I would point out that Minnesota showed dramatic gains on TIMMS not because of “new, more rigorous standards,” but because of that state’s decision to implement a coherent grade-by-grade curriculum in mathematics. William Schmidt took the lead in developing that curriculum (pdf file) and deserves to bask in glory for what he has done for the children of Minnesota. That is the most important lesson of 2007 TIMSS for the United States.
I'd love to hear more about this.
Here's some info about MN.
ReplyDeleteA while back we had a vertical meeting with math teachers from grades 4-8. The agenda was to familiarize ourselves with the standards for fractions outside of our own grade levels. The facilitators cut all the relevant standards into little strips, removing any identity as to the grade levels they came from. Our job was to put them back together again in the proper 3-8 sequence.
ReplyDeleteIt couldn't be done except at a gross level. Each year, and within each year as well, there are nuances on the nuances on the nuances. It was a good exercise in cross polination. In hind sight it was also a dramatic demonstration of the ridiculous nature of those standards. If the teachers charged with delivering them can't see clear annual goals then how can the kids?
I have our cities math curriculum from 1958 (I was in middle school then) and it reads precisely like the A+ international standard in the link. Interestingly, it is riddled with demands for mastery at key milestones, something that is totally absent in our present day constructivist, spiral curriculum.
Funny how 50 years of 'research' has taught us how to do what we already forgot.
Funny how 50 years of 'research' has taught us how to do what we already forgot.
ReplyDeleteAlso funny how the math of 50 years ago is said (by those pushing reform math) to have failed large numbers of students.
My suspicion has always been that the problem with the old math had little to do with the math and a lot to do with slouching towards the lowest common denominator in a totally non mathematical context so to speak. :>{
ReplyDeletewow - Paul - that's incredible.
ReplyDeleteAny chance you can post those standards?
Or at least passages from them?
Is there some place I could get hold of them?
I've just spent an entire day recovering from Tuesday night's board meeting. The new principal of the K-3 school gave a presentation & the school has been completely constructivized. There is nothing left of the school we knew.
And, yes, they are using "balanced literacy" to teach reading -- in collaborative groups, no less.
Balanced literacy in whole group instruction would be bad enough; these kids are basically teaching themselves balanced literacy.
They are ALL discovering patterns ALL THE TIME.
The classrooms have decodable texts (e.g. the Bob Books), but they don't use them. We the people have purchased decodable books that would actually teach our kids to read, and they are sitting unused. (We the people also purchased a decent spelling curriculum a couple of years ago that has apparently been abandoned in favor of word-study-via-looking-for-patterns.)
Also, the kids have WRITING PORTFOLIOS. They write the same GENRES every year, over and over. Each year they can open up their writing portfolio & pull out their GENRE PAPER from the year before, read it, and "see where they want to go as writers."
The fantastic news is that the board powerfully advocated for the kids on two subjects: (non)use of data and grade deflation. (Have yet to write my grade deflation in high performing school districts post.)
Unfortunately, the board doesn't know enough about balanced literacy or constructivism to realize what's being done to the kids. We saw lots of cute photos of cute kids sitting together at little round tables with nary a teacher in sight. Who can object to cute kids sitting quietly together at little round tables "working collaboratively"?
Still, as bad as that was, the good news outweighs it: board members weren't taking no for an answer on the subject of data & grade deflation. The administrators came back again and again with vague excuses ("The test might have been different last year") and every board member stood his (or her) ground.
I don't think that happens often in high performing school districts.
"Fourth-grade teachers in Minnesota also reported devoting more time on computation with whole numbers, fractions, decimals and number patterns, which is the major focus of fourth-grade math internationally. As a result, they covered fewer nonessential topics and achieved greater focus and coherence."
ReplyDelete"Minnesota’s eighth-grade teachers reported spending more than four times as much instructional time on algebra in 2007 than they did in 1995. Algebra is the major focus of eighth-grade math curriculum around the world."
These aren't difficult concepts.
Some would call this teaching to the test. Some believe that there is no connection between mastery of skills and understanding. I'm sure those people still exist in Minnesota. I would like to know the details.
Perhaps the change is not as large as I think. Does anyone have a link to their grade-by-grade standards for content and performance? Do they have a list of approved curricula?
Perhaps, by limiting the non-essential topics, teachers have more time to ensure mastery and still not feel like it's just drill and kill. Do they reject curricula like Everyday Math, or do they specify which sections to ignore. I can't imagine EM can be fixed easily. The big problem is that it allows kids to go for years before ensuring mastery (which never happens).
