In looking at the resent posts, I find it interesting that there is very little mention in the media of Singapore Math.
Could it be that there is not enough money to be made on pushing the Singapore Math Curriculum?
I just know that if results entered the media decicison making equation matrix we would be hearing a lot more about Singapore Math.
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Knowing what I now know - politicians have no more excuses. Singapore is clearly the best curriculum - it will educate kids. Science has followed math, because you can't very well have a decent science program if kids can't do the math that's required.
The best thing that could happen to public schools in America are for all states to put Singapore curriculum on the list of adoptable materials so school districts can purchase these textbooks with state funds. At least provide communities with an opportunity to do what is ethical.
The public has not been accurately informed about Singapore.
1. Singapore was written in English for non-English speaking students. It is written at an appropriate reading level. A full course of traditional standard algebra is taught in the eighth grade.
2. Singapore teaches standard algorithms and problem-solving methods.
3. Singapore problems were individually tested. The content stands by itself and it delivers what it promises.
4. Singapore is not just a vision; it is a complete curriculum.
Two million minutes is a wake up call for policy makers. Singapore has revolutionized education in Asia. The debate over math education and standards has everything to do with access to appropriate curriculum. Curriculum shapes our schools and it is directly responsible for the current crisis in American educational policy that has done more to resegregate communities, than bring people together. The scale and diversity of Asia, especially the Pacific Rim, is astonishing.
What is "a full course of traditional standard algebra"? Singapore's secondary curriculum is integrated. Some algebra is in 7th grade, some in 8th grade, some in 9th grade. Along with geometry and some trigonometry. It is true that most of what is considered algebra 1 in the US is covered by the end of 8th grade.
What is the source of the idea that "Singapore has revolutionized education in Asia"? The math curriculum is somewhat different in Japan, and I would guess China, though likely there are lots of similarities, but not because Japan or China is using "Singapore math".
Singapore is now "borrowing" from the US. It has changed its syllabus. The Primary Mathematics series available in the US, and what has been used in schools in the US so far, with some success, is from the older syllabus. The newer syllabus they have now allows calculator use by 5th grade, in order to promote more "problem solving" without having to do the math, and has less mental math, along with some other changes.
Singapore is a country, so it wasn't "written". They used one math curriculum, written by the Ministry of Education, up until 2001. For that series, it may very well be that the problems were individually tested. Now they have different series available, with different approaches and emphasis and difficulty levels, and I very much doubt each problem was individually "tested". They do all follow the same curriculum standards for each year, but with different authors there are different results. One of the newer series, for example, never specifically teaches finding the difference between two numbers as one interpretation for subtraction; it just sort of shows up when they look at length and start using bar models more, so the concrete introduction for that concept got lost, and that same series does not show a visual approach to the concept of a fraction of a whole number when the answer is a mixed number, as the Primary Mathematics does; it just shows an algorithm involving reducing the fraction so there is a step missing in the idea of concrete to visual to abstract in that particular istance. Another of the newer series never mentioned number bonds, which is used extensively in Primary Mathematics. There is not really such a thing as "Singapore" math any more than there is such a thing as "American" math.
In fact, there are now books in the US saying what Singapore Math is, and one of them includes another algorithm for multiplication, a cumbersome area model, that never was in the Primary Mathematics, the original series, and I do not know if it is a new thing in one of their newer series, but is in a US book about "Singapore math". There are now US books giving a step-by-step method for model drawing for solving word problems, but these steps are not in Primary Mathematics, and I have not seen them in any other math book from Singapore. So "Singapore math", or at least model drawing, is quickly being adapted into step-by-step procedures that perhaps make it easier to do the simpler word problems but don't work with the more complex ones, but is being called "Singapore math". So what is "Singapore math"? Is it following 8 specific steps for solving word problems, or is it using logical thinking and a flexible modeling approach?
Course 1 College Preparatory Math is the closest US textbook to a Singapore eighth grade textbook since the writers at UC Davis used ideas from Singapore to write a textbook that would teach eighth graders using age-appropriate language.
You are making a number of wild conjectures and again one only has to look at the results. Stop supporting the excuses being made by NSF-funded TEP professors -you haven't followed research protocols for years, why start now.
Singapore and CPM are like traditional, but they are written for younger audiences. The writers of the reform textbooks were writing for a much older audience - like for instance Core Plus which had assume initially that students had taken algebra in another course.
A traditional curriculum is a one-year algebra class using formal methodologies, is 13 units ,and usually finishes with quadratic equations. A first year teacher rarely finishes the entire program. During the year, students learn six standard methods of solving a system of linear equations. Reform math teaches non-standard methodology and not one method for solving a system of equations.
An eighth grader can solve a non-linear equation and factor quadratics, but not here in the state of Washington. That has to be depressing. I know graduating honors students in Washington that can't a simple algebra problem except by substituting letters with numbers. OMG
In California we had Title I kids who's language was other than English and they did well on the Golden State Exam - a test one takes after taking a 'traditional' algebra class. So I don't think you know what you're talking about.
