Prevention Equals Treatment, Dept.

NOTE: For those interested in math education issues, the Science of Math organization has been formed to do for math education what valid research has done for the science of reading. Consider becoming an affiliate of Science of Math to support the efforts of this organization.

A recent paper by Sweller discusses how and why inquiry based approaches harm student learning and is largely ineffective. This is not the first paper that Sweller has written about the subject (not to mention those written by Kirschner), but it may be the most definitive so far.  The paper has sparked interesting observations. In particular, I was intrigued by a friend’s remarks that the prevailing mindset in schools and districts is that only students with learning disabilities need direct instruction and that it functions primarily as a student services support.

In math education circles direct (or explicit) instruction has been painted as the prevalent currency of traditionally taught math. And those who seek to reform math education tend to deride and mischaracterize traditionally taught math as  1) consisting solely of direct/explicit instruction with no engaging questions or challenging problems, 2) focusing on rote memorization and no conceptual understanding, and 3) failing to teach math in any complexity. In fact, traditionally taught math employs some inquiry based approaches, while reform math teaching generally relies more on discovery/inquiry approaches than direct. (A paper by Anna Stokke (2015) addresses what an appropriate balance of direct and inquiry-based instruction should be and states: “One way to redress the balance between instructional techniques that are effective and those that are less so would be to follow an 80/20 rule whereby at least 80 percent of instructional time is devoted to direct instructional techniques and 20 percent of instructional time (at most) favours discovery-based techniques.” This was corroborated in a paper by Adam Jang-Jones (2019) which quantified the “sweet spot” between inquiry and discovery based approaches.)

Reform approaches in math in the lower grades (K to 6) have steadily grown over the past three decades. I had long wondered whether some diagnoses of math learning disabilities (MD) of students were in fact incidents of low achievement (LA) due to lack of access to effective instruction. In other words, did the inadequacies of reform math mimic cognitive deficits?

I was therefore surprised and delighted to learn, when I took an Introduction to Special Ed class in ed school, that there was no beating about the bush when talking about students with learning disabilities and other disorders. We learned that students with learning disabilities have been shown to overcome their learning difficulties when given explicit instruction along with other methods. This was mentioned in our textbook (Rosenberg, et al., 2008) and often repeated by our teacher—a tremendously kind teacher named Carmen. (Interestingly, this course was one that was not required as part of my certificate program.)

Of particular interest in this course was the topic of “Response to Intervention” (RtI). RtI is a procedure in which struggling students are pulled out of class and given alternative instruction which includes direct instruction and other evidence-based approaches supported by randomized control trial studies. If they improve under RtI, then the student is presumed to not have a learning disability and is returned to the normal class. If they do not improve, that is an indication that they have an underlying learning disability. (The procedure was established under the Individuals with Disabilities Education Improvement Act (IDEIA) passed in 2004).

I recall the discussion we had about RtI in which I posed a hypothetical to the teacher. “Suppose someone is doing poorly in a math class that relies on an inquiry-based math program,” I said. “And they pull the student out and give him RtI using direct instruction and other techniques, and this student does well.  What happens next?”

“Then the student is placed back to the class during math.”

“But then suppose the student does poorly again? Wouldn’t that indicate that he needs more direct instruction rather than inquiry based approaches?”

“It doesn’t work that way,” Carmen said.

“So he’s stuck with a program in which he doesn’t do well.”

“Right,” she said.  “But if he did poorly in RtI, then that would be evidence he has a learning disability.”

What Carmen was telling me was the Catch-22 aspect of special ed. That is, in schools that rely on programs that follow math reform principles, approaches used in traditional math teaching are generally not an option unless a student qualifies as being learning disabled. And if under RtI, a student does well with direct instruction this is taken as evidence that the student does not have a learning disability.

I suspect that the use of RtI is higher in schools that rely on reform-based programs. I would like to see research conducted to see if that is true. From where I and many teachers and parents sit, the effective treatment for many students who are LA, is also the effective preventative measure.

Based on conversations I’ve had with education professors, I believe the educational establishment will likely continue to resist recognizing the merits of traditional math teaching and direct instruction. The following statement from James McLesky (2015), one of the authors of the textbook we used in the special ed class and a professor at University of Florida’s College of Education, is typical of what I’ve been told:

If we provide only (or mostly) skills and drills for students with disabilities, or those who are at risk for having disabilities, this is certainly not sufficient. Students need to also have access to a rich curriculum which motivates them to learn reading, math, or whatever the content may be, in all of its complexity. Thus, a blend of systematic, direct instruction and high quality core instruction in the general education classroom seems to be what most students need and benefit from. 

Statements such as these imply that students who respond to a diet of more direct instruction constitute a group who may simply learn better on a superficial level. I fear that RtI will evolve to incorporate some of the pedagogical features of reform math that has resulted in the use of RtI in the first place.

I am hoping that the publication of Sweller’s latest paper and the reaction to it that I’ve seen so far, will result in an increasing recognition of the benefits of direct instruction specifically and traditional instruction generally, as well as the harm that can result from inquiry-based approaches. Unless and until this happens, the group-think of the well-intentioned educational establishment will prevail. Parents and professionals who benefitted from traditional teaching techniques and environments will remain on the outside — and the methods that can do the most good will continue to hide in plain sight.


McLesky, James. (2015) Private email to Barry Garelick. November.

Rosenberg, Michael; D. L. Westling, J. McLesky (2008). Special Education for Today’s Teachers: An Introduction. Pearson. New York.


4 thoughts on “Prevention Equals Treatment, Dept.

  1. Whatever happened to their advocacy of “different learning styles?”

    Blah, blah. Woof, woof.

    They lie about “traditional” math. They don’t show any proof that their methods work for STEM. All proper high school and college math are STILL traditionally taught. They don’t ask us parents what we had to do at home in K-8 to ensure “mere” facts and “rote” skills to help our kids into the AP/IB track in high school.

    They use a 19th century monopoly model for no choice in K-8 that disappears in high school – and so do their ideas. They want equality and that means equality of low expectations in class, but they ignore the unequal help affluent parents give at home. They just pretend that it doesn’t matter – or worse, they claim parental/tutor help for their own. I got to calculus in high school with absolutely no help from my parents. That was not possible with my “math bran” son. All of my son’s STEM-ready friends had to have help at home or with tutors.

    They won’t give it up because that’s all they have. They claim that skills and facts matter, but CCSS standards are so low that there is a huge gap and slope change to high school honors/AP/IB. With no proper algebra class in 8th grade, you have to cram five years of proper math into four. That’s not possible. If students don’t get help at home, a STEM future is all over.

    This is so stunning.


  2. It’s like treating someone for addiction by getting them out of the addictive environment, only to throw them back into that environment once it works.

    Liked by 1 person

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