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Western Initiative for Strengthening Education in Math WISE Math 
Apart from the “discovery math” program I see extremely many weaknesses and strangenesses of the Canadian school math (comparing to what I was educated in my time in the late Soviet Union).
For example, looking into current Ontario math curriculum I see that the order of operations is supposed to be studied in the grade 6 and brackets in the grade 7. What kind of math is it if the students are simply unable to write or interpret arbitrary arithmetic expressions until grade 7? How the distributive law of multiplication over addition is supposed to be taught without knowing brackets?What about factoring a difference of squares or a square of binomial without being able to use brackets?
In Russia brackets were taught in the first grade and the order of operations, well, as soon as children studied multiplication i.e. somewhere in the 2nd grade. I see here constant complains that children do not know multiplication table or long division algorithm, but overall what children are doing here does not look for me as math at all, just some playing with numbers. This is a result of the fact that children are not provided with some very basic tools to express math facts.
Just wondering where was the Canadian school math before “discovery math” was introduced. I believe there may be some people here who may tell me in which grade brackets were introduced in 1970th.
On the other side, nobody tried to teach us “probability theory” (especially before getting any sense of what the fraction is and how to deal with them – this is what is going now in ON schools), no graphic data representation, all these bar diagrams etc. Just clear pure math starting from grade 1 where each topic was built upon previously studied topics and all the studied things were related and not randomly picked up.
Well, some other points. Using of base ten blocks until grade 8 (as ON curriculum recommends) looks so pathetic.Fortunately, they did not exist in my time and I never needed to learn that 1 is a small cube, 10 is a column and 100 is a big square and was not obliged to constantly deal with them (so I never had a problem to jump immediately to understanding millions and billions). In Russia manipulatives were abandoned after first 3-4 months of the first grade, as well as I can remember.
Textbooks are awful. Full of colorful pictures and photos which distract the student (some researches exist about that) and which have very little relation to the discussed topic. Extremely heavy (so no chance to get them to home and back to school). Mostly filled with extremely wordy explanations and almost completely lacking math contents as per one page of the text. The way topics are presented makes me cry. Each topic, whatever chosen is linked to “real life”. Just any. By any price of getting ridiculous. Multipage index in the end of the book enumerating all real life application of math. Of course, almost no relating the math to physics and other sciences. I am talking here about “MathPower” 9th grade book which was released in 1999 i.e. before the new “discovery” approach was imposed. Since that for what I can see, the textbooks got much worse.
In my good old days I could take 4-5 textbooks and put them into my school backpack. They were cheap, small, light, and full of very clever contents. They had pictures which did not distract. And math books were full of math, not of belletristic.
To clarify some point on why I so like light books: Today Canadian children have their big heavy textbooks stored in the class room. Parents have very little information on what is the current curriculum exactly, say, they cannot easily know what topics are missed if their kid was absent from the school. Also, from what I can experience personally, no class notebooks are brought to home and homework is given on some separate sheets of paper. Most of the time, no grade marks are shared with parents on regular basis. Everything is built as if the goal was to isolate parents from their children and to not allow them being involved in the teaching process. I personally… well, I even do not know if my child has science or math textbooks at all and what are they, unless I ask the teacher explicitly about that. In my childhood my parents had full access to my textbooks (which I carried to school and back to home), notebooks, grade marks. Well, times are changing and things should not always be the same, no doubt. But all this lack of involvement and control from the parent side looks very problematic for me.
So, to the bottom line. The system is completely damaged. The curriculum is inadequate. The books are good only for their publishers who charge $100 for a heavy colorful book. And well, they even are afraid to put any math picture on the cover, no formulas, no polyhedra, putting instead some photos of bears and squirrels and transmitting by that a message that math things should actually be avoided (!!!). Is it a just o coincidence that on such a soil you’ve got this “discovery math” grown up?
Tom Pankratz, British Columbia, Grade 8 – 10 Math teacher
The standards and the assessment tools are being removed from education. No minimum competency that is required. We discussed having no final exams. Facts and recall are out, skills testing is in. Already no-one can fail grade 8, they just go to summer school and go to the next grade… and if they do not go to summer school they just go to the next grade. Not supposed to assign homework. Only supposed to give 3-4 summative tests per year. No percentages allowed…
I teach Grade 8 Math in BC. From Grade 1 to Grade 8 students can not fail. They were kept with their same age peers. That means I receive 30 students into Grade 8, at least 5 of which have not met expectations in math for three years, in spite of support. I asked why they ended up in a regular Grade 8 class when it was already clear they did not have the fundamentals necessary for success. I was told “There is nowhere else to put them”. So they usually go through another year of not getting it and fail. That is not the real problem. Now those same students are sent to summer school and passed to Grade 9 regardless of whether or not they pass…
Why is there not a remedial class for these students?
