Ontario’s math program for K-12 has come under fire the past few years. So much so that the current Premier of the province (Doug Ford) ran on a platform that included a “back to basics” math program.

The new math program was unveiled last week. A glance at its features showed that aside from the requirement that students know their multiplication facts, it appears to be the same mix of rhetoric for achieving “deeper understanding” of math.

A recent article talks about how a key aspect of the new standards is the Social and Emotional Learning (SEL) component.

Educators say the key innovation in the new curriculum involves teaching “social-emotional learning skills” throughout math. According to Ministry of Education documents, this means helping students to “develop confidence, cope with challenges and think critically.” For example, students will learn how to “use strategies to be resourceful in working through challenging problems,” says the parents’ guide to the curriculum. … Teaching those skills is a far cry from drilling times tables into students’ heads.

Interesting that the parent’s guide to the curriculum downplays the memorization of times tables, which was probably the biggest change in the new math curriculum from the older one. Actually, providing students with the necessary instruction to achieve success is what ultimately leads to confidence, motivation, engagement and–yes–critical thinking. Much of the thinking behind SEL, however, places the cart before the horse. The strategies talked about in SEL frequently include such things as telling students to say “I can’t do this…yet” and other motivational cliches. These so-called strategies are thought to give students a “growth mindset”.

The components of SEL are spelled out in the new standards. Specficially, they are:

- identify and manage emotions
- recognize sources of stress and cope with challenges
- maintain positive motivation and perseverance
- build relationships and communicate effectively
- develop self-awareness and sense of identity
- think critically and creatively

The standards state that these components will come about through implementation of the standards as they apply “mathematical processes”. What does that mean? Well, here are the mathematical processes the standards cover:

- problem solving
- reasoning and proving
- reflecting
- connecting
- communicating
- representing
- selecting tools and strategies

Taking just the first item in the bulleted list: “problem solving”. The reform-minded thinking is that if a student learns how to “problem solve” (the current lingo for what used to be called “solving problems; apparently the term “problem solve” confers more meaning and implies that there is “deeper understanding” rather than just “finding an answer” ) they will automatically be attending to the six components of SEL

Nice and neat, tied in a bow, and ready to use. The only thing missing, it seems, is the instruction for how to solve problems. For that matter the tools that allow one to reason and prove, or even to reflect also seem to be missing from the standards. The new standards leave out learning things like, say, the standard algorithms for adding/subtracting multidigit numbers, or multiplying and dividing. Instead, it talks about students learning “algorithms” for same–not the “standard algorithms”. This may seem like a nit-pick but it is not. “Algorithms” in the lexicon of the math reformer can be any particular procedure that produces an answer. This usually includes methods that are typically taught *after* mastery of the standard algorithms.

For example, adding 75 + 56. Rather than teach students to stack the numbers and to carry the excess to the tens place (or regroup, using a more reform-minded term) they teach students to first add 70 + 50 and then 5 + 6. Then add the two sub-totals of 120 and 11 to get 131. This is nothing new, and I’ve seen it taught in a 5th grade arithmetic book from the 1930’s (an era said to be when math was taught by “rote memorization” with no understanding). The method makes sense once mastery of the standard algorithm is accomplished. But teaching the strategy first rather than the standard algorithm is thought to provide the “deeper understanding” that the standard algorithm is believed to obscure.

The new standards supposedly provide students with the skill of making “connections among mathematical concepts, procedures, and representations, and relate mathematical ideas to other contexts (e.g., other curriculum areas, daily life, sports)”. Traditional or “back to basics” approaches are, according to Mary Reid, (assistant professor of math education at the Ontario Institute of Studies in Education). “just following procedure without really understanding why you’re doing it.” This “understanding uber alles” approach prevails in the math reformers’ view of how mathematics should be taught. It fails to recognize that procedures and understanding work in tandem, and also confers the mistaken belief that understanding must always come before allowing students to use more efficient procedures. In the case of the new standards, it looks doubtful that efficient procedures (i.e, standard algorithms) will be taught at all.

As far as the holy grail of “connections” is concerned, Robert Craigen, a math professor at University of Manitoba who has been involved in improving K-12 math education says this: “It’s amusing when they speak about “connections” as if this were something different from “isolated facts”. Actually it is the facts that *provide* connections. Everything else is only the educational analog of a conspiracy theory.”

We’ll see how this latest conspiracy theory plays out in Ontario.

Reblogged this on Nonpartisan Education Group.

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“The method makes sense once mastery of the standard algorithm is accomplished. But teaching the strategy first rather than the standard algorithm is thought to provide the “deeper understanding” that the standard algorithm is believed to obscure.”

Why? I don’t think I have ever used the standard algorithm in my adult life, but I use roughly this and similar methods every time I have to do mental math. Same story with the long division algorithm. I don’t think my knowledge of these algorithms has ever really helped me in a genuine way, either as a bridge to understanding or anything else.

I agree that times tables should be memorized, since knowledge of times tables allows you to reason numerically much more fluently.

I do disagree with the fuzziness of “reflecting, connecting”, etc, being standards, and think that any standards need to be more concrete.

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Students who master the standard algorithm first generally take to the short-cuts you mention. Students often discover these shortcuts on their own, as you probably did. The other way around, however, based on what we’re seeing in classrooms, can result in confusion.

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“I don’t think I have ever used the standard algorithm in my adult life,”

If that’s your idea of education, then I’ll wager you won’t like many other tradeoffs that criterion would cause.

I learned left-to-right calculation and estimation after learning the standard techniques and that’s what I use or else I will go for my calculator. However, there are many, many things about learning multi-digit multiplication and long division by hand that have nothing to do with being rote or providing an adult tool.

Adults take many things for granted understanding-wise that they now consider to have been rote learning. Learning to tell time? learning to count change? Was that learning rote? No. So many things tie together to build a bigger framework of understanding. School is not about providing only adult vocational tools. My adult life has nothing to do with whether I could dissect a frog or analyze a poem.

This doesn’t even take into account whether schools actually get students to master whatever they choose to teach. They don’t get the job done. We parents have to pick up the slack, and much of that has to do with enforcing mastery of what many people consider to be rote. Just ask us parents of the best students in high school what we had to do at home and with tutors. Enforce mastery of basic facts and skills.

The Common Core is a low slope from Kindergarten to no remediation in a College Algebra class. It’s easy to cherry pick and argue about details and overlook larger systemic problems and assumptions.

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Including emotional and social learning into an elementary maths curriculum is an “everything but the kitchen sink” tactic. One is left with the impression that the curriculum creators recognize that emotional and social skills are crucial to well-being, but have little idea about how to teach it.

Emotional and social skills are substantial skills in their own right and require rigorous instructional design methods (particularly formative assessments). Furthermore, the neural networks for these skills are most plastic in the first few years of life, and need to be developed by the primary caregivers. Unlearning mal-adaptive behaviors is difficult and costly.

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“It fails to recognize that procedures and understanding work in tandem, and also confers the mistaken belief that understanding must always come before allowing students to use more efficient procedures.”

I always tend to go to sports analogies, since my kids are all athletes – my youngest the most so. He has been able to throw a ball exactly where he wanted it to go since he was about 2-1/2. I am pretty sure he didn’t understand the physics of why the ball went where it did. He just knew that the way he did it worked. His “understanding” got better as he got older, but come on, just let the kids learn how to throw the darn ball!

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