Math 308 Fall 2008 Dr. Judy Rector Office: Draper 304C 985-3576 ext 3576 Home: 986-7496 Office Hours: MWF 10-11 1-3 T, 2-4 R Texts: Curriculum and Evaluation Standards for School Mathematics by NCTM Additional reading from research articles, NCTM Yearbooks, and the Mathematics Teacher (e.g. NAEP results, curricular issues, sample lessons) Students also self select activities books in geometry, algebra and problem solving. Grading Scale: 100-90% A s (A, A-)* 89-80% B s (B+,B,B-) 79-70% C s (C+,C,C-) 60-60% D s (D+, D, D-) 59-50% F * The + or - designation will be assigned at the instructor s discretion. Grading: 100 pts @ Tests 100 pts Development of a resource notebook 25 pts @ Lesson plans (e.g. develop lessons using problem solving, technology, manipulatives, cooperative learning, real life, interdisciplinary, historical) 20 pts Manipulative (construct a classroom set of materials) 25 pts Student interviews about beliefs about math and implications for teaching 25 pts Investigation of student error patterns in algebra 50 pts Van Hiele Analysis of students developmental levels in geometry 25 pts Software evaluation 25 pts Develop prompt and scoring criteria 100 pts Miscellaneous homework assignments (e.g. investigate use of manipulatives, evaluate sample lessons, observations, score student work using KERA criteria) NOTE TO RECEIVE A PASSING GRADE (C OR HIGHER) YOU MUST HAVE A C AVERAGE ON ALL TESTS IN THE COURSE) COURSE GOALS: The NCTM Standards and the subsequent KERA guidelines for teaching mathematics underlie the expectations for this course. The Standards provide recommendations both as to the mathematics content and methodology appropriate for teaching mathematics in high school. This course will try to model the suggested content and the student-centered methodology which includes problem solving, use of manipulatives, cooperative learning, and
application of mathematics to real life. Through in-class activities, students will learn of alternative approaches to teaching standard high school mathematics as well as become familiar with resources: manipulatives, software and activity books. Students will also be expected to become familiar with mathematics education organizations and begin through their portfolio to garner activities which exemplify the NCTM recommendations. The course also strives to intertwine an understanding of the mathematics content and methodology with the current research on teaching and learning mathematics. These goals along with the portfolio elements strive to prepare the perspective teacher for student teaching and for certification in secondary mathematics teaching. As a reminder of the connection between the professional education program, Math 208 and the teacher expectations under KERA, a copy of the TEP matrix entries directly connected with this course have been appended to this syllabus. Students are expected to become familiar with these objectives and the ways in which this course along with the other professional education courses seek to assist students in meeting these objectives. COURSE OUTLINE: I. Background reading and discussions A. Attitudes towards mathematics (student interviews) B. Affective issues and teaching C. NCTM Standards (Curriculum and Evaluation Standards for School Mathematics pp. 123-188, 189-247) D. NAEP results (Mathematics Teacher: April 1988 pp. 241-248, May 1988 pp. 337-347) E. Theories of learning: Cognitive and Absorption (Children's Mathematical Thinking: Ch 1, 3) F. Research on Conceptual and Procedural Knowledge (Conceptual and Procedural Knowledge: The case of mathematics: Ch 1, 7) II. Geometry A. Readings on teaching geometry topics: Van Hiele model and national test results (Learning and Teaching Geometry: 1987 NCTM Yearbook : Ch 1 and Mathematics Teacher September 1985 pp. 419-428, pp. 448-456, pp. 481-486) B. Student interviews on the Van Hiele levels of geometric development C. Activities using manipulatives, problems solving, and real-life applications (e.g. geoboards, dot paper, miras, pattern blocks, polydrons, geometric constructions, construct of 3-D models, using nets to develop spatial sense) D. Software: Geometer s Sketchpad for generating and exploring and developing proofs III. Algebra A. Reading on teaching of algebraic topics (The Ideas of Algebra, K-12: 1988 NCTM Yearbook : Ch 2,3,4; and Research Issues in the Learning and Teaching of Algebra pp. 33-59) B. Discussion of student difficulties in moving from arithmetic to algebra C. Activities using manipulatives, problem solving and real-life applications (e.g. base ten blocks to show factoring and completing the square, computer software Alge-Blaster, Mathematics Teacher May 1982, pp. 388-419)
D. Investigation of student error patterns in algebra (e.g. exponents, variable, signed numbers) IV. Precalculus and Calculus A. Reading on teaching precalculus and calculus topics (The Ideas of Algebra, K-12: 1988 NCTM Yearbook: Ch 5) B. Investigations of activities (Applications Yearbook, Mathematics Teacher) C. Technology: math modeling with Curvefit, graphing calculator V. Introduction to Problem Solving A. Reading about problem solving and cooperative learning (Problem Solving in School Mathematics: 1980 NCTM Yearbook: Ch 1,2,3,5) B. Paired problem solving activities (A Sourcebook for teaching Problem Solving; Problem Solving and Comprehension) and analysis of own thought processes C. Additional activities ( Attribute shapes to teach problem solving and introductory set concepts) VI. Basic mathematics A. Readings on teaching basic mathematics B. Investigation of activities C. Software: (Counting on Frank, Logical Journey, Math Blaster Mystery) In addition to the activities and readings, students will view and discuss Marilyn Burn s video tapes on using manipulatives in the middle school curriculum and view mathematics movies like Powers of Ten, Theorem of Pythagoras, Algebra for Everyone, and Story of Pi. ASSIGNMENTS: In additional to daily assignments students will be expected to develop elements for the Kentucky s Professional Portfolio, familiarize themselves with teaching and learning issues in the high school curriculum and refining skills needed for student teaching. POLICIES: Disability Statement: Any student who has a disability that may prevent him/her from fully demonstrating his/her abilities should contact Carol Barnett, PhD, LCSW, the Disability Services Coordinator at (859) 985-3212 to discuss accommodations necessary to ensure his/her full participation in this course. Attendance: Since the focus of the class centers on modeling mathematical activities and using manipulatives, it is essential that students be present, prepared and actively participate in all class activities. This attendance is expected in this class everyday. Any absences beyond three for the semester will adversely affect the student s grade in the course, potentially resulting in lowering the student s grade by one letter grade.
