Quebec Dominates in Math, Here Is Why Ed Reformers Should Pay Attention

The Canadian and Quebec Flags
Via Wikimedia Commons (CC-By-SA 4.0)

Paul Bennett had an interesting piece in Policy Options, a public forum run by the Institute for Research on Public Policy, a Canadian think tank located in Montreal, Quebec.

He notes that Quebec dominates the rest of Canada in math and have done so for many years. In spite of that, the other Canadian provinces don’t want to emulate Quebec’s success. 

He highlights a study conducted by British Columbia’s Ministry of Education into Quebec’s success. I wanted to highlight a couple of the findings that he writes about.

The first finding is that Quebec has a clearer philosophy and sequence. Bennett writes:

The scope and sequence of Quebec’s math curriculum is clearer, demonstrating an acceptance of the need for clarity in setting out a progression of content and skills focused on achieving higher levels of achievement. The 1980 Quebec Ministry of Education curriculum set the pattern. Much more emphasis in teacher education and in the classroom was placed upon building sound foundations before progressing to problem solving. Curriculum guidelines were much more explicit about making connections with previously learned material.

Quebec’s grade 4 curriculum made explicit reference to the ability to develop speed and accuracy in mental and written calculation and to multiply larger numbers as well as to perform reverse operations. By grade 11, students were required to summon “all their knowledge (algebra, geometry, statistics and the sciences) and all the means at their disposal…to solve problems.” “The way math is presented makes the difference,” says Genevieve Boulet,a professor of mathematics education at Mount St. Vincent University with prior experience preparing mathematics teachers at the Université de Sherbrooke.

Did you catch that? A clear scope and sequence was key, but not only that, an emphasis was placed on building sound foundations before tackling problem-solving. 

Now compare that to Common Core. We’ve noted Common Core’s Math Standards:

  • Delay development of some key concepts and skills.
  • Include significant mathematical sophistication written at a level beyond understanding of most parents, students, administrators, decision makers and many teachers.
  • Lack coherence and clarity to be consistently interpreted by students, parents, teachers, administrators, curriculum developers, textbook developers/publishers, and assessment developers.  Will this lead to consistent expectations and equity?
  • Have standards inappropriately placed, including delayed requirement for standard algorithms, which will hinder student success and waste valuable instructional time.

Bennett then notes Quebec uses stronger math curriculum:

Fewer topics tend to be covered at each grade level in Quebec, but they are covered in more depth than in BC and other Canadian provinces. In grade 4, students are generally introduced right away to multiplication, division and standard alogrithms, and the curriculum unit on measurement focuses on mastering three topics — length, area and volume — instead of six or seven. Concrete manipulations are more widely used to facilitate comprehension of more abstract math concepts. Much heavier emphasis is placed on numbers and operations as grade 4 students are expected to perform addition, subtraction and multiplication using fractions.

Fewer topics, they go in depth and students are introduced right away to standard algorithms. Common Core puts conceptual understanding before they master practical skills. Barry Garelick wrote about this in The Atlantic in 2012:

Under the Common Core Standards, students will not learn traditional methods of adding and subtracting double and triple digit numbers until fourth grade. (Currently, most schools teach these skills two years earlier.) The standard method for two and three digit multiplication is delayed until fifth grade; the standard method for long division until sixth. In the meantime, the students learn alternative strategies that are far less efficient, but that presumably help them “understand” the conceptual underpinnings.

Yet Quebec does not do this.

Canadian provinces are wise to emulate Quebec’s success in math, but we in the United States would be as well. 

A Common Sense Approach to Common Core Math

math_thumb.jpgBarry Garelick is providing a great service to parents and teachers who have no choice but to navigate through the Common Core Math waters.  Garelick has a degree in Mathematics from the University of Michigan and after retiring from the U.S. Environmental Protection Agency he sought out credentials to teach secondary math in California.

He started in August a series of articles entitled “A Common-Sense Approach to Common Core Math” found at The Heartland Institute’s School Reform News.  Right now there are three articles, but I’m sure there will be more on the way.

