1. American math students ...

It's now boiled down to "use a calculator or do it a lazy way."

I caught a news blurb on television and meant to share it with you all here. The way that mathematics is being taught in American elementary schools has drastically changed. We were all probably taught the foundations of arithmetic in similar ways, but I saw a method of solving a double-digit multiplication problem I didnt recognize, and wanted to know more. I found this youtube video.

In it, you'll get to see the methods in the text books that school districts are using to teach basic arithmetic. The lady makes a pretty good argument why this is a bad idea.

But mostly, I'm stunned at what the textbooks lead teachers to spend class time on, and how at the end of the video, parents are encouraged to import textbooks used in another country and work through that if their child is struggling. Im concerned. There should be no need to outsource basic math education.

What do you think this all means? Assuaging my worries is also appreciated.

2. I tutor algebra I students at my high school four days a week and the way they are teaching students now is complete rubbish. A lot of important details are hidden through abstractions (they call them "methods") that don't really teach the students much of anything. The students end up having little to no understanding of how and why things works the way they do because they simply aren't being taught everything they should know.

Of course the new math programs are imposed by the school and the No Child Left Behind act, and all of the math teachers agree that it doesn't really help the students at all.

3. Yes, go buy Singapore textbooks! We learn sigma notation for summation, abachler didn't!

4. This is (scary) news to me as the parent of a child who will be starting kindergarden this year with a little brother 4 years later. I've heard humor at the expense of "new math" but never understood what could be new about 2+2=4.

Apparently this isn't only in Washington State either. This place has links to sites for other states that are having issues like this.

Seeing the video that citizen linked frightened me actually. The examples she gives to show how multiplication and addition are taught seem bizarre. Putting emphasis on keeping track of the digit places isn't so bad when learning the basics, but I don't think problem clusters are a way to learn math. And I protest with all my being that a school, any school, should ever EVER promote using a calculator over learning the principles and concepts yourself. That is ludicrous! And one of the pictures in the math book showed a child confused about f(x) and h(n) (or something similar) floating by his head. GOOD GRIEF!!

I have a couple conspiracy theories about it all, but I won't air those just now.

I believe this is a natural consequence of not thinking (or not correctly anticipating) far enough ahead. It is a commendable goal, this "No child left behind". But rather than putting the burden on the students and their families to learn at least the minimum, the burden was placed on the school system, which reacted in the only way it could; make it easier to pass so children are more likely to pass. This had the effect of lowering the bar for everyone as this guy points out, and now we are starting to recognize the flaw in this situation.

I think in the grand scheme of things though, this will work itself out and we as a people won't be crippled by the less than stellar education some received. I hope so anyway, and I intend to make sure my sons learn properly. There will be a few victims, like the kids who were taught this way and never mastered the basics, but I have no idea how to fix that.

5. After watching the video again and thinking about my own Singapore brand of mathematics education, I posit that McDermott (McDermitt?) only has one main argument: the students in question lack practice because their syllabus is too concerned with appreciation of mathematics with respect to other fields.

To address her dismay that "most parents go: what's a cluster?", I would provide a counter example from Singaporean primary school mathematics: my uncle, an accountant, asked "what's a model?" when asked to help me. Guess what? The model method has been acclaimed as an excellent teaching method, after "Singapore Math received media attention and worldwide recognition in 1995 when Singaporean students were ranked first in an international study of mathematics and science education" (Teach Kids Math With Model Method). Clearly, the fact that parents are not familiar with a method should have no bearing on the validity of its use in pedagogy.

She scorns the TERC method of problem clusters, but that method is taught in primary schools in Singapore as a mental shortcut for specific calculations. In fact, I would argue that it is a closer precursor to algebraic manipulation than the other methods.

I agree that stopping at the partial products method is a Bad Thing. However, it seems to me as a useful intermediate step between a theoretical exposition of place-values and practical calculation with long multiplication.

The lattice method is perfectly fine, except that it can be tedious to draw up the lattice. The algorithm is essentially the same as long multiplication. (As a side note, it would help the students survive as book keepers if they are transported back in time and have to use Napier's bones. Then again, if the time machine brings them to Asia, they would be better off learning to use an abacus instead.)

Long multiplication provides a convenient form to express the calculation, and in this it has value by making practice less tedious. With more practice, students become more familiar with (numeric) symbol manipulation, and symbol manipulation is the essence of algebra, which is necessary to understand higher mathematics.

Therefore, if McDermott really wants it her way, she should not just be advocating the purchase of Singapore textbooks. Rather, she should advocate the purchase of mountains of Singapore assignment books and Ten Year Series past exam papers (model answers provided), just like what the students in Singapore are force-fed everyday.

