Enhancing Math Education Through Mathematical Modelling Frameworks

1. Real Maths in your classroom? Consider useful mathematical modelling frameworks and try a Desmos activity Cami Sawyer Massey University C.Sawyer@massey.ac.nz Rebekah Ward Massey University rebekah.ward.nz@gmail.com

2. What is mathematical modelling? Mathematical modelling describes how we can use mathematics to understand the natural world and phenomena. Grünewald, (2013) Modelling follows a cycle: 1) Define a “real world” problem 2) Select important aspects and variables of the problem 3) Form a model and find mathematically significant solutions 4) Translate the solutions back into the real world problem 5) Reflect on model, make any changes or adjustments 6) Finalise and communicate model

3. Why should we use mathematical modelling? • Help students develop problem solving skills • Provides a deeper interconnected understanding of mathematics Engage students in lessons, which have "relevance to the students' lives, an element of challenge… and the demonstration that mathematics is useful within practical situations" (Attard, 2014) • Group work is an important aspect of modelling, and allows ideas to be shared and refined by different thinkers. • A way of teaching students with a range of abilities - may help with equity - “complex modelling examples are not reserved for highly talented and high performing students” (Kaiser, 2007)

4. Programme for International Student Assessment (PISA) 2021

5. In NZ? Modelling version of PPDAC Problem • What is the question? • What am I trying to solve? Plan • What assumptions am I making? • What are the important variables? • What do I want my model to tell me? What does a feasible solution look like? Model • How do I make a mathematical representation of the problem? (Start with a simple model)

6. In NZ? Modelling version of PPDAC Interpret • Does my model give me reasonable results that are consistent with the real world? • Do I need to go back to my model and add complexity? Conclusion • In the context of the problem, what does my model tell me? • What are the limitations of my model? • What further questions are there?

7. Activity Rubric • For formative or summative assessment • Follows the structure of the modelling cycle. • Broken down into sections for each part of the modelling cycle. • under “plan”, the student’s ability to make assumptions, define variables, and use of mathematical knowledge is assessed. • It assumes that students are asked to participate in group work as part of the task. • Each part of the model is assessed, along with the individual student’s participation. • Students use of technology is not assessed, and the work that could be done using technology is not directly assessed.

8. Activity: Hot Drinks https://www.youtube.com/watch?v=pCkL9UlmCOE Play: 0 to 0.19 & 3:23 to 3:40

9. Activity: Hot Drinks https://www.youtube.com/watch?v=pCkL9UlmCOE Play: 0 to 0.19 & 3:30 to 3:43

10. Activity: Hot Drinks • How hot is a hot drink? • What is a temperature that is too hot? Why? • Too cold? Why? • How quikly does a drink cool down? • How cold does it get? • What if we add milk?

11. Desmos – Year 12 Activity Hot drinks: go to: student.desmos.com enter class code: JZRVC5 Raw data and more: https://tinyurl.com/Modelling-hot-drinks Give students more time and have them work in groups

12. Desmos – Year 12 Activity

13. Desmos – Year 12 Activity

14. Desmos – Year 12 Activity

15. Desmos – Year 12 Activity

16. Desmos – Year 12 Activity

17. Desmos – Year 12 Activity

18. Desmos – Year 12 Activity

19. Desmos – Year 12 Activity

20. Desmos – Year 12 Activity

21. Using mathematical modelling with your students? “Mathematical modelling is central and essential to providing high school students with the knowledge, skills, and dispositions needed to make greater sense of the world.” NCTM, 2018