Why can’t they fail?
Winnipeg, MB
Two other problems I see–
1. High school administrators who don’t ensure teachers have the credentials before assigning the course load (no, everyone can’t/shouldn’t teach grade 9 math).
2. What were once called “cheat-sheets”, now being allowed into pre-calculus provincial exams.
If readers want to be further worried, they should check out aspects of the BC Education Plan the government is attempting to push through by the late winter of 2013, in time for the provincial election.
I have concerns over the limited classroom time dedicated to grammar in the mid elementary grades. It was my experience that grammar was a daily, thorough,exercise-like arithmetic s to ensure the foundation for elementary education……..this issue added with the mathematics over complications in elementary school is just unacceptable…. .
I have been focusing on the general culture of the teacher training establishment, with most emphasis on its impact on general high school education. My own experience has focused on physics education, but the problems are very similar to those arising in math education.
Bad methodology is indeed relevant (I taught my own children to read at age three using Dr. Seuss and they were reading newspapers by the time they started school.) but my emphasis is more on teacher’s knowledge of content. Some observations.
1. Several years ago when I was a member of the Science Council of Canada’s Committee on Science Education, I discovered that some Canadian physics teachers found Newton’s Laws of Motion too abstract for their personal comprehension and invented their own replacement laws of motion, which were fundamentally Aristotelian physics.
2. While co-supervising a PhD student in physics education I discovered that objective research in the Faculty of Education could mean making subjective observations on class-room dynamics and then objectively counting the incidences of various observations.
3. When I was chair of the Graduate Class Review Committee at the U of R I found that a series of four new math classes requested by the Faculty of Education for their graduate level covered the same material as did one math class at the second year level in the Department of Mathematics. I was not able to prevent their approval.
4. The Canadian Association of Physicists had set up a Canada-wide physics scholarship program based on the results of a physics examination. Saskatchewan and Manitoba consistently under-achieved on the exam. Some of us in Regina set up a program to assist students who wished to prepare for the exam. We set weekly physics problems, marked submitted responses and published the correct solutions. The list of participants was dominated not by physics students but by physics teachers.
5. I taught first-year university physics for roughly 30 years. From that and from some of the forgoing it became clear that high school physics teachers viewed their task as one of “shoveling” a list of physics equations into students until they were full. Comprehension of the concepts behind the symbols in the equations and the implication of the equation itself received too little attention. The consequence was that students learned to approach the solution of physics problems by searching for equations with symbol related to the words in the problem, rather than by recognizing the physical concepts in the problem and the laws and theories that connected them. In effect, first-year physics primarily involved unlearning the sloppy mental habits that had been imparted in high school.
6. During the years that I sat as the Faculty of Science representative to the Faculty of Education’s faculty meetings I came to realize that Faculties of Education had come into existence because teachers had noticed that professions like law, medicine, engineering and business admin etc. commanded both more respect and more income and that they had four years or more of university level educational/training, and that teachers such as my mother and mother-in-law had only one or two years equivalent. Teachers decided to move to four-year programs but they didn’t have enough material to fill four years of education/training or their own professional jargon that helps identify members of a profession, so they filled up a four-year curriculum with a combination of newly invented “edu-babble” and diluted versions of academic subject matter that seems to channel people into Faculties of Education who probably don’t belong there.
I hope that you might find the foregoing supportive of your efforts to improve the enterprise of education.
Bev Robertson
Professor Emeritus, Physics, University of Regina
It is clear from Professor Robertson remarks that the problem lies with the Faculty of Education. It seems it is carrying empty briefcase to impress itself (most of us know it has ” edu-babble” ). The bad news is that professors from the Faculty of Education exert a great deal of influence in setting the direction of K-12 curricula.
One solution is to have a student complete an undergraduate degree in the faculty of the chosen discipline and then do a diploma in the Faculty of Education. We need to look at the root of the problem: the Faculty of Education.
Richard Askey, Professor of Mathematics, University of Wisconsin-Madison
Here are two links to comments on mathematics education in Finland from some university and technical college mathematics faculty.
http://solmu.math.helsinki.fi/2005/erik/PisaEng.html
http://solmu.math.helsinki.fi/2005/erik/KivTarEng.html
and a translation of a letter from thousands of Dutch university students in mathematics, physics, and computer science.
The problems are world wide and I am very pleased to read about people looking at these problems in Canada.
Lievemaria.nl was an initiative launched in early 2006 by all of the mathematics and physics student associations in the Netherlands. Following this action, on Tuesday, January 24th, then Minister Maria van der Hoeven adjusted her plans with regards to the second phase.
(See the latest press release, the e-mail conversation with a representative of the Minister, the exam that the MPs were presented, read the real letter
(pdf) or the short version below.)
