## January 20, 2007

### Today's Video

Update (Feb 7th): A second math video has been released. Check it out.

Unknown said...

Horrifying

Anonymous said...

Oh no. Maybe this is part of the reason I have students arrive in my Geometry class in 10th grade without knowing how to multiply.

Unknown said...

Total crap.

Pretends to be for the general public (which doesn't have the advantage of the daily reading of your site [and others]), yet doesn't explain anything.

It's all shock value. (Look at this! Is this what your Grandpappy taught you?!)

Here's a good question for you (and that stupid shill meteorologist): If everyone were taught the "partial products" method TO MASTERY--that is, students could do it EVERY TIME without error, would that make it less objectionable?

Seriously. If one were to answer "Well, the standard algorithm is more efficient," I would have to ask, Why? Because it's been practiced more? Or because it REALLY IS more efficient.

TurbineGuy said...

I have to admit that the partial products method isn't all that bad.

I taught my son (3rd grade) how to use it first, then after he has mastered it, I moved him on to the standard algorithm.

The lattice method reminds me of a bar trick. It works, but you can't easily figure out why.

I think the biggest points she scored in her video was the quote from the book about not needing to master anything since students could use calculators, and showing the umpteen page atlas' in the math books.

Unknown said...

Yeah, for what it sets out to do, it's very powerful. I just wish groups like hers could do more than exchange sound bites in front of the public.

Instructivist said...

I hope to see a lecture series soon, in which mr. person explains it all to the clueless masses.

KDeRosa said...

Oddly enough, I agree with all the points made in the comments.

This is a powerful video.

It, however, does not make the best arguments for why these programs are bad, i.e., lack of practice to mastery and unclear instruction.

But I'm not so sure that those points are amenable to effective presentation in a video, although I could be wrong. Someone needs to make a video showing why the "spiral" fails so badly with respect to teaching to mastery.

I don't so much mind that these non-standard algorithms are being taught, in fact, some I do like (partial products, even though the reason why it is taught is to mask nonmastery ("quick recall") of the multiplication tables). What I do find horrifying is that the standard algorithms are getting such short shrift (even though JD is right that kids could perform just fine if these algorithms were taught to mastery).

I posted a comment on KTM II from the DI listserv where Bob Dixon makes many of the same points that JD made -- the problem is much deeper than this video suggests qnd some of the points made in the video weak.

Instructivist said...

I see a budding idea: A collaborative effort to hammer out a script that addresses serious problems with progressive/constructivist math ed not covered or insufficiently covered by the video.

Then find a convincing personality to sit in front of a camera, hopefully with props, and put it on YouTube. It can be a low-budget affair.

The Penfield group already lists many good points of these major deficiencies.

One I can already add is the enormous time wasted with silly activities and projects like lining up a million objects for weeks on end to get a sense of big numbers.

There is no dearth of other good points.

Unknown said...

Instructivist,

I think that would be EXCELLENT.

Anonymous said...

I think I understand the rationale for the partial-products algorithm. It makes the kids better at mental math and estimating. Both of those skills are important.

But for many kids it's hard to do, for the reasons McDermott explained. So in our school system, which uses Everyday Math, most kids are using lattice multiplication, which really offers no advantages over the traditional algorithm.

Is the traditional algorithm more efficient than partial products? Well, if efficient means the fewest possible steps, then I guess not.

But when it comes multiplying very large numbers, the traditional algorithm is much easier. In a way, that makes it more efficient because, for most people, it's easier and faster.

For very large numbers, the traditional algorithm is certainly more efficient than drawing a big lattice.

The authors of Everyday Math would say get a calculator for very large numbers.

Anonymous said...

To tell the truth, I seldom whip out a pen and paper to do double-digit multiplication or division. Truth be told, without any TERC books, I do something that would be called partial products.

The lattices I defend for spatial learners. Being spatially "slow" myself, it would not have helped me as much as partial products or the "more efficient" traditional algorithm.

But for the lack of time to develop all 3, I would encourage all 3 to be presented. I think some will get the traditional way and some will get the other 2, and really, in school we're providing ways for students to find their own answers when necessary.

Anonymous said...

What concerns me about the algorithm issue is that math professors seem to favor the traditional ways. It sounds like they want kids to be very proficient with paper-and-pencil math. They also want the kids to know highly efficient, commonly used methods.

They say the traditional methods of multiplication and division are prepatory for more advanced math.

If the kid isn't going to take a lot of college math, maybe it doesn't matter which method he or she uses. But it may matter for the kid who needs lots of college math.

1citizen said...

