Dan Myer has a great post that contains the body of his brief presentation at the recent Critical Issues in Mathematical Education workshop organized by the Mathematical Sciences Research Institute.
In his presentation, Myer challenges the more narrow definition of mathematical modeling that is common in math education.
Modeling, in mathematics and all learning, Myer points out, is about taking our early knowledge of a pattern, applying that knowledge, discovering something new, refining our knowledge, and watching the pattern or model come into sharper focus.
We do this in math, certainly, but it is actually the same process we use with “learning anything – from short, abstract sequences of numbers to huge, abstract concepts like love, which you think you understand as a kid. It’s defined by your relationship to your parent or guardian. That’s what love is. Or love is everything but that.”
You go out and put your understanding of love to work for you as a young adult.
You find out something new that reveals the limits of your ideas of love. You revise and sharpen your ideas.
You put those ideas out into the world until you have that first traumatic break-up and you realize your model for love is even fuzzier than it was originally!
All these experiences help you revise your model for love – never completely, never correctly, never incorrectly, and always in process.
Yes, that is modeling and it’s an essential component in successful learning experiences. We see it at work in both formal and informal teaching. We see parents modeling behavior and decision-making for their children. We see teachers using models of their own life experiences to guide their students. We see it in movies, political speeches, and other forms of storytelling.
Someone shares a model or part of one, and someone else takes that model for a spin based on their own assumptions and knowledge. The feedback they gain from experimenting with the model helps them evaluate their understanding and revise their application of it.
This is at the very core of critical thinking and how we teach it across the curriculum.
As Myer points out in his presentation, “all learning is modeling.”
It’s true about love. It’s true about a sequence of numbers. It’s true about modeling itself. You came in here with a model in your head about modeling. You’ll test that model here at MSRI. Everything you hear and see and experience will change and strengthen your model for modeling.
We will all walk away with a different model for modeling than when we got here.
At TEL, we are just now beginning work on a series of experiential learning modules for our courses. These modules will make extensive use of the modeling to promote critical thinking at a deeply personal (relevant) level. I will share more specific examples of this modeling as our project develops but, at this early stage, here are four guidelines for our work.
1. Make models relevant — The models we share as part of experiential learning must seem relevant in order to engage learners fully. We see relevance a key motivator to encouraging students to take ownership (assume agency) of their learning.
2. Encourage experimentation — Students need the feedback that comes through experimentation in order to reconsider and revise their models. The greater ownership they have of this process — the more they control their experimentation and the greater relevance it has to their situation — the more valuable the feedback will be.
3. Provide frameworks that help learners apply feedback and assess their original understanding of the model — It is important to the learning process that we allow students to make their own interpretations of model feedback and to make their own model adjustments. That is what agency (which leads to mastery) is all about. At the same time, we may also need to provide different frameworks that students can use to organize and make initial sense of feedback.
4. Foster an atmosphere of model personalization and mastery — In the end, we want students to walk away from their experiential learning projects with a clear sense of “I got that!” We want them to feel that moving forward, they have another model in their personal knowledge inventory for understanding life and accruing wisdom.
Rob Reynolds, Ph.D.