We are angry. We see that we really can not function at the university level. Situations occur everyday where we find we have had too little math during high school. Because of this we have to take remedial courses, or even quit our studies. We hear that complaint from our teachers, but what can we do? We wish we had had more math in high school.
Now you are busy renovating education. Good idea! But we heard that you plan to give even less math. If you go ahead with that, then the new students soon won’t understand anything! It seem like a better idea to just give more math! We hope that you will consider this.
Sincerely,
10,000 students (mathematics, physics, and computer science)
Ottawa, Ontario
I think it is time to bring back the Euclidean geometry (both planimetry and stereometry) to our high school math.
I was shocked to find out the textbook asks the students to measure the internal angles of a triangle and verify the sum is 180 degrees. Math is a deductive, not an experimental, subject. What if the measurement turns out to be 179 or 181 degrees? Even if the measurement is 180 degrees for this triangle, how can somone be sure the next triangle yields the same result? However, the Euclidean geometry offers at least two versions of simple and elegant proof for the theorem.
The Euclidean geometry is the first course for a high school student to truly appreciate the axiomatic nature of the math. It also serves as the foundation for trigonometry and analytic geometry (ironically both subjects are taught at high school without this foundation).
I started teaching my daughter the Euclidean geometry after I realized the deficiency in the curriculum. I am using Kiselev’s books translated from Russian by Givental which are rigorous and demanding. So far we have finished the planimetry and we will start the stereometry soon.
I understand it is hard to re-introduce the Euclidean geometry to our high school at this point, since this generation of the teachers had little training on the subject. However, if we don’t take action now, the beauty of the Euclidean geometry will be lost forever, and our children will mistakenly think math can be done by measuring rather than reasoning.
As a parent, and not quite as accomplished in math, I taught my child the proofs such as all triangles have the sum of 180 degrees and other such proofs, to elicit a deep understanding and appreciation of math. My child, who is now 16, has a solid foundation to draw from, when dealing with the disconnected math curriculum, and inefficient math instruction and methods. Once my child was taught the basic arithmetic proofs, as well as the many drills and practices, she rose from a grade 1 level at the end of grade 3, to being part of top achievers in grade 6 math. Take note, my child is dyslexic, and during that period climbing the achievement ladder, my child lost a great many marks because her methods were wrong, even though her answers were correct. Bring back the old methods, including Euclidean geometry and the other mathematical proofs. The proofs became the key, in unlocking my child’s math abilities, as well as her love for math. A subject that she once detested with passion, and when I handed her the keys of proofs and laws, her hatred turned into love. Now, she makes math look easy, and as a parent I am amazed how fluent and comfortable she is doing her math homework, her way – the old-fashioned way of when I went to school..
From Jamie Samson, Oakville, Ontario:
I support this initiative but would like to see your mandate broadened to include all of Canada.
Common arguments against what you are trying to do include how well Canada does on international comparisons and ‘drill and kill’ takes all the fun out of math. How well students are prepared for post-secondary education is more important than how Canada does internationally. Showing factual information on this would be interesting. Doing calculations using pencil and paper is ‘fun’ for some students. Removing this from math education in an attempt to make it more ‘enjoyable’ for some students hurts the ones that need math the most. These are the students that will take courses like science, business and skilled trades.
From Frank, Saskatchewan:
Firstly, I do support what is being said. However the true lack of knowledge lies in the fact that there is a no failure policy, up to grade 9, in many school divisions. This creates a bottle neck in grade 10 lowering the strength of all students because the level of expectations lowers, simply because the teachers must show basic math operations, as well the teacher must also teach work ethic, due to the fact that the students haven’t been forced to stay behind in order to build their knowledge. I find that we should question the no failure policies more than anything.
As a retired high school math teacher, I totally agree with your comments. After the no-failure policy was introduced we soon noticed a sharp decline in the abilities of our incoming students from the elementary schools. Many students openly stated that it was a “free ride” into high school and that they did little or no work in the elementary school. Sadly, they hit the wall in high school math and most are never able to recover being so far behind. The cause was yet another ill-conceived idea that was mandated by the Ministry of Education that demotivated many students. Trying to make students continually feel good about themselves has damaged a generation of students so far.
The next lunacy is the latest statements made by several Ministry’s of Education that the use of cell phones in class should be allowed. I fought against parents and students endlessly trying to ban them from my classroom. Many of the students wanted to use the phones to play games, text their friends or cheat on exams. It is as if the students needed yet another distraction.to lower their concentration and achievement.
From Brock Cordes, University of Manitoba:
When students arrive at our classes at the University of Manitoba, perhaps some form of additional entry evaluation should have been set in place to enhance the capacity of those students to move with facility beyond entry level.
Hi Brock.
