Report on a US-Canadian Faculty Survey on Undergraduate Linear Algebra: Could Linear Algebra Be an Alternate First Collegiate Math Course?
Bibliographic record
Abstract
and 2015 [5]) and a rapid rise of interdisciplinary data science, with accompanying linear algebra curricular recommendations [1,6,10,15] that include, for example, exposure to the singular-value decomposition (SVD) and its popular cousin, principal components analysis (PCA).In 1993, the Linear Algebra Curriculum Study Group (LACSG [4]) published recommendations for a first course in linear algebra -emphasizing the importance of serving client disciplines and decreasing emphasis on abstraction by focusing on matrices, with a recommended core set of topics consisting of: operations on matrices, linear systems, determinants, properties of R n , eigenvectors and eigenvalues, and orthogonality.Recently, the National Science Foundation provided financial support to convene LACSG 2.0, bringing together experts on the teaching and learning of linear algebra along with representatives from client disciplines.Their forthcoming recommendations additionally emphasize the importance of linear maps, their compositions and inverses, as well as diagonalization and the singular value decomposition [12].Topics recommended for a second course by this group include an abstract treatment of vector spaces, matrix factorizations, inner product spaces, finite-dimensional spectral theorem, pseudo-inverses, operators, and Jordan form.The teaching of linear algebra, we note, has received considerable attention as a topic of research [7,14].We complement the above body of work with two useful perspectives.First, our survey, which gathers data on topic coverage and client populations, situates the above recommendations (and ours) in the context of what is
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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 | 0.005 | 0.017 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.006 | 0.001 |
| Scholarly communication | 0.003 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.028 | 0.004 |
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".