Here is an excerpt from his introductory article:

I believe that CC math, while not dictating particular teaching styles, has thrown gasoline on the ideological fire that has been raging for slightly more than two decades in education. I am referring to what is known as “reform math.” Reform math has manifested itself in classrooms across the United States mostly in lower grades, in the form of “discovery-oriented” and “student-centered” classes, in which the teacher becomes a facilitator or “guide on the side” rather than the “sage on the stage” and students work so-called “real world” or “authentic problems.” It also has taken the form of de-emphasizing practices and drills, requiring oral or written “explanations” from students on how they solved a problem (besides showing their work), finding more than one way to do a problem, and using cumbersome strategies for basic arithmetic functions. Math reformers say such practices will result in students understanding how numbers work—i.e., math is about “understanding,” not simply “doing”.

CC lends itself to such interpretations because of the words “explain” and “understand” in their content standards as well as eight overarching standards called “Standards for Mathematical Practice” that embody “habits of mind” of mathematical thinking. On the surface and to those unaware of underlying concerns and issues, the SMPs appear reasonable. But they are being interpreted to force students into developing “habits of mind” outside of the context of the material being learned—which again feeds into the reform math ideology.

In part I he addresses some selected First and Second Grade standards.  In part 2 he tackles Third Grade fractions.  In part 3 just published Monday he discusses drawing diagrams for dividing fractions.

I encourage you to keep tabs on future articles as well.

Algebraic Thinking for Those Who Don’t Know Algebra?

Barry Garelick’s article yesterday in Education News tackled the issue of teaching kids the “habits of the mind” that make up algebraic thinking before that student has learned algebra.  He said what happens instead is that particular thinking skills are taught without content to support it.

In essence you get math problems without math.

That sounds productive doesn’t it?

Garelick points out what purveyors of this approach are simply engaged in wishful thinking:

Giving students problems to solve for which they have little or no prior knowledge or mastery of algebraic skills is not likely to develop the habit of mind of algebraic thinking.  But the purveyors of this practice believe that continually exposing children to unfamiliar and confusing problems will result in a problem-solving “schema” and that students are being trained to adapt in this way.  In my opinion, it is the wrong assumption.   A more accurate assumption is that after the necessary math is learned, one is equipped with the prerequisites to solve problems that may be unfamiliar but which rely on what has been learned and mastered.  It would indeed be amazing if we could teach students algebraic thinking skills devoid of the content that allows such thinking to occur. I tend to believe, however, that a proper study of this will show what many have known since the time of Euclid: there is no such royal road.

We simply can’t put the cart before the horse so to speak.  If we do we’ll continually have frustrated students on our hands.

Kids Experience Testing Success When They Grasp Basic Math

An interesting story at Education News:

A study recently published in The Journal of Neuroscience finds that a strong grasp of basic mathematical skills can serve as a good predictor of student success on the Preliminary Scholastic Aptitude Test. The PSAT is an exam designed to gauge student preparedness for the SAT and is typically administered to kids in ninth and tenth grade.

To reach these conclusions, Daniel Ansari, Associate Professor in Western’s Department of Psychology and a principal investigator at the Brain and Mind Institute, used functional magnetic resonance imaging machines to monitor the brain activity of high school seniors. The MRI highlighted certain areas being utilized by students who were doing simple math exercise, and activity in those regions correlated strongly with their PSAT scores.

Read the rest.

Now, how does the Common Core Math Standards help this?

With the Common Core State Standards teachers are moved to the role of a facilitator.  Barry Garelick wrote late last year that not only will the Common Core Math Standards actually complicate math for kids.

With 100 pages of explicit instruction about what should be taught and when, one would expect the Common Core Standards to make problem-solving easier. Instead, one father quoted in the aforementioned article complains, “For the first time, I have three children who are struggling in math.” Why?

Let’s look first at the 97 pages of what are called “Content Standards.” Many of these standards require that students to be able to explain why a particular procedure works. It’s not enough for a student to be able to divide one fraction by another. He or she must also “use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9, because 3/4 of 8/9 is 2/3.”

