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For some reason, the lattice method of multiplication really annoys some people. I wish I could understand what appears to be an irrational rejection of a perfectly sensible approach that is just as mathematically sound as the "traditional" way most Americans were supposed to learn to do multi-digit multiplications. I recently had another fruitless "dialogue" (read: smash-your-head-against-a-brick-wall, you'll-get-further argument) with an entrenched foe of anything and everything viewed as tainted by the evil worm of fuzzy, reform thinking. I will try to edit it into something that some readers may find useful. What started this was the posting by another notorious reform opponent of a link to a YouTube video that shows a way to do multiplication by drawing a series of crossing lines. Of course, the underlying mathematics is the same as what makes the lattice method (and pretty much all methods I've seen taught) work. But the video appears to be presented ...

Reasons to be cheerful (part three) Summer, Buddy Holly, the working folly Good golly Miss Molly and boats Hammersmith Palais, the Bolshoi Ballet Jump back in the alley and nanny goats 18-wheeler Scammels, Domenecker camels All other mammals plus equal votes Seeing Piccadilly, Fanny Smith and Willy Being rather silly, and porridge oats A bit of grin and bear it, a bit of come and share it You're welcome, we can spare it - yellow socks Too short to be haughty, too nutty to be naughty Going on 40 - no electric shocks The juice of the carrot, the smile of the parrot A little drop of claret - anything that rocks Elvis and Scotty, days when I ain't spotty, Sitting on the potty - curing smallpox Reasons to be cheerful part 3 Health service glasses Gigolos and brasses round or skinny bottoms Take your mum to paris lighting up the chalice wee willy harris Bantu Stephen Biko, listening to Rico Harpo, Groucho, Chico Cheddar cheese and pickle, the Vincent motorsickle Slap and tickle Woody...

If you've been wondering about new entries on this blog, wonder no longer. After a month's hiatus, I'm back, blogging from a new perspective. I have taken a job at a public charter high school on the west side of Detroit and reentered the classroom full time after four years of doing professional development work, mostly with elementary and middle school math teachers. As you might imagine, if feels both strange and strangely familiar to be back. Unlike my two previous full-time positions in K-12, where I taught at an alternative high school with students whose average math and literacy level was between 4th and 5th grade, and at a middle college where I basically spent one or more semesters with students trying to get themselves in a position to pass an intermediate algebra course at the community college that sponsored our charter and physically hosted our school, this time around I've got one group of sophomores for Algebra 1, three classes of seniors for Algebra II,...

While not quite the Lincoln-Douglas debates, over the last several days, an old argument has been resurrected on math-teach@mathforum.org . Those not recently conversant with that long-standing free-for-all list likely don't know that after a decade or so as the wild west of mathematics education lists, where anything went and often did, in spades, the list owners have stepped in to bring peace, harmony, and bliss to this particular battleground in the Math Wars. Thus, the lion now lies down with the lamb, all is civility, no epithets are hurled, no ad hominem attacks launched, and decorum is the order of the day. And yet, intriguing undertones, sometime imported from more venerable and genteel locations such as NOTICES of the AMS, 54(2007), pp 822-3 There, one may find an exchange between Jerry Rosen, a founding member of Mathematically Correct and a Cal State Northridge mathematician and Sol Garfunkel of COMAP regarding old questions about who is to blame for the alleged contempo...

In 1998, as California was in its first year of a counter- revolutionary mathematics curriculum framework thanks to efforts led by anti- progressive mathematics education groups like Mathematically Correct and HOLD, Richard Rothstein's THE WAY WE WERE? The Myths and Realities of American's Student Achievement was published as a Century Foundation Report. The first chapter should be required reading for anyone who thinks s/he knows about the history of American public education. It explores and debunks many widely-believed myths about "falling" achievement in literacy, general academic knowledge, and the whole notion that our public schools are failing us, kids today are far less competent in basic skills than were those of previous generations, and that our lousy schools are paving the road to hell for our kids and our nation. In particular, Rothstein examines two currently hot-button topics - social promotion and bi-lingual education - and reveals many surprising r...

Last time, I explored some ideas about what comprises good mathematical questions in mathematics classrooms taken from MAKING SENSE: Teaching and Learning Mathematics With Understanding, by Hiebert, et al. In this entry, I want to introduce ideas from a book by Peter Sullivan and Pat Lilburn: Good Questions for Math Teaching: Why Ask Them and What to Ask [K-6] Sullivan and Lilburn's Criteria In the introduction to their book, Sullivan and Lilburn list three main criteria for good questions: a) They require more than remembering a fact or reproducing a skill; b) Students can learn by answering the questions, and the teacher learns about each student from the attempt; and c) There may be several acceptable answers. The first of these features, while not something everyone sees as important in all mathematics classrooms, is essential to non-routine questions. It takes no teacher skill to come up with questions that only ask for students to show that they have memorized a fact (e.g...

One glaring weakness in many American mathematics classrooms is the nature of questions teachers ask. This manifests itself in two pedagogical realms: first, the kinds of mathematical questions or tasks teachers tend to pose are often of a closed nature which call of nothing more than a calculation (or short series of calculations) and for which the answer is a single number that requires no further interpretation or thought on the part of the student. The second area of difficulty arises in the types of questions teachers ask when they want to help students who are having difficulty performing a given task (which generally consists of something like that mentioned previously, although this problem arises in more complex problem situations). My focus here will be on the the first situation: what kinds of tasks might comprise "good questions" for math students in elementary school? Mathematical Tasks In their book MAKING SENSE: Teaching and Learning Mathematics With Understan...