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The Math Crisis Starts in Elementary School

August 30, 2014 by .(JavaScript must be enabled to view this email address) at 06:30 AM


Following the appalling results of the latest EQAO report, we looked at the consequences of the low achievement of our grade-6 public school math programs. The kids that can't do grade 6 math aren't going to university to study engineering or medicine six years later, but it turns out that they aren't likely to be successful at a college either.

In 2011, the York-Seneca Institute for Mathematics, Science and Technology Education (YSIMSTE) published a report that reviewed the math load for various college programs across Ontario, both as stand-alone courses and math courses embedded into specialist courses such as accounting and electrical theory.

No surprise - they found that one needs some math to be a technician or a nurse, although maybe not calculus. However, a disturbingly large number of students at college are struggling with math that they should have learned in elementary school. And the colleges all realizing that, they are offering elementary-school math remediation courses. From the Seneca report:

"One in four of [students at risk of not completing due to low achievement in math] are studying college preparatory mathematics which covers concepts initially taught in grades 6 through 8 as part of the Ontario elementary school curriculum. These concepts include:
Order of Operations
Ratio and Proportion

The Seneca take-away is that it is our elementary schools that are failing in math education.  The problem starts very early.

Calculated Improvement

August 29, 2014 by .(JavaScript must be enabled to view this email address) at 07:09 AM

In trying to explain Ontario's poor math results, the Minister of Education betrayed her (and presumably the EQAO's) total lack of understanding of the problem when she said that the "students are struggling with problem solving, not basic math operations". more

Let me see if I have this right. The kids are using their calculators and manipulatives (allowed on the test) to get the right answers to the arithmetic questions, so therefore they are okay in arithmetic.

The EQAO officials and the Minister thus clearly have no understanding of the importance of fluency and automaticity when it comes to problem solving - even though mainstream research has long accepted this truth. Because working memory has a very limited capacity, when the kids tackle the problems they can't manipulate the numbers in their heads and get bogged down by their reliance on calculators and manipulatives. 

Here is a thought-provoking article from our archives. It concerns a school where the principal brought in school-wide math drills: the children increased not only their fluency and automaticity, but also their problem-solving skills. Here's what the principal of the school had to say.

"It is interesting to note that the use of the MATH program for just 10 minutes a day resulted in an improvement not only in basic skills but also increased achievement in all areas tested. It is my view that this is somewhat like the reading process. When a student is freed up from the laborious task of decoding most of the words in a passage, his comprehension improves. So in math: when basic computation can be done with speed and accuracy, more attention can be given to the process or problem. One of the unexpected results of the MATH program was the extent of the generalization that was evident in gains in math concepts and applications, including logical reasoning."

Lesson on Fractions:  One-Half isn’t enough

August 28, 2014 by .(JavaScript must be enabled to view this email address) at 05:18 AM

Ontario's testing body (EQAO) has released its yearly test results and grade 6 math is down another 3 percentage points. Click here for the highlights. Now just over half of the province's grade 6 students are deemed ready for middle school math (although of course they will all be promoted to grade 7 anyway, where they will struggle with math and drop it as soon as they can). 

Click here for Christina Blizzard's take on these results. She kind of says it all (but please note that Christina uses the word 'curriculum' to mean teaching methods and materials). H/T LDA

In Point of Fact

August 27, 2014 by .(JavaScript must be enabled to view this email address) at 05:16 AM

One of our readers has responded to our Remembering to Learn post about the importance of drilling to automaticity, suggesting that we post an excerpt from Daisy Christodoulou's terrific book Seven Myths About Education. The first of Ms Christodoulou's myths is FACTS PREVENT UNDERSTANDING, and here is an excerpt from pages 17-20.

"My aim here is not to criticise true conceptual understanding, genuine appreciation of significance or higher-order skill development. All of these things are indeed the true aim of education. My argument is that facts and subject content are not opposed to such aims; instead, they are part of it. 

"Much of the modern research into human intelligence was inspired and informed by research into artificial intelligence. To construct a machine that could think, scientists needed a better understanding of how humans actually thought.....'Our understanding of the role of long-term memory in human cognition has altered dramatically over the last few decades. It is no longer seen as a passive repository of discrete, isolated fragments of information that permit us to repeat what we have learned. Nor is it seen only as a component of human cognitive architecture that has merely peripheral influence on complex cognitive processes such as thinking and problem solving. Rather, long-term memory is now viewed as the central, dominant structure of human cognition. Everything we see, hear, and think about is critically dependent on and influenced by our long-term memory. 

