ࡱ> @B?a Xbjbj F3AbAbH: : 846<k$frrrrrMMM#######$%($MMMMM$rr%$Mvrr#M#:","r x:" #;$0k$D"R)W)"")",MMMMMMM$$MMMk$MMMM)MMMMMMMMM: B |:  GROSSMONT COLLEGE Official Course Outline MATHEMATICS 128 CHILDRENS MATHEMATICAL THINKING 1. Course Number Course Title Semester Units Semester Hours MATH 128 Childrens Mathematical 1.5 1.5 hours lecture: 24-27 hours Thinking 48-54 outside-of-class hours 72-81 total hours 2. Course Prerequisites A C grade or higher or Pass in Math 125 or equivalent or concurrent enrollment in Math 125. Corequisite None Recommended Preparation None. 3. Catalog Description An in-depth analysis of childrens mathematical thinking and understanding of operations (addition, subtraction, multiplication, and division), place value and fractions. Students will observe individual children solving mathematical problems. 4. Course Objectives The student will: a. Identify different strategies that children use to solve mathematics problems. b. Analyze childrens thinking in mathematics (meaning of operations, place value, and multiple meanings of fractions). c. Interview children to discern the childrens understanding of particular math concepts. d. Develop, conduct, and reflect on interview experiences with children. 5. Instructional Facilities a. Standard classroom equipped with: 1) Whiteboards 2) Overhead projector/document camera 3) Smart Cart b. Math manipulatives 6. Special Materials Required of Student Access to a computer with CD Rom/DVD player. 7. Course Content a. Role of multiple representations and connections among them in childrens understanding of mathematics. b. Significance of models of multiplication and division. c. Childrens problem-solving strategies for multiplication and division problems before instruction. d. Elements of counting. e. Importance and complexities of place value. f. Complexities of effectively teaching children difficult mathematical ideas. MATHEMATICS 128 CHILDRENS MATHEMATICAL THINKING page 2 7. Course Content a. Role of multiple representations and connections among them in childrens understanding of mathematics. b. Significance of models of multiplication and division. c. Childrens problem-solving strategies for multiplication and division problems before instruction. d. Elements of counting. e. Importance and complexities of place value. f. Complexities of effectively teaching children difficult mathematical ideas. 8. Method of Instruction a. Lecture. b. Small group discussion. c. Field investigation. 9. Methods of Evaluating Student Performance a. Written assignments where students analyze and reflect on both video and real experiences of children solving mathematical problems. b. Final project interviewing and audio taping a 5 or 6 year old child on number sense and interviewing and audio taping a 10 year old child on fractions and rational numbers. c. Written in-class final approach and final reflection. 10. Outside Class Assignments Watch and examine IMAP videos of children solving mathematics problems and write evaluations based on observations. Prepare reflection report. Write paper on interviews of children. 11. Texts a. Required Text(s): (1) IMAP: Select Videos of Childrens Reasoning. Englewood Cliffs, NJ: Prentice Hall, 2005. (2) Hiebert, James, Thomas P. Carpenter, Elizabeth Fennema, K.C. Fuson, D. Wearne, H. Murray, A. Olivier, and P. Human. Making Sense:Teaching and Learning Mathematics with Understanding. Englewood Cliffs, NJ: Prentice Hall, 1996. b. Supplementary texts and workbooks: None. Addendum: Student Learning Outcomes Upon completion of this course, our students will be able to do the following: Identify different strategies that children use to solve mathematics problems. Analyze childrens mathematical thinking by watching videos and conducting interviews. Communicate childrens ways of solving mathematical problems. 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