An Experiential Investigation of Algebraic Ideas Created and Implementedby Robert B. Davis
Bibliographic record
Abstract
Objective: To demonstrate instances of experiential learning of 6th grade students with Professor Robert Davis as the facilitator. Students first solve single order equations and then build on their learning to solve and justify the solutions of quadratic equations. Solving second order equations is generally an 8th or 9th grade strand, but through their own reflections and without intervention by the facilitator, students are able to understand the "secret" behind their solution. Description: Experiential learning is learning through reflection on doing, which is often contrasted with rote or didactic learning. Experiential learning can exist without a teacher and relate solely to the "meaning-making" (Holbrook Mahn 2012, p.101) process of the individual's direct experience. In Professor Carolyn Maher's published (1999) tribute to Professor Robert Davis two years after his passing, she quotes one of Prof. Davis' students who reflects on his own early education: "And once I had a teacher who understood. He brought with him the beauty of mathematics. He made me create it all for myself. He gave me nothing, and it was more than any other teacher has ever dared to give me." (p. 85)Reflection is a crucial part of the experiential learning process and Dewey wrote that "successive portions of reflective thought grow out of one another and support one another." (Kompf & Bond 2001 p. 55) Robin Alexander reinforced this idea when he wrote about creating a scaffold for further learning, and allowing for further experiences and learning. (2010)Facilitation of experiential learning is challenging, but a skilled facilitator asking the right questions and guiding reflective conversation before, during and after an experience, can help open a gateway to powerful new thinking and learning. The analytic is drawn from a set of 11 clips of Early Algebra of 6th grade students as Prof. Davis introduces the ideas of a variable, truth statements and legal substitutions. Students solve first order equations and with this experience they are able to solve second order equations; all without direct assistance from Prof. Davis. Finally individual students discover the "secret" for solving a special set of second order equations and since it is a secret all students are given the opportunity to arrive at a conjecture. No students are told the answer as they use their own experience to create justification.In conclusion I could not have produced this analytic without the long hours of editing video in the VMC by Kathy Spang and Patty Giordano. References:Alexander, R. J. (2010) Speaking but not listening? Accountable talk in an unaccountable context. Literacy Volume 44 Number 3 November 2010Giordano, P. (2008). Learning the concept of function: Guess my rule activities with Robert B. Davis. Unpublished doctoral dissertation, Rutgers University.Itin, C. M.(1999). Reasserting the Philosophy of Experiential Education as a Vehicle for Change in the 21st Century. The Journal of Experiential Education 22(2), 91-98.Kolb, D. (1984). Experiential Learning: experience as the source of learning and development. Englewood Cliffs, NJ: Prentice Hall. p. 21Kompf, M.,& Bond, R. (2001).Critical reflection in adult education. In T. Barer-Stein & M. Kompf (Eds.), The craft of teaching adults (p. 55). Toronto, ON.Maher, C. A. (1999) Mathematical Thinking and Learning: A Perspective on the Work of Robert B. Davis. Mathematical Thinking and Learning, I(1), 85-91Mahn, H. (2012) Vygostsky's Analysis of Children's Meaning Making Processes. International Journal of Educational Psychology, 1(2), 100-126.Spang, K. (2009). Teaching Algebra Ideas to Elementary School Children: Robert B. Davis' Introduction to Early Algebra.Unpublished doctoral dissertation, Rutgers University.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.006 | 0.011 |
| Scholarly communication | 0.005 | 0.003 |
| Open science | 0.001 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".