Integrated math

[abba12]

This isn't exactly an accelerated topic, as I think it applies just as readily to the learning challenged, but I figure many of you here have more experience with this kind of thing :)

 

I have been thinking about the structure of high school math. Here in Australia we have what I guess is called integrated math. We don't have an Algebra 1 course and a Geometry course etc, we have Math until 10th grade, and in 11 and 12 we have math A, B and C (A is for the kids who don't intend to use math much and covers the basics of algebra and geometry as well as practical and 'business' math, B is your 'standard stream' covering alg/geo/trig/statistics and a few other topics, and C is like an extension course, you must take B and C concurrently, and it gets into calculus etc.) but the topics are covered gradually over the course of high school instead of segmented into years. 

 

When I look at the scope and sequence of Alg and Geo/Trig books, I see topics that I covered as early as 7th grade, AND topics I never did end up covering at all (despite being gifted I finished school in 10th grade, which is still quite acceptable here). I always struggled to understand why you would study the advanced parts of Alg 1 before studying the basics of geometry but I never thought much about it, since it seemed to be the only options available in homeschool curricula, and I knew I didn't want to use our standard school textbooks.

 

But I am thinking more about it lately. Somewhere else on the forum someone mentioned the idea of doing, say, an Alg 1 book, Geo book and Number Theory book all at once, but spreading them out over 2-3 years, the idea being they would cover all the basic topics early (I think it was like 7th or 8th)  but wouldn't be struggling with the hardest aspects of any of the topics until they were older with a little more maturity.

 

This seems to make a lot more sense to me. Both for the accelerated student who is ready for more than arithmetic, but may not be mature enough to handle the harder elements of Algebra, and the learning challenged student who stalls out in Algebra and subsequently misses out on the parts of other topics he may have been able to handle. And for the standard student, doesn't it make more sense developmentally to go from basics in 8th to advanced in 12th than to go from easy to advanced in a single stream each year? Plus, it seems like it would help a lot with retention.

 

Has anyone handled high school math this way? Are there any homeschool curricula that do math like this or is it all segmented? Anyone have a reason NOT to do it this way? I'd love to hear how some of you who did multiple math streams handled it in a practical sense. I suppose with the way that American college standards and transcripts work it would actually be hard in a reporting sense, as you couldn't just put 9th grade - Geometry on the paperwork. I am grateful for a lot more freedom in high school requirements here in Australia!

[SorrelZG]

Curious about this, too.

[EndOfOrdinary]

We were planning algebra, geo, and number theory the way you were describing covering two years approximately. My son is visual and leans heavily to the geometry. While he can so simple algebraic equations, he will probably stall out if he does not do the algebra along side the geometry as necessary. Number theory helps with this integration as it is really about how the different numbers can be arranged in various groups.

 

I have not done this yet. We will be starting next January most likely.

 

The only snag I can see to the approach is personality. My son is a highly creative thinker, but not me. My personality really hates this approach. I am a linear box checker. I want to feel the rush of success that comes through progression of one subject before getting to the next. My brain rails against the murky waters and fuzzy lines that integration presents. It is much more realistic, but the crisp clean, non-creative lines of the separate subjects give me security.

[Monica_in_Switzerland]

The upper levels of Singapore are integrated... can't think of what they are called- NEM? 

[dbmamaz]

We used upper level singapore.  We started with NSM, which is discontinued, and half-way had to switch to DM.  I think they are discontinuing everything in favor of Discovery Math Common Core, but I think its still integrated.

 

The integrated system worked well for my teen (who is 2E).  He really hated algebra, so it was great that we never had to do algebra for more than 3 months straight without a break to do something else like geometry or stat.  

 

The only downside was that I wasnt sure what to do when we were done.  We only did through level 3b, which covers some trig, but not nearly as much as I covered in my high school pre-calc class.  4a covers calc and 4b is review.  So we didnt bother with 4 at all - he's headed to community college, so he's now doing a free on-line self-paced course called college algebra ,designed to help kids pass the community college entrance exams - its a good solid review (which he desperately needed) of algebra 2.  

