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