1. Quantitative Reasoning Reaction Rose Mary Zbiek - Penn State August 2013 Capturing a Tension Between Structure and Variability

2. STEM

3. M M

4. MEHTAMMEHTAM IENCESIENCES ATICATIC CSLACSLA

5. STEM Relationships Mathematics and Statistics Deductive reasoning & Probabilistic reasoning Structure & Variability (Peck, Gould, & Miller, 2013) Variance as inevitable Invariance as theorem (Sinclair, Pimm, & Skelin, 2012) Role of Context (Peters, 2010) Interpretive stance (van Oers, 1998; Johnson, 2013)

6. STEM Relationships STE M (dis)connect Math as tool for STE “apply mathematical routine to quantities” “preform mathematical calculation(s) ” (Waterbury Summit) STE as setting for Math Bacterial growth – exponential functions F=ma – rational functions  “Curricular math” in contrast to modeling (especially in U.S.A.) (Zbiek & Conner, 2008)

7. Freudenthal: “Children should be granted the same opportunities as the grown-up mathematician claims for himself” [or herself]. (1971, p. 424)

8. Practices & Processes STEM integration happens at the level of borrowed concepts (which might be “quantities” as numbers or measures) and appropriated procedures (which might be the “tools” applied).

9. Practices & Processes STEM integration happens at the level of borrowed concepts (which might be “quantities” as numbers or measures) and appropriated procedures (which might be the “tools” applied). Integrate based on practices or processes. CCSSM [“Use mathematics to model”] Guidelines for Assessment and Instruction in Statistics Education [GAISE] (Franklin et al., 2007)

10. What would be a learning progression (or landscape) if we strive for P-16 S,T,E,M co-develop with a focus on processes and practices?

11. Elaboration of “model” Math / Johnso n Math / Johnso n Stat/ Lehrer & Petrosino Stat/ Lehrer & Petrosino Quantification Measurement

12. Promise of Quantitative Reasoning Learning trajectories & learning progressions for STEM Johnson: Connections to other forms of reasoning Learning trajectories Essential Understanding (big ideas for teachers) Lehrer & Petrosino: Summary of Learning Trajectory for Data Modeling

13. Promise of Quantitative Reasoning Johnson (Reasoning/Essential Understanding series) Lehrer & Petrosino (Learning trajectory for data modeling) Number & numeration (EU) Multiplicative reasoning (R, EU) Proportional reasoning (R, EU) Algebraic reasoning (R) Function (EU) Difference among measures Shapes of same data Sample-to-sample variability

14. Promise of Quantitative Reasoning Johnson (Reasoning/Essential Understanding series) Lehrer & Petrosino (Learning trajectory for data modeling) Number & numeration (EU) Multiplicative reasoning (R, EU) Proportional reasoning (R, EU) [Statistics (EU) ] Algebraic reasoning (R) Function (EU) Difference among measures [Mean as fair share?] [Proportionality?] Shapes of same data Sample-to-sample variability [Symbol sense, Representational fluency]

15. Teacher Development/Support Train to know/to be able to do  Prepare to engage Example: Focus on process/practice, Acknowledge systems Mid-Atlantic Center for Mathematics Teaching and Learning [MAC-MTL] (NSF funded 2001-present)

16. MAC-MTL: Micro & Macro Levels Process-and-action approach (Zbiek, Heid, & Blume, 2012) Mathematical processes (generative acts such as defining and generalizing) Products (e.g., definition, generalization) Actions (performed on products; manipulating, linking, …) Teaching Triad (Jaworski, 1994; Potari & Jaworski, 2002) Mathematical challenge Cognitive and affective sensitivity to students Management of learning

17. Thank you for the insights and inspiration