High School Mathematics

22

By Maureen Dagg

Now that students have begun a new semester in our secondary schools, I thought I’d write about my observations as a high school math tutor for the past twenty-two years.  I feel that I have had enough experience here (having tutored kids at all levels of ability from four different school boards) to be able to make some useful comments and suggestions.

First of all, let me deal with the math taught in elementary school.   I am less familiar with it than with the high school curriculum, so it would be really helpful to have elementary teachers weigh in on this. It does seem that the Ontario government has finally noticed some “issues” and so they might be taking action.   I have heard mixed stories from elementary teachers, many of whom have been very frustrated with the lack of emphasis placed on actually knowing some basic arithmetic. In the meantime, I am getting tired of saying to kids:  “You don’t know your timestables and you can’t deal with fractions very well at all.  This is not your fault – but it IS your problem.”   And then I show them places where they can find extra practice sheets on these thing.   I have also occasionally resorted to drilling kids in timestables.   Don’t get the impression that these are kids who are “less talented” in math: on the contrary, these are really smart kids, and they don’t know their basics.

Parents, if you want to help your pre-teen kids know the math that actually matters (namely, arithmetic) please practice timestables with them and make sure they can do fractions.  And no, a calculator does not do a good job of fractions (do YOU think that 0.14285714 is easier to deal with than 1/7?).  They do need these two skills for high school math – especially for factoring quadratics and simplifying rational expressions.  Life is much easier on the kids who have their basics!  Arithmetic is the math they would need as adults, so worth knowing …!   (FYI parents, Superkids Math Worksheets is a great online source of worksheets).

Second, let me reassure parents that the high school math is not “dumbed down”, nor are they “shoving things down kids’ throats way earlier than they did it to us”.   You’ve just forgotten your high school math:  For most adults, it’s the elementary math that matters, because we use it.  We don’t use our high school math unless we have certain types of work, and so we forget it.  Our high school math curriculum is world class, and competitive.  The two textbooks that I’ve seen (the Nelson and the McGraw-Hill) are excellent, and very useful to kids who know how to use them effectively.

This comes to my concerns with some of what I’m seeing in high schools today:

  • Not using the textbook – and not following the curriculum
  • Not showing kids how to use the textbook
  • Teachers who fail to give kids extra support
  • SPLIT GRADE math classes
  • Shortened class times
  • Not using the textbook – and not following curriculum

Now, some people think that this is caused by a lack of textbooks for kids, but I’ve never actually encountered that in the kids I tutor.  What I have encountered are teachers who, for one reason or another, don’t bother to use the texts.  They hand out reams of paper, photocopied on one side, and often not hole-punched.  They don’t even assign homework from the text ,  preferring their own made-up questions.  It’s no wonder these kids need a tutor.

The biggest  issue with this is that it is extremely difficult to determine how well the teacher is actually following the Ontario-approved curriculum for math.  If they miss material, the student is going to have difficulty the next year.  And the one after that.  Math is cumulative, unlike most other subjects in school.  When kids are left with holes in their knowledge, it can be very stressful for them, and can affect their achievement level.  This, whether we like it or not, does affect how their future education unfolds.

In my experience, more often the teacher is going well beyond the curriculum, causing undue stress in students and having an effect on their achievement.  When this happens, kids might question their own competency and choose not to go into math-related fields, which is really unfortunate.  We need people in technology and other math-related fields.  A couple of years ago, the parents of students at a school in Kanata (mostly high-tech math geeks themselves) caused a huge uproar because the teachers were going way beyond the Ontario curriculum, and their kids were totally stressed as a result.  The Ministry got involved and the teachers were forced to back off.  I noticed a significant difference tutoring kids from that school after this happened.

Made-up-hand-out -questions often contain mistakes, and there is not usually any way for kids doing homework to check to see if they got the right answer.  There is also little or no time in class for “homework take-up” the next day.

Kids in my experience often aren’t very good at organizing large amounts of hand-outs.  Lack of hole-punching exacerbates the issue!  The text is a self-contained entire course, complete with lessons, extra explanations, reviews, practice tests, and answers.   And need I say, more environmentally friendly than all these handouts?

