Math: at what grade level do you start focusing on problem solving?

[poetic license]

At what point (grade level wise) do you start working on problem solving techniques with your kids?

 

Do you rely on using a particular curriculum (e.g. Singapore's IP, MEP, etc.) or do you use supplemental materials beyond your regular curriculum?

 

I've been reading the AOPS articles and am trying to think long-term beyond the typical school sequence to be able to prepare the kids for STEM fields, hence the questions!

[wapiti]

I definitely want to add problem solving before they get to prealgebra (once they get to the prealgebra level, I feel we're pretty well set with AoPS Prealgebra). Word problems are a start, but I don't think that's enough.  I started a list on anohter thread recently. So far, my list of problem solving materials for elementary level includes:

Contest materials:
Creative Problem Solving by Lechner
MOEMS contest problem books

Curricula:
SM CWP and IP
MM (for your basic word problems)
Beast
AoPS for prealgebra and up
MEP

Supplements:
Alcumus
Zaccaro books (which one is best?)
Hands-On Equations Verbal Problems Book
Kitchen Table Math Book 3 (?)
Martin Garner books (my ds9 is starting to get into the easier ones, especially the ones that don't look like they're about math)

as well as some thoughts mentioned in this thread.

Edited March 26, 2015 by wapiti

[Iucounu]

Preschool here (and before the start of any explicit math instruction), starting with games and puzzles, discussions involving logic, books, etc. The usual suspects for problem-solving enrichment include MEP (Sunshine Math is another freebie that's much less extensive but is also just problem-solving enrichment instead of a full curriculum), Ed Zaccaro's Challenge Math, Life of Fred, Singapore CWP/IP, etc.

[SunshineMom]

This is a wonderful thread about enriching math-thank you:001_smile:

[wapiti]

Around 18 months...you want them to get used to attempting to solve their own problems without being so frustrated they melt. The traditional childhood games, puzzles, and toys are where it starts.

 

This is a good point. RR talks about the importance of getting over perfectionism issues. While finding the right level of challenge and frustration is tricky, I do believe that the earlier one starts working on that, the better. I have a ds who is well behind his ability level in math due mostly to perfectionism issues (and a teacher who didn't challenge him even though she had the flexibility to do so, because she doesn't understand the issue).

 

It's a bit of a conundrum, how much problem solving to assign with a kid who tends to get frustrated. I know some try to avoid that entirely. I think it's important not to avoid it, but it's not clear how best to deal with it. Incrementally increasing frustration sounds good. 

[Runningmom80]

I feel like its been beaten into me (figuratively of course) to start now. :lol:

[Crimson Wife]

With my oldest, I started in 2nd, but with DS, I started in K. I have signed her up for a formal MOEMS prep class for next fall through a local co-op. DS was bummed that he couldn't do it too.

[Beth in SW WA]

Chess.

 

My dc start around age 5.

[poetic license]

With my oldest, I started in 2nd, but with DS, I started in K. I have signed her up for a formal MOEMS prep class for next fall through a local co-op. DS was bummed that he couldn't do it too.

 

What things did you start in 2nd and KG?

[crazyforlatin]

I've found that games such as Rush Hour and Tip Over require DD to think a few steps ahead, which is similar to solving a multi-level word problem. I didn't notice the improvement in her thinking skills until just last weekend when she was trying to solve an advanced level of Rush Hour with my brother, who happens to be a scientist. He noticed that these games would help her transfer some skills over to solving word problems.

 

I'm also thinking of getting similar games, specifically the one with penguins on ice using pentamino pieces.

[melmichigan]

Once they have their math facts down we really start to focus on problem solving so it has varied for each child.

[Crimson Wife]

What things did you start in 2nd and KG?

 

Singapore's CWP and IP, and the Zacarro Challenge Math books. DS also did most of MEP 1A in K and I'm toying with the idea of his doing MEP 2 over the summer.

[Miss Marple]

We were problem solving long before we started the boys in formal school. We played math word games in the car, in the kitchen, etc. By the time they started school they were familiar with various problem solving situations.

[slackermom]

We were problem solving long before we started the boys in formal school. We played math word games in the car, in the kitchen, etc. By the time they started school they were familiar with various problem solving situations.

 

I've also tried to use a problem solving approach with DD from the beginning, and math is part of our everyday life. When we do math problems together, we may solve the same problem 3 or 4 different ways, with a focus on trying out different tools and discussing the principles involved.

 

I like this article from AoPS. "We use math to teach problem solving because it is the most fundamental logical discipline....Problem solving is crucial in mathematics education because it transcends mathematics. By developing problem solving skills, we learn not only how to tackle math problems, but also how to logically work our way through any problems we may face."

Edited May 16, 2012 by slackermom
missing a word

[Spy Car]

Call it what you will, but developing creative problem-solving, logic, reason, and critical thinking has always been the fundamental goal of our home education, and "math" has always been at least as much about this as it is about arithematic. We learn math skills so we can problem-solve.

 

This was encouraged in toddlerhood with toys and games, and then expands upon with programs like Miquon and MEP in pre-K, with Singapore IPs, PGCM, CSMP, SMSG and other challenges thrown in. Most recently we've added Beast Academy and selected AoPS Prealgebra topics to the mix.

 

The goal is to develop a *thinker*.

 

Bill

[poetic license]

Call it what you will, but developing creative problem-solving, logic, reason, and critical thinking has always been the fundamental goal of our home education, and "math" has always been at least as much about this as it is about arithematic. We learn math skills so we can problem-solve.

 

This was encouraged in toddlerhood with toys and games, and then expands upon with programs like Miquon and MEP in pre-K, with Singapore IPs, PGCM, CSMP, SMSG and other challenges thrown in. Most recently we've added Beast Academy and selected AoPS Prealgebra topics to the mix.

