Annotated Bibliography
A working reading list for the three-paper program — grouped by the paper each source is load-bearing for, annotated with why it earns the slot, and tagged to the specific research question it supports.
This is a working document, not a final reference list. New entries arrive when a paper draft needs them; weak entries get cut when a tighter citation replaces them. The goal is twenty sources you actually use, not two hundred you don't.
Cross-cutting
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(2018). Make Eigenvalues Resonate: A Coupled Oscillator Project for Lower-Division Linear Algebra. PRIMUS, 28(1). doi:10.1080/10511970.2018.1484400
The anchor for Paper 01. Anderson's original MER project uses a two-mass spring-coupled pendulum as a verifiable bridge from matrix diagonalization to physical resonance. Our paper extends this to a three-degree-of-freedom case with an open-hardware BOM and a computer-vision tracking pipeline — explicitly taking up Anderson's written invitation in the Math 2BL S26 deliverables doc: "Project To-Do List: Under development (maybe you can help me develop this in spring 2026)?"
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(2024). Five Anti-Racist Learner-Centered Objectives for the Applied Mathematics Classroom. PRIMUS. doi:10.1080/10511970.2024.2369984
The anchor for Paper 03 and the evaluation lens for Papers 01 and 02. Anderson's five objectives (humanize the discipline, authentic modeling, transferable skills, student agency, assessment as learning) are operationalized into the 5×3 audit rubric in Paper 03, and mapped onto every MER 2.0 lab activity in Paper 01.
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(1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher, 15(2), 4–14.
Pedagogical content knowledge. The canonical citation for the claim that teaching a topic requires a different kind of knowledge than doing the topic. Frames every paper's positioning: what does a teacher of eigenvalues need to know that a user of eigenvalues does not?
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(2003). Design-Based Research: An Emerging Paradigm for Educational Inquiry. Educational Researcher, 32(1), 5–8.
Methodology anchor for all three papers. Each paper is design-based research, not a randomized controlled trial. This citation justifies (a) iterating the intervention during the study, (b) reporting on small-n pilots as contributions, and (c) treating the artifact itself as a research output.
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(1980). Mindstorms: Children, Computers, and Powerful Ideas. Basic Books.
The hands-on verification ethos. Papert's insistence that powerful ideas become learnable when students can make something do the thing sits behind Jeff Anderson's own "verifiable at a kitchen table" criterion. Cited in every paper's motivation as the intellectual lineage for the hardware kit, the SVD-first activity, and the modeling-co-pilot constraint.
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(2006). The $25,000,000,000 Eigenvector: The Linear Algebra behind Google. SIAM Review, 48(3), 569–581.
The tone target. Anderson cites this paper as the gold standard for "make abstract linear algebra concretely consequential." Every paper in the program tries to match its storytelling register: open with a concrete stake (a $25B valuation, a student's kitchen table, a ChatGPT refusal), then earn the math.
6 cross-cutting refs
Paper 01 — MER 2.0
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(2016). Introduction to Linear Algebra (5th ed.). Wellesley–Cambridge Press.
Baseline exposition of the eigenvalue decomposition for undergraduates. The MER 2.0 lab worksheet assumes Strang-level vocabulary: characteristic polynomial, eigenbasis, diagonalization. Used to calibrate what a Math 2B student already has in their toolkit at the start of the activity.
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(1968). Waves. Berkeley Physics Course, Volume 3. McGraw-Hill.
The classic lab-first treatment of normal modes. Crawford's home experiments with coupled pendula (Chapters 1–2) are the direct pedagogical ancestor of MER and of this paper. We cite Crawford to situate the kit in the home experiments tradition, which is exactly the lineage Anderson invokes.
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(1993). The Physics of Waves. Prentice-Hall.
The rigorous normal-modes reference for a 3-DOF coupled system. Georgi's Chapter 3 derivation of the eigenvalue spectrum of a one-dimensional mass-spring chain is the source of the matrix form used in the three-mass extension. Cited in the methods section as the validation target: our measured frequencies must match Georgi's analytical formula within our stated tolerance.
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(1963). The Feynman Lectures on Physics, Volume I, Chapters 24 (Transients) and 49 (Modes). Addison-Wesley. free online
Feynman's Chapter 49 frames modes as "the things you can do and have them stay that way" — the phrase we use in the student worksheet to motivate why eigenvectors matter physically. Used as the expository anchor for the "state the ideal model" step in Anderson's eight-step modeling process.
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(2000). The OpenCV Library. Dr. Dobb's Journal of Software Tools, 25(11), 120–123.
Standard citation for the computer-vision library used in the tracking pipeline. The paper's contribution is not the CV — it is that the pipeline fits in a single Python script a precalculus student can read. Bradski's paper is the required attribution for the library.
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(2007). Coupled Oscillators and the Double Pendulum as Pedagogical Tools. American Journal of Physics.
Working placeholder — confirm exact citation and DOI before submission. Serves as the physics-education parallel to MER, cited to show that the coupled-oscillator-as-lab tradition exists outside of math-ed journals.
6 refs · Paper 01
Paper 02 — Matrices → Networks
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(2019). Linear Algebra and Learning from Data. Wellesley–Cambridge Press.
