METHODS OF INSTRUCTION IN THE MATHEMATICS CURRICULUM FOR MIDDLE SCHOOL Math 410, Fall 2005 DuSable Hall 306 (Mathematics Education Laboratory) Dr. Diana Steele 357 Watson Hall Northern Illinois University DeKalb, IL 60112-2888 Telephone: 815-753-6755 E-Mail: dsteele@math.niu.edu Class meetings: Tuesdays and Thursdays 4:20-6:10 P.M. Office Hours: Tuesdays and Thursdays 3:00-4:00 P.M. and by appointment Purpose of the Course In this course, we will explore the teaching of mathematics, investigating both what to teach and how to teach it. The purpose of this course is to begin an inquiry into mathematics teaching and learning that will guide you in your first teaching experiences and give you tools that will enable you to continue to inquire and learn as part of your work as a teacher. Traditionally, a mathematics methods course is designed to teach preservice teachers how to teach the content of the mathematics lessons they experienced as middle-school students. But current national reforms in mathematics education are recommending that middle school teachers think in new ways about the content of their instruction (what to teach) and pedagogy (how to teach). This course is intended to launch you as a learner and teacher of mathematics in ways that correlate with these reforms. The purpose of this course is to help you learn to think of the mathematics you will teach from the perspective of the student who is learning. You will have the opportunity to explore the teaching of mathematics through investigating how students learn mathematics in the areas of whole numbers, rational numbers, measurement, geometry, probability, and statistics. The goal is to begin to help you develop ways of thinking about mathematics, about students, and about the teaching and learning of mathematics in each of these areas. At the end of your participation in this course, you should have new questions and insights about teaching and learning mathematics. You should have some new understandings of mathematics and some new mathematical interests. You should have ways of thinking about teaching mathematics that will help you make instructional decisions about curriculum, tasks, and tools. Organization of the Course We will explore what it means to do mathematics and what it means to understand mathematics through individual, small-group, and large-group mathematical problem solving. We will investigate ways to represent understandings of mathematical concepts, communicate reasoning about mathematical ideas, and construct mathematical arguments. We will read about and investigate ways students might represent mathematical ideas, communicate reasoning, and construct arguments. We will look at ways to help students build connections among mathematical ideas. We will also explore what it means to teach mathematics through a study of six principles that encompass the vision of current reforms in mathematics education. We will learn about the type of classroom environment that is conducive for mathematics learning. We will read about and discuss the importance of mathematical tasks, mathematical tools, the role of teachers and students in classroom discussions, and the assessment of students' mathematical understandings. Assignments throughout the semester are intended to further your understandings of mathematics and what it means to teach and learn mathematics in light of the current reforms in mathematics education. Through your experiences in this class, you will begin to build a rich foundation for the content and methods that will enable you to teach mathematics for understanding. You will leave this class prepared to continue in your lifelong learning about mathematics and about teaching and learning mathematics. 1
Course Goals and Objectives 1. Understand the content, methods, and materials necessary to teach middle school mathematics. 2. Learn about research on students' mathematical thinking and reform principles about teaching and learning mathematics. 3. Understand what it means to build a learning environment that supports the teaching and learning of mathematics. 4. Understand connections between mathematical concepts and procedures within a problem-solving environment. 5. Understand the role of mathematical discourse in students' learning to communicate and make sense of mathematical ideas. 6. Learn how to ask students questions and interpret their answers to gain insight into their mathematical thinking. 7. Learn how to assess students' mathematical thinking and plan instruction based on that assessment. 8. Learn to make instructional decisions about the use of curricular materials, such as textbooks, other resources, manipulative materials, and technology in the teaching of middle school mathematics. Course Requirements Required texts: Rubenstein, R. N., Beckman, C. E., & Thompson, D. R. (2004). Teaching and learning middle grades mathematics. Emeryville, CA: Key Curriculum Press Tsuruda, G. (1994). Putting it together. Portsmouth, NH: Heinemann. Recommended texts: National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. Attendance, Participation, and Mathematical Disposition. Attendance is an important part of your grade. This course is not a read-and-lecture class. Your active participation in each class session is vital to your learning as well as to the learning of other students in the class. I expect you to attend all class meetings prepared and to be engaged as an active, collaborative participant during each class session, whether whole-class discussion, collaborative-group activity, or individual reflection is involved. Being prepared means