However, if the range of topics is reduced, then maybe it's more likely that mastery will happen naturally. Teachers can still do some of their fuzzy discovery learning, but there is more time left over for mastery.
I can't imagine that MN K-8 teachers just decided that mastery is king, or that discovery learning has gone down the drain. It seems that the major change is a carefully-defined and limited curriculum, which gives teachers more time to do what they (deep down) know they have to do; ensure mastery of basic skills.
Recently adopted MN Math standards are available at the MN Dept of Ed. These were adopted in September 2008, so one might want to compare the 2003 standards with the 2008.
ReplyDeleteThere's also a nice alignment form for teachers and a CLEP guide for students.
Hi Catherine:
ReplyDeleteI only have hard copy on the standards. I'll scan them and email images to you for posting if that's OK. I dug them out and discovered they only cover grades 1 to 6. My remembery is faulty it seems.
There is an interesting quote to lead them off. Never really read it before but now that I have I'm blowing iced tea out of my nose. The quote is from the Sixteenth Yearbook in Mathematics. NCTM Bureau of Publications, Teacher's College of Columbia Universtity, N.Y. 1941. If I was a better writer I could have written this myself, yesterday! Funny how the wheels go 'round, eh?
Here it is...
"Atithmetic is a system of ideas. Being an idea, arithmetic exists and grows only in the mind. Being a system, arithmetic must be taught as a system. It cannot be left to individual caprice, but must be made the subject of explicit instruction. But it cannot be imposed on the pupil; it must be developed by his own individual responses and reactions: the pupil must be an active learner, but he must be taught; he must be subject to instruction, but the instruction must be individualized. And the two are not necessarily incompatible. The apparently conflicting demands of the number system and the interests and experiences of the individual pupil can be resolved into a consistent, basic theory of instruction."
I had to read that about three times before I grasped the eloquence and complete capitulation to DI put forth in that quote. Ken? Barry? Are you out there?
Now I'm just heading for my Scotch. It's not often you get to say I told you so with your adversaries very own pike.
Make that 'adversary's'. Apparently the scotch thing got going a bit early.
ReplyDeleteKen? Barry? Are you out there?
ReplyDeleteI'm right here, buddy. Drop me a line!
Here are some 1958 gems to whet the appetite. Just addition here but each strand is similar with insistance on mastery, spaced repetition, and skills maintenance.
ReplyDeleteGrade 1: horizontal and vertical addition facts through 10, with mastery
Grade 2: horizontal and vertical addition facts to 100, complete mastery.
Grade 3: Column addition to 4 addends and three places. Addition of US money in decimal form
Grade 4: Recheck mastery of addition facts, including review and complete diagnosis. Prepare for adding of partial products by giving oral drills in decade facts.
Grade 5: Check on mastery of addition facts. Provide diagnostices tests and arrange for differentiated practice. Provide a strong maintenance program.
Grade 6: complete mastery should be achieved. Emphasis should be on mental math including decimals
Here is what's covered in six years: Number System, Addition, Subtraction, Multiplication, Division, Fractions, Decimals and Percents, Measurement, Graphing.
These strands are all overlaid with appropriate problem solving and vocabulary for each year. I counted 'Mastery' or 'Complete Mastery' a total of 8 times. Notice that there seems to be a progression from introduction to mastery to maintenance. Instead of spiraling topics it spirals layers of expertise.
And lest you think this is all dry drill and kill, there is also an overlay of 'activities', for example, one for grade 4 "Collection of building plans and construction of a project from a plan". Here's another from grade 4 "exhibition and explanation of ancient ways of telling time".
From grade 5; reading making and using scale drawings (we scratch this in grade 7 with a delightfully childish tome called Stretching and Shrinking, actually it's more like a paper cut).
And here's a laugher from grade 5; imaginary spending of $25 or $50 at a grocery store. Chump change for my kids in the $250 gang garb.
$25 dollars at a grocery store! My head is exploding.
I better chime in to this discussion as a Minnesotan who has been watching this pretty carefully.
ReplyDeleteFirst, as to Diane Ravitch's comment:
I would point out that Minnesota showed dramatic gains on TIMMS not because of “new, more rigorous standards,” but because of that state’s decision to implement a coherent grade-by-grade curriculum in mathematics.
With due respect, I do not know what she is talking about, unless by "grade-by-grade curriculum" she means the "benchmarks" described below.
The very short history in Minnesota is this:
1998: Adoption of "Profile of Learning" as the first "standards-based curriculum policy" (our first state standards). 100% constructivist ideology. Became extremely controversial as soon as implemented. Finally ousted in 2003.
