How many times have you participated in a math talk at a professional development session with other adults and seen many awesome representations and strategies come out? Have you then gone back to your school, excited to try that same prompt with your students, only to find that the number of strategies is 1 or 2...or none, mentally?
So, what is the disconnect? Well, for one thing, students have varied prior experiences and so the models and strategies in their toolboxes also vary. More than that, though, is that once we learn algorithms, it is hard to go back to truly experience the building of conceptual models. Sometimes well-meaning parents teach their children to solve problems the way they learned, using the algorithm. Sometimes the pressure of high-stakes testing makes us feel like we need to introduce it so that students can tackle those questions independently. Whatever the reason, early introduction of algorithms happens, and it is harmful.
Algorithms are still a goal, eventually, but when we get there we want students to be able to think about what they're doing. Quantity gets lost in algorithms. Kids need to be doing mental checks and asking themselves, "Does this make sense?"
Fluency is bigger than answers.
(Based on research from Add it Up)
So, if students do not use the models or strategies I am hoping to see during my math talk, it is up to me to get them into our conversation. This is where my girl Missy comes in.
Take, for example, 16 x 25, as in the example at the top of this post. Rather than ask, "I want you to find the product of 16 x 25 in as many ways as you can," we can ask:
In this particular example, my goal is to help students see how we can break apart factors and use the associative property to make the problem easier to solve mentally.
Pam Harris has some great examples at her site, https://www.mathisfigureoutable.com/ that show lots of different visual models for various operations, like the one below, as well as problem strings to get those SMP juices flowing.
I wondered more about the idea of "learning backward" and came across a TED Talk by GM Maurice Ashley that really resonated. You can check it out here.
Toward the end of the talk, he mentions the adage of youth being wasted on the young, which made me think:
So, instead of being frustrated when students don't have the strategies and models we wish they did, let's work to "flip it and reverse it" by taking ownership of the solution with backward math talks to promote sense-making and rich discussion about mathematics.
I have found this planning template useful. You can access it here in Word form.
Happy planning! Please share any that you try in your classroom with me @anneagost!