It is obvious you don't understand what revolutionary is or for that matter what constructivist means. Your name's not Ginger is it? The revolution that UW TEP quackery refuses to see is a model for higher order thinking that works for younger children who are still learning English.
What does learning math have to do with using a calculator?
Singapore Math was developed by the Ministry of Education and it included world class standards, excellent curriculum, and textbooks. NCTM did nothing like that. Singapore provided exactly what communities needed. NCTM should suck it up and adopt Singapore.
In addition to having each problem carefully researched, students liked the Singapore curriculum -- that has to be the biggest difference between Singapore textbooks and the reform textbooks where I watched kids scrawl all sorts of ugly grafitti on the inside of book covers. That's how much they liked the DOE's exemplary curriculum.
You obviously haven't opened a Core Plus textbook, nor have you witnessed students using it in an alternative program where there is no teaching or learning happenning at all. Its truly a scene to remember where kids (18-20) haven't passed math since 7th grade and don't know their times tables. Gee, how long has Bergeson been in charge of this state. So you don't have a clue - you'd rob people of an education, before you'd admit to being wrong.
That exactly describes a support program in Washington State. To date, not one student has ever graduated from this program except when they were white and couldn't graduate from HS.
The OSPI website claims a 17% graduation rate - I don't see how the student turnover rate was over 100% during the year. This is nothing to be proud of and the leadership of this state deserves a good shakedown.
I'm having a hard time making sense out of some of your rant. When I see something worth responding to I'll be sure to write more.
Everyday Math prides itself on teaching anything but standard traditional algorithms. Students never get around to learning the algorithms they're supposed to learn. And when you do attempt to teach kids the correct algorithm they give you the NCTM speech - I learned an easier way to do math. Well okay if you can live with counting on your fingers than go right ahead. Have I got a bridge to sell you.
Pray tell? Can you slow down and explain what is a cumbersome area model?
Singapore for curriculum's sake means the Singapore curriculum, not just a country and yes, I've been there and its beautiful, especially as you approach the Straits of Malacca headed West(Are you a kid making a prank call?)
Here's my interpretation for you of the 'cumbersome' area model - in traditional algebra you learn to multiply binomials and the reverse - finding a factor to a rational function.
This is a visual model of the distributive property - so how one multiplies 51 * 49 = (50+1) (50-1) or 2500 - 1 and this is a trick that even Saxon uses. Integrated math does not teach the difference of two squares - simple, yet I count on many end of course exams where it appears 7 or 8 times.
Why do we teach this instead of FOIL? And by the way, the textbooks do use FOIL but only after students get the area model.
Models have rules that break down faster over time. The area model stays with students longer than FOIL because the rules for applying area models are not text-based and therefore don't require decoding (First, Outer, Inner, and Last), good curriculum writers avoid having students make easy mistakes), area models are visual. This can be taught to any group of teenagers regardless of language, so that's very important - we minimize decoding and maximize use with the appropriate models.
The area model has important uses in many other advanced math topics, not just factoring quadratics. FOIL only works for multiplying two binomials, so its classified as specialized knowledge or context-embedded. Most of reform math is context-embedded and that's why textbook consultants/professors go to great lengths to get on test alignment committees.
In elementary school the area model can be used to illustrate the distributive property. If I say justify factoring a trinomial then students know to use the area model - FOIL is not as good an answer, but I have other ways of knowing whether students can apply the area model.
Students confuse the area model with times tables. But which model has more application? - the area model.
This is not the same as when you have to multiply two numbers written in scientific notation. That problem curiously is one of the most missed questions on standardized tests.
Kumon is written in Japanese, but english-speaking IB students use Kumon problems. You don't have read Japanese to understand Kumon problems. Show me what US textbooks do with the area model - I doubt its anything. There's not enough practice to make an impact on student learning. In US schools its practically nothing and we see it by the results schools get.
Adopt Singapore and teach the professors.
Ick. So sorry. So much for my first effort at blogging.
I am neither a kid nor Ginger. And I have not been to Singapore.
I have taught with the Primary Mathematics, I have all the third edition books, all the US edition books, all the Standard edition books, and I know them very well, the ones that were written by the Ministry of Education.
I have the whole of one of the newer series now being used in Singapore, not written by the Ministry of Education, and have seen parts of others, and there are differences. I have studied the new syllabus for the new series coming out this year, which is the first time they allow calculator use in the fifth grade. My concern is that Singapore seems to be going the direction of reform math. And yes, I do have an idea what constructivist means, though I have seen different definitions.
Plus, as I said, I have several US written and produced books focusing on certain concepts of the "Singapore math" in a way that is not in the Primary Mathematics books, or even the newer series, but is being called "Singapore math", such as drawing bar models using a specific set of 8 steps or doing an area model for multiplication (bar models is in the curriculum, and is a powerful tool when logic and common sense is applied, but not so powerful if reduced to a specific set of 8 steps. But, maybe "Singapore math" has to be changed and adapted for teachers in the US. And still called Singapore Math. So what is "Singapore math"? Is it the curriculum as taught in the Primary Mathematics series? Is it what is now being used in Singapore, which is not written by the Ministry of Education? Is it the adaptations and changes and other things being called "Singapore math" in the US? That was the only point I was trying to make.
