Capturing a Tension Between Structure and Variability

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

2. STEM

3. M

4. MEHTAM IENCES C S L A A T I C

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” Quantification Math / Johnson Measurement Stat/ Lehrer & Petrosino

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