2003: Complete 180 turn; rigorous, content-rich standards put into place. Law requires "Benchmarks" in addition to "Standards."
Benchmarks are addressed in the FAQs on the Minnesota Dept. of Ed website. There it is stated that the purpose of benchmarks is to provide details about "the academic knowledge and skills that schools must offer and students must achieve to satisfactorily complete" the standards (Minn. Stat. § 120B.023 (2006). Benchmarks are intended to "inform and guide parents, teachers, school districts and other interested persons and for use in developing tests consistent with the benchmarks" (Minn. Stat. § 120B.023 (2006)). Benchmarks guide the test makers, but not all benchmarks are necessarily tested each year.
2008: Math standards tweaked, but in principle are the same "type" of content focused standards instituted in 2003.
Minnesota's math standard info can be found on the Minnesota Dept. of Ed. website. There you can find the grade by grade standards as well as benchmarks.
Re: Steve's comments on curriculum.
There is no state-approved curriculum. There are no state-approved textbooks to choose form, like in California. Each district can choose its own curriculum, period. So, the only across-the-board standardization comes in the form of the standards, the benchmarks, and the assessments (Minnesota Comprehensive Assessments) that are supposed to be aligned with the above.
I attended some meetings of the revisions committee that eventually produced the 2008 revision. My point was that there is no guarantee that great standards will translate into great curriculum or instruction at the district and school level. My case in point was St. Paul, which adopted Everyday Math around 2000 as being "exquisitely aligned" (or some such) with the Profile of Learning (constructivist standards) and was then sold as being aligned with the 2003 content-based standards!!
I have seen a document prepared for the St. Paul school district that purports to align all the EM sections with the standards, and shows teachers where they have to make adjustments. As you can imagine it's a big, complicated mess!
And, here is text from the St. Paul school district's website concerning mathematics education in middle school. You'll see some all-too-familiar themes:
The typical mathematics classroom in the Saint Paul Public Schools is one that is inclusive of regular education students, special education students, English Language learners, and gifted and talented. Teachers are aware of the multiple learning styles in their classroom and the instructional practices include group processes as well as direct instruction. Teachers have the flexibility to use the methods that they feel will best serve their students.
Disciplinary Literacy is an initiative that has been used in the Junior Highs Since 2004. This initiative trains teachers to facilitate problem solving in their classrooms. The activities are based on the University of Pittsburgh’s Principals [sic] of Learning. These nine principles focus on student learning and making all of us accountable for helping them be successful. Virtually all junior high teachers have been trained in Disciplinary Literacy and High School teachers are in the process.
St. Paul appears to never have let go of the Profiles of Learning.
All that said, I have to say I am really very surprised by how well Minnesota did on the 4th grade TIMSS and do not know what to make of it. Maybe they are doing something different in K-4 since my kids were there but Everyday Math still reigns in Twin Cities metro districts, at least (not sure about outstate). The state and SciMath, the quasi-governmental sponsoring agency, won't say anything about the schools/kids that were tested although it is supposed to be represtative.
It's 2008 now and Everyday Math babies are in high school and beyond. By and large our urban kids are not achieving our high state standards. The NEAP shows that we have one of the largest achievement gap in the nation. And there is even talk of postponing the implementation of Minnesota's graduation test in math, which is supposed to go into effect in 2009: 2/3 of our juniors just failed it!
From the article:
Kay is worried the math test will affect her daughter's chances of getting into college. "I can't tell you how upsetting that is to me," Kay said. "She is a good student. She gets good grades. She just doesn't get math."
And:
A passing score will not be set until after the test is given. Minnesota educators and national experts advise the department on where that score should be set; the education commissioner ultimately signs off on it.
Cassy, that MSU pointer claims all these great improvements in MN's scores on TIMMS. But neither that paper, nor Ravtich's note, nor the Fordham note on TIMMS points to any TIMMS report with the actual MN data. All I can find is the TIMMS overview which doesn't list any separate info for the states.
ReplyDeleteDoes anyone have a pointer that does show the MN breakouts?
Allison, here is a preliminary summary of results from the 2007 TIMMS produced by SciMath. Is this what you are looking for?
ReplyDeleteOr this full report from the US Dept. of Ed?
Thanks for your work, Vicky!
ReplyDelete"My point was that there is no guarantee that great standards will translate into great curriculum or instruction at the district and school level."
Exactly. Something else is happening. Maybe a lot more parents realize that they have to make sure that the basics are mastered. Maybe more schools have more time for the basics.