Our textbooks are written by teams of experienced, expert  teachers, and these particular high school texts happen to be really good.  Which brings me to my next issue.

  • Not showing kids HOW to use the textbook

I didn’t learn how to use a textbook effectively until grade 12, and it was only because of a single teacher, Miss Elizabeth Mausser.  In spite of being a math geek, I would open my book to the assigned homework, do the questions, look up the answers in the back, and that was it.

Miss Mausser actually took the time to show us our text, and often made reference to it while she was teaching.  We could see the lesson in the text while she taught it, and so we could choose whether or not we wanted to copy what she was presenting.  She encouraged us to find the “key notes” from each lesson in the text, and to refer back a page or two to see examples to help us with our homework.

I’ve been tutoring for over twenty years, and many of the kids I tutor are pretty serious math students.  Never have I encountered a student whose teacher has shown him/her how to use the text.  And nearly every student I tutor has commented on how much this simple tip has helped them.

This single thing made the biggest difference to my success in university, where I studied computer science and mathematics.   Knowing how to use the text effectively allowed me to help myself – and that is a powerful confidence builder.  So  parents, please sit down with your teen and just spend a few minutes flipping through the text to see how excellent a tool it is for students who know how to use it.

  • Teachers who fail to give kids extra support

Now, don’t go thinking I want to crap on teachers.  Because I don’t.  The vast majority of them are working extremely hard to keep ahead of several things (which I could write a lot more about).  But as we know, any group of people has its weaker members, and not putting that on the table is not just being politically correct.  It’s being irresponsible.

Suppose you’re the teacher, and you have a kid who had health issues, or family issues, or just hasn’t done math for over a year and now she has to get back on track. Would you just expect this kid to pony up and “get with the program”, or do you think you might at least toss her a few things to help? If the kid at least knew how to use the text effectively and was keen enough, the teacher might only have to point her to the Appendix of the text.  I know some math teachers who assign review questions from here at the beginning of the year for all of their students.

I think we can say (because we’ve seen teachers do this time and again) that most teachers would at least chat with the parents, or the student services folks, or something about a plan for this kid, right?

Sadly, this is not always the case, and kids are sometimes left behind … Teacher too busy?  Teacher doesn’t care?  Parents not advocating for their kid?  Schools intimidating parents who do?  Folks, if your teen is struggling, please don’t hesitate to advocate for him/her.  And yes, it is perfectly valid to expect a teacher to at least point a student towards review exercises that would help.  It is also valid to expect a teacher to be in the classroom before or after school to offer extra help.   Yes, I love tutoring, but the school is your first point of contact for help.

  • SPLIT GRADE MATH CLASSES

This is, by far, the most disturbing thing I’ve seen as a tutor.  At our own local high school, ADHS, there was an Academic Level grade 11/12 split math class last semester.  I’ve heard (but not confirmed) that there are more split grades this semester.   This is mind-boggling to me (but explainable – see my previous article on small high schools).  Suddenly, a highly competent math teacher  was having to teach the grade 11 (notoriously the hardest math of high school) and the grade 12 at the same time.

Is this possible?  Yes it is.  I have no doubt that, with excellent tools, this can be done.  But are those excellent tools in place?  No.  We seem to have put the proverbial cart before the horse.

Worse, the split grade class wasn’t carefully made with only the most mathematically competent students in it.  Imagine if you’ve always struggled to keep up in math class, and now the teacher isn’t even teaching a lesson or having time to give help.  Lessons are handed out as photocopies instead, and no one has shown you how to use the textbook effectively.

This might be an excellent tool:   Have the lesson video-taped in such a way that each kid can watch it on his own screen, wearing headphones, able to pause or rewind whenever he needs to review something.  The teacher is free to go around the class, helping individuals or small groups of kids.  Okay, this is actually ideal, and would be awesome!  BUT we don’t have that.  Not by a long shot.

Even the online (ELearning) lessons, which kids could be given access to, are woefully inadequate.  For this, the blame lies squarely on the Ministry’s shoulders.  It is not rocket science to produce lessons, being given by excellent math teachers, on each section of each textbook of the high school math – and have them online for kids.  Missed a class?  Didn’t understand the lesson very well?  You can see it again – and again and again.  The teacher would be free to actually help. As it is, and especially in this particular split-grade class, the teacher was so busy trying to get things taught that she would had no time during class to help anyone or to take up homework.