6. Long multiplication provides a convenient form to express the calculation, and in this it has value by making practice less tedious. With more practice, students become more familiar with (numeric) symbol manipulation, and symbol manipulation is the essence of algebra, which is necessary to understand higher mathematics.
Not to forget that it has direct applications to calculus... *shivers*

7. Thanks for contributing so much Laserlight. I'm very interested in Sigapore's program now.

It's not that I'm afraid to revamp the mathematics curricula, or that I have anything against Singaporean textbooks. I don't want to pretend that you didn't get the argument she put forth either. There must be better ways of teaching math than rote memorization of multiplication tables and so forth.

The point that I got seems to be that under reform math:

- There is little structure and guidance in order to learn whole concepts or formulae, in the worst cases avoiding these all together.
- Conventional algorithms are written off by proponents of reform math and are consequently avoided.
- Some of the alternative algorithms fall back on multiplication or addition skills that I have little confidence are being developed because of the above, plus calculator dependency. To solve a reform math problem you have to breakdown until you have a long string of subproblems you can solve.

Basically it lives and dies on the powers of factorization, but who knows when they're made aware of this, almost entirely because of how the books are written. I get the distinct feeling that reform math is the same type of shortcut stuff your math teacher would give you in grade school as nuggets of wisdom. I really don't see a reason to model a whole curricula after this, though.

8. It's even worse when it comes to English and spelling. If you're in the US, do all you can to send your kids to private schools.

9. Originally Posted by laserlight
After watching the video again and thinking about my own Singapore brand of mathematics education, I posit that McDermott (McDermitt?) only has one main argument: the students in question lack practice because their syllabus is too concerned with appreciation of mathematics with respect to other fields.
I think her main argument is their argument that methods really aren't necessary since we have calculators. The anecdote of the college students not knowing how to multiply 4 and 6 is entirely believable. I can't tell you the number of times I stand in a grocery line facing a flummoxed young adult cashier who was asked for \$20 cash back.

10. How about a lesson in Country Bumpkin Math.

11. I think her main argument is their argument that methods really aren't necessary since we have calculators.
That's what she's pointing out by calling out the lack of practice. Since calculators are perceived as a substitute for the ability to perform numeric symbol manipulation, the syllabus stresses appreciation of mathematics instead.

12. It also depends on the school. There are inner city and low funded schools who probably fill up math course time teaching for the reading portion of a standardized test.

13. You mind if I play the devil's advocate and spur things a little?
This will be somewhat long. Hope you enjoy reading it.

...

The problem these text books are trying to solve is one and one only; current math skills of the student population in generally is poor, comparatively to early years. And this has been happening long before these new (radical) methods were introduced.

One can argue standard algorithms aren't making a case of conveying basic math skills and promoting math as a "easy" discipline. I'm don't agree with this statement at all. But we'll get back to it shortly. First a critic of the proposed algorithms on both books...

On the books

Of the two, I think at least Everyday Math's is more coherent in the teaching method it proposes. The so called cluster problems are nothing more than putting on paper how we do mental math. Take a close look at their Partial Product algorithm for solving multiplication, or their version of the Long Division algorithm. Both algos use factorization, which is basically how we do it on our heads. Incidentally, the traditional and ancient Long Division method also uses mental math for the calculation of every digit. We can argue it's not a good algorithm, even though its the one I and my parents and their parents were taught.

The Terc Investigations based book is on the contrary completely laughable. There's no coherence in the proposed algorithms. Multiplication is taught by means of a cumbersome graphical Lattice which, while I was watching the video made me curious I must say as to what method they proposed for division. However disappointment came down like a rock when it was revealed to be nothing more than a skewed version of the cluster method proposed by Everyday Math's meshed with the Long Division graffiti. The Lattice Method for multiplication becomes a nightmare once you try operations like 353534*1256. Have fun drawing a 60 cell matrix and the diagonal lines to go along. Have fun adding all the diagonals. The division method, which I forget the name, is on the other hand dangerous. Very dangerous! Because it introduces the same graphical composition of the Long Division method, but then goes about solving the division in a completely different way (by means of a form of factorization).

Both books have another problem... space. Problem solving becomes curiously a large mantra of operations with the potential to fill in entire sheets.

On Calculators

Of the two books, if anything, I would at least want my daughter to be learning from Everyday Math's. At least the mental stimulation is there and it even seems to have the power to nurture her ability in mental maths, which will be what she will be doing most of her life if she later decides to not follow a scientific career. The only no-no I see is the fostering of calculator usage at such an early stage.