"I am really very surprised by how well Minnesota did on the 4th grade TIMSS and do not know what to make of it."
But that won't stop others from making some really big guess-and-check conclusions. I'd like to know exactly what is going on. It shouldn't be too difficult if we could see the raw data.
"The state and SciMath, the quasi-governmental sponsoring agency, won't say anything about the schools/kids that were tested although it is supposed to be represtative."
They can't do this.
Thanks for the links to the reports. I'll try to get some time to look at them.
well, the scimath link doesn't show where their data comes from. and the i will have to think more about what the us dept ed said, but i thought it said that the national sample was what was "Representative", not any given subsample. i don't see why MN is an unbiased estimator for the US, and lo! it wasn't, so that could simply mean that it wasn't a "representative" subsample of the sample in the first place --i.e. the schools they picked in MN were to adjust for various sample biases from other places as well...it's not like they have necessarily a lot of urban poor schools in the MN sample compared to in CA or NY or FL.
ReplyDeletestill trying to read the dept ed site before i jump to any conclusions that there's any real change here.
vicky, that dept ed link just goes to the summary. there's nothing in that summary report about MN at all. the scimath link doesn't yet talk of methodoogy or any actual data euther...
ReplyDeleteHere's a different link for the TIMMS 2007 data. It's the TIMSS 2007 International Mathematics Report by Mullis et al. available at the TIMSS and PIRLS International Study Center at Boston College. There's all sort of good stuff there that has kept me busy all evening! The International Database (maybe what you really want, although there is data in the International Report) will be available February 2009.
ReplyDeleteThe 2007 TIMSS Encyclopedia available on the same site gives lots of info about the participating countries and benchmarking entities. It's very clear in Minnesota's chapter that the state has no coherent grade by grade curriculum and that individual districts and schools have completely free rein when it comes to implementation of the standards, selection of curriculum, and instructional methods. Minnesota has standards--and they are good standards--but it's still up to the districts, one by one, to follow them.
Here's another interesting tidbit for Steve from the Minnesota Department of Education website. It's a Curriculum Alignment Sheet that local districts or schools can use to map their curriculum against the state standards. Like I said--you should see how this looks when Everday Math is mapped onto it.
Historical aside: under the old Profiles of Learning standards (pre-2003) our state Department of Education was named "Department of Children, Families and Learning." When the state got serious about the standards, it decided to take the fuzz out of the state education department name as well!
In the interest of full disclosure I should point out that Fordham gives the 2003 Minnesota state math standards a D. But, they were recently improved, addressing some of the weak spots, and even the 2003 version is so much better than the earlier one, most of us up here on the tundra aren't complaining.
ReplyDeleteStill, good standards are necessary but not sufficient. If there is resistance at the local level, implementation is a bear.
I guess it's time for me to really study TIMSS, if I only had the time. I can't begin to get even a feel for what is going on unless I go back to the basics. I started looking at some of the released questions, and I wasn't impressed by the difficulty.
ReplyDeleteFor example, a sample question in the 7th/8th grade test was:
Write a fraction that is larger than 2/7.
Even this one:
Divide 8/35 by 4/15
didn't impress me.
The first question I have is when are these tests administered, in 7th or 8th grade; at the beginning of the year or at the end? (Obviously, I haven't done much of my homework yet.)
I also noticed that not many of the questions would give me feedback about whether or not the student was properly prepared for algebra. Then, how many questions are on the test and how long are the students given? Do most kids finish the test with time left over?
There is also the question of how the raw score is translated into their reported score. This really bugs me about our state tests. They assume that nobody wants to see the details. The raw data gets translated into another scale and you lose all sense of the raw percentage score. It's kind of like redrawing a graph with a different y-axis scaling so that the slope looks steep (or flat - whichever makes the data look better).
Because of this, we all look at the relative numbers and don't have a clue whether the changes are significant or not. I don't know what the TIMSS numbers mean. If they go up 10 points, what change in raw percent-correct score does that mean? How many more correct questions does that mean?
This is what I hate about closing the academic gap. They shouldn't be looking at flattening the curve. They need to look at raising the whole curve.
A new post is up on my 1958 traditional curriculum with a challenge question for your enjoyment.
ReplyDeleteSteveH-
ReplyDeleteI believe the 2007 tests were administered in the fall of 2007.
Not only does:
Divide 8/35 by 4/15 or
Write a fraction larger than 2/7
not impress me, it makes me worry why the 8th graders did so poorly. Next week, when work is done, I'll have time to dig into the report. (Along with a 4 inch deep stack of articles.)