Thanks for dropping by. Just around the time you were leaving this comment, a Professor from Australia was leaving me a tweet with a similar take. Excellent thinking by excellent minds. ]]>

0*n = 0

n = 0/0 –> indeterminate: n could be any integer, including 0 (or 3)

So both 0 and 3 are factors of 0.

Maybe this could work? (These math puzzles were always the best part of class)

]]>I think it is all in how we define factor. The “goes into” idea is just shorthand. The definition i see is I think “n is a factor of k if there exists an integer m such that nm=k”. So 0 is a factor of 0.

I’m sure that there are times this fails. 0 is special it can have special rules.

]]>By and large, I agree with your likes and dislikes of the various elements of the Demana text and its peculiar proclivities. There is, however, one thing of real value that I think you overlook. I am referring to your concerns over the “introduction of cosine as x / r…” Although I don’t start of definitions of circular functions in quite this way, I introduce it as something similar – we define cosine to be the x-coordinate on the unit circle.

I think that it is extremely important, especially in a higher-level class like Precalculus Honors, to emphasize the notion of propositional logic and the deductive structure of mathematical knowledge right from the beginning. Kiddos often walk into Precalculus right off the boat from algebra, not really clear on this foundational way of viewing mathematics. So, when we start discussing the properties of sinusoids or trigonometric identities, we always boil our justifications down to the nature of the definition (and explicitly state that this is what we are doing).

In some sense, this is picking up students’ genuine mathematical education where Geometry leaves off.

]]>Thanks for sharing – this will probably make it to my department email share next week. I see a workshop not TOO far away…

]]>Thank you so much for dropping by and sharing these resources. I now have some fun reading material for the weekend!

I need to think about the idea of feeding some ask yourself questions to my students in a more thoughtful way. I have a habit of sort of stream of thought questions out loud. To a listener they might seem a bit random, in my head they are thought out in advance. If I can be more transparent about that planning process, that might give my students some clues/prompts to follow more effectively.

]]>Great post, thank you for sharing it.

As it turns out, one of the things we include in our curriculum are instructional routines and these routines include “ask yourself” questions. Basically, we include the ask yourself questions in our routines so that students get practice asking themselves these questions, but we don’t have students invent the questions to ask themselves, we give them those questions, and then we practice answering them (and seeing other people’s answers) in class.

My colleague Blue Taylor worked on this document which has A LOT of ask yourself questions aligned to three of the math practices.

David

]]>I realize this may be a cop out on my part, but I would suggest asking your schoolâ€™s physics and ap chemistry instructors how they develop that skill set in their students.

I would definitely like to hear of any effective strategies you learn!

apm

Twitter: @autismplusmath