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Unformatted text preview: Study Guide Final Exam ELM 410 Spring 2011 The exam addresses material from the second half of the semester, but there is some material that was addressed throughout the semester (see list below). Review your notes from class, the PowerPoint slides, and all class readings. Mathematics Instructional Quality Nine dimensions of Mathematics Instructional Quality ("A reflection framework for teaching mathematics" by Merritt et al.) You should be able to identify and describe the dimensions. You will not be asked to list the dimensions. Instead, you might be asked to describe problem solving, for example. Or, you might be given a description of one of the dimensions, and you would name it. o Structure, Multiple Reps, Mathematical Tools, Cognitive Depth/Demand, Problem Solving, Discourse, Explanation/Justification, Connections/Applications, Mathematical Accuracy In Framework handout: 1) Structure The extent to which a mathematics lesson is logically organized and conceptually coherent, leading students to a deeper understanding of mathematical concepts Lessons often did not provide time for sense-making U.S. lessons included non-connected mathematical components 2) Multiple Reps-Conceptualizing mathematical ideas in a variety of forms such as symbols, graphs, words, charts, diagrams, and physical manipulatives-Students generated multiple representations for mathematical concepts when supported by the teacher 3) Mathematical Tools- Representing abstract mathematical ideas through the use of appropriate hands-on items such as fraction strips, pattern blocks, counters, base ten blocks, compasses, rulers, and technological tools (e.g., virtual manipulatives) -The use of mathematical tools enhanced students understanding of concepts 4) Cognitive Depth/Demand-The level of thinking required of students to engage with the task-Higher cognitive demand increased students engagement with mathematical ideas 5) Problem Solving-Grappling with a task for which the solution method is not known in advance -Students practiced procedures in most classrooms, rather than engaged in problem solving -Students did not develop understanding through practicing repeated procedures 6) Discourse-A classroom environment in which students are expected to share mathematical thinking with their peers and the teacher using mathematical language-Teachers at higher performing schools promoted mathematical discourse among students about ideas, pushed for mathematical meaning, and valued student thinking 7) Explanation/Justification-Students providing reasons for their solution strategies and proof for their mathematical conjectures and ideas....
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- Fall '11