I thought the best thing about the video was that she actually named the offending textbooks. Most of the time, critics discuss the theory and philosophy which means nothing to most people. When an actual textbook gets mentioned, parents have a concrete reason to say, hey, my kid uses that!

Anonymous said...

"I just wish groups like hers could do more than exchange sound bites in front of the public."

They do.

The video was an introduction to the problem, not THE problem. She alludes to other problems, but, unfortunately, does not go into details, so the debate gets stuck on the not-so-important issue of which basic math algorithm to use. The only benefit might be to get parents to pay attention and do their homework. Something has to get parents out of their school-induced math haze.

It's about mastery, true mathematical understanding, and getting to algebra by 8th grade. I don't really care which algorithm is chosen. Mastery is where EM and TERC fail the most. This has been well documented. That's why most smart schools supplement these programs. But supplementation with more practice is not enough, they just don't get from point A to B.

Anonymous said...

"I think I understand the rationale for the partial-products algorithm. It makes the kids better at mental math and estimating. Both of those skills are important."

My take is different. I think they use simpler algorithms because they are easier to understand (they don't need to be efficient since everyone will be using calculators) and require less mastery of adds and subtracts to 20 and the times table. Forgiving division is all about not having to find the largest multiplier in your head. Partial products is about not having to do carrying (as much). They think that these simpler algorithms teach understanding better. They might at a superficial level, but students need much more than superficial understanding when they get to algebra.

I think they just don't want math to be a filter. They want to make it simpler and they want to eliminate the drill and kill (i.e. mastery). Oops, there's the rub. One can argue about the need for doing hundreds of long division problems by hand, but their lack of mastery and rigor philosophy carries over to topics that cannot be done by calculator.

I was in engineering at school when calculators became available for average students. Calculators were great and they really improved education (in college). Homework assignments became more complex because less time was needed for calculations. We could work on calculations that could never be done by hand. Calculators made college more difficult.

Unfortunately, K-8 schools want calculators to make teaching and learning easier. That's not what they are for. They should be used to attempt much more complicated and advanced problems. That's not what is happening. They are being used as avoidance tools.

Anonymous said...

I agree with Steve. Have you even tried to have a conversation with another parent about all of this? Even smart, college educated, super-involved parents start to get a glazed look on their face very quickly. This is why I just Save My Own.

I think the average parent is a lot closer to me in math ability than to many of you. This is important. They can't be reached through a lot of the nuances you speak about, but showing a long-winded algorithm that they've never seen before might get their attention. Finally.

Another thing that gets their attention is dropping test scores. I had a friend whose child's scores dropped about 30 points in one year. I mentioned to her that it was probably fractions. She said no, that he was great in fractions, but she did give him one of the online placements tests. Later she called me and told me that, in fact, he shut down at fractions and that she had no idea that he was so behind even though she kept up with his homework and he made all A's.

But this was a college educated, ex-teacher parent. She knows where he is headed. What about the other parents?

The rest will just resign themselves to the non-fact that little Johnny just isn't good at math.

Anonymous said...

"They say the traditional methods of multiplication and division are prepatory for more advanced math."

Let's put it this way. Students who have mastered the traditional algorithms have better basic math skills than those who (may or may not) have mastered algorithms like partial products. Is it a necessary condition for advanced math? No, but it's an indicator. It probably means that these students are going to be able to spend less time on basic math and more time on the the advanced topics. Is this the main argument against EM and TERC? No.

"If the kid isn't going to take a lot of college math, maybe it doesn't matter which method he or she uses. But it may matter for the kid who needs lots of college math."

Yes, but how do you know if a child is going to need a lot of math in college when they are in third grade?

Anonymous said...

"The rest will just resign themselves to the non-fact that little Johnny just isn't good at math."

"non-fact". Exactly. All school problems look external if you wait long enough.

Our schools say that "our kids hold their own", which means that they really don't want to know how much of that "holding" is done by parents and tutors.

Anonymous said...

"I mentioned to her that it was probably fractions."

It would have been better if the video focused on fractions, but that would have been more complex and many would just not understand.

I commented on KTM about the fraction work that my fifth grade son is getting in EM. Rote. Superficial understanding. Very little practice. Then quick, go on to the next topic.

The main sense I get from EM is low expectations and a slower pace. They cover a lot of topics, so it might seem advanced, but the explanations are simplistic and the expectations low. Slow and low masquerading as understanding and discovery.

KDeRosa said...