 

I am wondering if they are any less 'integrated' now that they are common core compliant?  

[amsunshine]

We currently use the upper levels of Singapore, which is integrated and we love it.  It starts with levels 7 and 8 in "Dimensions Math", which aligns with Common Core.  I don't believe they intend to publish any Common Core books after level 8.  We are currently in level 8B with my oldest and will continue on to levels 3 and 4 of "Discovering Mathematics", which apparently has a little bit of overlap in the first couple chapters, but we are fine with that.  After we finish level 4, I'm not sure where we will go, but my dds are young, so we have options.  Either AoPS or CC will likely be in our future.

 

Wendy, the teacher guides do have solutions for all the problems in the books/workbooks.  I find they are very clear and easy to use.  They don't have much in the way of teaching strategies, like the lower levels had.  However, I don't feel I need it.  The texts and the teacher guides are so clear and straightforward. 

 

 

[Lilaclady]

We are doing an overlapping integrated course. My dd is doing algebra and about half way through, she will start geometry. so she will do 3 days of algebra and 2 days of geometry until the book is finished. I feel the geometry book is tougher so I want to give her more time with the algebra.

[Crimson Wife]

I'm also not sure how user friendly it is for a homeschooler.  One can get TMs, but for example, do they contain solutions (not just answers)?  I need that.  I suspect a lot of homeschooling parents would prefer that.  I'm not a math teacher.  And all of the components together are quite pricey compared with other things out there that are easily available here.

The TM's for Discovering/Dimensions Math are pretty much ONLY solutions manuals. There is hardly any teaching guidance so they are very different from the Primary Math HIG's. That is why I wasn't originally certain how far I would get in teaching DM. I feel confident enough to finish out the algebra in DM 8 and the geometry in DM 3. But the harder algebra topics in DM 3 I'm not sure I'd be able to teach.

 

As it turns out, I'm in the process of switching DD from DM 8A to EPGY Beginning Algebra (uses the Lial book). We're not sure whether we will be able to continue HSing after the current school year. EPGY is much more likely to be acceptable for placement purposes at a B&M school. If she can finish up the beginning algebra course by August, she'd enroll in geometry. If she doesn't complete it, she'd presumably enroll in algebra 1 and the first part would just be easy for her.

 

If we are able to continue HSing, I'll probably have her finish up the EPGY Beginning Algebra and then run EPGY Geometry concurrently a review/extension of algebra 1 using the harder problems from DM 8 (and possibly AOPS Intro to Algebra).

[lewelma]

I have just switched to Singapore's DMCC too.  Younger loves it.  My plan is to work through it and the original DM (if grades 9 and 10 never materialize for DMCC) and then switch to a program that will work my son to the A levels for the CIE (Cambridge International Exams). There are heaps of textbooks for that level (just google CIE math)

 

Ruth in NZ

[quark]

Has anyone handled high school math this way? Are there any homeschool curricula that do math like this or is it all segmented? Anyone have a reason NOT to do it this way? I'd love to hear how some of you who did multiple math streams handled it in a practical sense. I suppose with the way that American college standards and transcripts work it would actually be hard in a reporting sense, as you couldn't just put 9th grade - Geometry on the paperwork. I am grateful for a lot more freedom in high school requirements here in Australia!

 

I'm going to format his transcript by subject. He will have subjects as main categories instead of 9th grade, 10th grade etc. I might include a column for year taken but I have seen subject-based transcripts that do not mention years courses were taken, just a graduation date. Or the span of four years that child was in high school. Or a span of five years if 8th grade work is included.

 

We don't use an integrated curriculum. Kiddo does math in multiple strands/ streams within the same day, moving from about 2 hours per day at Algebra 1 level to his current 4 or so hours a day (should hopefully drop back to 2 in summer). Within the hours he uses different math books: e.g. an Algebra book, a Number Theory book, some notes compiled by his tutor on discrete math topics and possibly some time spent researching math ideas on wikipedia or other sites.