Calculators are no strangers to European schools. We have been using them since shortly after I finished my studies (late 80s). However the traditional practice is to only allow them past 7th grade, and past 5th grade only allow them during exams. Before that, students are taught basic math skills without the use of calculators. Schools are allowed some level of freedom, but the usual practice is this. Of course not all calculators are allowed, depending on the teaching phase. All in all, they are not that bad as long as they serve the purpose of helping in the exactness of the end result and not as a replacement for the teaching method; something that I think goes more or less in the line of what Everyday Math's was suggesting. It however fails by wanting to introduce them below the 7th grade.

On Math Teaching

But the fact is that even Everyday Math's is not a book I would like my daughter to learn from. I would be in the first line of angry parents if such occurred.

I said earlier, and immediately rebuked it, that traditional algorithms don't help math teaching in our schools. At least in Europe (speaking from what I know) there's a growing concern with math results for the past decades. In Portugal, for instance, we've had years in which the national average for mid-school was... get ready... 80 in a 1-200 scale! That's national average, ladies and gentleman. Shocking at it may be, it's no more than the fact that universities had years in which they had to accept students that flunked on their math admission exams!

The problem has been discussed all over Europe extensively for the past years. At least two things are today common knowledge:

• Teaching Methods have to change to accommodate a more easily distracted student community and with a more active social life.
• Their parents (the group I belong) were the first generation of poor math students and are today completely incapable of following and helping their offspring in their studies.

This is, agreed by many, the major problem with math, but also general student results. So, I almost feel as natural the appearance of new teaching methods like the ones presented in that YouTube video as new solutions that are being tried out. Of course, the guinea pigs are real life students and I have to wonder if this is not the time for the federal government to regain control of education. It is as such in most countries in Europe, but I have a feeling in US, each state owns its own education policies, which can have devastating results if these type of books are actually being used in some states.

Anyway politics aside, and because my aged laptop is starting to page this web control and writing is becoming slow, it is my feeling these books are not addressing the problem from the correct angle. It's not the algorithms that need to change. Any of the solutions proposed is ridiculous because it is nothing more than Yet Another Algorithm. The real problem with Math as I've perceived it during my days and as I seem to perceive in my daughter's progress (thankfully a terrific student. I'm 7 feet tall with pride) is Environment. More than ever before math needs to be taught in a context and in a less abstract manner. I was taught math outside the real world. Never, even once, I was given a real life example where I could apply the skills being taught. This is not a good method in these days of neon lights, flashy movies, cellphone messages and a more self-aware, and I risk shallow (proportionately), youth.

It is my belief this is the real problem with math. Not so much in early school where results have been historically consistent, but starting with middle-school.

14. I can't agree with all of her arguements.

The cluster method may not be effecient for pen and paper usage but it is great for mental solving. For the 26 x 31 problem I would definately break that up into something like ((25 *3)+3)*10 + 20 + 6 so that it would end up being:
25 * 3 = 75
75 + 3 = 78
78 * 10 = 780
780 + 20 = 800
800 + 6 = 806

While parents might not be familiar with "clusters" (I know I've never heard the term before) a quick look at the book (oh no we can't do that can we?) should make it apparent what is going on.

I do agree that the reliance on calculators is troubling. I remember I had a professor for a math class (might have been linear or DE can't remember) that gave a problem that our big bad TI-89s would choke on but if you knew how to do it would only take you a minute or so.

As to the homework question she pointed out about 36 / 6. Well the problem wasn't to find the solution but to describe how you could go about solving the problem. Making sure students can logically get to the solution is much more important then the solution itself.

If anything my experiences tutoring everything from pre-algebra to Intro DiffEq showed the opposite of her point about math language. Most of the students I helped could only understand the symbolic language and couldn't do a word problem if their life depended on it.

I would actually encourage teaching multiple different methods to solve the same problem. People think differently and what works for one person may not work for another. Additionally, the type of problem can make one method more favorable then another.

15. Originally Posted by laserlight
Yes, go buy Singapore textbooks! We learn sigma notation for summation, abachler didn't!
Yes, this is the unfortunate truth, and I took great interst in math above and beyond what was taught in school. We simply don't have access to the resources. Part of the problem is the mistaken notion that all children are of equal capacity. While I don't think we shoudl abandon those that are not as academicalyl gifted, equally horrible is holding back those that are. We need a comprehensive multi-track educational system with a primary focus on core subjects like math science, art, and music with less focus on things like sports. The problem is that when you start talking about educational reform, people get emotional over it. Parents equate grades with success, not knowledge gained or skilsl acquired. So the kids don;t learn to think critically and grow up and fail to think critically about how ot improve the education of their kids.