professional development module created by the imspc project funded by the sass initiative of nc...
TRANSCRIPT
Implementing Mathematical Modeling: Learning Across Educational Levels
Professional Development Module created by the IMSPC ProjectFunded by the SASS initiative of NC Ready for Success
Agenda
9:00-9:30 Introductions & orientation to the project
9:30-10:30 For the Birds – a modeling task
10:30-10:45 Break
10:45-12:00 The modeling cycle & framework
12:00 – 1:00 Lunch
1:00 -2:00 Evaluating modeling tasks & improving the framework
2:00 – 3:00 Reframing questions as modeling tasks
3:00 – 3:30 Reflections & goal setting
Goals for the Day
In this module, we will collaborate to:
Develop shared meanings of notions related to mathematical modeling,
Explore a framework of teacher practices supporting students’ development as mathematical modelers,
Evaluate and adapt modeling tasks for use in your classrooms using the framework, and
Increase K-12 and college faculty awareness of mathematical modeling in the curriculum across educational levels.
Introductions
Share who you are, where you currently teach, and what your connection to mathematical modeling currently is. What brought you to this discussion?
For the Birds
The birdfeeder outside of my house at two different times. I don’t want to refill it too often, but want to keep the birds coming back.
For the Birds
What questions occur to you here?
For the Birds
How often should I fill the bird feeder?
For the Birds
Take a moment to discuss approaches you might take here. What information
do you need? What variable
quantities are you considering?
What assumptions are you making?
A modeling example
Here are the dimensions of the bird feeder.
Do we need to reassess or add any assumptions based on this additional information?
For the Birds
Consider an answer to our question. Be prepared to share your results and the process involved in finding it.
For the Birds
How satisfied are you with your answer? Are you confident enough to implement
it yourself? To recommend it to someone else?
How could you improve your model?
A modeling example
Do our solutions seem reasonable? What could we integrate that we chose to ignore?
Some examples: 7 inches from the top, there are only two holes –
will the rate remain the same? Could we make adjustments for hours when
birdseed will be eaten more quickly? What about the 2 inches at the bottom below
the bottom holes? From here, we may choose to reformulate
our question or our model.
CCSSM Modeling Cycle
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors. p. 72.
CCSSM Modeling Cycle
In this slightly adapted version of the CCSSM Modeling Cycle, the areas of the mathematical world and the real world context are made clearer.
CCSSM Modeling Cycle
When and how does the “teaching” occur when a task such as this is implemented in the classroom?
What might be the instructional purpose of using such a task?
What content might you teach with the For the Birds activity?
How would you expect student learning to proceed?
Framework for Faculty Practice
Using the Framework
You will find a collection of tasks for your group on your tables. Select one task to review using the modeling framework.
Identify key characteristics of the task using the language of the framework.
Consider what seems to be the target level learner for the task. How could it be adapted to address learners of another level?
Adapting or Creating Tasks
When examining your teaching materials, you may find that you have access to many interesting problems. However, if they aren’t actually modeling tasks, you may need to make some adaptations.
Consider the two examples that
follow.
Adapting & Creating Tasks
In these two tasks, an interesting task is made into a modeling task by revising the question or the given information.
What characteristics of modeling tasks do you see provided in the adapted task that were not present in the given task?
Framework for Faculty Practice