As a matter of fact, we are working on precisely this sort of thing. There are ongoing talks at UM about an entry exam, and a realistic chance of it happening soon. There are many details to work out, such as its content, exactly what it provides entry for (probably single “gateway” courses) and what alternatives/remedies are provided for those who can’t pass it.
Further, we are engaged in incipient discussions with U. Winnipeg about having common entry standards, which we think will send a strong signal to the public schools. At some point we will extend these discussions to U. Brandon, for a potential trifecta comprising a de facto province-wide standard.
WISE Math (R. Craigen)
At University of Waterloo, we have a math preparedness test, which tests students on material they should have learned in high school, as well as some basic problem solving. Additional support is offered to those who fail. I believe in certain instances remedial classes are required. It is multiple choice and only two hours, so it is not terribly comprehensive, but it is a good initial scan and has fairly low overhead.
Thx Alex. Yes, Waterloo’s model is among those we’re looking at here. This doesn’t fix the curricular problem but it does create a line in the sand and communicate our expectations more clearly to those designing the public school curriculum.
I notice you haven’t JOINed our initiative yet, and I’m guessing you support what we’re doing. If you agree with our mission statement, post a comment to that effect on our JOIN page.
–WISE Math (R. Craigen)
1. CALCULATORS:
I agree fully with Krista Markwart that calculators should not be used until basic skills are mastered. Students develop a very unhealthy dependency on calculators. I believe that this is one of the reasons why we see increased anxiety in students entering university. Many students feel that they cannot function without a calculator. They don’t trust their own ability. Calculators certainly do not promote understanding. It may be appropriate to use calculators for the experimental sciences such as physics, chemistry and biology but there is no need to use them in mathematics. I feel strongly that the schools should NOT allow the use of calculators in mathematics classes. Instead they should promote the use of the standard algorithms for addition, subtraction, multiplication and division. Once children/students have mastered the skill of using these algorithms they will feel much less anxious without their calculators and their confidence levels will have received a boost.
2. SUCCESSFUL REPETITION (or EFFICIENT SKILL DEVELOPMENT)
I agree with Blair Zettl that successful repetition rather than mindless repetition leads to proper training. Using the music analogy – one can practice a piece over and over for many hours making the same mistake(s) every time one practices it; thereby reinforcing the wrong way of doing things and in the end either never learning to play the piece properly or else having to spend many hours unlearning what was not learnt properly from the beginning. Unlearning is far more time-consuming than learning it correctly the first time around. It is thus vital that children in their early stages of development are guided very closely. They should receive regular assignments that must be marked by the teacher. The child must be given regular feed back so that bad habits do not develop. Mastery at each step along the way before moving onto the next step is vital for proper development of mathematical skills. This approach too will result in much lower levels of anxiety.
3. SEMESTERIZATION:
Long periods of time without exposure to mathematics are detrimental to the development, mastery and understanding of mathematics. Many high schools have introduced semesterization. As a result these students may not see any mathematics anywhere from 7 months to a year. Once they start the next grade of mathematics they may feel quite overwhelmed since they no longer recall much of the mathematics that was covered the previous year and on which the next grade depends. This has obvious consequences. With too little time available to recall and understand what was covered the previous year a student may find himself/herself in the situation where they either capitulate saying they can’t do math or else they may try to recall what they learnt in the previous year often getting their facts confused which in turn leads to a state of panic, anxiety and helplessness. Just as a musician will not be able to maintain a level of mastery by playing her/his instrument for only 5 months a year a student of mathematics cannot expect to maintain any level of mastery if they do math for only five months a year.
4. REGULAR TESTING:
If other provinces can perform significantly better on the CMEC tests there is no reason why Manitoba’s students cannot perform better. I would like to propose some type of regular testing for the western provinces. This will give teachers and students an indicator on how well they are doing and an opportunity to improve the way they are teaching/learning mathematics. I would also like to propose more programs for gifted mathematics students so that our province can compare more favourably with other provinces in the upper levels of the CMEC results.
I’d like to support your comment on semestered high school classes. I have a BMath and tutor students in my spare time and typically I need to teach two courses simultaneously, last year’s course (because they didn’t do well), plus their current course. When they’re in a semestered class there isn’t enough time in a week to fill last year’s gaps and set them up for success no matter how much the student and parents want to succeed.
Our children need to learn their basic math skills before using calculators. I also don’t think a lot of the teachers teaching “Math Makes Sense” don’t know how to teach it or even understand it.
WISE may consider working the following into the Key Objectives:
1. It is SUCCESSFUL repetition that leads to proper training. As with music and language, mindless, careless practicing leads to confusion and bad habits.
2. It may be worth mentioning that, while utilizing software as a didactic tool may be helpful, parents and educators should exercise caution and scrutinize such products to ensure they follow the desired curriculum, and support authorized methodologies.
Hi Blair,
Thank you for your feedback. We agree on both counts.
Anna Stokke