 

Please let me know if you'd like more info on what it has been like on a year to year basis for him. I wrote a longer post but deleted it because I wasn't sure how much detail you need. It works really well for him but his goals are quite clear...he wants harder math and is willing to work at it and is happy to unschool or be interest-led in subjects like language arts and history. It might look overwhelming, or maybe even inadequate, to others with different goals.

[Korrale]

I am am Aussie and I loved how maths was integrated. I actually don't know where all the lines are that divide of the Maths subsets. I thought they Saxon math was integrated. That was what I was planning to use. Ahhh. What I would give for my old math text books from high school. I loved those!

[Arcadia]

 What I would give for my old math text books from high school. I loved those!

 

The Bostock and Chandler ones (below are what my cousins had) were the other books used when I was in high school. The main ones I used were the low priced Asian edition that you can't find on Amazon.  I like my old additional math textbook 1987 edition, 

 

Further Pure Mathematics by L Bostock, F S Chandler and C P Rourke (1 Oct 1982)

Mathematics - The Core Course for A Level by L Bostock and F S Chandler (1 Oct 1981)

Mathematics - Mechanics and Probability by L Bostock and F S Chandler (1 Jun 1984)

Pure Mathematics 1: v. 1 by L Bostock and F S Chandler (7 Jul 1978)

 

I'll probable grab the CIE books later though for fun reading when I make a trip back home.

 

ETA:

Even growing up with integrated math,  I just read whatever I can get my hands on, including older cousins textbooks or reference books.  My kids are the same way so even if they are doing algebra, they are still doing topics outside of the books. 

[freerange]

We've used (& loved) books from Elmwood Press - http://www.elmwoodpress.co.uk/ & available from Amazon or (with free worldwide delivery) http://www.bookdepository.co.uk/

 

and material from www.cimt.plymouth.ac.uk/projects/mep/default.htm  

[MamaSprout]

We currently use the upper levels of Singapore, which is integrated and we love it.  It starts with levels 7 and 8 in "Dimensions Math", which aligns with Common Core.  I don't believe they intend to publish any Common Core books after level 8.  We are currently in level 8B with my oldest and will continue on to levels 3 and 4 of "Discovering Mathematics", which apparently has a little bit of overlap in the first couple chapters, but we are fine with that.  After we finish level 4, I'm not sure where we will go, but my dds are young, so we have options.  Either AoPS or CC will likely be in our future.

 

Wendy, the teacher guides do have solutions for all the problems in the books/workbooks.  I find they are very clear and easy to use.  They don't have much in the way of teaching strategies, like the lower levels had.  However, I don't feel I need it.  The texts and the teacher guides are so clear and straightforward. 

 

I'm reviving this old-ish post b/c I was looking at Singapore Math Website this morning and noticed this:

 

"Due to trademark issues, we will have to stop carrying Discovering Mathematics after December 31, 2014. This will affect all the Discovering Mathematics titles that we now carry. We currently have no plan to replace these titles. "

 

Is anyone else aware of this? With NEM discontinued, that means no Singapore after DMCC 8, unless they continue the Dimension series. I posted a Q on the Forum, but haven't gotten a reply yet. We are starting DMCC 7 next week. I might just do 7a as a pre-algebra and move to regular algebra if there isn't a clear path after 8.

 

Thoughts?

[Crimson Wife]

I wonder if this is a dispute between SGbox.com and singaporemath.com? Will it affect availability at RR and CBD?

[MamaSprout]

That's a good question, Crimson Wife. SGbox.com doesn't seem to carry Discovering Mathematics, though. I find their website tough to navigate. It feels like an off shore pharmacy that sells books.

[Arcadia]

I wonder if this is a dispute between SGbox.com and singaporemath.com? Will it affect availability at RR and CBD?

I think it is a dispute between Singapore Math and Star Publishing Singapore. Or rather a copyright issue with the original publisher.

 

Star Publishing SG publishes the Discovering Math series which is approved by MOE SG for school use. The covers look identical to what Singapore Math sells.

http://www.starpub.com.sg/product-discovering-mathematics.php

 

ETA:

Original publisher of discovering additional math

http://www.starpub.com.sg/product-discovering-additional-mathematics.php

[MamaSprout]

I think it is a dispute between Singapore Math and Star Publishing Singapore. Or rather a copyright issue with the original publisher.

