There is a lot of confusion in Utah when the state office of education says they adopted the “integrated” math method in order to be like the high achieving nations of the world, and then learns just how different Common Core and the integrated method are.
With permission I am reprinting this email from Ze’ev Wurman. Between 2007 and 2009, Ze’ev served as senior policy adviser in the office of Planning, Evaluation, and Policy Development, in the U.S. Department of Education. He has been involved in numerous standards reviews and understands the issues of Common Core and its failure to match up to high achieving nations standards.
This is Ze’ev’s explanation of integrated math as it exists in other high achieving countries.
First, I need to explain that what we call “integrated math” in the US is not at all like any math, “integrated” or not, they practice overseas. This is important because people peddling integrated math here claim that “this is what high achievers do overseas,” particularly for middle/high grades (7-9 there, 9-11 here).
What countries like Japan or Singapore do, is they spend a large part of the year (a semester, perhaps two trimesters) on teaching, say, algebra, and then they spend another large chunk (a semester or a trimester) on teaching, say, geometry. This way, the integrity and cohesion of the subject matter is preserved. Prerequisites are taught before they are needed, and generally things progress logically and hierarchically. Similarly, the geometry (or probability in higher grades) are mostly self-contained and may rely on what has been taught during the algebra period for the necessary prerequisite skills where needed. To Americans, used to teaching a full year of either algebra or geometry (those Carnegie Units still drive us!) this may seem “integrated.” Incidentally, in some instances there is even a separate teacher who teaches the algebra part of the year, versus another one who steps in to teach the geometry part.
But the American integrated program — and I am unaware of any exception — look very different. They are essentially programs that intermix the teaching of disparate content within the same units, or at most across short (4-6 weeks) units. The first type is often known as a Problem-Based Curriculum (or instruction) and works like this (think Connected or Investigations math): a “big” problem is posed that has multiple elements — geometry, calculations, perhaps a bit of graphing and/or algebra, perhaps a bit of probability or estimation. Then the class approaches the problem and as it “peels” it like an onion, the teacher is supposed to teach the kids the required knowledge as it becomes necessary. The idea behind it is that such problem-based instruction will offer a meaningful reason and justification to the students for the mathematical learning, rather than be taught as an “isolated skill” or “artificial (i.e., boring) non-real-life” problem. Unfortunately, it is essentially impossible to build a coherent curriculum around such large problems, because their needs for particular knowledge and skills do not follow any hierarchical and coherent progression. So you may need a bit about calculating a perimeter of complex figures, mixed with a bit about factorization and prime numbers (if the problem requires whole numbers as an answer) with some graphing thrown in. The result is that kids don’t develop knowledge and skills in a systematic and thoughtful manner, but rather learn disjointed bits and pieces of knowledge that rarely make sense or last for a long time. Integrated programs that are NOT problem-based have a different issue — they essentially interleave short units of different sub-disciplines, so teachers cannot build a solid base of the discipline’s body of knowledge, terms, and practices, before the class moves onto another sub-discipline that has a different set of terms and conventions. Again, think of the conventions in algebra versus geometry versus probability and stats. Consequently, no solid base of any discipline is developed because not enough time is spent to allow the student to internalize it over a lengthy period of time.
I am attaching a chart I collected from the 15 years of STAR administration. STAR offered both the course-based path through HS math, as well as an “integrated” one, and it had two separate sets of assessments for each path (same items, but partitioned differently across the years). As you can see, in the beginning about 25% of students were in integrated math in California. By 2013 there were fewer that 1.5% taking integrated. Nobody forced the school districts to abandon integrated — they just saw for themselves that kids in course-based math do much better, so they abandoned integrated in droves.
But nobody is paying attention to history :-)
(Click image for larger size – also see this article for the dramatic success of the CA standards)