Mathematical Complexity of Computational Modeling Experiences for - PowerPoint PPT Presentation

Mathematical Complexity of Computational Modeling Experiences for Elementary Students Kevin W. McElhaney, Gautam Biswas, Jennifer L. Chiu STEM+C PI Summit Challenges Showcase September 19, 2019

Curricular context: Modeling urban water runoff • Multi-week, 5th grade curriculum unit integrating earth science, engineering, and computational thinking (NGSS PEs 5-ESS3-1, 3-5ETS1-3) • Students develop a computational model of water runoff and use it to test and refine engineering solutions

Designing the runoff model SEPs CCCs (e.g., modeling, (e.g., Systems and information, system models, investigation) matter) Science DCIs Runoff model (Human impacts/ Runoff) Engineering DCIs CT concepts & practices (e.g., develop, (e.g., creating and testing test, refine computational artifacts, solutions) loops, variables…)

Basic runoff system model rainfall runoff s u r f a (rainfall – absorption) c e absorption (material dependent)

Runoff algorithm (time dependent) set StormDuration to... set ElapsedTime to 0 variable initialization set HourlyRainfall to... set TotalAbsorption to 0 set TotalRunoff to 0 simulation set TotalRainfall to 0 with stopping set AbsorptionCoeff to... condition Repeat until (ElapsedTime is equal to StormDuration) change ElapsedTime by 1 change TotalRainfall by HourlyRainfall change TotalAbsorption by ... set TotalRunoff to TotalRainfall – TotalAbsorption

Runoff algorithm (time dependent) set StormDuration to... Temporal variables set ElapsedTime to 0 require reasoning set HourlyRainfall to... about rates and set TotalAbsorption to 0 durations set TotalRunoff to 0 set TotalRainfall to 0 set AbsorptionCoeff to... Repeat until (ElapsedTime is equal to StormDuration) change ElapsedTime by 1 change TotalRainfall by HourlyRainfall change TotalAbsorption by ... set TotalRunoff to TotalRainfall – TotalAbsorption

Runoff algorithm (time dependent) set StormDuration to... set ElapsedTime to 0 Hourly vs. set HourlyRainfall to... total variables set TotalAbsorption to 0 set TotalRunoff to 0 set TotalRainfall to 0 set AbsorptionCoeff to... Repeat until (ElapsedTime is equal to StormDuration) change ElapsedTime by 1 change TotalRainfall by HourlyRainfall change TotalAbsorption by ... set TotalRunoff to TotalRainfall – TotalAbsorption

Runoff algorithm (time dependent) set StormDuration to... set ElapsedTime to 0 “set” vs. “change” set HourlyRainfall to... set TotalAbsorption to 0 set TotalRunoff to 0 set TotalRainfall to 0 set AbsorptionCoeff to... Repeat until (ElapsedTime is equal to StormDuration) change ElapsedTime by 1 change TotalRainfall by HourlyRainfall change TotalAbsorption by ... set TotalRunoff to TotalRainfall – TotalAbsorption

Runoff algorithm (time dependent) set StormDuration to... Repeat until (stopping set ElapsedTime to 0 set HourlyRainfall to... condition) is challenging set TotalAbsorption to 0 set TotalRunoff to 0 set TotalRainfall to 0 set AbsorptionCoeff to... Repeat until (ElapsedTime is equal to StormDuration) change ElapsedTime by 1 change TotalRainfall by HourlyRainfall change TotalAbsorption by ... set TotalRunoff to TotalRainfall – TotalAbsorption

Runoff algorithm (not time dependent)

Runoff algorithm (not time dependent) set TotalRainfall to... set AbsorptionLimit to... if (TotalRainfall is equal to AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is less than AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is greater than AbsorptionLimit) set TotalAbsorption to AbsorptionLimit set TotalRunoff to TotalRainfall – TotalAbsorption

Runoff algorithm (not time dependent) No rate-based or set TotalRainfall to... set AbsorptionLimit to... temporal variables if (TotalRainfall is equal to AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is less than AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is greater than AbsorptionLimit) set TotalAbsorption to AbsorptionLimit set TotalRunoff to TotalRainfall – TotalAbsorption

Runoff algorithm (not time dependent) set TotalRainfall to... No “change” set AbsorptionLimit to... if (TotalRainfall is equal to AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is less than AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is greater than AbsorptionLimit) set TotalAbsorption to AbsorptionLimit set TotalRunoff to TotalRainfall – TotalAbsorption

Runoff algorithm (not time dependent) set TotalRainfall to... Simpler conditions; set AbsorptionLimit to... no nesting if (TotalRainfall is equal to AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is less than AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is greater than AbsorptionLimit) set TotalAbsorption to AbsorptionLimit set TotalRunoff to TotalRainfall – TotalAbsorption

Designing the runoff model SEPs CCCs (e.g., modeling, (e.g., Systems and information, system models, investigation) matter) Science DCIs Runoff model (Human impacts/ Runoff) Engineering DCIs CT concepts & practices (e.g., develop, (e.g., programming, test, refine algorithms, variables…) solutions)

Designing the runoff model Grade-appropriate mathematics concepts SEPs CCCs (e.g., modeling, (e.g., Systems and information, system models, investigation) matter) Science DCIs Runoff model (Human impacts/ Runoff) Engineering DCIs CT concepts & practices (e.g., develop, (e.g., programming, test, refine algorithms, variables…) solutions)

Summary • Computational modeling experiences are constrained by grade-appropriate mathematics concepts, especially in elementary • Designers may be challenged to align multiple educational frameworks (NGSS, CS Framework, CCSSM) at specific grade levels • Argues for a broad definition of “computational model” for STEM+C education • model that leverages computational affordances (e.g., facilitates rapid testing and iterative refinement)

Project team UV UVA SRI SR • Chris Dittrick • Nonye Alozie • Sarah Fick • Satabdi Basu • James Hong • Ron Fried • Sarah Lilly • Reina Fujii • Anne McAlister • HeeJoon Kim • Jennifer Knudsen Vanderbilt ilt • Beth McBride • Ningyu Zhang Acknowledgements: This material is based upon work supported by the National Science Foundation under Grant No. DRL- 1742195. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.