Integrated math: algebra, geometry, and probability/statistics

[lewelma]

I am doing some planning for the future.  I'm looking to create a 3 year course in algebra, geometry, and basic probability/statistics, and would like some BTDT advice.

 

This is for my younger son, who is good at math, but likes variety. He has not like AoPS preA, and I think is more of a direct learner (plus he does not have that kind of intensity about math). He is currently doing preA through MEP secondary, which is integrated. I will stick with MEP this year, but I am finding that it is written with too many ability levels in mind, so there is a lot to sort through to get to the good stuff.  My goal is to keep somewhat within the NZ system by integrating maths, but not using the NZ textbooks (or even Cambridge) for these lower levels because they are just too algorithmic/formulaic (both NZ and Cambridge textbooks get better in upper levels), and my son finds that kind of material really dull.  He does need a challenge, but not too much of one. ;)  

 

I've heard good things about Foerster's algebra, and am looking for suggestions for geometry and basic probability/statistics. Geometry does not need to be proof heavy as NZ does not do geometric proofs, but it does need to be interesting/challenging.  For statistics/probability, we are talking really basic - so not high school level.

 

I would also like to get a feel for scheduling, testing, review, etc for an integrated course using multiple textbooks.

 

Given my son is young, I do have time for extras also.  So open to suggestions for fun resources.  This program would be for 6th - 8th grade, but include 'high school level' Algebra 1 and Geometry. Hope you guys don't mind me asking on the High School Board as I know there are so many of you with so many ideas and experiences.

 

Thanks,

 

Ruth in NZ

[Matryoshka]

Why not Singapore Discovering Mathematics?  It's for grades 7-10, and it's already integrated.  I have used both DM and Foerster's, and while I like them both, I think the level of problem-solving is definitely higher in DM, especially if you use the Workbook - it really extends the thinking.  I really, really liked it.  The only reason we went from DM to Foerster's Algebra was that I wanted a pure Algebra course so that dd could more easily integrate into the school here (she went to ps in 9th).

 

My youngest is using AoPS. The dd that did DM and Foerster's does not like AoPS' style - she likes less wordiness, and direct teaching.  Being familiar with both programs, I think some of the challenging problems in the DM workbook are up there with much of AoPS, but the teaching style is direct.  There are four different problem levels in the workbook, so you can pick and choose the number to do and the challenge level.  The text itself has the "main" problem sets (about equal to the basic level in the workbook); the workbook is optional but I really think adds a lot to the program.

[lewelma]

Goodness, I forgot that I had DM.  I bought it for my older who never used it.  I have the workbook too.  Off to get it out......

[lewelma]

Well, it's not DM, it is NEM.  What is the difference?

[Matryoshka]

Well, it's not DM, it is NEM.  What is the difference?

 

DM is newer.  The layout is "friendlier" and full-color; it looks a bit like a more mature version of Primary Math.  I've heard it rumored that the problem sets in the NEM text itself run harder than the problem sets in the DM text itself, but the DM workbook I think evens that out - although I haven't seen the full NEM program.

 

NEM also doesn't have solution guides above the 2nd level (actually I think only the 1st level is currently availalbe).  DM has them for all four - but they are switching to "Common Core" aligned DM here - the first two levels are out, levels 3 & 4 are still the originals.  But that's a US thing, and there's no reason for you not to stick with the original versions - maybe in NZ you can get the originals direct from Singapore, or imported via Australia?  I think some other vendors still have the originals for sale here in the US, but it seems silly to buy them from here since they originate closer to you...

 

Here's a comparison chart between the S&S of NEM, DM, and the new DM Common Core books - scroll about halfway down.  On the singaporemath.com website there are also sample pages of each to look at.

[lewelma]

Thanks! I can see what you mean about the workbooks.

 

Still interested in recommendations for individual texts.

[lewelma]

Matryoshka, I have a few more questions if you don't mind:

 

1) Did you buy the teacher's notes/solutions and the workbook solutions?  I can definitely teach this material, but am curious if it is more self teaching with a solution manual.  There are simple answers in the back of the textbook and workbook, right?  Did you actually use the solution books?

 

2) Also, where did the rest of the material in DM3 and 4 go?  From the scope and sequence, it looks like half of DM3 was integrated into DMCC 7 and 8.  Are they putting out a DMCC 9 and 10? And if so, when? 

 

3) Finally, do you know where I can buy the original Discovering Mathematics?  I'm not finding it anywhere.  Is it still made?  Or is it being phased out?  I don't want to buy materials that are being phased out as I want to trial the level 1 for a year before investing in all 4 years, and I don't want them gone before I need them. 

 

Thanks!

 

Ruth in NZ

 

edited to add: found it in the UK, although I am not quite sure what the 'express' in the title means:   http://www.mathsnoproblem.co.uk/mathematics/secondary-key-stage-3-and-key-stage-4/discovering-mathematics-express.html

[Matryoshka]

Matryoshka, I have a few more questions if you don't mind:

 

1) Did you buy the teacher's notes/solutions and the workbook solutions?  I can definitely teach this material, but am curious if it is more self teaching with a solution manual.  There are simple answers in the back of the textbook and workbook, right?  Did you actually use the solution books?

