This just in, Dept.

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
MATH CONTENT.

11 thoughts on “This just in, Dept.

  1. “For this analysis, we reviewed over 1,800 middle-grades assignments from over 90 math courses from 12 middle schools in six districts across the country …”

    They say nothing about textbooks, but I assume they are used. This could be a problem of teachers just assigning the basic skill sections of the textbook problem sets. I’m looking at my son’s old Glencoe Algebra I textbook and there many levels of questions, from basic skills to “Open Ended” questions just like they propose.

    However, the report says this about one comparison between the emphasis of basic skills (Assignment A) they see versus the “thinking” questions they like (Assignment B).

    “Assignments A and B are both opportunities for students to meet the standards. However, only providing students with problems in Assignment A limits their opportunity to engage in cognitively demanding tasks. …”

    In my son’s Glencoe textbook, all question variations are right there, so what’s their real problem – that teachers give up if only basic skill questions are mastered? Are they suggesting Assignment B questions IN PLACE OF or before basic skill mastery questions? Go ahead and assign more homework. Set higher expectations, but what are they really saying here; that more is more or are they saying that swapping their Assignment B for Assignment A will get them something for nothing? Um, no.

    My math classes have always focused on skills first because they contain all sorts of understanding. As you go further in every homework exercise set, you run into very time consuming open ended and “thinking” problems. Some might be helpful, but the ones they propose are not worth the time.

    Forget the fact that when they talk about CCSS standards in algebra classes, they are far removed from any sort of STEM level of preparation.

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  2. At the end, they ask…

    WHERE DO WE GO NEXT?
    “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.”

    This is completely wrong. This is all about them. This is NOT about looking at what works and what doesn’t – or asking us parents of their best students what we have to do at home or with tutors. What do colleges and careers want? They want good grades in the AP Calculus track, good SAT I and II scores, and many colleges want to see your AMC test scores.

    The traditional AP Calculus track works very well. The problem is how to best support ALL students on that track starting from Kindergarten. Educators and CCSS systemically fail this task, and no amount of understanding or rigor blather can hide that fact. CCSS is a NO-STEM Zone that starts in Kindergarten and Pre-AP attempts by the College Board are an admission of a 2+ generational approach to offering proper individual educational opportunities. Clearly, parents and tutors now have to do their jobs.

    It’s right there in black and white – CCSS NO STEM low slope math in K-8 and magic fairy dust Pre-AP math in ninth grade where students have to double-up in math. Then they have the audacity to talk about “social justice.” This report offers absolutely no critical thinking. They just claim to know what is needed for college and career readiness. Hello! At least look at what colleges want to see in applications for those applying to STEM programs like engineering. Then work backwards to the fairyland of K-8.

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  3. Pingback: More just in, Dept. | traditional math

  4. By “assignments” do they mean homework?

    Because it’s really important at lower grades to make sure homework is easy. If it’s hard you risk 1) them not doing it or worse 2) doing it wrong and thereby unlearning good habits. Possibly, 3) in well-off areas their parents or tutors will do it.

    Challenging problems should be confined to school time. Homework is for routine to build speed, strength and accuracy.

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    • homework shouldn’t exist at the lower grades, IMO. At the primary level, the only learning that should be occurring, is in the classroom, being taught by the knowledgeable teacher. Home time is very valuable for wee kids, and the quality of “homework” at this level is usually “busy work”. It’s counterproductive, and a massive intrusion on family time.

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      • Agree for lower grades K-5, say. But for middle and high school, homework plays an important role in building confidence and gaining practice as math grows more complex. Anti-homework advocates view homework at all grades as “busy work” which is definitely not the case.

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      • yes. For primary levels, don’t bother. For jr and senior high, be sure the homework is good quality review focusing on what classroom instruction depicted.

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      • The issue I have with the “no homework” policy our school has implemented is that parents have little idea what their kiddos are learning unless they take the initiative. For my son, it would be a no-learning zone if we didn’t also teach at home right now. He loves his special time with us too. Art of Problem Solving will launch their online Beast Academy very soon and he is so excited.

        My son’s math teacher is not strong with gifted math students and she struggles to find activities for him. She wanted to make him do the Bridges workbook 1 page at a time. He sat down a few months back and worked through a huge portion of the book. She wasn’t happy. I’ve sent his other books to school and he says he’s only allowed to work on them during free time, not math time. Bridges encourages lots of group work too. Sigh.

        I don’t like the idea that parents abdicate responsibility or authority to schools or teachers. It should always be a partnership.

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      • I don’t agree. Individual homework should exist in math for all grades. Homework need not be difficult or “busy work.” It establishes the routine of p-sets and enforces practice. Perhaps all necessary individual (!) skill work could be done in class, but I don’t ever see that happening. Maybe K-3, but I would need to see exactly what went on in class and see results of skill tests and quizzes so we parents get proper feedback. The rubrics I received for my son were completely meaningless.

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