reading the assigned chapters for each session and preparing questions and comments on each reading. If you are unable to attend a particular class session, please let me know before class. You are responsible for contacting someone in the class to find out what transpired in your absence. Excused absences are only those described in the NIU Student Handbook. I expect assignments to be completed on time even if you are absent. Assignments are due at the beginning of the class period. They may be turned in after the class period in which they are due for a maximum of half credit. Make-up quizzes may be scheduled only in the event of documented illness or emergency. Learning mathematics extends beyond learning concepts, procedures, and their applications. It also includes developing a disposition toward mathematics and seeing mathematics as a powerful way for looking at situations (National Council of Teachers of Mathematics [NCTM], Curriculum and Evaluation Standards for School Mathematics, 1989, p. 233). I will assess your mathematical disposition following the recommendations of Standard 10 in the NCTM Curriculum and Evaluation Standards: The assessment of students' mathematical disposition should seek information about their- * confidence in using mathematics to solve problems, to communicate ideas, and to reason; * flexibility in exploring mathematical ideas and trying alternative methods in solving problems; * willingness to persevere in mathematical tasks; * interest, curiosity, and inventiveness in doing mathematics; * inclination to monitor and reflect on their own thinking and performance; * valuing the application of mathematics to situations arising in other disciplines and everyday experiences; * appreciation of the role of mathematics in our culture and its value as a tool and as a language. 2
Course Assignments. You will complete a variety of assignments during the semester. They are as follows: Reflective Writing. You will prepare out-of-class and in-class reflective writings. All out-of-class reflective writings need to be typed. You will receive information about the reflective writings in class. Reflective writings and all other course handouts will be required to be kept in a 3-ring binder which you will bring to class in the last week. Illuminations Lesson. You will select a problem/lesson from the Illuminations website at nctm.org. This problem/lesson must be at the middle school level. You will write a two-page review of the problem/lesson you chose. The typed review should include the reason you selected the activity, a brief summary of the activity, and a discussion of ways (how, when, etc.) that you will use this activity in your teaching of mathematics. Your problem presentation should conform to the spirit of this course. This implies that the problem should focus on development of conceptual knowledge, problem solving, and active student learning. You will receive detailed information on this assignment in class. Questions for Student Assessment Interview. You will prepare questions to assess a middle school student on some concept. You will turn this typed report into me for feedback before you interview the student. You will receive information in class. Student Interview Report. You will interview a middle school student. You will assess the student on the concept that you have prepared. In this typed report you will describe your student's understandings and suggest appropriate instruction based upon this assessment. You should audiotape this interview. You will receive information in class. Collaborative Curriculum Evaluation. You will be required to examine some middle school mathematics lessons from mathematics basals. You will evaluate how these lessons fit into the framework of The Principles and Standards. You will be given and will also choose standards for each lesson and show how each lesson addresses these standards. You will prepare this evaluation with a small group. You will write a typed summary for each lesson. You will receive information in class. Cooperative Group Lesson. Working with a small group you will select and teach a lesson on a mathematics topic assigned to you. You will choose the activity/activities for the lesson from a given selection of resources. You will develop the lesson for middle-school students and adapt it into a 45-minute lesson that you will teach to our class. Your lesson should conform to the "spirit" of the Principles and Standards for School Mathematics (NCTM, 2000). This implies that the lesson should focus on development of conceptual knowledge, problem solving, and active student learning. You will prepare a detailed typed lesson plan that you will distribute to each class member on the day of the presentation. You will be asked to assess how your lesson fits into the framework of The Principles and Standards. Evaluation is based upon your preparation, knowledge, cooperative group work, and overall effectiveness. You will receive detailed information on this assignment in class. Final Exam. The final exam will be comprehensive. You must take the final exam with your fellow classmates at the scheduled time. You will receive further directions for each assignment throughout the semester. No assignments will be accepted after December 1. The grading scales will be approximately: Evaluation 90% and above 180-200 points A 80-89% 160-179 points B 70-79% 140-159 points C 60-69% 120-139 points D 3