I have taught using the secondary books too (none of the secondary books were written by the Ministry of Eduction, by the way) and like them very much, and have 5 different series on my bookshelf, and two editions of two of them, and the older ones are the most challenging, and it saddens me to see them getting easier. Yes, my kids could factor quadratics at the end of 8th grade, though the quadratic equations were taught at the beginning of the 9th grade books (Secondary 3). Three of the secondary books I have, from Singapore, have a different explanation for why multiplying a negative integer by a negative integer gives a positive integer so I wonder which one was used at UC Davis. I wonder which explanation is better. A real-world explanation using cash, one using the idea that (-1 x (-1) = -(1 x (-1)), or one using a pattern? Which one is "Singapore math".
So sorry, I was just reacting,in an apparently very poorly written way, to the term. I am well reminded why I don't blog, but I fell for it this time.
Where is the area model for multiplication taught in Singapore math at the primary level? Which is the level I saw it in the US book about Singapore Math. Do the teachers in Singapore use it at the Primary level? The distributive property is not formally taught at the Primary math level in the original books that have been used so far in the US, though partial products is used to explain multiplication, and it is used early on for mental math. But an area model is not drawn for multiplication, at least not in the textbook. When they get to mutliplying by a 2-digit number, they already thoroughly understand multiplying by a 1-digit number, and they use that and the idea of multiplying by tens to get two partial producat. Although it could be added as an alternative algorithm, even though it isn't in the textbooks. But I thought that one of the complaints against reform math is that too many different paper and pencil algorithms are taught as alternatives to the standard algorithm?
A more explicit explanation of the distributive property was specifically added the the new Standards edition for California, and that does use an area model.
There is an area model shown in at least two the secondary books for multiplying binomials (8th grade). One of the secondary level books doesn't have the area model, it uses cross multiplication. A fourth one shows algebra tiles. So it does seem to be used at the secondary level.
Hee Hee - you should blog, it makes you stronger and I think you are right that Singapore has changed. I'm not sure that it matters, because like college preparatory math it is always being edited and one hopes changes would be better.
I am not sure why some teachers make a big deal about how one teaches why the negative of a negative is a positive? For instance, teachers take for granted that explanations with number lines are sufficient, but using vectors is unnecessary and overly complex, most of the explanation gets muddled with lots of handwaving.
CPM grade eight develops a model for integers into a full blown model for solving algebra problems (unit 2). The algebra board looks like a tennis court - the equal sign is the fence or a double vertical line and going across the middle is a dotted line and then above the line are two quadrants labeled positive and two quadrants labeled negative.
Most teachers just use the two positive quadrants and we go about solving problems by balancing both sides of the equation, but then everyone goes well why do we have two negative quadrants below the dotted line when do those ever get used.
To construct the model we only used two rules:
1. double line represents equal
2. for each side, there is a positive and negative region.
when you read an expression sometimes you'll see this:
-(x-2)
most textbooks and teachers have you rewrite it first as - x + 2, except with CPM you can put x-2 in the negative region of the algebra model.
What's really cool is that students learn to put the negative region of one side of the model into the positive region of the other side of the model while they're solving the algebra problem. And this is faster (fewer mistakes are made) than other methods of solving the same problem.
So then what you do is generalize this manuever into two rules and one of the rules is always the following: -(- x ) = x or a negative tile in a negative region is the same as a positive tile on the same side of the equals sign.
(one flip rule)
The second rule is a tile in the negative region of the left side equals a tile in the positive region of the right side. (two flip rule)
Sorry without pictures you're going to have to do a bit of visualizing.
Five rules are all students need in order to solve algebra problems with this model.
But again, most teachers ignore the negative region and give the rule without explanation the negative of a negative is a positive and as we know well, this leads to all kinds of mistakes.
So 2 - (x+2) = 3 :using 2 flip rule
2 = (x + 2) + 3
2 = x + 5
x = -3
or using 1 flip rule
2 - x - 2 = 3
- x = 3
x = -3
Same answer but now you see why CPM has a negative region.
Anon6:01
Everyday Math, the problem with algorithms is that like for multiplication it teaches five ways to multiply two whole numbers together, but students don't learn to use the standard algorithm which works for all numbers. Also there is no instruction in fractions and NCTM presidents keeps saying its not important. Everyday math textbooks keep promising kids they'll get to long division, but that never happens until like maybe sixth grade.
Its interesting that you'd bring up cross multiplication and the area model. I think you mean similiar triangles. I know this is taught in CPM 7th grade. Another standard method involves comparing two fractions, often finding a common denominator, sometimes using Giant 1 (many students like this method) - many of them try to avoid using algebra for as long as possible.
What happens with students who cross multiply? First of all why does cross multiplication work? Students, especially younger children, don't understand why.
My recollection is cpm spent a long time trying to teach students how to solve ratios, but cross multiplying was one of the last methods of solving. For many teachers, that's the first thing they teach students and then often what happens students overapply in every problem they try to solve and for most problems you see on the WASL its a waste of time. The best method is using Giant 1 to find an unknown numberator or denominator.
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