Education Week ran an article about what the author called “Lesson Imaging” that used such phrase. The basic thrust of the article (and phrases like “unpack the learning goals”) was based on the premises stated in this passage:
Inquiry Mathematics and Science. Leading mathematics and science educational organizations (e.g., NCTM and NSTA) have called for fundamental changes to instruction to include a more student-centered classroom. Also, most state standards for mathematics and science education include requiring students to create viable solutions to problems through inquiry and communicate their reasoning (CCSS-M, NGSS).
As I have indicated in articles I’ve written, the Common Core website contains statements that the standards do not dictate pedagogy. For example here:
While the standards set grade-specific goals, they do not define how the standards should be taught or which materials should be used to support students.
And here:
Do the standards tell teachers what to teach?
Teachers know best about what works in the classroom. That is why these standards establish what students need to learn, but do not dictate how teachers should teach. Instead, schools and teachers decide how best to help students reach the standards.
Despite such advice, the prevailing interpretation is that Common Core does call for inquiry-based approaches as evidenced in the quoted passage from Education Week.
The Education Week article then notes that the publishing industry has responded to this “requirement”:
Textbook publishers have created materials that attempt to engage learners in more inquiry activities that foster the development of rich science and mathematics understanding. Along with a shift in educational goals, math and science teachers have been pressed to change from a traditional lecture, information-sharing classroom style to student-driven inquiry. Such a shift has been challenging for teachers because of the lack of resources to guide teachers in their pursuits.
Unstated in this article and in many others like it, is that the traditional practices of the past have not worked. And the articles that do state that, omit much in the way of evidence for such statement, aside from the standard “Many adults today cannot do basic math, so there’s your proof.” Such proof seems to neglect that if someone hasn’t done something in a while, they tend to get rusty and forget certain procedures, like finding percent of increase or decreases, or the formula for finding the volume of a pyramid or cone, or surface area of a sphere. The so-called proof also neglects that just as many adults today do remember their math facts, know when to multiply or divide, and know basic procedures with decimals and fractions. By contrast, many of today’s students–who have been taught using the student-centered, inquiry-based approaches championed by NCTM and other reform-based organizations over the past 28 years or so–cannot do basic math.
And this is why I found Tara Houle’s recent op-ed about the education problems in British Colombia so pertinent (and of which I wrote about a few days ago). Of note was this particular passage:
If we truly want to ensure our kids have a bright future, we must first build on the successes of the past, and bring that forward for them. That has not happened here. Successful methods of teaching mathematics have all been eradicated from British Columbia classrooms.
There is a rabid fervor promoting 21st-century learning, and insisting that inquiry-based learning take precedence over everything else. However, the fundamental principles of arithmetic are non-negotiable. Without mastering these crucial facts at the elementary level, any attempts at Math 10, pre-calculus or entry-level university mathematics will end in failure.
I wish the best for British Columbia’s education efforts as well as other provinces experiencing these same problems and hope they don’t continue to follow the pathway that the U.S. has been on. “Rich problems” are fine and in their place fulfill an important purpose. But there is no clear-cut or convincing evidence that this gives any insight into a great way to teach core material in this subject.
traditional math 
This is a nice statement of the problem – no requirement, no proof, and throwing out the baby with the bathwater.
These educational turf pedagogues want to change the learning process to one that is top down rather than bottom up from mastered skills. They claim that mastery does not include understanding – that it is rote. There is absolutely no proof of this. In fact, it’s the opposite. They alter reality to fit what they want, and what they want to see is really just a changed approach to what happens in the classroom. They rarely say anything about what should happen at home or individually. They send home notes to us parents telling us to practice “math facts” at home with our kids. Apparently it’s important, but what happens to all of those kids who don’t get that help at home or with tutors? It’s all over by 7th grade.
Textbook publishers offer different approaches depending on the demand. One thing I noticed was that the strongest algebra/geometry textbooks were labeled very simply, like Pre-Algebra and Algebra I. The lower expectation and simpler textbooks (from the same publisher!) added subtitles, like “Tools for a Changing World.” All of the best math students (with required help from home or tutors) end up in the non-simplified math tracks that lead to traditional textbook and skill-based AP Calculus track classes in high school. CCSS defines a NO-STEM K-6 world that is dominated by fuzzy, top-down, in-class ideas of learning that do not ensure the mastery of skills to get sorted into the 7th grade tracks that use traditional textbooks. They claim that their inquiry-based, group-oriented, learning process is somehow better with absolutely no proof. Do they ask us parents of the best math students what they did at home? No. They just use our kids as examples of success.
One simple thing that K-6 schools can do is to clearly define what skills, content, and understandings a child must show to get onto the top math track in seventh grade. I asked my son’s school (long ago), and they offered only a vague answer. I think a hidden part of the answer was that there were only a limited number of slots. This key turning point should not be so important, but it is. Students either get to a math track that offers any chance of a STEM career, or they get onto a low expectation one that can’t fix old problems – It’s kind of like the movie “Groundhog Day” for Algebra. No wonder they think traditional classes don’t work. Unfortunately, they get it backwards – their fuzzy K-6 ideas don’t work. Our high school created a very successful “Algebra/Lab” class where the “lab” part was used to try to fix the gaps and missing skills students were allowed to spiral along through K-6. (Thank you for that Everyday Math!) The lab class helped many kids, but the real solution would be to fix K-6 ideas of inquiry learning. Nope. There is a pedagogical wall between K-6 and high school. I saw first hand that traditional high school teachers did not want to even go there. The head of the math department who set up the algebra/lab class refused to blame Everyday Math, but she did not say that EM was just fine.
This doesn’t mean that a traditional approach could not be greatly improved, but as I realized when my son was in pre-school and I found out that our school used MathLand, they went in the completely wrong direction. Not even lowering expectations and making classrooms fun (?) gave them better results.
LikeLike