It can be challenging to plan activities for workshops with secondary math teachers. I like to have teachers first experience learning mathematics as my students do. There’s the rub – if I share an activity from my classroom, teachers already know the math. They can opt out of explorations designed to construct understanding – they know how the story ends.
Marc Garneau (@314Piman) and I have two strategies to deal with this. First, we can have teachers look at a familiar topic in a new light. For example, have teachers:
use an area model to represent multiplication of fractions
use pattern blocks to explore quotative division of fractions (and using common denominators)
A second strategy is to have teachers solve a problem that is similar, but not too similar, to something they teach. For example, I wanted to model how I use expert groups to have students develop the exponent laws in Math 9. Having teachers do this would be iffy. Instead, Marc and I came up with this:
Each expert group of teachers was responsible for learning and teaching one set of ‘pop’ rules. For example,
(a + c) ‘pop’ (b + d)
= 2(a + c) + (b + d)
= 2a + 2c + b + d
= 2a + b + 2c + d
= (a ‘pop’ b) + (c ‘pop’ d)
0 ‘pop’ a
= 2(0) + a
Later, we asked “Okay, so ‘pop-ifying’ is not in the WNCP curriculum, but where could you use this teaching strategy?” Teachers answered “It would be great for teaching exponent rules or log laws.”
This was my go-to review activity. I picked it up at an un-unconference as a student teacher.
First, have students get in groups of four. This is their home group. Have students number themselves from one to four.
Have students move and form groups so that each student in the group has the same number. This is their expert group. Each expert group is responsible for one part of a review assignment, such as this. For example, the 1’s (Adele, Ellen, Lea, and Oprah) may be responsible for becoming experts on solving quadratic equations by factoring, the 2’s on solving using the square root method, the 3’s on solving using the quadratic formula, and the 4’s on the nature of the roots. Emphasize that each member of the group must understand and be able to explain the solution to each question in this part of the assignment. I play up that I will only help students while they are in their expert groups.
(Classroom Management Tips: Ask just the first four home groups to move and form their expert groups. Have the remaining home groups remain seated until this is complete. You will be able to see if each student is moving to the correct group. I’ve used this activity in classes of 24 to 32 students. Plan for this. For example, 12 students will form three home groups of three and will move to form four expert groups of three.)
Have students return to their home groups to complete the assignment. If any student needs help with any question, he or she is sitting with an expert. For example,
Ashton needs help factoring when the leading coefficient is not equal to one?
Adele’s an expert.
Barack has difficulty using the square root method when there are brackets?
Beyonce struggles with simplifying expressions when using the quadratic formula?
Adele can’t remember which condition results in two equal real roots?
Beyonce can help.
I may have gone to the well one too many times with this as a review activity. Time to try Kate Nowak’s speed dating activity. Also, I’d like to use expert groups to have students learn, rather than review, concepts. I’ve used this activity, with some success, to teach exponent laws in Math 9.