Wednesday, September 7, 2016

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: 
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.


  1. This comment has been removed by a blog administrator.

  2. I will break this into small posts. I am a retired teacher with 32 years classroom experience. I have been retired for 4 years and now tutor. I am formerly from Co. Durham

  3. Ontario curric. uses vague and weak language. It does not emphasise that student should move from symbolic to abstract. I.E, from manipulatives and picture drawing to automatic recall of basic facts and thorough knowledge of topics. Language left very vague. No closure on topics and too long spent on single digits. The average student requires 4years to master fractional arithmetic. This curric does not provide enough time as most of work is started in Grade 7. Junior grades needs to be beefed up. Not enough time on simple algebra, decimals,percentage.

    1. I should have written "concrete to abstract" on line 2

    2. I lived in Gainford, Co. Durham.

    3. Near Teesdale? Beautiful place.

  4. Direct instruction is mentioned in the front pages of the curriculum that few read. But teachers are not supported in their direct instruction. Texts on Trillium List, materials provided from Ministry and school boards are constructivist. All workshops and PD I attended for 10 years was constructivist, as was that of others I have talked to. Grade 9 math teachers now get constrctivist (inquiry) PD. videos and other materials provided, authorized,made by the Ministry are constructivist. Data I collected based on a two week series of lessons I had to do as directed by principal and above were inquiry based. I never heard basic facts mentioned. It has crept back into the discussion over the last five years because of intense media pressure. Before that, the message was that Ss would not need those basics as computers would do that work. Public pressure has made an impact. Talk about 'balance' is disingenuous.

  5. My question is : Why is it that EQAO results are what put everything into question?
    I just can't quite accept that that test tells us everything we need to know about math success in Ontario. I have seen my students thinking change, I have seen their collaboration skills improve, I have also seen them become more curious, more involved and more passionate about their work. This to me are skills that will help them greatly and all of that has happened through the various strategies I use in class. None of that is evaluated by EQAO.

    Is a quantitative result enough to discredit the qualitative ones?

    1. Doesn't tell us everything is not equal to tells us nothing and can be ignored.

      A good question would be why doesn't increased passion, curiosity, and involvement result in better EQAO scores? Maybe it does and your sample is just too small at 25-60 kids a year in a population of 130,000 for grade 6.

      But either way are you really saying falling EQAO scores tell us nothing?

  6. The EQOA test is not a test of the basics, it is a test of problem-solving. I have never seen these tests, but have looked at sample questions. Knowledge questions are minimal. I strongly suspect that a Grade 3 student could earn a Level 3 on the EQAO test and be very deficient in fundamental arithmetic. This misleads parents. The EQAO is concerned with numeracy, not math as it is traditionally understood. Ss are to be prepared for future work; the emphasis on estimation,rounding, data, graphing, measurement. The PISA test is the same, perhaps less rigourous than EQAO. The Ministry, school boards, media , general public, admin. consultant, teachers, commentators, constantly conflate numeracy and math (arithmetic) as has traditionally been taught in elementary schools. Families pay a small fortune providing the essential funamentals for their children. Schools are providing numeracy and denying Ss equal opportunity. Colleges have seen a decline in arithmetic skills over the last 10 years (College Project). college math courses now routinely teach the arithmetic skills that should have been mastered in Grades 5, 6 and 7. Students pay for this course and they should have learned this material in elementary school

  7. My own children are 5 years apart and I have seen all the issues mentioned above play out at home. The younger one did not get the thorough grounding the older one did. Same school, same teachers, different approach taken. I see the same issues play out with all the students I tutor. Their parents pay me and their parents are well aware of the issues. Some of the students I have tutored have been mathematically talented, but were extremely frustrated because there were so many gaps in their knowledge. I have tutored from 2 boards and 2 different private schools. Multiple teachers involved. Always the same predictable problems.
    I taught 32 years, for the first 22 math ed. certainly had its issues, but I saw math ed. collapse. I am not just speaking about my class, but am basing my opinions on my personal experience of PD, thoughtful discussion, wide reading, from all perspectives. I have listened to parents, teachers, various experts and students. I have seen collapse.
    The devil is in the details.

  8. I am not advocating the fifties. there definitely is room for an inquiry approach, but it should be used much, much less, much more thoughtfully and it should be part of a structured, systematic and complete math programme. Math, not numeracy. There is nothing new under the teaching sun. Teachers have successfully and much more moderately used inquiry methods for decades. My own teachers used inquiry math methods in the sixties, but they used them very moderately and very thoughtfully.

  9. My views here are based on the thousands of concerns I have heard from numerous parents and teachers across British Columbia and Canada. As much as many consultants and proponents of constructivist learning try to make it sound how a balanced approach is utilized in the classroom, the truth is far from this perpetuated myth. The elephant in the room, which none of these believers mention, is the proliferation of tutors that many children now go to in order to learn their math facts. If a balanced approach DID exist, and if children DID master their times tables and learn fractional arithmetic in the classroom, why do hundreds of thousands of citizens/teachers/parents claim they do not? WHy do we have 4 math petitions across Canada - all asking that these fundamentals be taught properly in the classroom - be implemented in the curriculum, and the classroom?

    Many teachers have reported being unduly pressured to conform by over zealous Administrators who want 21st century learning in their schools. In all the flurry of Pro D workshops, i have YET to run across one which supports traditional, conventional methods for teaching math. Another "opinion" here by another "expert" does not change that.

    The evidence for direct instruction is overwhelming, whereas the link to the above "research" in the article cannot even be opened. I challenge anyone, to support evidence that empirically demonstrates direct instruction by the teacher, in the younger years, is not as good as other methodologies. In order to change that, one needs the 5 years I have been advocating for better math instruction, i have yet to read anything that would refute that.

    Another opinion blog doesn't really help the issues here. Get out and find out what the problems are in the home, and in the workplace. When employers report that 40% of their productivity is hampered by their employees' lack of BASIC skills such as arithmetic, it does not fill me with joy that we're doing something right.

  10. The argument provided here is a strawman. If you really cared to make your case you would take up Anna Stokke's challenge and counter her argument for 80/20 direct instruction verses discovery as the right balance. No informed critic of the status quo is making the arguments you claim.

    She also counters your correlation is not causation argument. Other scores such as reading have gone up while math has gone down and the time of the slide in math corresponds to time we have had the new curriculum. Sure that doesn't make it a certainty but it doesn't look good. To brush this off smells of blindness to even the possibility that the curriculum was a step in the wrong direction.

    Your arguments about what goes on in classrooms verses the curriculum betray the strawman in your piece. No one is arguing that there are no good teachers or no one is doing any direct instruction. The people who are arguing for change are not ignorant. They include many teachers who signed on to wisemath and other petitions and parents who got involved enough to see for themselves what is and is not done.

  11. As long as Ontario's curriculum does not mention addition & subtraction of fractions before Grade 7 and is handily outperformed in fraction-related material by by the US in both computational skills and comprehension skills ... I'll blame the curriculum (as at least one major factor) thanks, "Math Guy".