"When we encounter a problem we want to solve, we can use working memory and long-term memory to solve it. 'Working memory can be equated with consciousness. Humans are conscious of and can monitor only the contents of working memory. All other cognitive functioning is hidden from view unless and until it can be brought into working memory.' So when we want to solve a problem, we hold all the information relating to the problem in working memory. Unfortunately, working memory is highly limited. There is some debate in the literature about exactly how limited working memory is, but some of the most recent research suggests that it may be limited to as few as three or four items. That is, we can hold only three or four new items in working memory at any one time. This places a huge limit on our ability to solve problems....

"When we commit facts to long-term memory, they actually become part of our thinking apparatus and have the ability to expand one of the biggest limitations of human cognition. Anderson puts it thus:  'All that there is to intelligence is the simple accrual and tuning of many small units of knowledge that in total produce complex cognition. The whole is no more than the sum of its parts, but it has a lot of parts.'

"A lot is no exaggeration. Long-term memory is capable of storing thousands of facts, and when we have memorised thousands of facts on a specific topic, these facts togther form what is known as a schema. When we think about the topic, we use that schema. When we meet new facts about that topic, we assimilate them into that schema - and if we already have a lot of facts in that particular schema, it is much easier for us to learn new facts about that topic.

"Critics of fact-learning will often pull out a completely random fact and say something like: who needs to know the date of the Battle of Waterloo? Why does it matter? Of course, pulling out one fact like this on its own does seem rather odd. But the aim of fact-learning is not to learn just one fact - it is to learn several hundred, which taken together form a schema that helps you to understand the world. Thus, just learning the date of the Battle of Waterloo will be of limited use. But learning the dates of 150 historical events from 3000 BC to the present day and learning a couple of key facts about why each event was important will be of immense use, because it will form the fundamental chronological schema that is the basis of all historical understanding. Just learning that 4 X 4 is 16 will be of limited use. But learning all of the times tables, and learning them all so securely that we can hardly not think of the answer when the problem is presented, is the basis of mathematical understanding. If we want pupils to have good conceptual understanding, they need more facts, not fewer."

A Conflict of Interest

August 26, 2014 by .(JavaScript must be enabled to view this email address) at 06:08 AM

On the right is a picture of the headquarters of the Michigan Education Association (teachers' union). It looks like an expensive building, probably a nice place to work in and costly to maintain. For sure, the union has lots of well-paid staffers with cushy jobs.

In 2012, Michigan became the 24th right-to-work state. This means that Michigan workers no longer have to belong to a union if they want to work at certain jobs, including teaching. However, the Michigan Education Association says it will use any means possible to hold on to its members - for example, the union will accept teachers' resignations only in the month of August (a fact not, of course, advertised by the union). more  more

This raises the question of whose interests the union is looking out for. I can't really see how it helps the union's individual members to prevent them from leaving when they want to. But it's easy to see that the union would be better off with the maximum number of members - more union staff positions, higher salaries, more clout, and so forth. 

What about the others?

August 25, 2014 by .(JavaScript must be enabled to view this email address) at 04:58 AM


I read with interest the piece on the Huffington Post website. It's a pity, but the fact is, that even though the schools and teachers know what the legislation is with regards to helping ALL students learn, in the interest of expediency they don't always adhere to the requirements. I have a lot of experience with this.

I became a teacher in 2002, so that I could help my daughter from within the system. She has a learning disability (Auditory Processing) that prevented her from handling the volume of work required in school. Nonetheless, she is a bright gal who has gone on to become an Early Childhood Educator.

Every year, I had to advocate for her, ensuring she was getting the attention that was rightfully hers. As well, I was her scribe and interpreter. Once things were explained in a different way, she was able to understand the concept. As she got older, she understood what she needed (she's extremely visual), so she would ask her teachers to present the information to her in another way. With one of her math teachers, she tried this; however, the woman was incapable of translating her work into anything other than the gobblygook written formula that made sense to people who learn with her own style, but not for those who learn visually. As you can imagine, my daughter did very poorly that year.

Another time, she was given a take-home art exam that even I had trouble interpreting (I'm a high school English teacher). The instructions for this exam were written in paragraph form with no highlighting. My daughter's reaction to it was, "It's just words, Mom." The words made no sense to her (due to her disability, she needs chunking of info and highlighted words for the main ideas). I compare her confusion to mine when I do a jigsaw puzzle. To me, those pieces are "just colours". Consequently, in order for her to complete her test, I was required to break down what the teacher was asking into separate questions.

I am an educated person who understands the limitations and struggles teachers face on a daily basis. Nonetheless, teachers have to be accountable to ALL students. Although I was able to help my daughter because of my own skills and abilities, imagine those students whose own parents had similar difficulties in school. Of course, these students would believe that school is "stupid" and the teachers are "idiots". If you can't even understand the instructions, how are you going to continue with the work?

My mother, who grew up in a disadvantaged home during the Depression, always told me that her mother was illiterate. Nevertheless, my mother stressed education for her children, so my sisters and I all have post-secondary degrees.

