Sense Making and the Development of Other
Mathematical Practices
http://mathforum.org/workshops/cmc-2014/
Steve Weimar
steve@mathforum.org
What are we currently thinking about and trying to
figure out with the mathematical practices and the
development of these with students?
What I am thinking about
What do we mean by “learning the mathematical
practices”? (and what does this have to do with learning
math, more generally?)
What might it look like if the students were explicitly
working on this and accountable for competence and
improvement in the practices?
What I am thinking about
Focus on two practices: Sense Making, Looking for
Structure
What do we mean by these practices?
What is the interaction between Sense Making and
Looking for Structure?
What does it mean to get better at them?
How is this facilitated?
(graphic organizer for recording)
Plan
Engage a scenario with sense making (Notice and Wonder)
Add notes to our graphic organizer about Sense Making
Pick a wonder/problem and work on it
Compare and contrast, looking for structure
Add notes to our graphic organizer about Looking for
Structure
Reflect on the process and what helps facilitate
Revise/tweak the process
Do a different type of problem
Interaction of Sense Making and Looking for Structure
Notice and Wonder:
You have 7 cups of
dog food. You use
two-thirds of a cup of
dog food at each
meal.
Fraction +1 Scenario
Start with a fraction: add 1 to the numerator and 1 to the
denominator
Three Piece Spaghetti
Break a piece of spaghetti into three pieces.
Try to make a triangle with the ends of the pieces
brought together to make vertices.
Find a value for x.
When I first posted this problem, I neglected to mention that it can be done with
introductory geometry concepts (supplements, transversals, similarity, 180 degrees
in a triangle, etc.) and no trig.