Professional Development Module created by the IMSPC Project Funded by the SASS initiative of NC Ready for Success

9:00-9:30Introductions & orientation to the project 9:30-10:30For the Birds – a modeling task 10:30-10:45Break 10:45-12:00The modeling cycle & framework 12:00 – 1:00Lunch 1:00 -2:00Evaluating modeling tasks & improving the framework 2:00 – 3:00Reframing questions as modeling tasks 3:00 – 3:30Reflections & goal setting

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.

Share who you are, where you currently teach, and what your connection to mathematical modeling currently is. What brought you to this discussion?

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.

What questions occur to you here?

How often should I fill the bird feeder?

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?

Here are the dimensions of the bird feeder. Do we need to reassess or add any assumptions based on this additional information?

Consider an answer to our question. Be prepared to share your results and the process involved in finding it.

 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?

 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.

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.

In this slightly adapted version of the CCSSM Modeling Cycle, the areas of the mathematical world and the real world context are made clearer.

 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?

 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?

 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.

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?