advanced math |

‘Redefining What’s Possible’ is a series of blogs that highlights stand-out tech tools being used at KCS.

The other day a student asked to use my office at lunch to work on math. By the end of lunch recess, I learned he used the time to do three different versions of his homework assignment, persisting until he got the full set of questions right.

Homework has a patchy record in this profession. It always has. One big glitch with it is when students have homework that they, unknowingly, don’t do correctly. This can happen to anyone when learning something new, and is particularly common in advanced math when the concepts to be practised are far removed from the rest of our lives. Traditional math homework has students carry on regardless (because it’s due and will be checked), with more than a few doing it incorrectly. In essence, these students practise doing it wrong. That’s right – despite best efforts, homework helps some become proficient in doing it incorrectly. Hopefully, mistakes will be picked up by both teacher and students the next day, whether in class or extra help. Hopefully, correct practice will then be fully established. The students will all ably move on to the next concept to be practised at home that evening. That is the ideal.

Unfortunately, the ideal can be elusive, and most of us know that for a fact. Multiple obstacles could be at work, and differ from student to student – the well-practised incorrect method; students not paying full attention during homework correction for any number of reasons; students not getting enough practice doing the work correctly; students not getting enough direct, immediate feedback, among others. A quantum leap in homework effectiveness would give students fast direct feedback on their homework, make reinstruction readily available whenever needed (24/7), and make it easy to redo homework, multiple times if necessary, until it’s done well.

That’s where one innovative technology is redefining what’s possible. Every student wants to learn and do well, but many traditional practices don’t readily support it for all. There are many reasons why the Math Help Services program in grades 7 and 8 is making a positive difference to student learning, but one significant reason is the difference with homework. Students find out immediately after completing a set of questions how they did. They learn right away in the privacy of their home (or my office) which questions were right and which were wrong. They have unlimited access to multimedia instruction and step-by-step examples to correct misunderstandings. And with the click of their mouse they can request and receive a new set of homework questions on the same topic. Trying a second or third time, homework marks invariably go up. The students learn the concept with however many questions they need, and are ready to go on.

There’s an additional benefit this technology provides that’s soundly rooted in brain research. Math Help Services lets the teacher create regular concept reviews with questions from all concepts previously taught. Research has clearly established the power of extended, mixed practice of learned concepts over intense, repetitive practice of just single concepts. The former leads to mastery, the latter leads to the all-too-common math affliction, “I don’t remember how to do it!” And like all other homework, the students can access as many versions of the concept review as they need to get the mark, and mastery, they seek.

Was the one student in my office an anomaly? No. The majority of our grade 7 and 8 students take advantage of doing homework assignments multiple times, as needed, forging through different question sets until they nail them.

That ideal isn’t elusive. It’s here and making sure math gets learned.

Andrea Fanjoy,
Assistant Head, Academics
You can follow Andrea on Twitter @afanjoy.

You’ve likely already noticed that math is a hot topic in mainstream media these days. While newsrooms haven’t always been following the subject, we have.

Monitoring the profession from a global perspective, and debating strengths and limitations of our current practice, are part of the day-to-day work at KCS. This determination to do our best for every student over the years has led to a number of initiatives, such as:

Constantly growing collection of tools for differentiating instruction in the classroom, so all students can learn what they need at the level that’s right for them
Introduction of math workshops (small-group dedicated instruction) in grades 6 to 8
Introduction of JUMP Math in grades 2 to 5, where we think it’s the best fit
Introduction of the online math program Math Help Services in grades 7 and 8, where we think it’s the best fit
The use of Khan Academy to help support differentiated instruction
Widespread participation in the Brock University Caribou Math Challenge
The use of the University of Waterloo Math Problem of the Week in multiple grades for rigorous problem-solving
Introduction of computer programming with Visual Basic through our electives program, a language that requires significant use of advanced math

These are on top of our longstanding commitment to ensuring students master their basic math facts; avoiding the use of calculators except when appropriate and in the oldest grades; having ample experience with problem-solving; and enjoying generous use of concrete materials in their youngest years.

In the Family Satisfaction survey, a number of parents asked about our math program, in particular math in our older grades. I’m happy to report that our Canadian Achievement Test scores from last year are the best ever in the school’s history, with our senior students on average achieving in the 91st percentile across Canada in math concepts, and the 93rd percentile in computation and estimation. In fact, from grades 3 to 7, the grades that undertake the CAT test, the average percentiles were all at their highest ever, ranging from the 84th to the 94th percentile. We regularly hear from alumni and their parents that our students do very well in grade 9. Any feedback to the contrary is explored to determine what, if anything, can be done better.

Our math teachers have worked tirelessly over the years to help every student master what they need to know. For students who can’t get enough math, we won’t stop looking for more to give. For students who find math a relatively daunting challenge? Attentive teachers, with multiple tools, some being online, is great news for them too. And when news media have moved on to other issues, we’ll still be learning, debating and improving what we do.

Andrea Fanjoy,
Assistant Head, Academics
You can follow Andrea on Twitter @afanjoy.