 

Star Publishing SG publishes the Discovering Math series which is approved by MOE SG for school use. The covers look identical to what Singapore Math sells.

http://www.starpub.com.sg/product-discovering-mathematics.php

 

ETA:

Original publisher of discovering additional math

http://www.starpub.com.sg/product-discovering-additional-mathematics.php

 

Okay, I see. It looks like from the sample CBD has the Starpub version available. We may go ahead and just switch to that after 7A.

 

I do like the looks of the CC edition. I'd stay the course if there were a "CC 9" in the works that wrapped up  Alg 2, Geometry and maybe Statistics.

 

Thanks!

[kiwik]

Any NZ textbook would be integrated. Really though you just do short blocks of each subject. I can't see why (apart from price) you couldn't do the first 1/4 of each book one year then keep on like that. You would need algebra, statistics, geometry, trigonometry at the very least to cover NZ early high school then calculus at least after that.

[MamaSprout]

Any NZ textbook would be integrated. Really though you just do short blocks of each subject. I can't see why (apart from price) you couldn't do the first 1/4 of each book one year then keep on like that. You would need algebra, statistics, geometry, trigonometry at the very least to cover NZ early high school then calculus at least after that.

 

This is true. I would need to find 4-5 texts I want to live with for the next 4 years to do that (Americans split Algebra into 2 different years).

 

Not a bad idea, really. Especially if you thought you might need to push through and finish up a course to go into B & M school.

 

For us, for now, Singapore is working well. The CC edition uses American terminology and at least somewhat covers the same ground as the American course sequence, while most other "quality" integrated texts align with O levels. The Singapore format is appealing to younger students. The books are somewhat smaller than the American high school texts.

 

I'm glad the DM series isn't going away completely.

[Mike in SA]

Not all American courses split algebra into two courses.  Look for "Beginning and Intermediate Algebra" texts for a combined view.  "College Algebra and Trigonometry" is not quite the same as precalculus, as college algebra tends to go deeper (like an "algebra 3" course).  AoPS' "Introduction to Algebra" is both algebra 1 and 2.

 

Some geometry courses include trigonometry, but you have to be careful to find one that does so at sufficient depth.  Often, trig is taught in depth only in precalculus and calculus (calculus itself doesn't need much time, but integration techniques using trig do).

[Tanikit]

We had integrated Math in South Africa too - I know calculus did come later in our high school career, but we certainly weren't doing only Algebra or only Geometry any particular year. I have not thought what I will do with my children when they get there though so will follow this thread - having done integrated myself though I might be tempted to speed up the book I was on just to get a break from one type of Math for a while so finding something more integrated would probably be wise - of course my DDs might disagree entirely by then.

[Korrale]

The beauty of intergrated vs side by side courses is that what is being learnt in one math stream will be applied and built upon by another.

 

This is a first grade example from my sons maths work...

He learnt to count by 5s then a few lessons later he learns to count nickels, then a few lessons later he is doing time, and lessons after that he is doing fractions. Now he is constantly reviewing counting by 5s, nickels, time, and fractions. But you can see how it builds upon each other. He has quite a few curricula and workbooks that don't work like this. They would have a chapter based upon number sense, which would cover skip counting, then a chapter on addition, then a chapter on subtraction, a chapter on measurement, a chapter on time and money, a chapter on geometry with fractions.

 

Many would consider this spiral, and due to the constant review it is. But every single lesson covers all these elements of Maths. Not all spiral does that.

[lewelma]

I will argue the other side.  For gifted students I think that the isolated courses allow students to move further more quickly.  In an integrated program, there is quite a lot of review because you come back around to a topic only once or twice a year.  It also takes some time to get into the swing again when a new topic is started.  At least this is what I have seen when I was a Math teacher in NZ teaching integrated math. 

 

A gifted student does not need all that review, and can just power through more advanced topics more quickly without it.  In a good series, like AoPS, there is review of Algebra in the Geometry book because a lot of the problems use algebraic relationships instead of just numerical ones.  And in my ds's Number Theory class, there are often combinatoric topics and vice versa. 

