyment - I've done graduate level maths [way in the past] but graph theory never really featured for some reason. Thanks for your continued consideration.
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