>Readers will see the story of Cathy's honest struggle to improve >her mathematics teaching. Students' work "objectively" speaks >for itself throughout the book. There's plenty of "data" of this >sort dispersed throughout.
It was in today's mail and a quick read. In fact, a look at the now mouldy but high-sounding rhetoric during the CLAS rebellion is a pretty good summary. Here's another for which I can't take credit but that is entirely appropriate; the plural of "anecdote" is not "data". In fact, in some cases it's not even plural. Forty five pages(!) of Shelli's portfolio with nothing but an occasional encouraging comment, "This shows evidence of a good understanding of fractions!"
Actually, that's not quite true. Deprecating students' use of pencil and paper arithmetic appears to be OK. Isn't this your writing in Fig. 9.33? "Shelli, This works for you when you're doing paper and pencil, but it's a *hard* way to do mental computation." That was beyond Cathy's(?) more encouraging comments that concluded with "This is a good way!" Neither comment reflects the fact that when Shelli did the 10 x 25 in that problem, 25 x 15, she got 350 so the answer was off by 100. At least she demonstrated that she does know the standard base-ten multiplication algorithm, a fourth grade standard in California that I saw being met nowhere else in the book.
Most informative is *her* assessment of your own assessment that "Children Invent Arithmetic Concepts (P. 144). From Fig. 9.33, Jan 13: "When we do mental computation all the problems are different and since some are easy and some are difficult, the ones that are difficult are hard for me and I don't always do them. I just wait until I see other people do it then I realize how easy they really are." And four days later, "I don't really think I've made any progress I've just stayed the same. I like it but I can't find a better way to do the problems. I just do them the way I was taught. Like this: ..." (and proceeds to do the 25 x 15 conventionally, tho incorrectly.)
Glancing down other California Math Content Standards, I cannot begin to tell from the work presented - even for Shelli, let alone the rest of the class(!) - if they have been met or not. Use of < >, negatives on a number line, decimal arithmetic, factoring small whole numbers, division by a single digit, etc. The fifth grade CA Standards appear to not have been met by a wide margin, powers, use of parentheses, division with positive decimals, arithmetic of fractions including division of fractions and expressing quotients in simplest terms, and many, many others. I saw no evidence of multiplication and division of fractions at all. To what extent the percent standard is met would be speculative since I saw no use of percents in her portfolio. It is mentioned in the text in your discussion with Michael, J.R., Sean, Joseph, and the class on P. 145. Your parenthetical statement is indicative of the flavor:
"[These ten-year olds are making sense of percent without ever having been taught percent formally. We were to discover over and over again throughout the course of study that kids are powerful sense makers when they are given situations to make sense of.]"
Although that's a motherhood and apple pie statement that is absolutely true, I see no "data", not even a singleton *anecdote*, that verifies any level of student understanding here. "The children worked to invent procedures and make sense of their information. On a recent California Assessment Program (CAP) test, only 50% of eighth graders tested were able to successfully answer the question, 'How much is 100% of 32?'" You then follow with some math ed political rhetoric, "... might it also be that teaching rules and procedures can interfere with children's sense making processes?"
I asked my daughter [going into 6th grade in a few weeks] to read that "eighth grade" problem. She didn't really answer it, what she actually said was, "I'll bet a third grader could answer that question! What are they doing at that school!?!" Her private school remains very close to the California Standards and was so before they were ever written. Fifth grade Number Sense 1.2 is "Interpret percents as a part of a hundred, find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number. The clarifying example given is:
"A test had 48 problems and Joe got 42 correct.
1. What percent were correct? 2. What percent were wrong? 3. If Moe got 93.75% correct, how many problems did he get correct?"
