Sunday, April 15, 2012 | Categories: Episodes
On Cross Country Checkup: teaching math
As Canadian students continue to slip in international rankings of math skills, more children are being enrolled in tutoring programs to get them through the school year.
Is there something wrong with the way math is being taught?
With host Rex Murphy.Blog entry by Emily Burke
I struggled with Math. I had to go summer school in grades 11 and 12 to take Math (and English). Math is logic and rules. I put in high school year book, in ambition and probable fate, to get a PhD in English and Math. As a training Industrial radiographer I had to learn different series of time, distance and shielding using math.
Victoria, British Columbia
The absolute basics of math are not reinforced, so students are horribly disadvantaged in the world. We all know the young (and maybe not so young) cashier who cannot make change when the electronic cash register fritzes out. When I handed back quizzes in my university English classes--quizzes marked out of ten--quite a few students would whip out their calculators to determine the percentage. A young engineering student questioning his grade had no idea how to work out a percentage without using his calculator--I had to show him.
Most students will never need more than the basics of algebra, geometry, trigonometry, set theory, vectors, etc. They will need excellent mental arithmetic, a thorough understanding of banking, credit card company, and stock market practices, and training in financial responsibility. Most schools are teaching them nothing of the sort, so they are prey to the corporations, especially the credit corporations who rely upon their ignorance of compound interest.
Victoria, British Columbia
I was put into an advanced math program in 1958 taught by Mr. Batt. Future Engineers were going to be in great demand. The first thing he did for two weeks was to teach us English comprehension. How to read a math question. Periods and commas meant something and how to break down the question into manageable parts. Guess what. Our results soared.
North Vancouver, British Columbia
What I don't much understand Rex, is why kids in school don't start off counting money. Every kid knows money by the time they are old enough to begin schooling. Then go from there...
Victoria, British Columbia
A simple word problem for you:
Less money for education + parents not knowing the new way Math is taught therefore unable to help their child = Canada ranked #10 in the world. In closing, Until our government realizes that education is more important than War we will continue to lag behind.
Moncton, New Brunswick
I cannot help but note that our teaching of mathematics has been deficient for some time, as demonstrated by our own Federal government minister's inability to use basic arithmetic to add up the cost of an F-35 fighter jet.
I'm an engineering professor at Ryerson. We should be teaching math with modern tools. Tools like Maple allow us to show students general physical systems that automatically derive the underlying math behind them. This allow the students to see the system in motion *first*, then shows them the math that governs its behaviour. Most important, arbitrarily complex systems can have their equations derived, so we're not just stuck with the same three examples, all the time. Maple is produced by a Canadian company and it's one of the key math education products out there that can help us teach better.
First, I was the chairman of the math and science department in a private school and, more recently, a math and science tutor.
One of the things that I see wrong with math training is that in many cases the emphasis is in "rules and procedures" instead of realizing what math is a way of thinking and a way of communicating, precisely, concept and ideas between people. In many ways, math is a language.
As with any language, there are rules of grammar, memorization of vocabulary But an emphasis should be made into teaching people to translate from their language into "Math". One of the things I used to stress for my students is the ability to "think in math-speak", and had quite a bit of success with my students. As we progressed in more advanced content, it was so that we could express more complex ideas. "Word problems" actually became "translation".
As with any language, it provides another way of seeing the world, of thinking about it. It is not something that exists as something aside from everything else.
White Rock, British Columbia
It is not really hard to define what mathematics is essential. For everyday literacy, some basic rules, estimating ability, statistics, interpreting graphs, etc. This is akin to learning how to read at a basic level. Then there is the training for those who want to become mathematicians. Finally, there is math for fun: sudoku, puzzles, and higher level math. So there are math users, creators, and consumers. Our society needs to change its attitude towards math. Many otherwise intelligent people say openly that they were "never good at math." Imagine those same people saying "I was never good at reading." This would go a long way towards making math mainstream. Actually, young children love numbers and patterns.Teaching methods prescribed by education boards can of course turn people off. Math need not be drudgery.
I was a victim of the "New Math" in the 60s and only survived due to the intervention of my Grandfather, who had taught Math for many years. I learned more in two cram sessions with that old man than I had in 11 years of misguided trendy revisionism.
Although an Olympic-class curmudgeon, Grandpa maintained that the supposed inferiority of girls when confronted with Math was an unfounded concept and that girls, properly taught, could manage Math as well as could boys.
I wish I had taken advantage of his expertise earlier; he had held back on assisting his grand-daughters, wishing not to confuse them with his "old-fashioned" methods.
My late father-in-law, a retired sea-captain, was an unofficial Math teacher on the Isle of Barra, teaching navigation. He was able to entrance the most recalcitrant pupil into the world of Math by stealthy means, dressed up with the romance of the High Seas.