Final: Final exam will be comprehensive. Date Fri Dec. 12 at 10 am. Final Grades: A student s grade may be raised by one letter grade above the actual percent earned if in the instructor s opinion the student has shown exceptional improvement since the beginning of the semester or if the student has shown outstanding work on the final exam.
TEP Performance Goals and Indicators Matrix for Mathematics Education 1 Teachers demonstrate their understanding of the centrality of inquiry in a learning community; the critical role of communication in inquiry; and the confidence that grows with the development of our ability to participate in a community of inquiry. 2 students can identify pedagogical strategies that encourage constructive dialogue in the classroom and can incorporate these in planning for 7 students recognize the importance of learners conducting their own inquiries 8 students can identify ways of organizing that emphasize both cooperative and independent inquiry 10 students can identify strategies that develop students thinking and communication skills and can incorporate these in planning for 2 Teachers demonstrate both a general knowledge of all subject matter in the school curriculum in order to understand the interrelationships among disciplines, and an in-depth understanding of the subject matter for which they are directly responsible, including the origins, development, and structure of each discipline; its core concepts and principles; its pedagogical framework; and its application in daily life. 1 students demonstrate in their planning the knowledge and ability to make explicit both the boundaries and connections between subject matters 2 students demonstrate a knowledge of the structure of subject matter and are able to plan for in a way that makes the structure explicit for students 3 students recognize subject matter as dynamic, not static or finite, and make al plans to represent subject matter this way 4 students have accurate knowledge and understanding of subject matter, including its ambiguities and paradoxes MAT315, 321
6 students are aware of many different sources of knowledge (nature, books, non-print media, other human beings, other cultures) and utilize these in planning for 7 students are aware of the different ways in which knowledge is preserved and accessed (books and libraries, in works of art, in museums, in the natural environment) and utilize these in planning for 8 students can identify the dynamic connections between subject matter and students lives and plan for so as to make these connections explicit 9 students find the questions in content that inspire their own inquiry 10 students demonstrate increasing ability to maintain disciplinary coherence and integrity while organizing subject matter into developmentally appropriate, integrated units of 11 students are aware of technologies and appropriate applications within their subject areas 348 348 All MAT courses, esp. MAT 492 330 MAT 315, 308 and 492, 220, 225, 330, 314, CSC 205 12 students are aware of the core concepts and principles described in Kentucky's second learning goal, and possess a deep understanding of those in their particular field(s) 13 students can determine essential questions both in a discipline and in particular topics of study 14 students can articulate criteria for determining what knowledge is worth knowing 348 (Especially) 3 Teachers demonstrate that they understand that authentic learning requires experience (direct and vicarious), inquiry, time, interest, self-correction, and external criticism
1 students can identify pedagogical strategies that emphasize student experience and can incorporate these in planning for 2 students recognize the important role that interest plays in determining students learning and can identify strategies helpful for incorporating student interest in al plans 3 students are aware of pedagogical strategies that help students think about their thinking and can incorporate these in planning for 6 students demonstrate an awareness of a variety of al strategies, resources, and technologies, and can incorporate these in planning for 480 4 Teachers demonstrate understanding of the historical, social, psychological, and philosophical bases of common schooling in the United States to inform their own philosophy of education and their pedagogical practice 1 students demonstrate knowledge and understanding of different philosophies of education and are able to identify al strategies consistent with each philosophy 2 students can adequately articulate their developing philosophy of teaching 3 students demonstrate knowledge and understanding of different learning theories and are able to identify al strategies consistent with each theory 5 students can identify strategies that are appropriate for different learning styles and levels of development, and can incorporate these in planning for 6 students recognize the importance of high expectations for all learners 100 and all subsequent EDS courses MAT 208 100 and all subsequent EDS courses 480 480 100 and all subsequent EDS courses (especially 480) 5 Teachers demonstrate responsibility for their own professional development and for their own learning as a lifelong process.
3 students follow through on their professional development plan 4 students demonstrate reflective thinking as they communicate about matters related to teaching portfolio 100 and all subsequent EDS courses