An Inquiry-based learning method used by mathematician Robert Lee Moore. Students generally aren’t allowed to read any texts on the subject1; instead, they’re given basic axioms and definitions, and asked to find proofs themselves for the sequence of theorems which might otherwise be presented in lecture. Lectures are absent; during class meetings, students are asked to prove the theorems they’re assigned. Students are meant to work alone2, and they prove theorems in class individually, rotating only when one student can’t complete the proof.

Moore sums up his approach with this principle, typical of inquiry-based learning: “that student is taught the best who is told the least.”

I expect this would induce a very strong version of the Self-explanation effect. Related, also, to the reciprocal instruction method. Like all inquiry-based methods, I expect that low-knowledge students would really struggle.

Reminds me a bit of a much more formal version of Constance Kamii’s “Young Children Reinvent Arithmetic.” But much more explicitly focused on agency and fostering a passion for inquiry; e.g. McLaughlin (2008):

Much of the points that highlight aspects of the author’s modified Moore method may be summed up as it accents, celebrates, encourages, and attempts to hone an internal locus of control.

For McLoughlin, in particular, part of the point of this method is that it encourages students to *do* mathematics—not just in the sense of writing proofs for theorems which would normally be given in a textbook, but also in the sense of actually doing original work in mathematics: Enabling environments focus on creating opportunities for growth and action, not on skill-building.

1 Both Chalice (1995) and Cohen (1982) report sometimes relaxing this.

2 Cohen (1982) has undergrads work in teams of 2-3.

- Moore method - Wikipedia
- Chalice, D. R. (1995). How to Teach a Class by the Modified Moore Method. The American Mathematical Monthly, 102(4), 317–321. https://doi.org/10.1080/00029890.1995.11990577
- Cohen, D. W. (1982). A Modified Moore Method for Teaching Undergraduate Mathematics. The American Mathematical Monthly, 89(7), 473–490. https://doi.org/10.1080/00029890.1982.11995481
- Good, C. (2006). Teaching by the Moore Method. MSOR Connections, 6(2). https://doi.org/10.11120/msor.2006.06020011
- McLoughlin, M. (2008). Inquiry Based Learning: A Modified Moore Method Approach To Encourage Student Research. 11th Annual Legacy of Robert Lee Moore Conference, Austin, TX.