Constructivizing STEM

by Robert Pondiscio
February 22nd, 2012

The following guest post is by Katharine Beals, who blogs about education at Out in Left Field, where this post also appears.  — rp.

It’s hard not to detect a certain worry among those who write STEM articles for Education Week that the drive to educate students for careers in Science, Technology, Engineering, and Mathematics might include a drive to increase core scientific and mathematical content at the expense of things that Constructivists hold dear. Things, for example, like “model building,” “data analysis,” and “communicating findings.”

These are what Jean Moon and Susan Rundell Singer, in their backpage Edweek Commentary on Bringing STEM into Focus, want to be sure schools are focusing on:

Re-visioning school science around science and engineering practices, such as model-building, data analysis, and evidence-based reasoning, is a transformative step, a step found in the NRC report, which is critical to STEM learners and teachers, both K-12 and postsecondary. It puts forward the message that knowledge-building practices found under the STEM umbrella are practices frequently held in common by STEM professionals across the disciplines as they investigate, model, communicate, and explain the natural and designed world.

Not that this is all that Moon and Singer care about. They also care about big ideas, which they divide into two categories: “crosscutting concepts (major ideas that cut across disciplines)”, and “disciplinary core ideas (ideas with major explanatory power across science and engineering disciplines.” The former include “scale, proportion, and “quantity or the use of patterns;” the authors don’t cite any examples of the latter.

Besides “practices” and ”ideas,” the authors mention “strategies” and “tools” (again, without specific examples). What they don’t mention is underlying content, except to say:

Lest some believe this is setting up another false dichotomy in science or mathematics education between content and process, let us quickly add a strong evidentiary note: Epistemic practices and the learning and knowledge produced through such practices as building models, arguing from evidence, and communicating findings increase the likelihood that students will learn the ideas of science or engineering and mathematics at a deeper, more enduring level than otherwise would be the case. Research evidence consistently supports this assertion.

I’m curious what “research evidence” means, but I gather that it doesn’t include the research evidence that cognitive scientist Dan Willingham cites in support of the idea that students aren’t little scientists and need a foundation of years of core knowledge before being ready to function as actual scientists.

In promoting their ideas as “transformative,” the authors are overlooking the fact that the kinds of constructivist practices they desire are already standard in many schools (particularly those held up as models for others). If they want to promote something truly transformative for STEM, they should instead be advocating a reinstatement of the years of solid, content-based instruction in math and science that many of our K12 schools used to offer (and that one still finds in schools in most developed countries around the world).

Katharine Beals, PhD is the author of Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School. She teaches at the University of Pennsylvania Graduate School of Education and at the Drexel University School of Education, specializing in the education of children on the autistic spectrum. She blogs about education at Kitchen Table Math and on her own blog, Out in Left Field.

Singapore Math Is “Our Dirty Little Secret”

by CKF
October 6th, 2010

The following guest post is from Barry Garelick, co-founder of the U.S. Coalition for World Class Math, an education advocacy organization that addresses mathematics education in U.S. schools.

The New York Times ran a story on September 30 about Singapore Math being used in some schools in the New York City area.  Like many newspaper stories about Singapore Math, this one was no different.  It described a program that strangely sounded like the math programs being promoted by reformers of math education, relying on the cherished staples of reform: manipulatives, open-ended problems, and classroom discussion of problems.  The only thing the article didn’t mention was that the students worked in small groups.

Those of us familiar with Singapore Math from having used it with our children are wondering just what program the article was describing.  Spending a week on the numbers 1 and 2 in Kindergarten?  Spending an entire 4th grade classroom period discussing the place value ramifications of the number 82,566?   Well, maybe that did happen, but not because the Singapore Math books are structured that way. In fact, the books are noticeably short on explicit narrative instruction.  The books provide pictures and worked out examples and excellent problems; the topics are ordered in a logical sequence so that material mastered in the various lessons builds upon itself and is used to advance to more complex applications.  But what is assumed in Singapore is that teachers know how to teach the material—the teacher’s manuals contain very little guidance.  Thus, the decision to spend a week on the numbers 1 and 2 in kindergarten, or a whole class period discussing a single number is coming from the teachers, not the books.

The mistaken idea that gets repeated in many such articles is that Singapore Math differs from other programs by requiring or imparting a “deep understanding” and that such understanding comes about through a) manipulatives, b) pictures, and c) open-ended discussions.  In fact, what the articles represent is what the schools are telling the reporters. What newspapers frequently do not realize when reporting on Singapore Math, is that when a school takes on such a program, it means going against what many teachers believe math education to be about; it is definitely not how they are trained in ed schools.  The success of Singapore’s programs relies in many ways on more traditional approaches to math education, such as explicit instruction and giving students many problems to solve, in some ways its very success represented a slap in the face to American math reformers, many of whom have worked hard to eliminate such techniques being used.

