New boss, old boss, Dept.

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:

1. identify and manage emotions
2. recognize sources of stress and cope with challenges
3. maintain positive motivation and perseverance
4. build relationships and communicate effectively
5.  develop self-awareness and sense of identity
6. 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.

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