Elementary Mathematics Methods Winter Quarter 2009 (Wednesdays 4-7PM) Lisa Rollins, NBCT [email protected] CCOOUURRSSEE OOVVEERRVVIIEEWW “Research in mathematics education has consistently found that understanding and skills are best developed when students are allowed to wrestle with new ideas, to create and defend solutions to problems, and to participate in a mathematical community of learners.” ~John Van De Walle Much of the work we will engage in this quarter may differ from the way that you learned mathematics. Please approach this class with a curiosity about how children think mathematically and allow yourself to explore your role as a teacher in a mathematics classroom. This class will familiarize you with many instructional practices that are shown to improve student learning. CCOOUURRSSEE GGOOAALLSS • To strengthen your own understanding of mathematics and how students learn by doing mathematical tasks in a learning community (Doing mathematics) • To actively engage in writing to learn by responding to given prompts (Reflective journaling) • To discover that children bring important mathematical ideas to the classroom and that making sense of mathematics through discourse deepens their understanding (Interviewing students) • To design learning opportunities for students that will draw out their ideas and build understanding (Lesson planning) RREEQQUUIIRREEDD TTEEXXTT Van de Walle, John A. (2007) Elementary and Middle School Mathematics: Teaching Developmentally Sixth Edition. Boston: Pearson Education. AASSSSIIGGNNMMEENNTT EEXXPPEECCTTAATTIIOONNSS  This class is centered on class discussion, close careful observation of students and classrooms, and engaging in math tasks.  Each week you will have a reading assignment along with selected reflection questions to respond to in an informal journal format.  As a mid-term project, you will need to have a student interview formal paper submitted on February 4th  As a final project, you will need to have a complete lesson plan submitted on March 4thWeek and Reading Assignments Writing To Learn QuestionsDate Assigned (20- 30 pages weekly) (5 prompts weekly) WEEK 1 (1/7/09) page xvii Van De Walle’s Note To Students Opening Journal Entry in Class Ch2 p12-20 Exploring What It Means to Do Mathematics p20 (#3 #4 #5) Ch3 p22-34 Developing Understanding in Mathematics p34-35 (#4) For Discussion (#3) WEEK 2 (1/14/09) Ch4 p37-59 Teaching Through Problem Solving p59 (#1 #7 #8 #9) For Discussion (#1) WEEK 3 (1/21/09) Ch9 p120-140 Developing Early # Concepts & Number Sense p141 (#7 #8 #11 #12) For Discussion (#2) WEEK 4 (1/28/09) Ch10 p143-162 Developing Meaning for the Operations p163 (#1 #11 #12 #14) For Discussion (#1) WEEK 5 (2/4/09) Ch11 p165-185 Helping Children Master the Basic Facts p185 (Choose 4 from #1-14) P107-109 Calculators in the Mathematics Classroom p117 (#2) WEEK 6 (2/11/09) Ch5 p61-75 Planning for the Problem-Based Classroom p76 (#1 #5) Ch6 p78-93 Building Assessment Into Instruction p93 (#1 #6 #10) WEEK 7 (2/18/09) Ch15 p259-290 Algebraic Thinking :Generalizations, Patterns & Functions p291 (#3 #4 #5 #12) For Discussion (#1) WEEK 8 (2/25/09) Ch17 p316-331 Computation With Fractions p331-332 (#9 and choose 2-3 more)WEEK 9 (3/4/09) Ch18 p 333-350 Decimal & Percent Concepts and Decimal Computation p351 (#1 #4 #8) Closing Journal Entries BelowWEEK 10 (3/11/09) *Please bring a copy of these two responses with you to classLast Day of Class 1.What are the most important ideas that you learned in this class No reading assignment that you will take with you into your classroom? 2. Is there any new idea from this class that changed or shifted how you previously thought about math instruction? Please describe your new way of thinking about this topic.Conducting a Mathematics Interview (Due Week 5 – February 4, 2009) 9 Interview two children (one at a time) using problems from the suggested list. Don’t just pick haphazardly from the list of suggestions. Think about what you want to learn about the student and make appropriate selections. 9 The problems should focus on number sense. They could be about problems that can be solved with whole number addition, subtraction, multiplication or division. 9 Write up one interview using the guidelines below. SOME IDEAS ABOUT TALKING TO STUDENTS 1. Tape record the conversation and keep all artifacts of the interview. 2. The problems that I provide are a guide. You are encouraged to adapt in order to make them appropriate for your students. You can also do follow-ups for the problems – just keep track of what you do and why, so you can explain it in your write-up. 3. You do not have to pose all of the problems to a child in one sitting. 4. Make sure the students have a variety of materials to use: paper and pencil, some type of unit counter and possibly some type of ten counters. 5. Before you start asking the student to solve a problem, let them know why you want to talk to them. “I’m really trying to learn more about how kids solve problems. I’m going to ask you a bunch of questions and I’ll probably ask you to explain what you were thinking about so I can learn more. This is going to help me as a teacher. It’s okay if you don’t know how to do a problem – just say so and I bet we can work through it together. I’m not worried about whether you get the answer right. I’m really interested in how you think about the problem.” Telling them that you’d really like their help with an assignment you have for school often helps break the ice as well. Try to make them more comfortable. Some kids are not used to people asking them why they did something, and so they may think that if you ask them to explain, they must have done something wrong. 6. Make sure you let the students know they can solve the problem in any way that they wish. Try suggesting to the child that s/he talks aloud while solving the problem. Some children will not be comfortable doing that, and some will. If you cannot tell what the student did to solve the problem, follow up with clarifying questions like: Can you tell me how