Don't Blame the Curriculum

The announcement of Ontario's EQAO results was followed with a predictable tsunami of opinion as to what is wrong with Math in Ontario schools. The media looked to various 'experts' for their thought, many of whom criticised the 'discovery-based' curriculum as being the cause for low math scores. I noticed that many of those making these points are not experienced Ontario teachers with a working knowledge of the Ontario curriculum. I read that the teaching of facts is optional. I read further that the teaching of algorithms is frowned upon. I also read in one tweet that the real culprits were the educational consultants who were forcing bad methods on unsuspecting teachers and students.
Well, I am one of those consultants and have been one for nearly ten years. I have a Math degree and a Masters in Mathematics for Teaching from the University of Waterloo. In these last ten years I have worked in hundreds of classrooms with thousands of students from kindergarten to Grade 12. In doing so I have learned so many things that I wish that I knew when I started teaching in 1990: not that I was doing a bad job back then, but because I would have done a much, much better job.
I have also run various Math nights for parents in our school board, helping them get to grips with their own math phobias as well as giving them strategies to help their children with their Math.
As such, I feel that I have to address some of the myths that have recently been stated.

Myth 1) Teaching of Facts is Optional
No it isn't. It is clearly in the curriculum.

Myth 2) Teaching of Formal Algorithms is not Allowed.
No, they are there in the curriculum too.

Myth 3) The Ontario Curriculum is Discovery-Based.
No it is not. Read the front matter and it will say that direct instruction is part of good teaching. This (and the need for students to be fluent in their math facts) has been emphasised in many different sessions that the Ministry has run that I have attended.
There is a great word that is used throughout the curricula though: 
Develop
This is a much more powerful word than 'Give'. Sometimes, a student led activity will develop the formula, sometimes a teacher-led activity will be used.

Now I am sure that there are some people who want to argue that developing formula is 'discovery-based' and thus a waste of time, that we should just give the formulas to the students instead. This attitude (whilst bordering on elitist) is also easily disproved: when I have developed formulas with students and parents and then ask them 'Would you have preferred it if I just gave you the formula and told you not to worry about why it works, just memorise it?', they always reply 'No!'. 

Myth 4) Low scores are a result of the discovery-based curriculum
Even my grade 9 students know that correlation does not mean causation. Yet this is the conclusion I have seen many folk jumping to. Yet none of these people can back up this claim unless they have gone into the classrooms to see how math is being taught there. Even if a curriculum is 'discovery-based' (whatever that means) that certainly does not mean that every classroom will be discovery-based.

Now this doesn't mean to say that we don't need to improve Math teaching in Ontario: of course we do. We can always get better. As educators and parents, we need to actively seek out the most effective ways for teaching Math. Countries that tend to do well on international Math tests such as PISA and TIMSS have math curricula that emphasise both the conceptual and the procedural aspects of learning Math. This is backed up by research which maintains that these are bidirectional: it is not necessarily so that we need to learn all the facts and rules before we can learn to solve problems. Likewise, it is not necessarily true that all of our facts and rules are learned after we have solved some real-world problems.
And, of course, it is very important that students are given good opportunities to practice what they have learned. But what constitutes good practice? Again, research points strongly toward spaced practice. We need to think about how we can incorporate this into our schools.

Having worked in Ontario schools, I know that there are some brilliant Ontario teachers who are getting great results (EQAO and otherwise) with their math students. These are the people we need to look to when searching for answers on the best methods of teaching and learning Math. And when we do, we will see that there is a lot of common ground in the methods that they use to deliver the curriculum effectively.

So as an experienced, qualified Math teacher I will say this: it is not about 'back-to-basics' and it is not about 'discovery-based' Math. It is about balance. The Ontario curriculum (whilst it might need some fine-tuning) allows for this.