In my ideal math class, kids would watch and read a lesson ahead of time (put the lesson as homework!) and class time would be devoted purely to doing math. Want to get really good at math?  Try out the questions on your own, then get together with others to figure out whatever gets you stuck.  The teacher can work with small groups when necessary, and even grab everyone’s attention to explain something that she sees most people getting wrong.  Class time devoted to learning through doing math, not trying to keep up with a lesson.  And lessons that you can rewind … pause … use the text …. Maybe watch with friends so that you can help each other….!

But … none of this exists, amazingly.  An American fellow named Khan started making just such videos for his cousins to use, while they were in high school and he lived far away.  Khan Academy was born, and has such videos.   The issue for us is that they aren’t linked carefully to our particular math curriculum, so it’s more difficult for students to find exactly what they need.  But if a computer geek can make awesome online math videos for kids to learn math … why can’t we produce such things for kids to use?

  • SHORTENED CLASS TIMES

We’ve seen a gradual erosion of time that kids actually spend in class for each subject.  When I went to high school, we didn’t even have semesters.  Classes were short – but we had 8 subjects all year long, 40 minute periods, and a rotating timetable.  So we had all year to cover each subject, and 3 sets of exams (you could be exempted from the final exam if your marks were high).   Now, with semesters, we’ve started out with 76 minute periods … and now they’ve been cut down to 60. This allows for an MSIP (Muli-Subject Instructional Period) to occur.  The real reason behind this was a complex issue regarding the staffing of the library (another small high school problem).

It’s difficult to really tell how kids are doing with these changes, because along with changes come different ways of evaluating kids and measuring success.  Graduation rates look great: certainly higher than they were when I was growing up (4 of my 7 siblings never finished high school).   The fact is, the more gifted learners will fly through our system no matter what we toss at them.

But we can’t keep squeezing kids, cramming more and more into them without adequate supports for both teachers and students, and expect competent, confident graduates.  What we are getting, it seems to me, are increasing rates of anxiety and depression.

I write this simply out of concern.  Kids are more likely to succeed when they are properly supported.

Parents of kids currently in the system might find this summary list useful for math:

  • In elementary school,
  • make sure your kids can add, subtract, multiply, and divide (long division being the least important of the four).
  • make sure they know their timestables, and how to add, subtract, multiply and divide fractions.
  • don’t worry about helping your child with homework that you find confusing! I’ve had calls from parents who find the elementary math confusing, simply because of the new methods of teaching it.  Imagine the kid when he brings home math, and his Dad and Mom can’t help him because it is all about explaining how he got the answer, “determining ranges” and “discussing”.  At the end of the day, can your child add?
  • It’s cool to do useful things with kids, like figuring out how much carpeting it would take for their bedroom and how much it would cost! Estimating the cost of things – in other words, doing the math that matters.  Measure stuff!  Double the recipe!
  • In high school, encourage your teen to look through the text book to actually understand how it is set up. In the textbook, you will find
  • each lesson is carefully laid out, followed by exercises
  • useful boxes of “key points” from the lesson
  • review exercises
  • sample tests
  • Cumulative Reviews for several chapters at once
  • Also, you will find in the Appendix, reviews of essential skills from previous math courses.
  • And, of course (this goes without saying), answers in the back.

The textbooks currently on offer are excellent.

  • If your teen’s teacher isn’t using the text, demand to know why. It is perfectly valid to have the teacher show you, step by step, how he is following the Ontario Curriculum.   If he is going beyond it, you are within your rights (and your child’s) to ask that the curriculum be followed.  As far as I can tell, not following the curriculum is not strictly legal.

Math matters – well, it matters to me, anyway!  It’s pretty well known that it is one of only a few subjects (music being another one) that is cumulative and requires much practice.  Math teaches us how to think in a particular logical fashion, and therefore enables us to be better problem solvers.  Understanding how to approach a math problem can make you better at writing English essays!

We don’t need it to be needlessly hard though.  And some of this stuff that I’ve brought up is doing just that.