My experience tells me that innumeracy in Canada and Scotland, for that matter, is no new phenomenon and that a return to unfashionable methods, put in practice by excellent teachers, couldn't possibly hurt!
Liverpool, Nova Scotia
As a secondary math teacher starting in 1978, and currently a tutor I have seen great changes and not for the best in our mathematics students today. Students do not know their number facts and have to multiply 4 timers 6 using a calculator in Grade 11 Academic (the highest level in Ontario) They have no idea of how to handle fractions. We do not have time to teach them critical thinking because we now have, since 1999 a way of evaluating that includes 4 categories and each school can decide how to weight the categories. Teachers no longer have to prove they can even do the math while in Teacher's College as I had to do in 1977. Many teachers of math at the elementary level have no training beyond what they had to take in high school which up until 1999 was 2 credit courses. Students coming into Grade 9 math are therefore often afraid of and unfamiliar with the concepts they should know. The other major problem is the high school curriculum has changed drastically in Ontario and I find as a tutor that many secondary school teachers do not stay current with the curriculum as it is today in 2012.
I had the pleasure last week to drop into a grade three classroom where students were excited about math. They were sharing math equations that they had thought up for a number that they chose. Some students were using concepts well above the curriculum square roots, factorials, division, the Fibonacci series, fractions and decimals. Others were operating at the curriculum level but showed real number sense as they shared long mathematical sentences involving both adding and subtracting. There was excitement in the air. Most importantly, with only one exception every child knew his or her facts. The learned their facts using multiple strategies and they did know them automatically.
In the early eighties I helped start a Montessori preschool in Naramata, BC as I had a 3 year old daughter. Part of the reason I got involved in Montessori is the way they taught Math, and I wanted my daughter to have a different experience with math than I did. She loved using the special Math materials, such as the Golden Beads, which provide hands on visual experience of the decimal system. I still have some of her carefully done pages where she added up ten digit numbers, using different colors and columns, and she was starting to understand multiplication and division, all while "playing" with the wonderful materials that Montessori uses to teach Math (or any subject for that matter.) She loved math and was well on her way to learning it, all before the age of 5.
Unfortunately, the school closed so she went to first grade at the local elementary school, where math was taught in the usual way, and part of the program was a daily "Speed Drill". In order to get a sticker by your name, which was on a chart on the wall, you had to get the problems all right within the time given, and if you didn't, no sticker. Erica did not know how to deal with this type of "learning" and Math became something associated with stress, failure, and public humiliation, as she had no stickers after her name. Within the first weeks of first grade she came home telling us she hated school and wasn't going back. These feelings about math stayed with her for the rest of her school years, and it is bittersweet to remember how she used to love it.
Learning abstract concepts like math is greatly helped with hands on visual way of practicing the skills, especially in the early grades. It is the same with language, or any subject. Positive reinforcement vs. testing and feelings of failure is the key. Learning should be fun and fulfilling too.
Let's all get together and save the CBC from the current cuts. We need shows like yours to keep us informed and thinking.
Armstrong, British Columbia
I have not used my real name on the contact information because as a teacher I have not jumped whole heartily into the math program our district has spent a fortune buying into. I use to love teaching math. I would explain everything using manipulatives, it is easy to do at the elementary level. (The hardest concept to teach is dividing by numbers smaller than 1 at this level) The program we are supposed to use now unnecessarily complicates things, is brutal for bad readers, and lacks opportunities for practice.
None of this is required by the curriculum. After a few years of trying to be loyal to program, I now just teach to the curriculum and expose the students to the program so they won't be lost in coming years. The curriculum says that the kids should be memorizing the facts, so do it.
The publishers have made a fortune selling textbooks. They will love this discussion and the push in the media. That means they can come out with a whole new set of 'new' textbooks and make another fortune.
As a parent of a student who just finished the system with straight A's in math, his/her traditional powerhouse teachers that ignored any airy fairy programs are the ones that kept him/her on track through his/her 13 years in the system. He understood why, his teachers could explain.
Prince Rupert, British Columbia
Students have been getting the wrong end of the yardstick forever with the very notion of a classroom. The idea of a class room full of students is a matter of economics rather than caring, compassion and reality. Every one of my private students is different, has different experiences, different talents and different communication skills and so every one of my students over the last thirty or more years has gotten different exercises, different pieces and a personal level of attention unheard of in the poisoned political "public" education system where the opposite of the old cliché apply, the needs of the few, or even the one, outweigh the needs (of the economy) of the many as far as music education goes, and if it is even taught anymore.
The discussion so far today more than supports my conviction to be a private music teacher rather than a public one, a hopeless shepherd in a field of mediocrity that is the public system.