 

I'm sure it depends on the curricula, but for more advanced students I would keep to the one topic a year system.

 

Ruth in NZ

[kiwik]

No I agree. The main downside to the using 4 to 5 texts approach apart from the initial cost is you would lose at least a week to review every time you changed books. It would add up over 4 years. Doing two books concurrently may be easier. You could do algebra 3 days and geometry 2 or something. I find it a bit annoying at primary too.

[NittanyJen]

I think it is a dispute between Singapore Math and Star Publishing Singapore. Or rather a copyright issue with the original publisher.

 

Star Publishing SG publishes the Discovering Math series which is approved by MOE SG for school use. The covers look identical to what Singapore Math sells.

http://www.starpub.com.sg/product-discovering-mathematics.php

 

ETA:

Original publisher of discovering additional math

http://www.starpub.com.sg/product-discovering-additional-mathematics.php

 

Interesting!

 

FYI, my last email communication with Singapore Math confirmed from their end that they will support only K-8 math for the time being once their current stocks sell through, so if anyone is planning to use through DM4, find them now (one of the texts, either 3 or 4A has already sold out; I think I got one from Rainbow).  They will continue 7-8 Dimensions Math.

 

They did not specifically address their uppermost math program, the Additional Math, that adds in the rest of trig and the beginning of calc, but the email specifically said they will focus on only K-8 "for now."  I took that to mean they will not support that last level either and bought it while I was at it.  I didn't know about the starpub group.

 

My younger DS is working through 7B now, and I love the integrated approach.  Since the divisions are artificial, this just makes more sense to me.

[NittanyJen]

I will argue the other side.  For gifted students I think that the isolated courses allow students to move further more quickly.  In an integrated program, there is quite a lot of review because you come back around to a topic only once or twice a year.  It also takes some time to get into the swing again when a new topic is started.  At least this is what I have seen when I was a Math teacher in NZ teaching integrated math. 

 

A gifted student does not need all that review, and can just power through more advanced topics more quickly without it.  In a good series, like AoPS, there is review of Algebra in the Geometry book because a lot of the problems use algebraic relationships instead of just numerical ones.  And in my ds's Number Theory class, there are often combinatoric topics and vice versa. 

 

I'm sure it depends on the curricula, but for more advanced students I would keep to the one topic a year system.

 

Ruth in NZ

 

The Singapore Math series uses a continuously integrated model just like it does during Primary Mathematics, eliminating the need for review.  Once something has been introduced, you use it constantly in the word problems and examples thereafter, so you never "lose it."  The algebraic concepts are used in the geometry sections and the geometry concepts are used in the algebraic sections, which is, truly, part of the entire point and beauty of the integrated approach.

 

I did experiment with "monstering together" a course this year for older DS who is not using Singapore-- one week of Fred algebra 2, one week of AoPS geometry.  Although I liked the geometry book, he ended up hating switching gears each week, and he didn't want to do two math books concurrently.  We did end up dropping AoPS so he could just finish Fred, and he'll do Fred Geometry when he's done.  So I think I agree with Ruth in terms of a program that isn't designed to go together from the outset-- his problem sets weren't designed to work together beautifully as they are in Singapore Math, so mentally, it was just a clash for him rather than being an integrated anything.  We didn't have a review issue, but it just didn't run smoothly and they were not complementing each other as I did not have the time to invest in working them into one another; we just did one and then the other.

 

So . . . done right and done very thoughtfully, it can be a really beautiful, elegant thing.  Lacking that degree of planning and insight, it can just be an ugly clash that detracts from the program and I think Ruth is spot on-- one topic a year would be better than a clash and clamor.

[MamaSprout]

This thread is going over at the high school board, and does have some updates from SingaporeMath.com. similar to Jen's correspondence, but may be of interest.

 

http://forums.welltrainedmind.com/topic/521727-if-you-have-used-discovering-mathematics-singapore-math-would-you-please-share-your-perspective-on-pacingscheduling/