Spatial-numeric method application to the movable wedge problem for Physics First pedagogy
Abstract
The objective is to solve the college physics problem of a block sliding down a movable smooth wedge without friction anywhere using a spatial-numeric perspective. The drawing method used the sum of the normal force and weight of the block to find the wedge acceleration. The drawing method results are equivalent to the algebra method results within drawing accuracy. The result of a geometric construction with regular drawing uncertainly was shown for the case without any horizontal applied force. For the case of a given horizontal applied force, an additional numeric graphing method was shown with additional drawing uncertainty in the result. The geometric construction without graphing resuted in solving the horizontal applied force case via scaling in the concept of modified gravity experienced by the block on the wedge’s slant edge, assuming a pre-requisite knowledge of algebra and trigonometry. The presented spatial numeric method and results imply a Physics First pedagogy of using the spatial numeric abilities, with the inclusion of the pre-projectile problem, pre-traffic-light problem, and post-collision problem in a one-semester syllabus.
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Chen, J. W. (2010). A Web Based Bayesian Van Hiele Problem Solver For Computer. ASEE Annual Conference & Exposition 2010 , Louisville, Kentucky. https://peer.asee.org/16631
Chabache, E., Cao Y., Miao, Y., Groisman, A., Devreotes, P., Rappel, W. (2021) Coupling traction force patterns and actomyosin wave dynamics reveals mechanics of cell motion. Mol Syst Biol, Dec;17(12):e10505. https://pubmed.ncbi.nlm.nih.gov/34898015/
Conrad, B.N., Pollack, C., Yeo, D.J., Price, G.R. (2023). Structural and functional connectivity of the inferior temporal numeral area. Cereb Cortex, May 9;33(10):6152-6170. https://pubmed.ncbi.nlm.nih.gov/36587366/
Dehipawala, S., Kokkinos, D. S., & Taibu, R., & Tremberger, G., Cheung, T. (2022) Excel optimization pedagogy using Van Hiele learning model of spatial abilities with Force Concept Inventory Test MRI and haptic learner data for COVID-19 online challenge. ASEE Middle Atlantic Section Conference 2020 Spring, Newark, New Jersey. https://peer.asee.org/40053
Dworak, E., Revelle, W., Condon, D. (2023) Looking for Flynn effects in a recent online U.S. adult sample: Examining shifts within the SAPA Project. Intelligence, Volume 98, 101734, https://www.sciencedirect.com/science/article/pii/S0160289623000156
Fernandez-Ruiz, A., Sirota, A., Lopes-Dos-Santos, V., Dupret, D. (2023) Over and above frequency: Gamma oscillations as units of neural circuit operations. Neuron, Apr 5;111(7):936-953. https://pubmed.ncbi.nlm.nih.gov/37023717/
Hawes, Z., Ansari, D. (2020). What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior. Psychon Bull Rev, Jun;27(3):465-482. https://pubmed.ncbi.nlm.nih.gov/31965485/
Hawes, Z., Sokolowski, H.M., Ononye, C.B., Ansari, D. (2019). Neural underpinnings of numerical and spatial cognition: An fMRI meta-analysis of brain regions associated with symbolic number, arithmetic, and mental rotation. Neurosci Biobehav Rev, Aug;103:316-336. https://pubmed.ncbi.nlm.nih.gov/31082407/
Hoyer, C., Girwidz, R. (2020). Animation and interactivity in computer-based physics experiments to support the documentation of measured vector quantities in diagrams: An eye tracking study. Phys. Rev. Phys. Educ. Res. 16, 020124. https://journals.aps.org/prper/pdf/10.1103/PhysRevPhysEducRes.16.020124
Jaramillo, S., Kuo, E., Rottman, B.M., and Nokes-Malach, T.J. (2021). Investigating causal inference difficulties with a simple, qualitative force-and-motion problem. Physics Education Research Conference 2021. Part of the PER Conference series Virtual Conference: August 4-5, 2021Pages 197-202. https://www.per-central.org/items/detail.cfm?ID=15752
