http://hdl.handle.net/2027.42/58605 Search the Channel search http://deepblue.lib.umich.edu/simple-search http://hdl.handle.net/2027.42/64280 Title: How Do You Know that You Know? Making Believe in Mathematics<br/><br/>Authors: Bass, Hyman<br/><br/>Abstract: Knowing in a discipline means not only knowing its products, and their uses, but alsoabout the genesis of its knowledge, how that knowledge is warranted, and how contraryviews are reconciled. This shapes the entailments of teaching and learning of thatdiscipline whether at age 8, 18, or 80. This lecture will focus on the discipline ofmathematics, illustrating what mathematicians do when they seek to “prove” a claim,taking note of the challenges presented by the advent of computer-based proofs. Provingis a fundamental mathematical practice, learned by few students, and then only late intheir education. I will consider how proving could shape the early learning ofmathematics, including the use of “generic” proofs. Examples from elementaryclassrooms will illustrate why the warrants for shared knowledge in a field matters for thecurriculum at any point. http://hdl.handle.net/2027.42/62487 Title: WHAT NONVERBAL INTERACTIONS WITH DIAGRAMS TEACHERS PERCEIVE AS MEANINGFUL ELEMENTS OF STUDENTS’ MATHEMATICAL WORK<br/><br/>Authors: Herbst, Patricio; Chen, Chia-ling; Weiss, Michael; Aaron, Wendy http://hdl.handle.net/2027.42/62486 Title: Tasks that embody knowledge, tasks that probe teaching<br/><br/>Authors: Herbst, Patricio http://hdl.handle.net/2027.42/56005 Title: Finding social justice in education policy: Rethinking theory and approaches in policy research<br/><br/>Authors: St. John, Edward P.<br/><br/>Abstract: Employing a critical-empirical approach to the study of college access, the author explores the role of policy researchers in seeking educational equity.