NSF Awards: 1441024
2018 (see original presentation & discussion)
Grades K-6
Our video will showcase a project called IMMERSION:Integrating Mathematical Modeling, Experiential learning and Research through a Sustainable Infrastructure and an Online Network for teachers in the elementary grades (2014 – 2017) where three research sites collaborated with school districts in diverse settings find relevant context to engage young modelers; encouraging open-endedness and creativity in mathematical modeling; and discovering how mathematics can be an instrumental tool to make sense of and make important decisions in the real world. Students tackled community problems that they cared about and solutions gave them a sense of empowerment.
A National Science Foundation Sponsored STEM-C Program (NSF-1441024) through George Mason University, Montana State University, and Harvey Mudd College
Daniel Damelin
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?
Jennifer Suh
Associate Professor of Math Education
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!
Michael Belcher
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!
Jennifer Suh
Associate Professor of Math Education
Great question Michael! We did measure teacher attitudes using a combination of attitudinal scales: the Attitudes to Mathematics and Mathematics Teaching Survey (White, Way, Perry, & Southwell, 2005/2006); the Beliefs about the Nature of Mathematics scale (Tang & Hsieh, 2014); and the Beliefs about
Learning Mathematics scale (Tang & Hsieh, 2014). The Attitudes to Mathematics and Mathematics Teaching Survey is a 20‐item instrument that examines 5 factors: 1) Open and Creative nature (OC), 2) Conservative and Rigorous nature (CR), Learning through Student Initiative (SI), 4) Learning by following Teacher Instruction (TI), and 5) Utilitarianism in Teaching (UT). On average, teachers had high OC and SI factor scores across all three measurement occasions. This suggests they tended to regard mathematics as open and creative and believed students should have an active role in the learning process. In contrast, the teachers had low mean TI and UT factor scores, indicating they did not believe mathematics was best learned by following teacher instruction and/or doing what is deemed practical. With regards to the conservative and rigorous nature of mathematics, teachers’ mean factor scores across all three measurement occasions were consistently close to neutral.
To estimate changes in participants’ OC, CR, SI, TI and UT factor scores across time, we used linear mixed models for repeated measures in SAS® software1, Version 9.4, We founds that there is moderately strong evidence that, on average, over the duration of the workshop, teachers’ OC factor scores increased (95% CI: 0.18 ± 0.11, F(1,71.81) = 10.29, p= .002) and their CR (95% CI: ‐0.27 ± 0.19, F(1,71.72) = 7.69, p = .007) and TI (95% CI: ‐0.18 ± 0.13, F(1,71.24) = 8.02, p = .006) factor scores decreased. These changes translate to small (Cohen, 1988), but “educationally significant” (Hill, Bloom, Black, & Lipsey, 2008) effect sizes ranging from 0.33 to 0.35. No meaningful changes in mean factor scores occurred during this time for the other two factors, SI and UT. In addition, there were not any meaningful changes in mean factor scores from the post‐workshop to the post‐study group measurement occasion. This suggests that the changes observed during the course of the workshop were sustained until the end of the study group experience.
This was exciting for us because it showed that our teachers' attitude that mathematics is an open and creative (OC) process increased at the same time their attitudes about mathematics being about Conservative and Rigorous nature (CR), and Learning by following Teacher Instruction (TI) decreased. The factor Learning through Student Initiative did not change but the mean scores across all three measurement time point was as high (m1=5.22; m2=5.21 and m3=5.25) as the Open and Creative nature mean score which is promising because teachers having the belief that students should learn through student initiatives complements and guarantees the success of enacting mathematical modeling.
Carrie Willis
"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.
Padmanabhan Seshaiyer
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.
James Diamond
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.
Jennifer Suh
Associate Professor of Math Education
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!
Jim Hammerman
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?
Megan Wickstrom
Thanks, Jim, for your comment. You are correct that different curricula is more aligned with modeling than others. We have seen that teachers are tending to use modeling as an additional challenge or unit in their classroom, not necessarily tied to what they are currently doing in mathematics. I have witnessed the reverse effect. Several of our teachers in Bozeman, after learning about modeling, advocated for a curriculum that had more, as they called it, "modeling" like tasks. We have seen that a key motivator for student engagement tends to be authenticity. If the problem seems important to students then they want to dive in and work toward a solution, even if that means learning new mathematics along the way.
Padmanabhan Seshaiyer
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.
Further posting is closed as the event has ended.