I am the chair of mathematics at an Ontario secondary school.
The teaching of mathematics has been damaged by several factors: the prevailing use of calculators since early elementary school, the curriculum being tied to graphing calculators and computer programs, the rise of standardized tests and the decline of enrolment in computer science courses. The usage of calculators at all levels degrades fundamental understanding of how numbers go together. This leads to students not understanding fractions or integers, which damages all further mathematics concepts. Standardized tests mean that we spend more time teaching towards the test and less time teaching the reasoning behind the concepts. The declining enrolment in computer courses means that there are less courses that back up the concepts of algorithms and logical thinking.
Teachers teach the curriculum mandated by provincial governments. As ridiculous as it sounds, teachers are our students' first bastion of defence against the will of the ivory tower. Provincial governments are in the business of having students succeed, by which they mean pass their courses and graduate. They are not in the business of giving our students quality education. The only people doing that are teachers who maintain their integrity and standards.
I am extremely grateful to the Edmonton Public School Board for the alternative programs that are publicly funded. My 14 year old daughter has been in specialized programs since kindergarten, and I am convinced that these programs are largely responsible for her academic success. From K-Grade 6 she attended an academic program called Cogito, and now in junior high she attends a girls program called the Nellie McClung Program. We could not have easily afforded private school for our daughter, but if these specialized had not been available, we would have found the money. I do not feel that the teachers in mainstream programs have the time or resources to give our students an even adequate education. As far as "rote" memorization goes, (I hate the term) I would have never gotten through my Physical Therapy degree if I had not memorized anatomy and physiology!
Listening to today's discussion, it occurs to me that we all "memorized" the alphabet by singing the ABC Song. Singing is fun and it never felt to me like "memorization"; it was just singing a song. I have always struggled with memorization and would have welcomed a song for the Times Tables. Is there such a song? If so, why isn't it used to teach the multiplication tables? Why isn't it widely known? If there is no such song, why not? Is there no musician anywhere who could write it?
Metchosin, British Columbia
I could tell you a long story about the frustration of getting a basic education for my child from the public school system in Vancouver. However, suffice to say that I've been "forced" to take the job on myself - in spite of the fact that I already have a full time job. One point I'd like to make is that there's no reliable testing to make sure that the schools are effectively covering curriculum that's been prescribed. Letters are sent home to parents from the classroom teachers every year before the uniform testing saying that it's a disservice to the kids, schools, and teachers to allow the children to take the tests and this letter is accompanied by a permissions slip that opts the kids into the test rather than opts them out. So there's no accountability. Does your guest have an opinion about the politics of the situation?
Vancouver, British Columbia
I am a father of a grade 7 girl. We were assured, like previous callers, that we shouldn't worry - that our daughter's multiplication table skills would "gel" in later grades. Interestingly, she did very well in grades 1 to 4 at which point we identified her inability to multiply to a "9 x 9" level. We began drilling her at home and bought a computer program which was entertaining enough to engage her and she has managed to attain a reasonable proficiency. However, the struggle delayed her development of other skills, particularly division.
Some years back, BC experimented with something called "whole language" geared toward teaching basic language skills. Children were encouraged not to worry about spelling (perhaps in some prescient anticipation of the telephone texting which would not arrive for another three or four decades ), but rather to focus on "whole words" . Many, many children did not learn to spell let alone read competently. The program/approach was dropped and with the benefit of hindsight might be viewed as a failed "experiment" on a huge cohort of kids.
The whole language experiment failed. I feel that our kids are, or have been, subjects in a similar "experiment" with respect to math. Stop! We Must return to fundamentals and ensure competency with the times tables, along with at least addition, subtraction, and division, during the first 3 or 4 years of school.
Forest Grove, British Columbia
When I was in primary school in the 1980s, my mother would get me to help her in the kitchen. I would be asked to figure out how much of each ingredient we would need to make some multiple of a batch of some recipe. For example, if the recipe called for 2 cups of flour to make 24 cookies, how much did we need to make only 12 (or if I was lucky, 48!). Similarly, when we went to a fast food restaurant, I would be told that I could get whatever I want (within reason, of course) as long as it cost less than such and such an amount. I had a vested interest in knowing my math and how to apply it! We cannot simply offload all of the responsibility for math instruction to teachers and blame the school system when the progress is poor.