When I read your blog on the Huffington Post site, I remembered that this is one of my goals in life:  i.e., to help others have their children succeed too. (By the way, I have two other children. They were both above-average students who had little difficulty in school. The older did well in university and works as a Events Planner, while my younger chose the trades and is an Electrician).

Do you have any suggestions for me? Should I post blogs myself? Should I approach the schools to advocate from within? I am really concerned that all children reach their own potential and that the schools need to aid that path to success.

Sunday at the Movies (You Can Learn Anything)

August 24, 2014 by .(JavaScript must be enabled to view this email address) at 05:56 AM

Simple but profound.

The biggest bang for our bucks

August 23, 2014 by .(JavaScript must be enabled to view this email address) at 05:51 AM

We live in a real world where resources are limited. Much as we might like to, say, make it possible for every medical condition to get optimum treatment or ensure that no child goes hungry, there isn't enough money to do this. Therefore, we have to prioritize and spend wisely.

New Zealand's John Hattie stands ready to help governments make wise choices when it comes to education spending. Dr. Hattie has analyzed dozens of possible reforms in terms of which ones have been found to increase student learning, have no effect, or decrease student learning (yes, some do).  more

Reducing class sizes? Very small effect. Labelling kids? Negative effect. Constructivism and discovery learning? Very limited effect. Curriculum re-writes? No effect. Transformational principals? Negative effect.

Unfortunately, these are the sorts of policies that look good and appeal to politicians. Even more unfortunately, the single reform with the biggest pay-off when it comes to student learning is ... better teachers - something that politicians don't seem to be able to wrap their minds around. However, it's not rocket science.

Given that almost all Canadian teacher and principal recruitment and training, both pre-service and in-service, is dreadful, governments should be developing alternative routes to teacher and principal certification and in-service training. This is a reform that would actually save money while enormously increasing student learning.

Curriculum Guidelines

August 22, 2014 by .(JavaScript must be enabled to view this email address) at 06:20 AM


I was visiting a Head-of-Math at a Scarborough high school in the early 1990’s; he knew that two of his last-year graduates had enrolled at our college that fall and he asked how they were doing. I told him that they were two nice young men, but they didn’t appear to know any Trigonometry. He looked shocked and apologized sincerely; he said he had to guess which subjects the grads would need for further education and he had not taught them Trigonometry. I responded: “How could you not teach Trigonometry when it was clearly listed in the curriculum”, and had been since I started teaching in 1969. For our part, the Civil/Resources programs were designed to build on the abilities supposedly gained by the students in the high schools. No one at the Ministry had told us, at the colleges, that the curriculum was now only a “guideline’'.

The Head-of Math gentleman replied that “the Ministry document (curriculum), was not a curriculum, but only a guideline”. He further explained that when the province introduced the “child-centered” approach to education, elementary school grads came to the high school with very little preparation and could not work at the level needed for success in high school – the high school teachers were then told to consider the curriculum only as a guideline, and “just do the best you can” – this was in the 1970’s.

Without a background knowledge in Trigonometry – which included Statics, the students, at college, had little hope of passing subjects such as surveying, highway geometrics, statics and subjects in the structural design option. Other programs in the Engineering Technology Division had the same problems we did and the Division’s failure rates sky-rocketed as the years went on.

Finally, The Conservative Party, responding to suggestions from groups like the one I belonged to (EAQE), reduced Ontario’s elementary/secondary education to 12 years - as it was in most of the countries on earth. The logical way to reduce the number of years was to replace Grade 12 with the Grade 13 subjects down to Grade 8 which would become a variation of the old Grade 9. The old Grades 1 to 8 would be compressed to seven years. What actually happened? It seems to me that they simply lopped off Grade 13 and did very little to replace it. We never dreamed that something like that could happen in this day and age or we wouldn’t have suggested it.

This nonsense has to stop before we completely ruin our ability to compete with other countries  - who do value effective education (including learning how to think) .

All Kids Should Have the Same Opportunities in Education

August 21, 2014 by .(JavaScript must be enabled to view this email address) at 07:46 AM


Malkin's latest article in the Huffington Post is right on. Why is it so difficult for the heads of our system to understand that equality in the economic market begins with support for every individual according to their requirements! Not what some "authority" thinks is sufficient. Check out some very successful persons in our society and you discover they had to leave "the system" in order to become successful.

It is my belief and that of many professional people that failure to spend the time and effort early is the main reason for criminals. Two police officers spoke to some young people at our church and stated most teachers can identify future problem children by Grade 3. However, teachers claim they don't have the time, money and resources to deal with those problems.

Then why are we able to spend thousands of dollars later when the child comes in contact with the law. First, to make sure they get a "fair" trial and second, keep them in prison for years at $80,000 to $110,000 annually. Does that make sense? Why is that so difficult to see and understand?

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