 

The goal is to develop a *thinker*.

 

Bill

 

What's the bolded one? SMSG?

 

I agree with your post. I am really glad to hear the suggestions from everyone because my education did not proceed in this way. I've probably griped about this on these boards before, but I've been in GT/STEM magnet schools until 8th grade, finished up to Calculus with straight As, but am terrible at math. I have so little understanding, so little number sense, and no problem solving skills. :( I really want to do better for my kids, and re-learn for myself as I go along.

[stripe]

 

School Mathematics Study Group material can be found here, within this site, an archive of "new math" books from the mid-20th century.

[Spy Car]

What's the bolded one? SMSG?

 

I agree with your post. I am really glad to hear the suggestions from everyone because my education did not proceed in this way. I've probably griped about this on these boards before, but I've been in GT/STEM magnet schools until 8th grade, finished up to Calculus with straight As, but am terrible at math. I have so little understanding, so little number sense, and no problem solving skills. :( I really want to do better for my kids, and re-learn for myself as I go along.

 

School Mathematics Study Group. This was the best of the (wrongfully) dreaded "New Math" of the 1960's. The SMSG brought together some of the best math-minds in the country and they released textbooks to serve as models for textbook publishers. The materials are archived on-line and available to download free in electronic form. Top-notch stuff IMO!

 

Bill

[LittleIzumi]

Beyond the toddler toys ;), we start logic in K and also use logic/problem-solving-heavy math (MEP, Miquon).

[wapiti]

I recently ordered a few of these books from Singapore: Process Skills in Problem Solving, which I'm hoping will offer more in terms of problem solving than the CWP and IP books (while the CWP and IP books would be a step in the right direction, they might not be quite what I have in mind). The lower grade levels were improved recently, though I believe the 5th and 6th grade ones will not be updated until later this year.

 

UPS just dropped off my box. These books look very good - very explicit teaching. Much of the book involves various kinds of bar models, but there's also quite a bit on other approaches ("heuristic"), though different things are taught in different levels. Just glancing through the TOCs, I like what's in Level 3: look for a pattern, draw a picture, work backwards - these are the very subtopics in Ch 15 of AoPS Prealgebra.

 

The answers are in the back. The books are not very long at all, so it shouldn't be difficult to find the time to add them as enrichment. I wish they had more problems, however.

 

Keep in mind that I have not seen CWP or IP, so I can't compare.

[Five More Minutes]

UPS just dropped off my box. These books look very good - very explicit teaching. Much of the book involves various kinds of bar models, but there's also quite a bit on other approaches ("heuristic"), though different things are taught in different levels. Just glancing through the TOCs, I like what's in Level 3: look for a pattern, draw a picture, work backwards - these are the very subtopics in Ch 15 of AoPS Prealgebra.

 

The answers are in the back. The books are not very long at all, so it shouldn't be difficult to find the time to add them as enrichment. I wish they had more problems, however.

 

Keep in mind that I have not seen CWP or IP, so I can't compare.

 

I ordered them too ... I couldn't resist. They haven't arrived yet, but I'll be interested in hearing more about what you think about them. I'm imagining that they may work as enrichment, or as a springboard for problem-solving math labs that we work through together.

[Crimson Wife]

School Mathematics Study Group. This was the best of the (wrongfully) dreaded "New Math" of the 1960's. The SMSG brought together some of the best math-minds in the country and they released textbooks to serve as models for textbook publishers. The materials are archived on-line and available to download free in electronic form. Top-notch stuff IMO!

 

Bill

 

Is it any easier to understand than CSMP? I think my DS would really like CSMP-type math but I've never been able to make much headway in figuring out how in the heck to teach it.

[poetic license]

Those who use SMSG, what components do you single out for use?

[Spy Car]

Is it any easier to understand than CSMP? I think my DS would really like CSMP-type math but I've never been able to make much headway in figuring out how in the heck to teach it.

 

Yes, much easier to follow. I really enjoyed our play with CSMP, but as time constraints have increased the voluminous teacher books and unconventional methods became too much for me to pull off.

 

The SMSG materials are much more straight-forward. There is still a good-deal of "set-theory" work (as was typical of New Math) but it is very easy to grasp and implement. I use it as a change of pace and often go several grade levels up looking for interesting diversions.

 

Bill

[Spy Car]

Those who use SMSG, what components do you single out for use?

 

There are teachers books at every level that are valuable for parent/teacher education and the full series to glean problems from. I don't know anyone on this forum who uses SMSG as their main math program (but it could be done). I grab ideas for our "Math Lab." The materials come out of the same zeitgeist as Miquon and share the low-tech look.

 

Bill

[stripe]

I used parts of year 3 of SMSG (and parts of Singapore IP for y2) with my son between MEP Y2B and MEP y3a. We did it for about a month. He liked the graphing a lot.

 

The K book is for the teacher only. Lots of hands on ideas. No worksheets. The other one has a teacher's manual and a student text. The problems have tons of room on the page. Lots of white space.

 

Btw one of the links on the new math website to a book is wrong. That book doesn't seem to actually be there. I found a poor quality copy on ERIC. My old post about it

 

I found that the link for Unit 57 of "Mathematics for the Elementary School" (for year 3 part 2) is wrong at http://ceure.buffalostate.edu/~newmath/SMSG/SMSGTEXTS.html. It links to Unit 54.

 

I located this unit (in a fairly bad quality scan) at ERIC, here.

 

I also observed in at least one book (year 3??) that the book, after it finishes, repeats, backwards. So don't blindly print off the entire 400+ page file. Check it.