Burnaby, British Columbia
My Grandchild was having difficulty with exponents. Honor student. I Helped him and discovered the textbook was atrocious. As I liked math and was good at it I was appalled. It was like a horse designed by a committee that turned out to be a camel. At the same time I was alerted to a website called Khan Academy which was developed by a Ph D in physics after he was helping is nephews and nieces with their homework and discovered what a dogs breakfast the system being used was. He is being funded by either Microsoft or Google and now has instruction up to and including university level math and physics courses. I can attest to the fact it is absolutely remarkable and have passed it on to many people in the education system as well as students with great results. The system is free and they have a method to let any school the want to use this system. You may not be surprised but to my knowledge the only schools that use the system free are the expensive private schools that are not controlled by unions. By the way my grandchild moved from a 70 in math to the 90s.Thank goodness we have someone leading the way out of this math conundrum and every one of our schools could be using this instruction.
As a secondary school teacher with 20 years experience and the father of five teenagers I am amazed that we continue to believe that the model of instruction where student's do not have control of their learning and yet does not achieve results is perpetuated. The Khan Academy offers free online tutorials that have been used by a variety of primary and secondary institutions and my own kids to good effect. Check out the TED lecture. Very useful tool!
It is not uncommon for students in my grade 10 Jr. Engineering to not know what 1/2 of a 1/2 would be - some students cannot successfully complete the first drawing on the first day due to their weakness in math - I regularly offer my own CAD & Engineering students a financial bonus of $144 to learn their 12X tables with the caveat that they fail the course unless they successfully memorize - Parents often respond angrily to me that their child does not need to know their 12x tables and mind my own business!
Quesnel, British Columbia
I found the majority of students who didn't graduate and are now adults don't know very much Math. If I ask, what is 7 times 8, it will take some adding to find out. After the answer of 56 is arrived at, if I then ask what is 8 times 7, there is another ling calculation. If I then ask, how many 7s are in a 56 or how many 8s are in 56, there is no understanding that they already know the answer.
The answer to 3 times 8 takes less time to figure out than 8 times 3 because 8 plus 8 is 16 and then 8 more is eventually 24, while 3 plus 3 is 6 and then 3 more is 9, etc. The question 8 plus 3 is easier to calculate than 3 plus 8 when your only strategy is to count.
I think understanding math is important and so is acquiring the basic tools that assist in reaching the understanding of concepts.
Good luck with the pendulum that has swung so far.
You ask about the joys of mathematics. I'm a young actress in Vancouver, I have a B.F.A. in Film and Theatre. I graduated from high school almost ten years ago, so it wasn't that long ago that I went through the B.C. system. My brother, much older than I am, has a PhD in Physics and was always very, very good at math. I was never gifted in the subject. I was near the top of my class until about mid-high school, but I never enjoyed it, and often repeated that common refrain of, "Why do I need to learn this when I'm never going to use it as an adult?"
But, you know what? In first year university I realized how wrong I was. Since high school, my everyday life has required me to use more math than I ever would have guessed as a teenager. I've used long division in film editing; fractions and trigonometry when I renovated my house; arithmetic in my head every day as I calculate event costs, create production budgets, count cash; percentages whenever I go out to a restaurant or bar. I do use calculators occasionally, but as much as possible I do it in my head -- it's usually faster.
I disliked math as a child, but now being able to work these problems out successfully fills me with pride and satisfaction. There's a real joy to working through problems and finding tidy and neat solutions.
As a visual learner, the real clincher for me was when I discovered the abacus. I already knew my math basics - times tables, etc. - but learning a new way to implement them, with my hands and in front of my eyes, made everything so very clear. I don't know why this tool has been so completely abandoned by the western world that I hadn't a clue how to use one until my mid-twenties. I wish visual-learning children struggling with arithmetic had ready access to these.
Great program -- I listen most weekends.
Vancouver, British Columbia
I worked on Provincial Curriculum from 1969 to 84. I am just completing 50 years of teaching mathematics, mainly in Ontario, from elementary to teachers College and first year university. Since retiring 16 years ago I have run a program for students who love mathematics. We have about 300 registered this year. My first comment is that Mathematics is not just a utility subject. Let students enjoy the History and people of Mathematics. The Ontario Math curriculum is boring and out of date. Trig is still being taught as if we were in the nineteenth century. Teachers are not given the opportunity to share the mathematics they enjoy, as the curriculum is totally prescriptive. I could go on, but my main request would be to let good teachers teach what they want to, as long as the basics are included. A guide would be prescribe two thirds and leave one third to the teachers. Unfortunately with semestering and no grade 13 time and continuity is at a premium. Math contests are a great way to inspire and encourage students. I have had several student on the Canadian International Mathematics Team.
I am a third year education student at the University of Winnipeg, and although I believe there are deficiencies in Manitoba's math programs, I do not think a step backwards to rote learning is the answer. Using rote with children does not teach them skills, it teaches them how to regurgitate information. Students need to learn to use all resources, and yes, that may mean a calculator, to grasp both simple and complex concepts.
