This article in The Windsor Times (which serves Windsor, California) explores the changes in math education going on in that school district. There is a discussion of how the “integrated math” option of Common Core is superior to the “old ways” of doing things:
“Part of the issue is the substantive changes to the curriculum itself, which everyone agrees is better in the long run and significantly more rigorous that previous versions but is also significantly different. Gone are the old paradigms of Algebra I, Geometry, Algebra II/Trigonometry, followed by AP Calculus for the elite few. In its place now exists Integrated Math 1, which incorporates early concepts of both Algebra and Geometry, with slightly more emphasis on Algebra, Integrated Math 2, which introduces more advanced concepts of Algebra and Geometry, with slightly more focus on Geometry, and Integrated Math 3, which takes both sets to the next level and along with some Trigonometry.”
Excuse me, did you say “everyone agrees” the new curriculum is better? Everyone, you say? Sorry. Go on.
” “The belief is that students who have grown up in the integrated model will be much better equipped and have a much more extensive math education that those without. However, students at all levels are struggling with the staggered roll out from the old model to the new.
” “We are no longer asking them just to compute,” Director of Educational Services Lisa Saxon said. “They have to think about numbers in a different way, explain, defend and justify their answers, and undertake a completely different level of rigor.”
Excuse me again. I teach algebra and believe me, I don’t just ask students to “compute”. Where are you getting that? As for defending and justifying their answers, and this completely different level of rigor: I’m aware some people think there are such things as “math zombies” who operate from a “rote” level of executing procedures. I would suggest that there is also what I call a “rote” level of understanding in which students mouth the explanations the teachers want to hear. Is that what you meant?
traditional math 
“We are no longer just asking them to compute” is a refrain at least 150 years old. It’s pretty tired by now.
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“Gone are the old paradigms of Algebra I, Geometry, Algebra II/Trigonometry, followed by AP Calculus for the elite few.”
“Elite few?”
“The belief is that students who have grown up in the integrated model will be much better equipped and have a much more extensive math education that those without.”
Whose belief?
“much better equipped”
Than the “elite few?”
This is where their thinking falls completely apart. They like to call the elite kids “zombie math” students as if they would be better off in an integrated math curriculum. Dream on. Colleges love these “zombie” students. You don’t get an admissions advantage for going through an integrated math program. Colleges want your traditional math grades, SAT I and II scores, AP Calculus score, and your AMC scores. They are zombies only in the fantasy world of ed school demagogues.
They don’t even make a case that integrated math is better for certain students at lower levels. Colleges aren’t giving better admittance advantage to those students. Why is that? Many educators love the idea of K-16 education as if their domain of influence include colleges – as if their fuzzy ideas of education (their turf) dominate over the content knowledge and skills of professors in colleges. That doesn’t even fly in high school. Integrated math lost that battle. It’s over. Been there. done that.
Could there be other high school curriculum paths that would be better for some students? Possibly, but first they have to clean up the low expectations and lack of mastery in K-6. A better high school path is not one that tries to adapt to the systemic problems in K-6. These pedagogues love balance, but never seem to much care about ensuring the skills part. In addition, they have to link to the requirements of college and vocational degree programs – not the other way around.
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Their idea is that if you do well in math, then you are “elite” and somehow learn differently. Either that, or they claim that they are students who are turned into “math zombies” that only some high school teachers and college professors want just to show good grades and scores on tests like SAT, AP, and AMC. We are never shown any model or class of students taught using their techniques who are better at math. We are only given empty hypotheses. I would be their biggest supporter if they had any proof, but their hypotheses drive their interpretation of reality – a reality they know nothing about. Could it be that their ideas might work better for some students who learn differently? Maybe, but you can’t slow down coverage and change the need to link up to advanced education requirements and skill levels. Using hand puppets for math could work better if you lower expectations and redefine where you dump these students off in the end.
Some high school students might be better off with a different approach to math credits if they are not going on to a higher level education that has specific entrance requirements, but I would suggest a different approach than even integrated math. One option would be to offer a course on personal finance and investing taught in a traditional format with a textbook and nightly individual homework. This would be one that helps them master the ideas and skills of investment classes, allocation, investment horizon, risk, return, and correlation, not one that has the discovery of the importance of compounding as a major goal. You can’t replace mastery of skills, content knowledge, and rigor with simple discoveries and hope for engagement and transferrence.
Their claim is that they somehow know better than those who define the admission requirements for colleges and vocational schools. This is a philosophy that is not driven down from above or even the job world. Sure, they can find business leaders who claim that they want students who can think and analyze, but what does that mean and what is the reality? The reality is that businesses want people who have skills and can do specific jobs and tasks. I remember 35+ years ago talking about all of the accomplishments and projects that I completed on my resume. No. They wanted to see my list of skills and specific courses. They cared about the projects I completed in the sense that they got a better understanding of my skill level. Doing those projects proved those skills and showed how well I understood the material. Accomplishments may look great on your resume, but your interviewers will grill you on the details of your skills to see if you are a skill leader or a faker. There is no such thing as rote skills. There is no generalized discovery or inductive transferrence ability that replaces those skills. Experience and insight are built upon mastered skills that are applied over time. Project managers don’t just materialize out of thin discovery air. They come up the path of hard work and learning the skills of people and project management. Those are not generalized transferrable top-down discovery methods.
These educational demagogues claim to have found a magic approach that they own and use to define their special turf. That’s really what they are looking for. It doesn’t match reality, but that doesn’t stop them. It doesn’t match the requirements of colleges and vocational schools, so they go off to business leaders to find words that seem to back up their beliefs. However, they never show successful classes of students who have followed their path.
Education is bottom-up, not top down. Concepts might be great, but meringue does not form or create the base of a pie. Having taught college courses on systems analysis, I call a technique I created “Outside-In Systems Development.” This is a process that starts with a top-down analysis (given trained workers – not as a education technique) that stops before “analysis paralysis” sets in to create a solution from the bottom up using a prototype development technique. The prototype system is where the real work and learning takes place. The top-down analysis only gets you going in a good direction. Hands-on prototyping might sound like a good educational technique, but not if it’s built on nothing. That’s just a bad vocational education because most vocational schools require at least success on the Accuplacer test. At the other end, “hacking” at MIT is built upon real skills and P-sets. It’s not a foundational educational technique.
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