Mr W's Math Study Guides


When our children wish to excel at sports or music we expect their teachers to instill proper skills and get them to practise, practise, practise. We would not hire a teacher who stressed “discovering” or “finding a strategy”. We build on what others have discovered. When a ball is hit to a third baseman he concentrates on getting the runner out…not how to field the ball or how to throw it….the basics were practiced long before. When a forward on a hockey team is on a breakout he isn’t thinking about what an offside is….that was dealt with and practiced over and over. When the pianist in a jazz group sees D#m7 there is no time to think about it….all that practice and rote take over and the job gets done. Math should be taught the same way. In elementary school, basic skills should be learned and practiced so that our children are not at a disadvantage when entering High School.


 The views I’m expressing here are NOT coming from of an “expert” (there are too many of them around) but someone who has been involved as a student, math teacher, parent, author, and tutor of mathematics for more than 60 years. The world has changed a lot since I learned and memorized basic number facts back in the 1950’s but those basic skills have served me well over the years and are still valid as I do research on Google, upload my Math Videos to YouTube, develop Math Study Guides and help High School and University students navigate the world of mathematics. As I look at the changes that have been made to the math curriculum not only in Ontario but elsewhere in Canada (and beyond our borders as well) I wonder how things could have deteriorated the way they have. I’m not yet (but almost) cynical enough to believe there has been a deliberate attempt to dumb down the population to make us easier to control but one of the main reasons for what I see as the decline in standards is the following. The Ministry of Education has to keep changing the curriculum and approach to maintain the illusion of progress……you can’t say “by golly, this works really well….I think we should keep this the way it is”. So they decide that rote is a bad idea in grade school, long division is old-fashioned, Grade 13 should be eliminated, use of calculators should be encouraged and so on and so on….. I know there are lots of parent organizations trying to bring common sense back to our curriculum but they are either stonewalled or bamboozled by educational jargon. Does anyone really care? The answer is yes, but I wonder if anybody ‘up there’ really cares about the students or is it all about change for the sake of change!


In the movie ‘Oh God!’ with George Burns and John Denver, George (God) made the following remarks:
“A beautiful bird and I put the kneecaps on backwards…….I think I could have found a better way for a skunk to defend himself…..and mathematics, that was a mistake. I should have made the whole thing a lot easier.” Well the first two I can agree with, but the math thing ......... definitely not God's fault ! What could be easier than ‘if I have 7 cookies and I eat 3 cookies, how many cookies do I have left?’. Cookie Monster can explain that as well as I can. Or how about ‘if the temperature is -2 degrees and it drops 3 degrees how cold is it?’. The difficulty is not in the question or even in coming up with an answer and it’s certainly not God’s fault if it gets messy. It’s the fault of the bureaucrats and text book writers who make a simple idea so darned complicated that half the teachers don’t know what to make of it. Last week I saw diagrams in an Ontario textbook ‘explaining’ addition and subtraction of integers that would baffle Stephen Hawking……not that he couldn't see what was going on but he would be amazed that something so simple could be so bizarre in its explanation. Why all the little blue and red circles as if the negatives and positives are little balls bouncing around annihilating each other? IT DOESN'T HAVE TO BE THAT DIFFICULT!!


All parents I talk to about elementary school math text books tell me that they find the explanations confusing and that they are often unable to help their children with homework. This is totally unacceptable! If a textbook which is addressing basic concepts such as adding, subtracting, fractions, decimals etc. is making a parent feel stupid and helpless the book isn’t worth the paper it’s printed on let alone the hefty price tag for those colourful, picture laden books that presently pass for text books. The endless little rectangles and squares for multiplying, the blue and red circles for integers…….and what’s with all the colourful pictures that have only the most remote connection to what is supposed to be taught! How many times has a student said to me “Is that all we have to do?” or “Why didn’t they just say that?” In my book ‘Get Ready for High School Math’ I cover all the material I feel is necessary to know when entering Grade 9 and it’s not really that much. I sometimes feel that as far as math is concerned most students would benefit more from playing sports and games like Monopoly and chess for their first 10 or 11 years…. and we could formally teach them all they need to know for high school when they reach the age of 12.  That way we wouldn’t have to correct all the confusion the textbooks instill in students and their parents during the early grades. 


In Grade 10 mathematics we expect students to do what we call factoring trinomials. In order to do this they must be able to come up with solutions to simple arithmetic problems such as: Find 2 numbers that multiply to 63 and have a difference of 2. OR Find 2 numbers that multiply to 45 and have a sum of 14. Once they have those numbers they can then concentrate on the main job which was to deal with the trinomial. The problem for many students is that in the earlier grades rote learning was not emphasised and the frustration begins. At this point many students who are capable of mastering the Grade 10 content are discouraged and they begin to give up. I have observed this problem so many times when trying to help students and an article on a recent neurological study of how rote learning frees up the brain for higher levels of reasoning has confirmed what I believe is a real shortcoming in our education system. How can the average student succeed when they are not given to basic tools needed for success?


"Lies, damned lies, and statistics" is a phrase describing the persuasive power of numbers to bolster  weak arguments. I was reminded of this phrase when Stats Canada revealed that inflation in Canada was 1.3% in 2015. Since I called this website ‘Not Another Math Question’ I will not bore the reader with endless equations and the numbers. But in every area I looked, hydro, water, communication, food (cauliflower at $7 a head, and don’t get me going on the price of hamburger), insurance ,car repairs…all were up well over the so called ‘average’. On the flip side the price of gasoline is dropping….making a drive to Florida cheaper…a great idea until you realize it costs $1.40 for a US buck. They also use the argument that the price of a 4K TV set is coming down. Tell that to the pensioner that just passed on the cauliflower. So what am I saying here?   Just making the point that you can prove anything with numbers.


Who would ever forget the laughter when the latus rectum was mentioned during the study of conic sections in the 1950’s Ontario grade 13 Analytic Geometry Course. But no longer is the latus rectum a topic of discussion… fact most students in Ontario now have never even heard of conic sections. For some unknown reason (at least unknown to me) the parabola is the only remaining member of that family…the hyperbola and ellipse having disappeared into oblivion. When I became a teacher of mathematics I enjoyed the continuity of the course as it was then. I had a plastic cone showing the different shapes generated when you slice the cone at different angles. But as time went on the parabola has became the be all and end all of conic shapes. They are studied to death in Grades 10 and 11 under the latest fad called ‘transformations’ (which incidentally made a short appearance back in the 1970’s). I am always amazed by the fact that our educational gurus decide that something that is so important in the study of math is suddenly unimportant. It only goes to support what I have said all along…… we have an education department whose only reason for existence is to keep changing courses to give the appearance of progress. 


 While working with a boy (let’s call him Karl) in Grade 7 he expressed his disappointment in the fact that he would never be able to write because he was not being taught cursive writing. Karl is a very fun loving kid, always has a joke for me, but expressed sadness that his school had the policy that cursive writing no longer had a place in the curriculum. I repeat CURSIVE WRITING IS NO LONGER BEING TAUGHT in his school. I realise that most communication is done now through computers. I rely on my computer for many things…I have 2 e-mail addresses, 2 websites, 2 YouTube channels and get most of my news from my computer, but I am so glad that I know how to write. Karl at a very young age realises that too. Cursive writing is an extension of our personality….not that we would write entire volumes in hand writing (although some authors do), but we should be able to write a short note to a friend or relative, maybe a message of condolence or congratulations, or a diary of events. I have my grandfather’s diaries and enjoy seeing his handwriting. So call me old-fashioned…..a stick in the mud….. but I believe cursive writing is important and apparently a student in grade 7 thinks it’s important too!