Javanmardi, Y., Agrawal, A., Malandrino, A., Lasli, S., Chen, M., Shahreza, S., Serwinski, B., Cammoun, L., Li, R., Jorfi, M., Djordjevic, B., Szita, N., Spill F., Bertazzo S., Sheridan G., Shenoy V., Calvo F., Kamm R., Moeendarbary E. (2023) Endothelium and Subendothelial Matrix Mechanics Modulate Cancer Cell Transendothelial Migration. Adv Sci (Weinh), Apr 13; e2206554. https://pubmed.ncbi.nlm.nih.gov/37051804/
LeGresley, S., Delgado, J., Bruner, C., Murray, M., and Fischer, C. (2019). Calculus-enhanced energy-first curriculum for introductory physics improves student performance locally and in downstream courses. Phys. Rev. Phys. Educ. Res. 15, 020126. https://journals.aps.org/prper/pdf/10.1103/PhysRevPhysEducRes.15.020126
Liu, D., Mohattala, H. (2021). A study of undergraduates' understanding of vector - decomposition of forces on inclined planes. Physics Education Research Conference 2021. Part of the PER Conference series. Virtual Conference: August 4-5, 2021 Pages 233-238. https://www.per-central.org/items/detail.cfm?ID=15758
Mason, R., Schumacher, R., Just, M. (2021) The neuroscience of advanced scientific concepts. NPJ Sci. Learn, 6, 29. https://doi.org/10.1038/s41539-021-00107-6
Nakakoji, Y., Wilson, R. (2020) The Interdisciplinary Learning in Mathematics and Science: Transfer of Learning for 21st Century Problem Solving at University. I Intell., Sep 1;8(3):32. doi: 10.3390/jintelligence8030032. https://pubmed.ncbi.nlm.nih.gov/32882908/
Naufal M., Abdullah, A., Osman, S., Abu, M., Ihsan, H., Rondiyah, R. (2021) Reviewing the Van Hiele model and the application of metacognition on geometric thinking. International Journal of Evaluation and Research in Education (IJERE), Vol 10, No 2: June 2021. 597-605. https://ijere.iaescore.com/index.php/IJERE/article/view/21185
Nordine, A., Krajcik, J., Fortus, D. (2011). Transforming energy instruction in middle school to support integrated understanding and future learning. Science Education, Vol 95, Issue 4, 670-699. https://onlinelibrary.wiley.com/doi/10.1002/sce.20423
Okano Y., Kase Y., Okano H. (2023) A set-theoretic definition of cell types with an algebraic structure on gene regulatory networks and application in annotation of RNA-seq data. Stem Cell Reports, Jan 10;18(1):113-130 https://pubmed.ncbi.nlm.nih.gov/36400029/
Pujawan, I. G. N., Suryawan, I. P. P., & Prabawati, D. A. A. (2020). The Effect of Van Hiele Learning Model on Students’ Spatial Abilities. International Journal of Instruction, 13(3), 461-474. https://doi.org/10.29333/iji.2020.13332a
Sabo, H., Goodhew, L., Robertson, A. (2016). University student conceptual resources for understanding energy. Phys. Rev. Phys. Educ. Res. 12, 010126. https://journals.aps.org/prper/abstract/10.1103/PhysRevPhysEducRes.12.010126
Sadler, P., Tai, R.(2007) Transitions: The two high-school pillars supporting college science. Science, Jul 27;317(5837):457-8. https://pubmed.ncbi.nlm.nih.gov/17656706/
Sevgen, A. (2013) Mass on a moving wedge. http://www.phys.boun.edu.tr/mooc/?p=41 (Also on Yutube https://www.youtube.com/watch?v=xuXwWjbnVPg
Sevgen, A. (2014) Mass on a moving wedge: analysis with energy-momentum arguments. http://www.phys.boun.edu.tr/mooc/?p=165
(Also on Youtube https://www.youtube.com/watch?v=INft7uHGszc)
Wingard, J. (2022). Higher Ed Must Change or Die. Inside Higher Education, August 15 https://www.insidehighered.com/views/2022/08/16/higher-ed-must-change-or-die-opinion
Zhan M, Pallier C, Agrawal A, Dehaene S, Cohen L. (2023) Does the visual word form area split in bilingual readers? A millimeter-scale 7-T fMRI study. Sci Adv., Apr 5;9(14):eadf6140. https://pubmed.ncbi.nlm.nih.gov/37018408/
Zhu. M., Abdulzahir, A., Perkins,M., Chan, C., Krause, B., Casey, C., Lennertz, R., Ruhl,D., Hentschke, H., Nagarajan, R., , Chapman, E., Rudolph, U., Fanselow, M., Pearce, R. (2023). Control of contextual memory through interneuronal α5-GABAA receptors. PNAS Nexus, Volume 2, Issue 4, April 2023, pgad065, https://doi.org/10.1093/pnasnexus/pgad065
Authors
Dehipawala, S., Shekoyan, V., Holden, T., & Cheung, T. (2023). Spatial-numeric method application to the movable wedge problem for Physics First pedagogy. Momentum: Physics Education Journal, 7(2), 299–310. https://doi.org/10.21067/mpej.v7i2.8562
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