Singapore Math does not rely heavily on manipulatives as so many articles represent.  It does make use of pictures, but even that is misrepresented. Singapore makes use of a technique known as “bar modeling”.  It is a very effective technique and is glommed onto as the be-all end-all of the program, when in fact, it is only a part of an entire package.  People mistakenly believe that all you have to do is teach kids how to draw the right kind of pictures and they can solve problems.  (In fact, there are now books written that provide explicit instruction on how to solve problems using bar modeling—meant to supplement Singapore’s books. That such books rely on a rote-like procedure is ironic considering that reforms criticize US programs as being based on rote instruction.)  Pictorial representation is indeed a gateway to abstraction, but there are other pathways that Singapore uses as well.  Singapore’s strength is the logical consistency of the development of mathematical concepts. And much to the chagrin of educators who may have learned differently, mastery of number facts and arithmetic procedures is part and parcel to conceptual understanding.  Starting with conceptual understanding and using procedures to underscore it is an invitation to disaster—such approach is making profits for  outfits like Sylvan, Huntington and Kumon.

The underlying message in articles such as the Times’ is that math education is bad in the U.S. because it is not being taught according to the ideals of reforms—and the reason it is successful in Singapore is because it is being taught that way.  Never considered is the possibility that the reform minded methods and textbooks written to implement them are one of the root causes of poor math education in this country.  Katharine Beals in her blog “Out in Left Field” does an excellent job describing this.

A friend of mine recently admonished me for my criticism of the article.  At least schools are using Singapore Math and it is getting worthwhile publicity, he said.  Fortunately, the logical structure and word problems in Singapore’s books are so good it will work in spite of the disciples of reform.  My friend is right.  If the education community wants to think that Singapore Math is student-centered and inquiry-based and the realization of US reforms, let them think it.  For those of us who know better, it will remain our dirty little secret.

Barry Garelick is an analyst for the U.S. EPA and plans to teach math when he retires this year.  He has written articles on math education in Education Next and Educational Horizons.

Teaching Grammar By Osmosis

by Robert Pondiscio
August 16th, 2010

OK, fess up.  You don’t know what a dangling participle is, and you couldn’t pick the past perfect tense out of a police lineup.  Neither can I.    But you know nouns from verbs.  And you can probably tell the difference between a complete sentence, a fragment, and a run-on.  Consider yourself part of a vanishing breed.  Writing at Betrayed–Why Public Education is Failing, Robert Archer, a high school English teacher in Spokane, Washington estimates that fewer than 10% of his 10th graders have command of basic grammar.

“Honestly, it’s gotten to the point that trying to make my way through the grammatical land mines that await me anytime I assign a writing assessment becomes so painstakingly tedious that even the solid content of any given essay becomes lost in the ghastly-writing-skills shrapnel. (And don’t even get me started on the spelling skills of this generation of non-phonics-learning texters! OMG!)

“When high school students cannot use their own language correctly, their overall communication skills—both in written and oral form—suffer tremendously,” writes Archer, who blames curriculum developers for his students’ poor skills.  Somewhere along the line, he writes “teaching grammar has become something that we teachers can simply ‘imbed’ into the reading and writing curriculum.”  Trouble is, it’s not working. 

“I’m sorry, but in my experience, the term “imbedded” is nothing more than educationalese for ‘not ever specifically taught.’ Somehow, this grammar-is-imbedded movement is supposed to help students naturally take in what proper grammar is (i.e., grammar by osmosis). It’s very much a hyper-constructivist approach to education; the students are supposed to “discover” proper grammar on their own as they read good pieces. Then, somehow and some way, they are to emulate these proper mechanical structures in their own writing. And if the students don’t quite “take it all in,” the teacher may take 2.5 minutes here and there to show them what a damn verb is.”

“When I’m hoping for nothing more than 3-4 grammatically correct sentences being strung together at a time as the sign of a “good” paper, then my expectations have dropped far, far too low,” Archer concludes.  “Yet, sadly, this is exactly to what I’ve resigned myself.”

Preach it, brother.  And teach it.

Renegade Parents Teach Math! (Teachers Too.)

by Robert Pondiscio
July 16th, 2008

Uh-oh…the secret’s out.  If you want your child to do well in math, teach ‘em long division at the kitchen table after school.   Traditional formulas have been supplanted, the Associated Press has discovered (long after the horse has departed the barn) by concept-based curricula aiming to “teach the ideas behind mathematics.”  This is leading “renegade parents” to teach basic math formulas on the sly at home. 

Renegade teachers too, as Matthew Clavel described in a terrific piece in City Journal some time back:

If school officials knew how far my lessons would deviate from the school district-mandated math program in the months ahead, they probably would have fired me on the spot. But boy, did my kids need a fresh approach….Not one of my students knew his or her times tables, and few had mastered even the most basic operations; knowledge of multiplication and division was abysmal. Perhaps you think I shouldn’t have rejected a course of learning without giving it a full year (my school had only recently hired me as a 23-year-old Teach for America corps member). But what would you do, if you discovered that none of your fourth graders could correctly tell you the answer to four times eight?

You’d teach them the algorithms, like Clavel did, I did, and countless others.  The idea that teaching for understanding precludes automatic recall and traditional methods of instruction–that children haven’t learned unless they ”construct” their understanding of math–is one of those mindless orthodoxies that have squeezed out common sense and strewn failure in its wake.   Watch a 4th or 5th grader struggle with partial sums addition and lattice multiplication and you’d quickly revert to time drills and memorization too. 

If I run into one of my 5th graders even 20 years from now, I will ask him or her, “Do you know how to divide?”  I’d bet my rent money I’ll get the answer, “Does McDonalds Sell Cheese Burgers?”  Sue me.  Take away my teaching license.  But I’ll bet they can divide.