Design of Modeling Sessions for PSTs
Design of Modeling Sessions for PSTs
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Background
Background
Mathematical Model - A representation of a mathematical system or scenario that is used to gain understanding of real-world problems (Bliss et al., 2014)
Benefits of Mathematical Modeling
Help students see the importance of mathematical understanding (Blum & Ferri, 2016)
Deepen mathematical understanding (Anhalt et al., 2018)
Raise interest and build awareness of real-world applications (Cirillo et al., 2016)
Bolster problem-solving skills, encourage creative & critical thinking (Gann et al., 2016)
Opportunities to express, modify, and refine ways of thinking (Lesh et al., 2003)
Cirillo et al. (2016) adaptation of Blum (2011) Modeling Cycle
Methods
Methods
Research Questions:
How did Pre-Service Math Teachers (PSMTs) respond to the design of our mathematical modeling sessions?
How did our sessions impact their view on the teaching and learning of mathematics?
Participants: 26 PSMTs in a math methods course during Fall 2021
Data: Video/audio recordings of sessions, Student work, Surveys
Analysis: Thematic analysis and pre- & post- survey comparison
Session 1
Atomistic Modeling Task, “Seeking Shelter”
Engage students with parts of the modeling cycle
Opportunity to look at a real-world problem through a social justice lens
Participants experience the open-ended nature of mathematical modeling
Overview on Mathematical Modeling
Review modeling process and criteria for an effective task
Look at various modeling cycles and how a modeling task differs from a word problem or an applications problem
How to scaffold modeling tasks
Seeking Shelter by Citizen Math
Student Feedback on Session 1
“Mathematical modeling is the way in which we use math to model real world outcomes. A mathematical model can lead us to conclusions and predictions about what happens in the world around us. It can be a messy process, but is one worth doing, because it requires us to think on a large, more powerful scale.”
- Abigail
“[Modeling] really has the students investigate and create their own solutions that make sense to them. It moves away from memorizing procedures and formulas and moves towards more conceptual ideas.”
- Robert
Session 2
Warm Up - Brainstorming with Mindmaps
Holistic Modeling Task - “Having Kittens”
Low-floor, high-ceiling task
Complete modeling cycle experience
Follow-up discussion on implementing modeling in a classroom setting
Student Feedback on Session 2
“I feel more confident in seeing how to facilitate math modeling.”
- Jen
"I am worried about the time constraint within classroom and not giving too much guidance.”
- Amy
“This lesson had more scaffolding than the last lesson but still had plenty of room for productive struggle.”
- Zoey
“It was helpful because we got to model however we wanted and then each group shared what they did, so it showed how students do not all think the same and often have different ideas.”
- Iris
Findings
Findings
How would you rate today’s modeling session in terms of enjoying the task?
How would you rate today’s modeling session in terms of learning about the modeling process?
The role of the teacher is to tell students exactly what definitions, formulas, and rules they should know and demonstrate how to use this information to solve mathematics problems.
Students can learn mathematics through exploring and solving contextual and mathematical problems.
How well prepared do you feel to enact mathematical modeling in your future classroom?
PSMTs:
Generally have little prior knowledge of mathematical modeling
Gain experience from engaging with modeling tasks themselves
Benefit from collaboration
PSMTs still had concerns about:
Time constraints in the classroom
How to best support students
Possible student frustration
Balancing freedom and providing constraints
Future Research
Giving PSMTs the opportunity to engage collaboratively in modeling themselves
Providing more examples of modeling tasks across different mathematics courses
Having PSMTs observe a teacher implementing modeling with grade-level students
Discussing implementation of modeling tasks
Having PSMTs find and evaluate modeling tasks
References
Anhalt, O., C., Cortez, R., & Bennett, A. B. (2018). The emergence of mathematical modeling competencies: An investigation of prospective secondary mathematics teachers. Mathematical Thinking and Learning, 20(3), 202-221.
Bliss, K. M., Fowler, K. R., & Galluzzo, B. J. (2014). Math modeling: Getting started and getting solutions. Society for Industrial and Applied Mathematics (SIAM).
Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (Vol. 1, pp. 15-30). Springer.
Blum, W., Ferri, R. (2016). Advancing the teaching of mathematical modeling: Research-based concepts and examples. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 53-64). National Council of Teachers of Mathematics.
Carlson, M., Wickstrom M., Burroughs E., & Fulton, E. (2016). A case for mathematical modeling in the elementary school classroom. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 121-130). National Council of Teachers of Mathematics.
Cirillo, M., Bartell, T., & Wager, A. (2016). Teaching mathematics for social justice through mathematical modeling. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 53-64). National Council of Teachers of Mathematics.
Gann, C., Avineri, T., Graves, J., Hernandez, M., & Teague, D. (2016). Moving students from remembering to thinking: The power of mathematical modeling. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 97-106). National Council of Teachers of Mathematics.
Hirsch, C. R., & McDuffie, A. R. (2016). Annual perspectives in mathematics education 2016: Mathematical modeling and modeling mathematics. National Council of Teachers of Mathematics.
Lesh, R., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. S. (2003). Model development sequences. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 35-58). Lawrence Erlbaum Associates, Inc.
Maiorca, C., & Stohlmann, M. (2016). Inspiring students in integrated STEM education through modeling activities. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 153-162). National Council of Teachers of Mathematics.
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