Effective Math Instruction: Hiding in Plain Sight

traditional math

This article originally appeared in Education News in 2015. It received about 80 comments, most of them indignantly negative, which told me I was probably on the right track. I revised the article to bring it up to date and it is now included in my book “Math Education in the US: Still Crazy After All These Years”, which I heartily encourage you to purchase–in fact get several copies and send them to people who disagree with you on educational matters. They’ll never forget you.

I include this article here because there has been much talk lately on Twitter about how reading is not taught properly (due in large part to a great article written by Emily Hanford in the New York Times). The first line of my article echoes some concerns being discussed now. I extend the argument to math.

In a well-publicized paper that addressed why…

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Worked Examples and Scaffolding, Dept.

traditional math

In teaching procedures for solving both word problems and numeric-only problems, an effective practice is one in which students imitate the techniques illustrated in a worked example. (Sweller, 2006). Subsequent problems given in class or in homework assignments progress to variants of the original problem that require them to stretch beyond the temporary support provided by the initial worked example; i.e., by “scaffolding”. Scaffolding is a process in which students are given problems that become increasingly more challenging, and for which temporary supports are removed. In so doing, students gain proficiency at one level of problem-solving which serves to both build confidence and prepare them for a subsequent leap in difficulty. For example, an initial worked example may be “John has 13 marbles and gives away 8. How many does he have left?” The process is simple subtraction. A variant of the original problem may be: “John has 13 marbles…

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Research Tutorial on Locating Obscure, 2008, Common-Core-Related Paper


The purpose of this post is to offer a glimpse into how I located an obscure document once my originally-posted link was deemed dead. In this case, my efforts led to a solution that I thought I would share in case it might help other researchers, not only with the research process, but also with access to the actual document of interest.

magnifying glass

On May 05, 2014, I wrote a post about the Common Core State Standards (CCSS) in which I linked to a 2008 paper that CCSS creators David Coleman and Jason Zimba wrote on behalf of the Carnegie Commission. At some point, the link I originally posted to the 2008 Coleman-Zimba-Carnegie paper went dead. (One receives a privacy error message, but bypassing the safety warning only yields the site’s home page.)

The paper itself is an obscure one; I was first made aware of it from reading this 2013…

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Imbellus Assessments: Out of the Gate with $23M and McKinsey & Co. as Client


On January 11, 2019, Mark Bauerlein of the James B. Martin Center posted a piece entitled, “Be Wary of This Test,” about a testing startup, Imbellus, which has an impressive website deficient in any substance. Even so, Imbellus already has $23M in venture capital funding behind it.

According to Bloomberg, Imbellus was incorporated in 2015.

Imbellus is also on Twitter, with the last posting in June 2017.

The founder of Imbellus, 26-year-old Harvard dropout, Rebecca Kantar, is featured as one of Forbes’ “30 Under 30 2019 startups with $15 million plus in funding.”

What Kantar purports to do is create a cognitive assessment to rival– and apparently replace– the likes of the SAT and ACT. From Kantar’s Imbellus site:

Imbellus is reinventing how we measure human potential.

We build simulation-based assessments to evaluate how people think, not just what they know.

For nearly 100 years, college admissions…

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Wish List, Dept.

traditional math

I have
written a number of entries regarding “understanding” in math. I have discussed
various misunderstandings about understanding in math. There are two statements I haven’t addressed,
which for me raise many questions.

I have heard
many people express the thought that “Calculation is the price we used to have
to pay to do math. It’s no longer the case. What we need to learn is the mathematical

And often on
the heels of this statement I will be told that they had done well in math all
through elementary school, but when they got to algebra in high school they hit
a wall. Or, similarly, they did great in
high school, and hit a wall with calculus.

There is
much information that we do not have from such statements.

  • Was the education they received
    really devoid of any kind of understanding and all rote?
  • Are there people who…

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Oh, Lordy! Bill Gates Will Invest in Common Core-Aligned Curriculum

Diane Ravitch's blog

Bill Gates never gives up, and he sure isn’t abandoning his Common Core baby.

But he is not investing much. Only $10 million to train teachers to use Common Core curricula.

For this multiBillionaire, that’s not an investment, it’s more like throwing a few coins out there. Maybe it’s just a signal to his grantees that he is not yet ready yo throw in the towel.

Edweek reports:

The Bill & Melinda Gates Foundation plans to invest in professional development providers who will train teachers on “high quality” curricula, the philanthropy announced this afternoon.

The announcement fleshes out the curricular prong of the education improvement strategy the influential foundation laid out in late 2017, a major pivot away from its prior focus on teacher performance.

The investment, at around $10 million, is a tiny portion of the approximately $1.7 billion the philanthropy expects to put into K-12 education by 2022…

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How is Understanding Measured? — traditional math

I have written about understanding in math, and the education establishment’s view of it. With all this talk about how it is important for students to “know math” and not just “do math” the question arises: “How do we measure a student’s understanding as opposed to their ability to go through procedures?” That is, how […]

via How is Understanding Measured? — traditional math

#MakeAmericaDebateAgain: A Stronger, Healthier Republic Requires Open Debates — IVN.us

#MakeAmericaDebateAgain: A Stronger, Healthier Republic Requires Open Debates It’s 2019 and the United States of America still has a democracy problem. A few powerful studies have summed it up differently, but the heart of the problem is that despite Lincoln’s claim that we ever had a government of, by, and for the people, we have always had unrepresentative and unresponsive government. In recent…

via #MakeAmericaDebateAgain: A Stronger, Healthier Republic Requires Open Debates — IVN.us

Is Sweden’s education system falling apart? If so, what is to blame: vouchers or progressivism? — relinquishment

Sweden adopted an expansive school voucher system in 1992. Since then, Sweden’s PISA scores have tumbled. Sweden’s PISA scores shot up a bit in 2015, which is good to see. But it’s worth exploring why they dropped in the first place. There are two main theories why the scores dropped: some blame the voucher system and some […]

via Is Sweden’s education system falling apart? If so, what is to blame: vouchers or progressivism? — relinquishment