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Sunday, 26 October 2014

What is "New Math"?


Last week my father emailed me to ask what I thought of Mr. Anthony Quinn who is running for one of our School Board's Trustee positions. I told my dad I would look up Mr. Quinn and then get back to him with my opinion. I found the following from one of Mr. Quinn's campaign newsletters that I would like to discuss here.



This "news" piece really bothers me because it is rife with misconceptions and incorrect information. The current Math curriculum that we use in Ontario was written in 2005 and is an updated version of the older curriculum written in 1999, so why it is being called "new math" is something I am having trouble understanding. An analysis of curricula of high-achieving regions around the world indicates that our Math curriculum is aligned with those that are the most successful in the world. But in addition, it is my understanding that the gap between our highest achieving students and our lowest achieving students is smaller than anywhere else in the world. 

I am also struggling to determine where the term "discovery math" comes from. I have been an Elementary school educator for 13 years, and until now, I have not heard that term before. I did a search of our Math curriculum document and I found the word "discover" in two places:

Students who are willing to make the effort required and who are able to apply themselves will soon discover that there is a direct relationship between this effort and their achievement in mathematics. Pg. 4 of the Ontario Math Curriculum, 2005

and 

Graphs and statistics bombard the public in advertising, opinion polls, population trends, reliability estimates, descriptions of discoveries by scientists, and estimates of health risks, to name just a few.
Pg. 9 of the Ontario Math Curriculum, 2005

Certainly, as you can see, the term "discover" does not figure largely in our current Math curriculum in Ontario. However, Mr. Quinn seems to be under the misguided notion that students are expected to "discover" math concepts on their own, which is very much NOT the case, and he would know this if he were to have a look at our Math Curriculum document. In fact, if he were to scan the verbs used in our overall and specific expectations for Math he would find terms such as: identify, describe, construct, create, analyse, compare, connect, extend, and determine, just to name a few. 

Mr. Quinn also has an italicized quote that suggests that students are not expected to know their multiplication facts. Quite the opposite is true. Here is an example of an expectation from our Grade 4 Number Sense strand:

– multiply to 9 x 9 and divide to 81 ÷ 9,
using a variety of mental strategies (e.g.,
doubles, doubles plus another set, skip
counting);

If someone were to ask me what is the difference between the expectations in the Math Curriculum currently being taught from what was taught in the 1970's I would have to say that when I was growing up, I was expected to have rote memorization of my multiplication facts whereas students today are expected to have conceptual understanding of mathematical operations and can represent them in a variety of ways, as well as use them to solve problems. 

Students today are not only expected to solve questions like ¾ ÷ ½ = ?, they are also expected to be able to represent a real-life situation where that expression would be needed to solve the problem. I wonder how many people educated in the 1970's are able to do that? I was taught "Yours is not to reason why, just invert and multiply". Students today ARE expected to reason and they are expected to be able to explain why multiplying by the inverse fraction provides the solution for the division of fractions. 

I have spoken at several schools' Family Numeracy nights as well as at the Halton Catholic Parents Conference and each time I begin by asking how many parents in the audience think of themselves as "Math People". Invariably, less than half of the people in the room raise their hands. I want ALL of our students to see themselves as "Math People". Learning Math the way I did simply did NOT achieve that result. So I disagree strongly with Mr. Quinn's statement about "fixing something that wasn't broken"; there was something very "broken" in the way that Math used to be taught thirty and forty years ago. 

As Dr. Christine Suurtamm said at a recent symposium I was fortunate enough to attend, the mathematical thinking we are teaching is so complex, we definitely do not support "discovery" learning. But we do support the generation of student algorithm. We are supporting students actively participating and thinking, not just being passive consumers regurgitating and performing rote procedures. Kids need to do the math to learn the math. They need opportunities to makes sense of the mathematical skills they are learning. If you look at the curriculum, you will see it includes traditional algorithms and mental math, and in addition, the thinking involved in doing the math. 

Our current EQAO data indicates that students are actually doing quite well in using procedural knowledge. The area they are having difficulty with is in solving multi-step multi-strand problems. No amount of rote procedural knowledge is going to help them think their way through these types of problems. Students need to have deep conceptual understanding of number sense, including operational sense, place value, and proportional reasoning to be able to successfully solve the types of problems they are currently struggling with. They need to develop a facility in composing and decomposing number.

Our students need procedural fluency, which implies much more than merely knowing their Math facts. Yes, they need to know those facts, but that is not enough. Procedural fluency is the ability to perform math operations flexibly and see the connections between those operations. Rote memorization of a procedure does not mean that you have conceptual understanding of that procedure. 

Do we need to learn more about teaching and learning Math in Ontario? Absolutely! We need to support our teachers in developing their own conceptual understandings and pedagogical knowledge in Math because they are victims of what I will call the "old Math". We need EVERY student to achieve at high levels in Math in Ontario and we are not there yet. I'm sure if Mr. Quinn took the time to read the Board's Improvement Plan, he would see that a philosophy of continuous improvement exists and that no one is suggesting "there is nothing we can do".

I am sure that if Mr. Quinn is elected as a trustee he will dedicate himself fully and devote himself to representing the voice of our parent population. I hope that he, and all of our trustees, will take the time to look at our Math curriculum so that they can provide the informed support that is very much needed if we are to improve student learning in Math.

I will leave you with a typical question from the Junior EQAO Math Assessment. I ask you to consider - could you have solved this question when you were in Grade Six? Can you solve it now?