Gifted Issues Discussion homepage Forums Learning Environments OMG! Video about Everyday Math and TERC math

This video was posted in 2009, but I thought I'd post it again, given that we have a lot of new members and given that EM pops up pretty frequently here.

Personally, I had forgotten the horror.

Math Education: an Inconvenient Truth

Blech...EM is taught on our school district. Thanks for posting the video, Val.

I don't find her case compelling at all. Her examples make the conceptual students appear incredibly dense in their guesses. Her personally created examples for TERC illustrate an unrefined bumbling approach. Investigations is a philosophy of developing skills in algorithm development and fit finding; much more meta-skill focused.

That lattice method looks as silly as long division to my way of thiking, but ultimately I want a context where my son can have the freedom to discover his own methods and traditional math isn't it.

We've found that too. Dd14's algebra II class no longer allows calculators either and, while she knows how to multiply, do long division, etc., it never really became an automatic second nature type of thing b/c they touched on how you do it and then gave the kids calculators as early as 2nd grade. I view it as a big handicap to have to stop and think, 'how do I do that again?' which is hard to convince the kids b/c they've been told for years that they can just rely on the calculator and demand proof of a situation in which they'd need to do long division sans calculator.

I thought that her point about the abusurdity of devoting an entire long chapter called "Calculators" was very compelling. This was 30+ pages in both the 4th and 5th grade textbooks.

I was also convinced of the foolishness of devoting even longer chapters to geography lessons in in EM textbooks. And of course I have to say this: geography is an important subject. But it just isn't math (which is why they call it "geography" and not "math").

I was equally impressed by the quotation from the EM teacher's guide. To paraphrase, the guide announced that expecting children to master something like division is just asking too much. Besides, calculators are better!

If you have a better algorithm for long division, I'd love to see it. It would be great. But IMO, the TERC & EM methods simply call for guesswork, are inefficient, and ineffective with large numbers.

I think this is a good point, depending on what "traditional" means. Still, I loathe EM as implemented in our district. It's extremely dumbed down, and I see a lot of the failings discussed in the video and mentioned by Val.

I think Singapore Math has a lot of strengths, and if it is fully implemented there is a fair amount of self-directed investigation that happens, even though it is also a straightforward mastery curriculum overall. SM supplies plenty of problem solving practice, including many problems that are not at all cookie-cutter in design and require some thought.

I think that a focus on investigating number relationships and arithmetical methods can be excessive, and that's part of what I see wrong with Everyday Math for a math-gifted student. For instance, DS was forced to "explore" number bonds ad infinitum, and didn't get anything at all from it. I certainly wouldn't want him taught rote, inflexible problem-solving skills, but for some of the basic arithmetic I don't see the harm in building a strong skill-based foundation and moving on to the good stuff.

In addition, I had the sad experience of having to tell DS7 to ignore all attempts to teach him mental math strategies at school. He has always been good at mental math, and SM honed that further with an almost uniformly straightforward approach. Attempts to teach mental math strategies the EM way at his school really messed him up and slowed him down at one point.

Maybe these programs are good for more average children, but I can't recommend EM to anyone for use with a talented math student.

kcab, he's almost 7.

My base stance is from the rarity of people I've encountered who can do math in their head at the rate I can. I have a wide range of shortcuts and algorithms I use and constantly select different paths as I calculate. I do things automatically like keeping track of how much my groceries cost.

One of the more interesting fMRI studies of gifted kids is one showing how the brain goes haywire seeming to select the correct solution heuristic and then the brain highly focuses in that area. I'll encourage my son to try and be fast as I think that's a good path for internalizing more effective heuristic selection strategies.

If a child is floundering, then sure a single effective and consistent algorithm is great.

Val,
Most of her message was along the lines of saying the way we learned was best. Because she says so (and people who walked seven miles uphill in the snow...) and uses extreme examples of making investigations look silly. I'd question the Everyday approach (and their book content) which most of her critique is oriented towards but she takes aim at investigations by proxy.

Algorithms are best that work for the person. Some algorithms are more effective if someone has a strong working memory others use methods to reduce memory load.

I think it would probably be just fine even for a child who's not floundering. Most of the world's great math thinkers weren't taught with Investigations, anyway, so I don't think it's necessary to do the amount of exploratory work that the curriculum seems to require with basic arithmetic. I also don't think that a personally discovered or picked calculation method is always going to be the best for a particular student, since I don't think that beginning students are so wise as to always pick what will work best (this is why I don't believe in radical unschooling for the masses, either). And while I think it's good to develop fundamental problem-solving meta-skills, I don't see much point in spending a lot of time developing basic number sense and calculation skills this way. A little time, maybe, as fun enrichment, but not a lot of time.

But my feelings on this might be because my son nearly instantly grasped so much of arithmetic, and has never shown any problems learning or remembering procedures like long division either. ETA: Every child is different, and I can see that for many children it's probably appropriate to start developing problem solving skills with the main tools they have available early on-- basic number manipulation. I can see some sense to it.

I have started consistently asking DS to work out how to do some algebra operations on his own before a new skill is introduced, though. I also ask him to do a fair bit of the algebra in his head, to improve his memory and let us go a bit faster. I wish I could actually encourage him to do more in his head, but he needs some practice on doing neatly organized written work too.

Traditional here meaning Long Multiplication and Long Division as her examples of "how it ought to be" in the video.

As a disclaimer: I carry a large bitter chip on my shoulder because my sight division got broke by "showing your work" for Long Division in like 4th grade. Maybe a year or two later I would've understood how I did it, and it might've survived that crucible.

That sucks. I also remember things I've read here and elsewhere about students graduating from high school with shaky understandings at best of such important topics as division, the meaning of an equals sign, etc. I also credit that focusing on rote teaching of an involved process like long division might confuse and dishearten students, and get in the way of learning the underlying concepts (besides potentially missing out on a chance to develop problem-solving skills). I get it.

Still, looking at the videos on the following page, I think DS would literally scream if he were forced to sit through something similar:
http://investigations.terc.edu/curriculum_clrm/earlyalgebra/earlyalgebra.cfm

Now, it might well be that the general didactic approach used by these teachers would work fine for him, just that he'd have to be able to go at a faster pace, and of course not have to learn what he already knew that way. The students do seem engaged well enough in those short videos.

ETA: I think that the last video on this page also would cause extreme frustration for DS:
http://investigations.terc.edu/curriculum_clrm/mathpracticestandards.cfm

I might be missing the point of it, but I think the approach in this particular video is garbage. I don't think these students are becoming stronger mathematical thinkers in any substantial way, or even really getting better at multiplication here. I think it would be demeaning for a lot of students to be forced to verbalize a lot of this extremely basic stuff, such as that 30 is 3 10s. I think that that particular video mainly shows wasted instructional time.

But that's not an indictment of the entire curriculum, just an example of one way that it might be implemented poorly. Actually, now that I think about it, this sort of approach might make it difficult to implement in-class enrichment for the brighter students. It's so... plodding, and the students seem to be expected to plod together. But in a classroom filled with students with a similar pace of learning, even that might not be an issue.