I'm a Math/Physics teacher in Vancouver. In my experience the provincial requirements have been in obvious decline (in both math and science) for the last 20 years. I don't put up with it. I still make the students follow the more stringent requirements from the early 90's. If things don't work out for people it is nothing to do with the students and their abilities-genetics don't change on that sort of time scale! A common practice is to "change the curriculum" in each grade and-in the process-drop some aspect like geometry or logic. Ridiculous. Teaching is messy and doesn't work the same way for everyone, but it certainly doesn't get better by watering down the subject area.
Vancouver, British Columbia
I teach chemistry at university and see a lot of problems with the math skills of students coming in. Don't get me started on science instruction. Sticking to math (and many other topics) I believe that many issues are due to the need for instant gratification that many people have and a tendency for people to look for the easy route. We have many tools that make our lives easier, but we rely on them too much. With math this is the calculator. Students have no business using calculators until they get to higher grades where they are dealing with combinations, permutations, statistics, scientific calculations with enormous and tiny numbers, logarithms, and trigonometry. The problem or solution lies so much with the teacher. Here is a horror story... One of my wife's colleagues has a son in grade 5 or 6. The class was working on math problems and this student was (as he should have been) doing it all correctly in his head. The teacher, rather than celebrating this, said to the student something along the lines of "stop being an arrogant show off doing this all without a calculator". This teacher and ones like them are also a big problem. The sooner they're removed, the better.
Before I get to my main point; the reason estimation is being taught is that when you get to the finding the answer - the estimate will let you know if your answer is reasonable (for example, if you estimate that the answer will have three decimal places, but your answer only has one, then you'll know that you had a problem in your calculations). Teachers who accept the estimated answer are not understanding what estimation is for or not explaining it clearly to their students and parents.
As a new teacher (24 years ago) teaching a split grade 5/6 class, I learned math all over again from the text book and I learned why I got the answer (such as multiplying or dividing fractions). I had many A-HA! moments when all the learning during my elementary school days finally made sense. We need a balanced approach to math - time to learn math with manipulatives to learn how and why we get answers and time to practice. I can truly say that in the Ontario curriculum, there is no time to revisit and practice concepts. The curriculum in all areas is so busy that teachers are rushed to get through the content. Children don't learn at the same speed and using the same learning style, the curriculum needs to be simplified so that the most important topics need to be taught with the appropriate time given for learning and practice.
What some people don't realize is there is quite a bit of research which shows doing multiplication tables and learning cursive (another process deemed antiquated) improves brain fluency, fine motor skills and focus. I had the opportunity to sit in an elementary school classroom recently (I'm a secondary science teacher). In the class there was a flip chart with instructions on ways to think out how to figure out simple math problems. For example 8 + 13 was broken down as follows: 8 plus 10 is 18 then if you add 3 it is 21. What shocked me was that is how I naturally worked on math problems. It was never instructed, it was a coping skill that I personally developed. I don't believe I would have responded if I was taught this. For each problem I had a set of methods that I would apply depending on need. They were abstract and worked for me, I would never expect my students or my own children to work that way. They need to find their own path, and be provided with the basic skeleton of skills to personalize and develop their own methods
Vancouver, British Columbia
Here is my story, recently I was waiting my turn in a medical clinic and there was an elderly couple sitting beside me. The man had had a stroke and his female partner was giving him a math exercise. Nothing very difficult, simply counting backwards from 100 by 2 he did quite well until he got into the 80's there was a young girl sitting there as well she was a university student and she exclaimed that she was unable to do that simple task without a calculator. Everyone was shocked I asked her was she did for a living and that is when we found out she was a university student specializing in special education I simply couldn't help myself and exclaimed god help us all
I am a mother of grade 12 student. I am an engineer , and I was educated in Poland, where the attitude towards school was quite different than in Canada. Grade school children know it is their job and their duty to study and do as well as they possibly can. In Canada my daughter brought home the attitude of " what's wrong with being average?" which had completely stunned and terrified me. We need to expect and demand more from children in grade school. More work, more practice, more results. An average grade 6 student in Poland would definitely have much more math skills than an average grade 9 or even 10 student in Canada. I think this is a problem.
High school system is not helping either. My daughter had math in grade 10 fall semester, then the next math subject she opted for was spring semester in grade 11. The developing mind of the 16 year old was not exposed to math for a full year! This is a fundamental problem because math should be taught in smaller portion but regularly.
I have home schooled my children for several years, from mid-elementary to high school. I chose to use the Alberta curriculum because we have provincial achievement exams, and they need credit for high school math. What struck me is how much is in the curriculum. Where is the time to drill basic concepts? In high school they introduce a concept, give a couple of questions for practice and move on to the next, more complex concept. What they learn in high school is way beyond what I learned in high school. Are students supposed to be way smarter than we were? I'm not sure the average student is capable of absorbing everything they are supposed to. Hence students taking remedial math classes after high school.
