From “Education Dive” (as in “deep dive”, “deep understanding” and other ridiculous jargon which unfortunately permeates the edu-world), a summary of a shocking new study:
Less than 10% of math assignments in the middle grades require “high levels of cognitive demand,” and only about a third of tasks expect students to show their thinking when providing their answers, according to a new analysis of more than 1,800 assignments, released today by The Education Trust.
Oh dear! Say it ain’t so. What kind of high level cognitive demand do you want from a homework assignment? What’s wrong with practicing procedures or solving word problems that escalate in difficulty–even if they aren’t the “open ended” variety? (Open ended, as in “The area of a rectangle is 24? What are the dimensions of the rectangle?” Things like that, which supposedly get at “depth of knowledge” rather than the dreaded procedural “plug and chug”, which supposedly never scaffolds to higher difficulty problems.)
And what do they mean by showing their thinking? A written paragraph? Showing work is not enough, I guess. Can’t the teachers assess students’ reasoning by asking questions in class, like “Why did you subtract those two numbers? How did you come up with that approach?” No, students now have “some ‘splainin’ to do!” Assignments that are “answer-focused” to use the jargon of the study, do not allow students to communicate their thinking.
And from the report itself:
Unfortunately, our analysis revealed that although roughly three-fourths of all assignments at least partially aligned to the grade- or course-appropriate math content, they also tended to:
- Have low cognitive demand
- Over-emphasize procedural skills and fluency
- Provide little opportunity for students to communicate their mathematical thinking
And this tendency was often worse in higher poverty schools.
Which concludes with:
This analysis of middle-grades math assignments show that
schools and districts across the country are falling short when it
comes to providing their students with high-quality math tasks
that meet the demands of college- and career-ready standards.
The high percentage of aligned assignments demonstrates
that teachers are adjusting from the “mile-wide” philosophy
of previous standards movements and embracing the focused
prioritization of content that the math standards provide. These
high rates of alignment should be celebrated and strengthened.
However, alignment on its own is not enough to meet the high
bar set by rigorous college- and career-ready math standards.
And another “conclusion”:
AS OUR DATA SHOW, WE AS EDUCATORS MUST DO MORE TO PROVIDE STUDENTS WITH QUALITY MATH ASSIGNMENTS THAT PROMOTE COGNITIVE CHALLENGE, BALANCE PROCEDURAL SKILLS AND FLUENCY WITH
CONCEPTUAL UNDERSTANDING, PROVIDE OPPORTUNITIES TO COMMUNICATE
MATHEMATICAL UNDERSTANDING, AND ENGAGE STUDENTS WITH OPPORTUNITIES FOR CHOICE AND RELEVANCE IN THEIR MATH CONTENT.
Wow, it has all the right words doesn’t it? And how does data show that we need to engage students with “opportunities for choice and relevance in their math content”? It might show that there is not much opportunity for such choice, but does it show that we need to provide such opportunities? There are teachers (not just me) who will tell you that if students know enough to be able to tackle the problems given, they won’t care if it’s relevant or not. OK, don’t believe me.
Look, I use a 1962 Dolciani algebra textbook to teach my algebra class. The word problems are plenty challenging for my students, though I’m fairly certain that the authors of said study would find such problems lacking in “real world relevancy” (as if my students care) and low cognitive demand. Yes, I hear you saying “But they’re not from poverty and they would do well anywhere.” Really? Got proof of that?
For my 7th grade class, I use JUMP Math, which uses micro-scaffolded approaches, but doesn’t skimp on the conceptual understanding behind the procedures either. It has been given bad reviews by those who hole math reform ideologies in high regard as being “too procedural”.
Which brings me to one final question. Did the study in question look at how the students are doing on standardized tests? And, oh yes, what types of approaches are used at Learning Centers, by tutors and by parents at home. What is it that successful students are doing? Do they explain their work? Spend time on open-ended problems? Are do the stuff that’s held in disdain? Any data on that anyone?
AS OUR DATA SHOW, WE AS EDUCATORS
MUST DO MORE TO PROVIDE STUDENTS
WITH QUALITY MATH ASSIGNMENTS THAT
PROMOTE COGNITIVE CHALLENGE, BALANCE
PROCEDURAL SKILLS AND FLUENCY WITH
CONCEPTUAL UNDERSTANDING, PROVIDE
OPPORTUNITIES TO COMMUNICATE
MATHEMATICAL UNDERSTANDING, AND
ENGAGE STUDENTS WITH OPPORTUNITIES
FOR CHOICE AND RELEVANCE IN THEIR