Gifted Issues Discussion homepage Forums Recommended Resources Need some guidance re: Life of Fred

It is interesting that parents (including my wife and me) are trying to prepare their children to thrive at elite colleges when their children are so young. I think a great book for parents trying to ensure their children are competitive with children from "academically advantaged homes" is "What High Schools Don't Tell You" by Wissner-Gross.

I would agree with this. There are many aspects of constructivist approaches that I have come to appreciate relative to the traditional, algorithim/property memorization style of instruction I recieved, but there are some significant weaknesses as well. One of the greatest weaknesses I see is that students don't learn the same appreciation for precision and efficiency. It's interesting to me that constructivist approaches in all areas emphasize focusing on process vs. content without recognizing that learning and applying rules is itself a process that needs to be developed. I definitely favor a combined approach to instruction in all areas. As it relates to math specifically, I think that constructivism--at least as it is applied--overlooks the fact that while some students/adults work best by gathering parts and constructing a whole understanding, other students and adults work best by deconstructing the whole,examining the parts, and then imagining or exploring different ways to work those parts to get the same, or a similar, result.

For sure we don't want students to look at problems like 101-99 and set it up with a standard algorithm (something I too have seen students do on multiple occasions), but I think we do want students to have efficient tools for the computations that aren't easily done without pencil and paper. I like to work on having students identifying for themselves problems that they need algorithms for and problems they don't need algorithms for so that they are in the practice of considering the tools they have and choosing the best tool for the job.

Re: fractions. Fractional understanding is probably the area in which I most support an almost universal constructivist approach, at least with initial concepts. If a student can't grasp the relative size/meaning of a fraction, I question the wisdom of teaching them to solve equations which include fractions.

I so want to read this now!

ABSOLUTELY. I think that principle goes for pretty much every subject, too.

I am not a teacher and for all of my DDs various issues it would never occur to her to do any sort of long process with 101-99. Surely the failure to see the simplicity of this question is far bigger than what method of math curriculum is in use? Is that something that is taught or needs to be taught? Surely anyone that can could knows when two numbers are two digits apart and so knows that 10-8 is 2, 9-7 is 2 and 101-99 is 2? I am genuinely curious here. Is it common to not just see how this works? I would honestly never have imagined this as a problem. Though I guess it is similar to my never having realised that children could "read" without comprehension, which I now know is a real problem but it would never have occurred to me and I still can't understand how it works.

Yes, it can

Yes and no. It is bigger than just curriculum, because it represents and fundamental lack of understanding in the number system. BUT some curriculum do emphasise that kind of rote behaviour without understanding more than others do.

Jenbrdsly, is constructivism a philosophy that has been mangled in Everyday Math?

I have not seen Everyday Math, but I can tell you that the Dale Seymour Investigations series which many schools in CA use to use, is a Constructivist program.

I think Dale Seymour Investigations was formerly known as TERC Investigations , and lots of parents and math professors dislike it:

http://www.nychold.com/terc.html

...

Mathematically Correct Second Grade Review of TERC [then Dale Seymour] Investigations in Number, Data, and Space. Some observations and conclusions: "Poor focus, lots of child centered discovery activities and no meaningful mathematical content. [...] [T]he authors accept that some children, at the end of second grade, will still add and subtract by drawing pictures and counting, or by counting back and forth on a `100 chart.' [...] With the exception of some discussion of counting by 2's, 5's and 10's, multiplication is not obviously introduced. [...] This program is totally dedicated to discovery learning and away from mastery, depth, or any skill or understanding... There is nothing to recommend about this program."

Mathematically Correct Fifth Grade) Review of TERC Investigations. Excerpts: "This program received the lowest rating of Mathematical Depth of the fifth-grade programs in this review. [...] The quality of presentation for this program also received the lowest rating among the fifth-grade programs reviewed. The lack of a student text by the fifth grade contributes to this as it leaves students without such resources as a glossary or the opportunity to review prior instruction independently. [...] Although there is a fairly reasonable number of student worksheets, the actual work expected is severely limited in depth and scope and is unlikely to support mastery of content."

Mathematics Program Reviews Comparative Summary for Second Grade and likewise Comparative Summary for Fifth Grade, by Mathematically Correct. The previously cited MC program reviews of TERC Investigations are part of a comparative review of eight mathematics programs for both 2nd and 5th grade. For both grades two of the eight programs (Everyday Mathematics and TERC Investigations) are deemed to fall far short of the Mathematically Correct review criteria, and in both cases the Investigations in Number, Data, and Space curriculum is rated unambiguously the worst of all that were reviewed.

TERC Hands-On Math: The Truth is in the Details. An Analysis of Investigations in Number, Data, and Space by Bill Quirk. This is a detailed analysis of the mathematics in TERC's Fifth Grade teaching materials. Bill Quirk writes: "But math is a vertically-structured knowledge domain. Learning more advanced math isn't possible without first mastering traditional pencil-and-paper arithmetic. This truth is clearly demonstrated by the shallow details of the TERC fifth grade program. Their most advanced `Investigations' offer probability without multiplying fractions, statistics without the arithmetic mean, 3-D geometry without formulas for volume, and number theory without prime numbers."

This is why people have a negative knee jerk response to the notion of "constructivist math". Investigations is one of the reasons my children are homeschooled. I have compared the output expectations of Investigations and Singapore math very carefully and there is *no* comparison. Investigations is beyond a joke. And I'm not just talking about the number of problems or that Singapore actually teaches the standard algorithms. The depth and complexity of the problems is markedly different.

My personal understanding of "constructivism" is that it refers to what goes on in the learner's head and does not refer to the mechanism for getting there. I think the whole discovery learning thing is a misinterpretation of constructivist theory.