As a math tutor I teach "old school" methods. Rote, memorization, and lots of practice. I struggled in math all through school. I did graduate Grade 13 with 3 math courses. It all came together when I went to college. I had a great teacher and managed a 90 % in his advanced calculus course. So when a student struggles I feel for them. I use all of my old textbooks from the 60's and 70's. My students always ask me "Why can't our textbooks be this good". Our textbooks in Nova Scotia are "garbage". The methods of discovery used in math are really poor. It took Pythagoras 17 years to develop his theorem and the school board wants students to do the same thing in 3 periods. It's time for parents to take back the education system from the bureaucrats.
Lawrencetown, Nova Scotia
Not enough focus is given for the kids to learn the basic math skills before they get into the more difficult math. These days word problems are a large part of today's math. Not enough time is allowed for kids to learn the new skill before they are forced to go on to the next. Therefore, when you have a kid with high functioning Autism, you are forced to hire tutors to teach the skills at a cost of 3000.00 per year. the govt. haven't listened to the math professor from MUN.
Spaniard's Bay, Newfoundland
One problem is that too many students are forced in to school before they are ready. Then, when they have problems they are passed on from grade to grade with less and less understanding as they go along. When they reach high school they then fail the courses. Some students need to start school later and some need to be held back until they are at grade level. Only then will they succeed and be able to live up the inflated sense of self-esteem with which their parents have endowed them.
Here's what happened to my nephew in the primary school system. He graduated from Gr. 12 with a secondary school diploma but had no math skills whatsoever. The system basically passed him through each grade without failing. When he graduated and tried to find work he found out that his lack of math skills were so atrocious that he was unable to get employed. He wanted to get into plumbing but his math skills were too weak. He decided to improve his math skills by signing up at Oxford Learning. Their assessment was that his math skills were at a grade 7 level at best. He was so discouraged with having to learn with other students who were 13-14 years old that he became extremely depressed. He was going thru a difficult time in his life and this additional humiliation sent him spiraling into depression. In the end he took his life. I blame the school system. Virtually none of his teachers took any time to address the issue head on. They could not care less. The elephant in the room, which no one wishes to speak to, is the PhD's who 'dream' up the curriculum and appear to be completely divorced from the actual process of teaching and how kids learn. Just as in the corporate world you have people that discard the tried and true processes and wish to 'leave their mark', there are educators who do the same. They basically need to justify their salaries.
I have a Bachelor of Math and I am also a teacher. When I started teaching I was dismayed by the frequency of students knowing the "rules" but having no idea when they apply. I jokingly described this as "a race between their heads getting full of rules and them graduating high school." It is my hope that the new curriculum will provide more opportunity for giving students understanding of mathematics and the so-called rules to be used. Note that when the folks at WISE math talk about incapable students who have been taught the "new" math, they are misinformed--no students taught in the "new" math in western Canada have reached university yet! That won't happen until September of 2013.
Math, as I see it, is part art, part science, part philosophy, and part science fiction. As a youngster I had no problem with arithmetic, but when they introduced 'new math' was lost and remained so through high school and university. My mind could not grasp the 'concepts'. Most of my teachers along the way were Gym specialists, who taught math as their secondary subject. I am was a superb athlete by the way.
I can fix just about anything, and can solve most problems and think theoretically and am a whiz at business concepts, but math is a no go, nadda.
My husband on the other hand is a 'genius'. He taught math at college and university for many years. Can't put in a light bulb, but can solve complex mathematical problems at the snap of a finger.
Teaching math, to those who had for many years been messed over by teachers who did not get math themselves, for him, was eye opening and a pleasure. So many of his students said they never got it before.
So I agree with so many of your callers. Teachers are a key part to students actually getting it.
Many teachers are thrust into teaching math at the elementary level because there is a body needed in the class, not because they are good math teachers.
I taught Math for more than 30 years. I have been hired (in the past) to train teachers in new curriculum and teaching methods. Let me say there are many sides to the issue. First I want to say there is a great problem with math teaching today. I will mention a few issues. Standardized testing and moving to US style teaching. This move to evaluate teachers and systems by a standardized test forces teachers to teach to a test rather than teach a subject to students. If my desire is for a student too look good on a standardized test you might teach only the concepts that will be on the test. Administrators put extreme pressure to meet these curricular objectives. Teacher Training, at the elementary level most schools use a classroom teacher approach and often these teachers are specialists in English. These teachers are not equipped to handle the "New" Math teaching systems. Students have changed, society has changed and instead of 4 or 5 kids in a family, from my generation now you have usually only 2. Modern conveniences have removed the need for children to perform many chores at home. When parents used to give their children chores to do the child often needed to organize their chores. Our sports and recreation were child created, now it is often parent organized and planned. The students do not come to school with the problem solving skills from a generation ago.
