Reflecting on Practice: Making Connections that Support Learning Unit 2, Session 4 2016 Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute How People Learn 2.Teachers must teach some subject matter in depth, providing many examples in which the same concept is at work and providing a firm foundation of factual knowledge. To develop competence in an area of inquiry, students must: (a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a conceptual framework, and (c) organize knowledge in ways that facilitate retrieval and application. Reflecting on Practice Park City Mathematics Institute NRC, 2001 Back

Yesterday we focused on structure… What do you think is meant by the word “transfer” in relation to learning? Reflecting on Practice Park City Mathematics Institute

Yesterday we focused on structure… What do you think is meant by the word “transfer” in relation to learning? “ the ability to extend what has been learned in one context to new contexts” (e.g., Byrnes, 1996:74). Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute What have we considered so far in our work in Reflecting on Practice that would support transfer? Looking at progression … what do they know to apply in he new grade level Changing the lens in the new context If you’re goin to transfer something, you have to have a high level of understanding… they can’t transfrer unless they truly understand it. Sequencing the problems, to try to have students make meaning without teacher interference. The iea of experts versus novices in terms of the organization. The necessity of practice Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute More generally, what kinds of learning experiences lead to transfer? Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Transfer is about being able to use knowledge in new contexts and situations. One way to know what your students know is to put them in a place they have never been before. The problems do not have to be novel problems but problems for which students have not developed a routine nor practiced. For example, Students who have been studying factoring might be given the following: 2x2- 3x+k has (x-3) as a factor. Identify k. Students studying the central limit theorem with skewed distributions can be asked to investigate uniform distributions Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Worksheet The worksheet contains ten problems. With a partner, choose two of the problems and identify the content area and grade level you might be teaching if you were to give the problem to students as a "place they have never been". Be ready to explain why these would push your students into a new space. Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Why is it important, as part of classwork and on assessments, to give students problems that are unfamiliar but use the same mathematical ideas they have been studying? Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Illustrative Math MARS Project MathPickle.com from Gord Hamilton OpenMiddle.com Nrich.maths.org PISA/NAEP/TIMSS NCTM Illuminations Robert Kaplinsky Problem Based Learning Art of Problem Solving discussion boards Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Organizing ideas A key to making connections is being able to organize what you are learning… Note taking on keyboard is not as effective as taking notes by hand. Teacher-provided notes (through PowerPoint, Smartboard files, or photos of whiteboards) are not as useful as student-generated notes Students need to be deliberately revisit and interact with their notes by themselves to really benefit from taking notes. Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Note taking on keyboard is not as effective as taking notes by hand. Teacher-provided notes (through PowerPoint, Smartboard files, or photos of whiteboards) are not as useful as student-generated notes Students need to be deliberately revisit and interact with their notes by themselves to really benefit from taking notes. Identify strategies for implementing these findings with your students. Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute We’ve focused these past 4 days on Key Finding 2. What are some other ways we can promote organization, coherence and connections? Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Note taking – by hand Students recall more lecture material if they record it in their notes (Bligh, 2000). Note takers score higher on both immediate and delayed tests of recall and synthesis than students who do not take notes (Kiewra et al., 1991). The more students record, the more they remember and the better they perform on exams (Johnstone & Su, 1994). Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Providing notes: can impede learning because they constrain student engagement with the material making them less likely to make connections between idea units that they would have otherwise made (Peper & Mayer, 1978; 1986) may dissuade students from taking generative notes in their own words, which can make their learning inefficient. reviewing instructor notes did not impact memory performance for a later test (Fisher & Harris, 1974). Reflecting on Practice Park City Mathematics Institute

Design interaction with notes The largest factor associated with optimal review is for the learner to transform their notes in some interactive way, rather than simply reading or copying their notes (Bjork et al., 2013). The quality of summaries produced by learners after reviewing their notes was the best predictor of later test performance,(Hadwin et al., 1999). Methods or exercises that encourage learner interaction or engagement with content during review improves learning, even the act of trying to understand a peer’s notes has been found to be beneficial (Kiewra, 1989). Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute References Association for Psychological Science. Take notes by hand for better long-term comprehension .php/news/releases/take-notes-by-hand-for-better-long-term-comprehension.html DeZure, D., Kaplan, M., & Deerman, M. Research on student notetaking: Implications for facilty and graduate student instructors. http://www.math.lsa.umich.edu/~krasny/math156_crlt.pdf Friedman, M. Notes on Note-Taking: Review of Research and Insights for Students and Instructors. Harvard Initiative for Learning and Teaching Harvard University http://hilt.harvard.edu/files/hilt/files/notetaking_0.pdf Reflecting on Practice Park City Mathematics Institute