It’s an odd pedagogical agenda, based on a belief that conceptual understanding must come before practical skills can be mastered. As this thinking goes, students must be able to explain the “why” of a procedure. Otherwise, solving a math problem becomes a “mere calculation” and the student is viewed as not having true understanding.

This approach not only complicates the simplest of math problems; it also leads to delays. Under the Common Core Standards, students will not learn traditional methods of adding and subtracting double and triple digit numbers until fourth grade. (Currently, most schools teach these skills two years earlier.) The standard method for two and three digit multiplication is delayed until fifth grade; the standard method for long division until sixth. In the meantime, the students learn alternative strategies that are far less efficient, but that presumably help them “understand” the conceptual underpinnings.

I’d be interested as these are implemented if we see a rise in kids needing math tutoring away from school.

Common Core Math Standards Making the Simple Complicated

mathBarry Garelick wrote at The Atlantic about the Common Core Math Standards.  Basically he says that kids are required not to just learn how to make a calculations, but also how to explain why they are doing so.  The standards actually elevate this above learning how to solve math problems.  Garelick points out a couple of emails he has received as anecdotal evidence that the implementation of the standards are falling flat.

The first email was from a parent:

They implemented Common Core this year in our school system in Tennessee. I have a third grader who loved math and got A’s in math until this year, where he struggles to get a C. He struggles with “explaining” how he got his answer after using “mental math.” In fact, I had no idea how to explain it! It’s math 2+2=4. I can’t explain it, it just is.

The second from a teacher…

I am teaching the traditional algorithm this year to my third graders, but was told next year with Common Core I will not be allowed to. They should use mental math, and other strategies, to add. Crazy! I am so outraged that I have decided my child is NOT going to public schools until Common Core falls flat.

Garelick then goes on to explain why the Common Core Math Standards complicate math needlessly for students:

Many of these standards require that students to be able to explain why a particular procedure works. It’s not enough for a student to be able to divide one fraction by another. He or she must also “use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9, because 3/4 of 8/9 is 2/3.”

It’s an odd pedagogical agenda, based on a belief that conceptual understanding must come before practical skills can be mastered. As this thinking goes, students must be able to explain the “why” of a procedure. Otherwise, solving a math problem becomes a “mere calculation” and the student is viewed as not having true understanding.

This approach not only complicates the simplest of math problems; it also leads to delays. Under the Common Core Standards, students will not learn traditional methods of adding and subtracting double and triple digit numbers until fourth grade. (Currently, most schools teach these skills two years earlier.) The standard method for two and three digit multiplication is delayed until fifth grade; the standard method for long division until sixth. In the meantime, the students learn alternative strategies that are far less efficient, but that presumably help them “understand” the conceptual underpinnings.

Be sure to read his whole article.

Barry Garelick: Common Core Math Standards, A Mandate for Reform Math

Barry Garelick, a TAE advocate, wrote an op/ed for Education News.  Here’s an excerpt:

Mathematics education in the United States is at a pivotal moment. At this time, forty-five states and the District of Columbia have adopted the Common Core standards, a set of uniform benchmarks for math and reading. Thirty-two states and the district have been granted waivers from important parts of the Bush-era No Child Left Behind law. As part of the agreement in being granted a waiver, those states have agreed to implement Common Core. States have been led to believe that adoption of such standards will improve mathematics and English-language education in our public schools.

My fear (as well as that of many of my colleagues) is that implementation of the Common Core math standards may actually make things worse. The final math standards released in June, 2010 appear to some as if they are thorough and rigorous. Although they have the “look and feel” of math standards, their adoption in my opinion will not only continue the status quo in this country, but will be a mandate for reform math — a method of teaching math that eschews memorization, favors group work and student-centered learning, puts the teacher in the role of “guide” rather than “teacher” and insists on students being able to explain the reasons why procedures and methods work for procedures and methods that they may not be able to perform.

Read the rest here.