Now obviously these are simply three of many factors, I have only given a broad statement and of course nothing is as simple as this. The overarching issue is the moving of control from local schools and parent groups to a Provincial Dept. of Education mandate is the over arching issue. I need to go. I have students I tutor coming soon.
Thank you for discussing such an important issue.
On your comment, why aren't the professionals (teachers) able to decide how to teach math the main reason is they don't have the know how. School boards around the country aren't basing their recommendations on curriculum on a hunch. They base it on research. Math should be about discussing, exchanging and communicating concepts during problem solving not remembering rules and methods.
I wanted to echo Mike's sentiments about how math was taught (in the 80s and 90s). I too struggled with the speed tests done in primary classrooms. You were given 2 minutes to write out your division, addition, subtraction or multiplication. You were not permitted to write your work out, you were only permitted to write the answer and were forced to quickly do the math in your head. I failed every one of these tests, even though I knew the answers. In grade 2 I was labeled bad at math, despite understanding it. This stuck with me from year to year and until I shunned it all together.
I think learning like that destroyed any hope of a lot of people from my generation had of understanding math (by being labeled bad at it), so a more balanced approach would be welcomed by myself for my son when he enters school in a year.
East York, Ontario
I believe that have been ignoring the field of computer programming which has been and still is lumped in with mathematics as a kind of side topic whereas it should be tackled as an additional subject. Programming concepts can and should be taught from very early years and if we do not soon correct this lack in our education system we will miss the boat.
Halifax, Nova Scotia
I am an elementary school teacher in Ontario and I currently thoroughly embrace the methods of teaching math that are encouraged today. Coming from math experiences in my own schooling where I was told simply to "do not ask the reason why, just invert and ,multiply", I see the necessity of teaching foremost for understanding using whatever strategies that work, whether they be student generated or not. Once the understanding of the basic concept ( such as multiplication or division is in place, then it is possible to move towards the mastery of the standard algorithms because now those algorithms sense. It does not help a student to simply follow the procedure, or try to memorize the steps for long division if they do not understand that to divide means to share equally. Students need to experience division and multiplication and fractions in meaningful problem based contexts and develop their understanding of the concepts by struggling to find a solution that makes sense, not simply apply a rule or procedure that has been demonstrated to them.
Students who learn through problem solving are also learning a life skill, many employees look for people who know how to think, not simply unquestioningly follow procedures.
I am a teacher in my 5th year of teaching with the public school board here in Toronto. I teach in the primary grades. I have always enjoyed Math and done well in it myself. However, I found teaching the curriculum here in Ontario quite challenging. Last spring I took a university course at night school: the first part of a 3-part teaching specialist in Math. It was a revelatory experience.
When I started my course work (under the wonderful instruction of Pat Margerm at York U - one of the leaders in pushing the teaching of Mathematics forward) I was blown away by my own lack of depth in terms of my own understanding of the developmental continuum in how concepts are learned and developed in students. The experience made me realize that we as teachers need to seriously 'up our game' if we are to be truly effective Math teachers.
Earlier this year, I had an experience that confirmed for me that this new teaching paradigm for Math is worth the huge investment that we must personally make as teachers. While discussing the solutions during the 'consolidation' phase of a lesson, I asked the students to share what strategy they saw their classmates using. I had chosen a piece of work in which the students had used the strategy of 'doubles' and 'near doubles' at least 2 times in their solution. A grade 2 student raised his hand confidently. I called on him and the words that came out of his mouth blew me away and warmed my heart: "They are composing and decomposing the numbers," he said. I looked again and realized that while I was expecting an individual strategy, he was speaking to a mathematical 'Big Idea' that we had explored earlier in the year, one of the concepts that underlies many, many aspects of Math. I would argue that this level of understanding (and, yes, he wasn't just using big words he'd heard) was possible because of our work with new models of the teaching of mathematics. In this case, we have been using the Bansho method from Japan.
Many of your guests today have spoken to both that which is being left by the wayside, and the ineffectiveness of the 'new' models of teaching Math. I am sympathetic to both of these concerns, but I would caution against abandoning the newest, 'cutting-edge' methodologies. Most of these methods are not theoretical, but have been developed through much research. What they do need in order to be successful, are well-trained, skilled teachers. Until we teachers are masters of our subject matter, we won't be able to move students forward, no matter what the technique we employ. My own experience was extremely rigorous, but also extremely empowering.
