Topics:
-The student outcomes on the syllabus. How has the work we've done thus far related to those outcomes?
-The Hand Squeeze Activity. What was that all about? Connect to the course outcomes and the state and national standards.
-The van Hiele Model. In addition to the van Hiele developmental levels, several interesting problems and tasks* were discussed in class. You should be comfortable with the content of these tasks, but also recognize how they are connected to the van Hiele levels and what the implications for teaching are. You also need to be able to discuss the activities as they relate to the Phases of Learning as described in the chapter. *including triangle and quadrilateral classification, properties of diagonals of quadrilaterals, handout including area of a triangle partner activity and area of a parallelogram (all on geoboards), 1" square tiles perimeter and area problems, cubes and 2-dimensional representations of 3-D models
-The introduction to NCTM's Curriculum and Evaluation Standards for School Mathematics presented a vision of teaching and learning in mathematics classrooms that varies greatly from most classrooms youÕve experienced and observed. Be prepared to describe what a classroom environment that models the Standards might look like.
-Know the New York State Core Curriculum Standards and the Math A key ideas (by name and number). You should have solid knowledge of what the Key Ideas are and how the content is split up among those key ideas. The new standards are divided into 5 content standards and 5 process standards and you should know these. (see link on homepage) You should also be familiar with the format and scoring guidelines for the Math A assessment (general and calculator).
-The National Assessment of Educational Progress provided us with much data on student knowledge and understanding of perimeter and area as well as an abundant source of non-routine tasks. Be familiar with some of the tasks and the broad implications this assessment has for mathematics education.
-The Core-Plus materials and the TI-83/84 calculator as a tool for exploring equations, tables, and graphs and how the tasks relate to the NCTM Standards.
-The manipulatives we have used thus far and how the tasks and their use in general relate to the NCTM Standards. (geoboards, square tiles, cubes, colored counters, algebra tiles)
Question Format:
The questions will be mostly short response with a couple of extended response questions. These are an attempt to conform to two guidelines. First, this course has the multiple foci of content, learner, and pedagogy. Thus, the questions will attempt to assess your knowledge and understanding within each of those domains. Second, the questions will be at the varying cognitive levels of knowledge, comprehension, application, analysis, and synthesis. Thus, you might be asked to state the 7 key ideas of the NYS Learning Standards, or to discuss why a certain task is suitable for students working at one of the van Hiele levels, or to discuss how a given problem or activity meets or does not meet the state content and process standards, or how certain activities model the state and national standards as well as address aspects of the van Hiele learning model.