The structural anchor for Paper 02. Part I.8 ("Four Fundamental Subspaces") and Part III ("Low-Rank and Compressed Sensing") provide the SVD-first scaffolding the activity inverts: rather than deriving SVD from the subspaces, we hand students a trained network and use SVD to reveal its learned structure. Cited in the methods section as the linear-algebra level we assume.
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(2015). Neural Networks and Deep Learning. Determination Press (online). neuralnetworksanddeeplearning.com
The definitive free introduction to MLPs, and the exact text we are inverting. Nielsen derives backpropagation first and interprets weight matrices second; our paper flips this. Cited both as prior art and as the explicit foil — we walk the reader through which of Nielsen's steps require multivariable calculus and which do not.
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(1998). Gradient-Based Learning Applied to Document Recognition. Proceedings of the IEEE, 86(11), 2278–2324. doi:10.1109/5.726791
Origin of the convolutional approach and a canonical citation for handwritten-digit classification. We cite it to acknowledge the CNN-shaped hole in our activity: the SVD-of-a-dense-MLP story is an honest simplification, and this paper is where the reader is sent if they want the full convolutional account.
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(1994). A Database for Handwritten Text Recognition Research. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(5), 550–554.
Origin paper for the USPS handwritten-digit dataset used throughout the activity. Chosen over MNIST because USPS is smaller (16×16 vs 28×28), which means a single-hidden-layer network with visible weights fits on one screen and trains in under a minute in Colab — both pedagogical wins.
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(2016). Deep Learning. MIT Press. deeplearningbook.org
The canonical graduate-level reference and the textbook our activity is not trying to replace. Cited to mark the scope boundary: a precalculus-first community college student does not need Goodfellow before they can look inside a trained network — and the paper's contribution depends on that claim being true.
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(2014). Neural Networks, Manifolds, and Topology. colah.github.io (blog). free online
A stylistic benchmark for geometric intuition about what a trained network is doing. Olah's illustrations of nonlinear boundary warping inform the visual language of the student worksheet: we tell students that a weight matrix is a map, and SVD tells you which directions the map stretches.
6 refs · Paper 02
Paper 03 — Anti-Racist AI Tutor
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(2023). ChatGPT for Good? On Opportunities and Challenges of Large Language Models for Education. Learning and Individual Differences, 103, 102274. doi:10.1016/j.lindif.2023.102274
The survey anchor. The most-cited early synthesis on LLMs in education, and the paper reviewers will compare Paper 03 to. Our contribution is the audit framework — this paper catalogs opportunities and challenges but does not operationalize any of them into a measurable rubric. Cited to position Paper 03 as the missing operationalization.
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(2019). Should Robots Replace Teachers? AI and the Future of Education. Polity Press.
Critical-theory framing. Selwyn argues that the "tutor vs. teacher" dichotomy is the wrong frame; the real question is which student-led practices a tool enables or forecloses. Paper 03 adopts this framing directly: we ask "which practices does the constrained tutor make easier," not "is the tutor as good as a teacher."
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(2004). Design Research: Theoretical and Methodological Issues. Journal of the Learning Sciences, 13(1), 15–42.
The canonical methodology citation for design-based research in learning sciences. Paper 03's two-arm pilot is a design-based study, not a causal experiment; this is the reference reviewers will expect to see in the methods section when the n is small and the intervention iterates during the study.
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(2020). Historical Threads, Missing Links, and Future Directions in AI in Education. Learning, Media and Technology, 45(3), 223–235. doi:10.1080/17439884.2020.1798995
Historicizes the current LLM-in-education moment. Williamson's argument that AIED has always been entangled with behaviorist assumptions is cited to motivate why an anti-racist learner-centered framing is a substantive departure, not rhetorical ornamentation.
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(2023). Using AI to Implement Effective Teaching Strategies in Classrooms: Five Strategies, Including Prompts. SSRN Working Paper. SSRN:4391243
A reference example of prompt-engineered classroom tutors. The Mollicks' prompts are the baseline our constrained tutor improves upon: they scaffold pedagogy but do not operationalize any anti-racist learner-centered framework. Cited as the "state of the practice" that Paper 03 builds on.
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(2023). Science in the Age of Large Language Models. Nature Reviews Physics, 5, 277–280. doi:10.1038/s42254-023-00581-4
Caveats about LLMs as scientific collaborators apply directly to LLMs as modeling co-pilots. Cited in the risks section of Paper 03: the failure modes the authors flag (confabulation, authority laundering, reasoning short-circuits) are the exact behaviors our audit rubric's "violates" column is designed to catch.
6 refs · Paper 03
What's missing
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No empirical student-cognition work on coupled oscillators.
Paper 01 would be stronger with a citation to an existing study of student misconceptions around normal modes — if one exists. Currently searching the PER literature for a Rebello-style study. If none exists, Paper 01's pre/post instrument becomes more than a measurement: it's a contribution.
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No citation yet for "visible weights as pedagogy."
Paper 02's central move — show students what a trained weight matrix looks like — is not yet attributable to a specific published precedent. Candidate: Zeiler & Fergus's feature-visualization work, but that is on convolutional filters, not dense MLPs. Still searching.
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No prior operationalization of the five anti-racist learner-centered objectives.
This is load-bearing good news for Paper 03: if no prior paper has converted Anderson (2024)'s five objectives into a behavioral audit rubric, then the 5×3 matrix in rubrics/ai-tutor-audit.html is a novel contribution. To verify before submission.