When I went to enginerring school, some-what powerful calculators were readily available. But the thing was that they did you almost no good at all until the very last step when the problem got simplified to show the answer. Ideally, you wouldn't even substitute values in for the variables until the last step either which made the whole calculator issue moot anyway.

Anonymous said...

"To tell the truth, I seldom whip out a pen and paper to do double-digit multiplication or division. Truth be told, without any TERC books, I do something that would be called partial products."

When I do calculations in my head (exact or estimate), I use different techniques than the traditional algorithms. I often attack a multiplication problem left to right. I keep going depending on how many significant digits I need. I think my mastery of the traditional algorithms helped this mental math ability.

TERC and EM try to teach basic understanding, but without mastery, there is no ability to estimate, accurately or otherwise.

Anonymous said...

"But the thing was that they did you almost no good at all until the very last step when the problem got simplified to show the answer."

Moot. yes. That's what happened. Some students had calculators and some didn't. The tests turned to all symbolic. Calculators were not even necessary. In the early days, our department had an HP programmable desktop calculator that we could use for homework.

Eventually, when the TI calculators got to be less than \$100, professors started to assign many more homework problems that required calculators. Some homework required the calculator for numerical (like Simpson's Rule) techniques, rather than analytic techniques, but the tests all evolved to make the calculator unnecessary.

Anonymous said...

Oops,

That was me.

Anonymous said...

SteveH,

I agree with you that the MAIN problem with Everyday Math is the lack of practice. I bought some fifth grade materials on Ebay to see what's coming next year.

At this point, I shouldn't be shocked, but I am. As Wayne Bishop said, the fifth grade material "has the flavor of a survey."

I don't know how anyone can learn math this way.

Anonymous said...

I think one of the main issues here is the unwillingness to recognize that different approaches work for different individuals. It's not (or shouldn't really be) about which one works for me, therefore which one works for everyone or is generally more logical - rather, it should be about what teachers find most useful in their classrooms, with the range of children they're working with, and what the parents can latch on to. Instead of approach-bashing, can't we be a bit more constructive about how we address these growing chasms?

(As an aside, I substitute taught in a school system and had no idea what was going on with the math curriculum _and_ math is one of my strong points. Perhaps there *is* something to be said about creating a culture of transferrable math skills.)

Anonymous said...

"I think one of the main issues here is the unwillingness to recognize that different approaches work for different individuals."

This is not one of the main issues. The video doesn't get into it enough, but the main issue is mastery of basic skills. This includes much more than basic arithmetic. My son has Everyday math in 5th grade and the main problem is low expectations and lack of practice. This is done on purpose! EM's coverage of fractions is very poor and "rote" in many cases. It doesn't matter what "style" of learner you are, the coverage is poor.

"Instead of approach-bashing, can't we be a bit more constructive about how we address these growing chasms?"

Schools are not "constructive" or pragmatic about the process. They are in charge and do not like anyone having any input into the curriculum or teaching methods. They are the masters of bashing. It seems that they can't take what they dish out.

The purpose of the video was to get everyone's attention - perhaps provoke parents into finding out more. And there is a lot more to find out. This is not a matter of finding a balance between skills and understanding.

Unknown said...

Ken says:

"When I went to engineering school, some-what powerful calculators were readily available."

When I graduated from high school, my grandfather -- a math teacher -- got me one of the first calculators on the market (very expensive, bulky, and heavy), a HP with reverse polish logic (no equals key). I found it extremely useful as an undergrad.

Even back then, when calculators were first coming out, people were predicting that they would degrade math skills. I poo-pooed them.

I'd like to apologize for that. I was wrong, and they were right. But it never occurred to me that anyone would even think of substituting calculators for math knowledge.

Anonymous said...

Hi, Ken.
Thanks for posting the video.

What bugs me about all this conversation is the entrenched diatribe. People stake out positions on this, and then try to defend that they're right and the other guy is wrong.

Point one: kids should learn that math is more than a single "algorithm". There is always more than one way to skin a cat, and higher order mathematics recognizes multiple paths to the right answer.

Point two: Mr. Person is right that this video only fuels the math wars, and moves us (i.e., the general public) away from any reasonable discussion of mathematics instruction.

Point three (from personal experience): My sixth grader is taking Algebra 1. He is being taught by an "old school" teacher, age 62, who is teaching only formal math. My son is doing all these problems, but he has no idea what any of them mean. So he gets confused. The abstractions mean nothing to him, so he gets frustrated and hates memorizing the "formal algorithms" used to solve the abstract problems. My wife has begun tutoring him using Connected Math, only because he then learns a context or story in which all these formal math problems actually become tools to solving interesting puzzles. To sum up, both sides of the math wars are right. And both are wrong.