Your final grade will be determined as follows: Percent of total grade Points Possible Attendance, Participation, Mathematical Disposition 10% 20 Reflective Writing 15% 30 Illuminations 5% 10 Preparative on Student Assessment Interview 15% 30 Report of Student Interview 15% 30 Collaborative Curriculum Evaluation 10% 20 Cooperative Group Lesson 10% 20 Final Exam 20% 40 Total 100% 200 Performance Standards for Student Work Level Standard to be achieved for performance at specified level A B C D F Fully achieves the purpose of the assignments while insightfully interpreting, extending beyond the assignments, or raising thought provoking questions. Shows clear understanding of the concepts. Communicates effectively. Substantially completes purposes of the assignments. Displays clear understanding of concepts, even though some less important ideas may be missing. Communicates successfully. Purposes of the assignments not fully achieved; needs elaboration. Displays understanding of major concepts, even though some less important ideas my be missing. Limits communication to some important ideas. Results may be incomplete or not clearly presented. Important purposes of the assignments not achieved; work may need redirection. Assumptions about the purposes may be flawed. Gaps in conceptual understanding are evident. Approach to assignments may lead away from their completion. Results may be incomplete. Attempts communication. Purposes of the assignments not accomplished. Shows little evidence of appropriate reasoning. Presents fragmented understanding of concepts. Week 3 Illuminations Review due September 6 Week 4 Reflective Writing Due September 13 Semester Schedule for Assignment Due Dates 4
Week 6 Reflective Writing Due September 27 Week 9 Preparation of Student Interview Due October 18 Week 10 Curriculum Evaluation Due October 25 Week 11 Reflective Writing Due November 1 Week 12 Report of Student Interview November 8 Week 13 Cooperative-Group Lessons Begin on November 15 Throughout the semester Other Reflective Writings Due Final Week Final Exam at 6-7:50 PM on Tuesday, December 6. Note: Changes and adjustments may be made to this syllabus when judged appropriate by the instructor. Such changes, should they occur, will be announced in class. Students with Disabilities: NIU abides by Section 504 of the Rehabilitation Act of 1973 which mandates reasonable accommodations be provided for qualified students with disabilities. If you have a disability and may require some type of instructional and/or examination accommodation, please contact me early in the semester so that I can provide or facilitate in providing accommodations you may need. If you have not already done so, you will need to register with the Center for Access-Ability Resources (CAAR), the designated office on campus to provide service and administer exams with accommodations for student with disabilities. The CAAR office is located on the 4th floor of the University Health Services building (815/753-1303). Academic Conduct: Academic honesty and mutual respect (student with student and instructor with student) are expected in this course. Mutual respect means being on time for class and not leaving early, being prepared to give full attention to class work, not reading newspapers or other material in class, not using cell phones or pagers during class time, and not looking at another student's work during exams. Academic misconduct, as defined by the Student Judicial Code, will not be treated lightly. Reminders: General Classroom Etiquette * Turn off pagers, phones, etc. * No palm pilots, PDA's, etc. can be used for any in-class work including quizzes, exams * Plan to arrive on time, stay to the end of class, and be in the classroom for the entire session * Only students who are registered for this course should attend this class * Come prepared for class (see p. 2 of this document) * Give your attention to the presenters in this class, whoever they may be. 5
MATH 410 s Schedule--Fall 2005 (Tentative) Class Day Date Topics s # 1 T 8/23 Orientation 2 TH 8/25 Introduction TLMGM p. xxii-p. 6; Tsuruda Ch 1 3 T 8/30 Approaches to learning and Tsuruda Ch 2; teaching; problem solving 4 TH 9/1 Approaches to learning and Tsuruda Ch 3, 4; teaching (continued); reasoning and proof 5 T 9/6 Algebra; assessment TLMGM p. 7-10, unit 1.1; Tsuruda Ch 5 6 TH 9/8 Algebra; communication TLMGM unit 1.2; 7 T 9/13 Algebra; planning and organizing TLMGM unit 1.3; Tsuruda Ch 6 8 TH 9/15 Algebra; qualitative graphs TLMGM unit 1.4; 9 T 9/20 Algebra; rational numbers TLMGM unit 1.5; TLMGM p. 73-76, unit 2.1 10 TH 9/22 Algebra; rational numbers TLMGM unit 1.6; TLMGM unit 2.2 11 T 9/27 Algebra; rational numbers TLMGM unit 1.7, p. 71-72; 12 TH 9/29 Rational numbers TLMGM unit 2.3; 13 T 10/4 Rational numbers; representation 14 TH 10/6 Rational numbers; connections TLMGM unit 2.4; 15 T 10/11 Rational numbers; number and ; Tsuruda Ch 7 operations 16 TH 10/13 Rational Numbers TLMGM unit 2.5; 17 T 10/18 Rational Numbers; proportional reasoning TLMGM unit 2.6, p. 130-131; 18 TH 10/20 Geometry TLMGM p. 133-137, unit 3.1 19 T 10/25 Measurement TLMGM unit 3.1, 3.2, 3.3; 20 TH 10/27 Measurement; asking questions TLMGM unit 3.4, 3.5, 3.6; 21 T 11/1 Geometry; tasks TLMGM unit 3.7; TLMGM p. 205-208, unit 4.1 22 TH 11/3 Geometry; Probability and TLMGM unit 4.2; Statistics 23 T 11/8 Probability and Statistics; TLMGM unit 4.3; assessment 24 TH 11/10 Probability and Statistics; TLMGM unit 4.4; assessment; Cooperative Group Lessons begin 25 T 11/15 Cooperative Group Lessons TLMGM unit 4.5 26 TH 11/17 Cooperative Group Lessons TLMGM unit 4.6, 6
27 T 11/22 Cooperative Group Lessons TLMGM p. 258-259 TH 11/24 No class, Thanksgiving Holiday 28 T 11/29 Cooperative Group Lessons 29 TH 12/1 Open Final T 12/6 7