logarithms – Chris Hunter

Last year, one of my former student teachers told me about Tarsia, a software program that allows teachers to create jigsaws (and more). He remembered that I created similar jigsaws using MS Word (no small feat) and experienced this joy himself as a new teacher. I wish I knew about this tool several years ago.

Tarsia includes an equation editor for entering matching expressions. Teachers may also enter distractors so that corner and edge pieces are not easily determined. The activity cards are scrambled when outputted, ready to be cut out by students.

Here’s one that I quickly created:
logarithms jigsaw (normal)
logarithms jigsaw (larger)
logarithms solution

In my classroom, I often used jigsaws to review a topic. In addition to providing students with opportunities to practice, these activities get students talking mathematically. As a teacher, I am able to listen to students making mathematical arguments about whether or not pieces fit together and observe them checking and revising their work. Also, eavesdropping on these mathematical conversations will tell me if there are topics that need to be discussed further (e.g., rational exponents).

Formulator Tarsia (for Windows only) can be downloaded here.

Recently, a video showing a snappy way to add fractions was shared on the BCAMT listserv. Thankfully, it was panned.

This “butterfly method” also appears in Elizabeth DeCarli’s Ignite presentation, this time to help illustrate that “meaningful representations are greater than cute mnemonics.”

In my previous post, I wrote about one way in which my Math 10 teacher tried to make math memorable for his students. (Yes, I realize that since I still remember this, he was successful.) I also wrote about how this didn’t build any understanding.

As a teacher, sometimes I’d be frustrated/puzzled by what I heard from my students. Negative exponents send numbers “to the basement” (or upstairs if they’re already in the basement). The “Front Door Bomber” has one bomb for each person in the house (the distributive property). Why is a negative times a negative a positive? “When something bad happens to a bad guy, that’s good.”

The Good, the Bad, and the Ugly — When something bad happens to a good guy…

But I, too, was guilty.

I’m not talking about the usual suspects, FOIL and SohCahToa. I’m talking about “bacon and eggs”. Secondary math teachers can see slides 3 and 4 below and figure it out. Others probably stopped reading two paragraphs ago.

I imagine my students’ calculus professors being frustrated/puzzled by this. That makes me smile. A little. On the inside.

Aside from being unnecessary, two times out of three it’s incorrect and misleading. For example, in slide 8, is x the exponent or the answer?

I’ll no longer use FOIL in my classroom. Through algebra tiles, I’ll emphasize an area model. I’ll have a tougher time letting go of SohCahToa. It does help students memorize the definitions of the three primary trig ratios. However, whenever I asked my Math 10 students what they knew about trigonometry from Math 9, they would just say “It’s that SohCahToa thing”. No mention of big ideas or similar triangles. Suggestions?