When I was an elementary student in rural Ontario in the 1960s, there was emphasis put on learning multiplication tables and practicing page after page of questions that utilized such facts. The problems in the text books were simple and I knew that if I had just practiced multiplication, the problems that followed would inevitably involve multiplication. Not too much thinking required in terms of problem-solving, but Rex is correct, I did and do know my multiplication facts. And I agree with anyone who says that knowing basic math facts makes the math concepts that follow easier to deal with.
Throughout high school, I was successful in Math, but I cannot say that I really understood the underlying concepts. I was very capable at following steps and showing all my work, thus helping me achieve 80-90% in these subjects.
I thoroughly enjoy listening to Cross Country Checkup and do so regularly. In my second career, I am an Intermediate teacher, and I feel very uncomfortable with what I am hearing. I work conscientiously to deliver the best lessons I can for the students I teach. I agree that students should know their basic math facts. However, I also agree that other math skills, such as estimating and problem solving are also important. I never have a calculator in the grocery store, but if I have a finite amount of money with me, I will estimate what items I can purchase with that amount. I estimate the amount of tax I will be charged while I am waiting in line at the cash register to ensure that I won't be overcharged. If I want to paint a room in my house, I need to understand that area is the concept that I will use. I will estimate the area of the walls before I purchase the paint. So when people think estimates have no place in a math classroom, I disagree.
The final point I would like to make is that teachers have a legal responsibility to teach the curriculum as laid out by the Ministry of Education in their province. I don't pick and choose what I teach. I follow the curriculum and teach the variety of students in my classroom to the very best of my ability.
I understand that parents are frustrated when their children are struggling. As a parent, I struggled to help my children when they were in school from K-OAC. Remember, too, that the majority of teachers are trying to do their best at delivering the curriculum to their students in several different ways in order that students can understand.
I am currently a grade six French Immersion teacher, and I have been teaching for 28 years. I have taught kindergarten, grade 1, 2 and right now I am in grade six. When I first started teaching grade six, I will have to admit that I was terrified to teach this subject, having never been "good at math" after grade six myself. I had to work hard myself and constantly sought out help from my colleagues to know what to do.
Nine years later, I love the new math as it's called even though it isn't really new. The same processes are required to understand math now as there ever were. And for me, it's only now in my life that I could begin to think of math as an exciting subject. I wish I had felt that way when I was in school, or I wish I had understood the subject ias well as I do now ( grade six level I mean).
My natural aptitudes fell in the French, art, English areas and because math wasn't easy to me, I didn't make a very great effort to become good at it Had I worked harder or asked more questions, or had the math been taught the way it's being taught now, I might have done better.
The flaw with the way we are teaching now is not the program itself, it's that we are trying to do so many things that we cannot spend enough time to really help children develop the numerous concepts that need to be covered each year.
When I went to school, it was largely " readin' writin' and arithmetic" in the classroom. It was boring but we sure practiced.. . Now I am teaching math, art, social studies, science, religion, - in the French language and English language arts. The students also have physical education and music classes. Add to this sessions to help students understand what good character is, discipline sessions, fun days, many students out for vacation or other reasons on a regular basis I may have missed a few subjects there but you can imagine how difficult it is to cover everything. I cannot see how children can be bored but I have heard the word!
I agree wholeheartedly with the callers who pointed out that to succeed with anything, it requires hard work and consistent practice. People who have an aptitude for anything still have to work at it, it never comes as easily as others might think. It's just that people who have an aptitude for a subject tend to like it and that keeps them going with it.
I wish I were going to school now for all the options that a child has. But it would still be nice to slow it down a little and be able to work quietly on problems and have a chance to figure out what you don't know.
Very interesting and thoughtful comments. Thanks to the young callers, They were great.
Logy Bay, Newfoundland
As a Math teacher for 10 years, I found the problems with teaching Math can be listed as: the curriculum, which is weak; using the calculators by students who were not taught properly the basics in Math; and the teacher who is not encouraged to "go the extra mile."
My philosophy when it comes to Math is expose and challenge, and believe me it worked very well with most of my students. The least I did was to teach them the curriculum, but I did introduce the concepts of grades 10 and 11 to students of grades 6, 7, 8, and 9. For example, I made sure my students understood the very basics of numbers and all operations deal with them. Then, in Algebra, I gave them the basics of how to solve the equations from all grades up to 11, meaning students from grade 7 and 8 were able to sole linear equations not only by eliminating, graphing or substitution, but also by using matrices. My grade 7, 8, 9, and 10 students were introduced to different topics in matrices, including solving equations by Gauss-Jordan elimination and by applying Cramer's rule. These topics are only covered by student in grades 11 in IB programs. My best achievement is that my students love Math, or most of them.