It is truly amazing that, six years after the CLAS anti-assessment disaster folded, you are still being hired around our state to help districts that are using MathLand and busy trying to write their own math standards "because the state standards are too shallow." From the flyer of your next appearance, MATHEMATICS FOR THE FUTURE, A Community Math Night, "You are invited to attend a very special evening event with Dr. Ruth Parker, ...", Mountain View in the Silicon Valley tomorrow night (August 22nd). This is an upper middle class neighborhood so concerned parents tend to have compensating opportunities available but it is also close to the home of HOLD. Right there, under their very noses. Undermining California's amazing progress. Amazing in itself.
At 02:26 PM 8/20/00 -0700, Ruth Parker wrote (and I responded):
>...for those who have not read the book, ... > It's a conversation worth having though.
Guilty as (gently) charged and it should be arriving soon. I look forward to that conversation. In the meantime ...
>Students' work "objectively" speaks for itself throughout the >book. There's plenty of "data" of this sort dispersed throughout.
It can, of course. That's all I use in my classes and am pretty confident that my assessments are objective, consistent, and reasonable. I would not begin to assert that a sample or some samples of one particular student's work is indicative of much of anything, however. I would consider *all* of the students' responses to a given item to be meaningful and objective and the over-all class grade distribution to be meaningful and objective, as well, but I might be hard pressed to convince someone who doesn't know me that such is true, much less someone (our Rebecca perhaps?) who does know me and believes that to be damning enough.
You mentioned the early demise of CLAS so I pulled out the 4th grade (all 5 forms were mailed to me anonymously at the time) and some of the items, and their expected responses, seem far from objective. For example, one item on one form has the student listing all possible combinations of coins (not pennies) that would be appropriate responses to, "Please deposit 40 cents to complete this call." That, in itself, is more of an intelligence and situation familiarity item than an objective assessment item but give it a pass. It's the following page that is the real outrage, a full blank page with only the heading, "Explain how you know that you have found all possible combinations," and the standard instruction box at the bottom, "Check your work to make sure you did the following: ..."
A decent presentation of a systematic solution to the item itself would eliminate any need for any response at all! I assume creative writing would be recognized (such as the "write a letter to the principal" item the previous year) but a blank page following an informative table on the previous page would not have been. The fact that this item only appears on one of the five forms of the test also makes one wonder about any sense of objectivity.
Or here's another from a different form of the test: "Your friend Jimmy is just beginning to learn more about numbers. He does not understand what 3 x 5 = 15 means. Use drawings and words that could help Jimmy understand," followed by two blank pages and the standard instructional box at the end.
That was the *only* assessment of multiplication conceptual and computational competence on that form of the test. Some of the other forms had none. Again, this was to be a test of grade 4 mathematics.
I do hope that your implied support of the "objective" assessment of CLAS is not consistent with the objective assessment of student performance as reflected in your book.
At 02:26 PM 8/20/00 -0700, Ruth Parker wrote: >on 8/20/00 1:23 PM, Wayne Bishop at email@example.com wrote: > > > At 09:39 AM 8/20/00 -0700, Ruth Parker wrote: > > > >> I wrote it in '92 and there are some things Cathy and > >> I would choose to do differently, today, but it paints a > >> fairly clear picture of what I think a more powerful mathematics > >> classroom can look like. > > > > I tend to ignore descriptions of a "more powerful" mathematics classroom > > without a context of objectively obtained student performance data, > > reported over time and against the backdrop of parental socioeconomic and > > educational levels. The Jaime Escalante student performance in AP Calculus > > come to mind as do the top several Inglewood schools on the CAT-5 and now > > SAT-9. Do you have that kind of data on her classroom? Thanks in advance, > > > > Wayne. > > > > > > > >Readers will see the story of Cathy's honest struggle to improve her >mathematics teaching. Students' work "objectively" speaks for itself >throughout the book. There's plenty of "data" of this sort dispersed >throughout. I'll be happy to entertain the question, "What do we know about >these students' performance in mathematics?" I'd have to write volumes to >try to do so for those who have not read the book, and I just don't have >time for that right now. It's a conversation worth having though. >Ruth Parker