 

I bought the Teacher's Guide, which ended up being pretty much just the solutions.  The notes are so minimal as to be non-existent.  I did not end up using them that much, as the math in the text was mostly straightforward enough that the answers in the back were usually enough.  Looking at the samples of the newer CC version, it looks like the Teacher's Notes/Solutions include classroom activities as well, but I don't know how useful those would be?  But this is coming from someone who never got the HIGs for PM...

 

What I did not buy that I should have bought was the solutions manual to the workbook.  I don't think it was out yet at the beginning of the year when I purchased the materials, and I hated to buy it mid-year, esp. as it wasn't cheap.  But gosh, I could have really used the solutions for some of those tough problems.  I did also buy the test bank and gave her tests every so many chapters.

 

2) Also, where did the rest of the material in DM3 and 4 go?  From the scope and sequence, it looks like half of DM3 was integrated into DMCC 7 and 8.  Are they putting out a DMCC 9 and 10? And if so, when? 

 

At singaporemath.com, they're still selling the original DM3 and 4 (also found the same at Christianbook.com) - so the sequence right now is 7,8,3,4.  They're in the process of switching over, I'm not sure at what pace.  I don't think(??) the originals are being discontinued in Singapore (??) - the switch here is because of Common Core (CC), which is irrelevant elsewhere.  Can you get them directly from Singapore?  Does anyone import them to Australia? I'd think that would save you on shipping to boot... ?

 

3) Finally, do you know where I can buy the original Discovering Mathematics?  I'm not finding it anywhere.  Is it still made?  Or is it being phased out?  I don't want to buy materials that are being phased out as I want to trial the level 1 for a year before investing in all 4 years, and I don't want them gone before I need them. 

 

They're still selling levels 3 and 4 here, I'm guessing until the 9 and 10 levels are finished... but I still don't see why they'd phase them out elsewhere? 

 

 

edited to add: found it in the UK, although I am not quite sure what the 'express' in the title means:   http://www.mathsnoproblem.co.uk/mathematics/secondary-key-stage-3-and-key-stage-4/discovering-mathematics-express.html

 

Here's the publisher's website in Singapore.  Looks like there's a brand-new 2nd Edition out there.  The Express refers to a level?  Although I have no idea what that level is??  Maybe contact them directly?  There's contact info on that website.

 

[Arcadia]

 

 

edited to add: found it in the UK, although I am not quite sure what the 'express' in the title means:   http://www.mathsnoproblem.co.uk/mathematics/secondary-key-stage-3-and-key-stage-4/discovering-mathematics-express.html

Express is the four year secondary school course which is 7th-10th grade.  Normal would be doing the express course stretched out to five years.  DM ends at GCSE or O Levels.  The Additional Math program is for 9th-10th grade and has a separate GCSE exam.

[Brad S]

Ruth,

 

My DS sounds a bit like your younger.  We really liked the Jacobs Geometry (3rd edition).  You can alter the amount of proofs covered by problem selection.  Although I have not actually seen Singapore's newer Discovering Math series, I'd look into it if we were doing it over again, but I'd make sure it included some data analysis and statistics or supplement.  We found it hard to find good age-appropriate statistics materials for 5th graders.  A lot of newer US math textbooks, for all their flaws, are now including that material, at least from middle school onward.  The Practice of Statistics, by Starnes, Yates, and Moore (4th ed.) is a very good textbook.  Although it's for AP, it might be usable by a 6th grader with a little help. Though it's a bit expensive, you could probably use it as a supplement now and then for a course later.  We were looking for similar materials a couple years ahead, and this is where we ended up: 

 

http://forums.welltrainedmind.com/topic/486905-math-options-after-algebra-2-for-12-13yo/?p=5404097

 

Best wishes.

[Arcadia]

  We found it hard to find good age-appropriate statistics materials for 5th graders.  

Unit 9 Data Analysis of the MEP GCSE is easy for a 5th grader.  The statistics portion of the A Level section is okay for a child who likes statistics.  Anyway MEP is free to download.

[lewelma]

Thanks Brad for the Jacobs rec. I currently have his algebra text, so it might be easy to blend it with his geometry. Why the third edition?. I was also a statistician in a previous life, so I we certainly find some sort of stats somewhere for both my kids to do before they leave home!

 

Arcadia, we are currently using mep year 8, so I will definitely look up a few years at the stats material. I had not even thought of that idea and it is excellent. I would actually stay with mep through highschool if it were written differently. I really like it but am finding it very difficult to implement with any sort of independence component especially because the easy and difficult problems are all mixed together and only identified in the teachers manual so there is quite a bit of flipping around.

 

Thanks!

[Brad S]

Ruth, I know that a few math types prefer the 2nd edition since it has more proofs, but Jacobs apparently thinks the 3rd edition has a better approach.  The 3rd edition is very appealing and we spent more or less time on proofs for individual sections as seemed appropriate -- as a math type myself, I thought the coverage was sufficient.  I would skip the algebra review, however, in Jacobs Geometry, and use something else as they're mostly just drill problems in the algebra review.  If you do integrated math, you won't need to review the algebra since you'll already be doing it in parallel.  By the way, I think Jacobs's Geometry book is far better than his algebra book.