I think the debate about theory/derivation of formula vs. application/usefulness of formula is an interesting one, and can go either way depending on the class, the level of the students, and the type of formula. For myself, if I’m learning the Quadratic Formula in grade 11 math, it’s neat to see where it comes from, but I’d rather see examples of how it works, and how to use it to calculate roots of quadratic functions. Once I know that the formula was created to solve for the x-intercepts, I’m good to go and should start practicing. However, if I’m learning a new physics equation, say Work = Force x Distance, I’d like to see the derivation, showing me an older formula that I already know (Force = Mass x Acceleration) is used to find work, meaning that Work is actually equal to Mass x Acceleration x Distance. A lot of students seem to think that formulas are just magical things that were discovered one day, and showing them some theory/derivation certainly can’t hurt in some cases.

Of course, these would just be my preferences, and everyone is different.

Secondly, I think your idea of having teachers write professional upgrading tests every few years is a great idea. It brings a measure of accountability, which the government and public should like, and (most) teachers should embrace it too. If teachers are truly passionate educators they should be learners themselves, and if they want what’s best for their students, they’d recognize that learning new techniques and writing a test every few years is not only good modelling, but valuable experience. You said secondary teachers should attend courses but I think all K-12 teachers could benefit from some math upgrading every now and then.

If you’re teaching math 6 or 7, for example, you should know a variety of techniques for demonstrating and solving questions with/in order of operations, fractions and decimals, geometry and algebra, to name a few. And you should be able to demonstrate that you’re capable of writing a test using the techniques you’re supposed to teach For some elementary school teachers, they might not have taken a math class since their first year of university, which could have been five, ten, or thirty years ago. As teachers, we should be reminded of what it’s like to learn (or re-learn) something new every so often. It makes teaching easier.

Lastly, I’d like to add myself as another person who can attest to the ‘annunciation of foreign instructors’ point you brought up. It’s definitely common in BC, in K-12 and post-secondary.

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