So why are we still at war? Why are we fomenting discord in math education when actually, we all seem to agree that a combination of "formal algorithms" and context are important features of instruction? Why do we insist on talking trash, implying it's "my way or the highway"?

In order to grow up like Mr. Person (a guy who clearly LOVES math), we have to instill in our kids at least two things: knowledge (of algorithms, for example) and a rich sense of how those cool algorithms can be used to solve real puzzles...like the ones Mr. Person posts on his site.

Let's spend less time on the diatribe and more time helping our teachers (and parents) to understand that formal math without the context is self-defeating, and at the same time, "discovery" of mathematical concepts is inefficient when handy "algorithms" will serve kids better when they understand where and when to apply them.

John Barth said...

Which of these methods permits you to do math quickly your head? In terms of practical application of arithmetic (in work, travel, shopping, figuring a tip) , my brain relies on memorized multiplication tables and something more akin to an algorithm. Fewer steps, fast answers.

KDeRosa said...

Mark, I'm not a big fan of the consensus/balanced approach. It isn't working well for Reading and I can't imagine it'll work well for math. We need to find what works and use it, disgarding all the remaining crap.

Unknown said...

The problem isn't as cut and dry as the books are bad. If we get rid of the books everything will be okay. For an articulate video response by a math professor. Check out these YouTube links.
Math Education: A response Part 1
Math Education: A response Part 2
As an educator in Japan, a country that does exceptionally well on international tests, I can tell you that the reason that the students do well on international tests is because the education system is geared directly to test taking (for enterance exams starting with middle school.) Whether or not that is translating into better pratical understanding is an open question. I can tell you that there certainly doesn't seem to be any shortage of bad math and reasoning skills with the students and people I meet when compared with my native country of Canada.

Anonymous said...

What for engineers, scientists, programmers, mathematicians, etc.???
America doesn't need that! The owners of the country don't want that!
Americans should be FAT, STUPID, UGLY IGNORANT- WORKERS!!!
Smart enough to do the paper work and strong enough to take care of the heavy stuff.

KDeRosa said...

xander, The good professor is attacking a strawman in this rebuttal. No one believes that math should be taught without understanding. Teaching algoithms does not preclude teaching them with understanding. The issue is how to best teach that understanding. The primary criticsm of the curricula mentioned in the video is that the lack a coherent sequence of instruction and do not have sufficient distributed practice to achieve automaticity in students.The result is that students do not gain the requireed mathematical understanding. Memorizing one's multiplication tables and learning the common algorithms to mastery IS a necessity because our working memory is extremely limited (magic number 7 +/- 2). If students do not have this basic knowledgecommited to long term memory the cognitive load required to peform higher math, such as algebra, willbe too much for their working memory constraints regardless of their understanding of math. Moreover, our brain is predisposed to learn new informationin concrete terms first and only later is the brain able to structure the concrete examples around a dep abstract structure. It is at this point that the student acquires understanding. A further mistake the professor's makes is not realizing that novice students do not learn like expert mathemeticions and do not have the deep well of domain specific math content knowledge that is necessary to learn math in a way that can tolerate the haphazard sequence and minimal practice/rehearsals employed in these curricula.

I suggest that the professor read the "ask a cognitive scientist" articles written by Daniel Willlingham in the AFT journals (online) and reevaluate his position.

Shinigami said...

how would you go on about multibplying or dividing using those stupid partial product or quotient.

Unknown said...

SORRY, BUT THE CREDIBILITY OF THE PRESENTER OF THIS VIDEO (LADY AGAINST REASONING IN MATH) IS SHATTERED WHEN SHE WRITES THAT 133 DIVIDED BY 6 IS 22 AND 1/6 !!!!!!i GUESS SHE IS A PRIME CANDIDATE FOR MORE REASONING IN MATH. SOMEHOW SHE BECAME A QUANTITATIVE PROFESSIONAL (?), AND SHE DOES NOT SEEM TO UNDERSTAND SIMPLE, BASIC FRACTIONS. PRETTY SAD SHE IS TRYING TO INFLUENCE OTHERS WITH HER FRUSTRATION, BUT OBVIOUS SUPERFICIALITY IN ADDRESSING SUCH COMPLEX ISSUE.

KDeRosa said...

THE CREDIBILITY OF THE PRESENTER OF THIS VIDEO (LADY AGAINST REASONING IN MATH) IS SHATTERED WHEN SHE WRITES THAT 133 DIVIDED BY 6 IS 22 AND 1/6

Er, that's what it is.