The real-world contexts for their mathematical modeling is a great idea, and they don't just do problems on paper. The physical and community aspects of the work seem to be important for student engagement. Can you talk about differences in student engagement from prior math courses? Are you collecting any data about this?

Thanks Daniel for your interest! Our project was specifically measuring teacher knowledge and attitudes towards mathematical modeling and viewing mathematics as a creative process. However, we have conducted multiple interviews with classroom teachers and asked questions specifically related to the difference they noticed in student engagement. The emerging themes from these multiple interviews in regards to student engagement include- 1) Students' affective "attachment" to the math modeling task- these "in vivo" codes include "care about the math"; "ownership"; "building a relationship with math"; 2) Students' persistence on the task- these in vivo codes include "Spent all their recess time"; "continued on with the project beyond the scope of our time allotted for the task"; kept asking teach 'when will we get to work on our MM task?'; 3) Students typically "disengaged" showed a interest in tasks, motivated to learn the math saying "Teach me the math so I can solve the problem." We want to include an interest inventory and attitude towards mathematics in our future studies. These narrative actually are just as powerful for us because it was this proof of student engagement that teachers noticed that convinced them to continue on with this "ambitious" teaching practice! 

This is a fascinating project. I love that students have an opportunity to engage fully in the modeling process. In your summary, you talk about your focus on teacher knowledge and attitudes towards mathematical modeling. In your measures, do you include questions targeting teachers' perceptions of whether students are learning the intended content (e.g. skip counting) as they engage in the modeling process or of whether teachers feel the added time required for modeling activities is well spent? I wonder if these perceptions influence teachers' attitudes towards mathematical modeling. Along those same lines, have you measured whether students are making gains in their understanding of either the content or the modeling process?

Thanks and great work!

"Am I ever going to need to use this math in real life?" is something we often hear from students. These models show how we use math on a daily basis, in all aspects of life. I liked how it was mentioned that teachers would spiral back to a previous scenario, once higher level skills had been taught. 

Hi Carrie, thanks for your comments. Yes our project was able to help realize the simple philosophy of a real-world problem driving students to discover the mathematics rather than the traditional approach of teaching the mathematics first and then solving the problem! This  not only helped students to become good communicators and collaborators but also helped them become better critical thinkers and creative problem solvers.

Hi. Thank you for sharing this. Embedding math work in community-based challenges or projects seems like such a terrific format for elementary-aged (or any aged, for that matter) students. Is there ever any kind of follow-up? For example, do the students and teachers ever find out how many meals they actually wound up contributing to? I can imagine it would be very helpful to hear feedback from the community organizations at some point.

Thanks James for your inquiry! Actually, the projects come to reality for all our students. The students who solved the "ordering the bus for a field trip" problem helped the teachers with the planning and they went on their field trip. The students who ran the coin drive and used the money to optimize the meals for the community also had a chance to give to their community! This was the prize at the end of all the hard work and critical thinking!!! Students were truly invested and their math modeling paid off double fold in fun and caring ways!

You mention integrating these modeling tasks into different kinds of curricula. I imagine some of these are more aligned with the modeling work that you're focusing on than others. Can you talk a bit about how that's making a difference in how easily or well students are taking to these modeling problems, or taking up mathematical modeling as a way of thinking about other math problems?

Thank you for your comment Jim. Yes, we have observed in the project that mathematical modeling has helped students to become better critical thinkers and creative problem solvers. The open-endedness in the approach, the flexibility in the assumptions they can make, the opportunity to do research, the ability to collaborate and make decisions on what is "best" has definately helped students to take up mathematical modeling as a way of thinking about solving math problems. For educators this paradigm shift also allows seeing students not just as consumers of information but students as producers as well as peer-reviewers of information.