Mathematics Methods
Winter 2005
Instructors:
Dan
Julie Kern
Thad Loef
Megan
Angela
Addresses TPE’s 1(a),2,3,4,5,6(a),7,8,9 and 13.
Principles:
This course will build on the principles of the Teacher Education Program.
- Social justice guides our theory, practice and inquiry
- A reciprocal dynamic between theory and practice
- Collaboration with schools and communities
- Teaching has moral, cultural and political dimensions
- Collaborative inquiry is imperative as we develop communities of practice
- Supportive environments are essential
Goals:
- Continue to develop detailed knowledge about the development of children’s mathematical thinking
- Continue to develop your perspectives on the teaching and learning of mathematics
- Continue to develop an understanding of the mathematical content in the elementary grades.
- Continue to develop a repertoire of pedagogical moves related to the above
- Continue to develop a repertoire of tools, including technological tools that support the development of mathematical understanding
- Continue to develop a sense of equity and access inside and outside of the mathematics classroom including issues of language
- Continue to reflect on your role as a mathematics teacher in an urban school and community
Course Materials: Making Sense, Hiebert et. al
Children’s Mathematics, Carpenter et. al
California Mathematics Standards/NCTM Standards (we will provide)
Handouts (other readings etc…)
Student Responsibilities:
Class participation. You are expected to attend and participate in class. We will be engaging in discussions and activities in class that can not be “made up” outside of class. If you cannot be in class you must send an email to the instructor prior to class. IF you miss more than one meeting you will not pass.
Student assessments: As a part of the follow up you will be expected to complete at least one student assessment. You are expected to pose problems, record student responses and bring descriptions of the student work to class. The student work will be expected along with a short summary of what you noticed and what problems you might pose next to support the student’s learning.
Reading: Each week you will have reading and you will be expected to be prepared to discuss it in class.
Reflection: Each week you will be asked to reflect on a question at the beginning of class. The reflection question attempts to engage you in drawing connections between the readings for the week and actual classroom practice (your own practice). The questions will also highlight the challenges of teaching mathematics in an urban school and ask you to struggle with what this means for you.
Mathematics assessment: Before passing the class you will be expected to pass a mathematics assessment; the assessment will be given out a the beginning of the quarter. The assessment items will ask you to demonstrate understanding (a standard algorithm will not suffice). You will need to complete all mathematics assessment items by the end of the quarter or you will receive an incomplete until such time that you can complete them with understanding.
Collecting tasks and assignments: Throughout the course you will be engaging in tasks or responding to reflection questions during class and at times throughout the week. You must save all documents that you are asked to turn in so that you may turn them in as a set at the end of the quarter. When the work is returned, you are expected to look over the comments and respond to any questions. All assignments will then be turned in a second time at the end of the quarter.
Grading: You will be graded on the basis of your adequate completion of all assigned tasks. If you turn in all assignments – completed – you will pass the course (providing you have been coming to class). If you turn in an assignment that is missing parts of the assigned task or needs to be more thorough, you will be given your assignment back with comments and questions and asked to complete it. If you turn in the all the completions requested – again you will pass.
Schedule:
We have designed this year’s mathematics methods course in a way that focuses initially on the details of children’s mathematics thinking and then uses that information as a way to ground learning about the teaching of mathematics. We cannot cover all that you will need to know in 20 hours of methods. So we have chosen to focus on what will prepare you to begin and learn as you teach. As we address student thinking we will be also asking questions and discussing critical aspect of teaching and learning of mathematics: equity (racial, SES, gender, language), the use of mathematical tools and pedagogically meeting the needs of all students. So we will meet for three days at the beginning of the quarter to intensively focus on student thinking. We will then meet three times during the quarter to continue to make sense of students’ mathematical thinking in relation to teaching and learning in urban school classrooms.
Day 1: Thursday 9-1, Focus: Counting and direct modeling
The first session will focus on issues of counting and direct modeling. We will count collections, represent our counts, examine student work, and watch classrooms engaged in counting. We expect you to develop a sense of students’ trajectories in counting, begin to develop an understanding the role of counting in mathematics, begin to develop a repertoire of counting tasks, and develop a sense of the issues in counting for different students (particularly second language learners). We will build on issues of counting to discuss problem solving and what we know about the initial strategies children use to solve a range of different problems. We expect that you will be able to detail direct modeling strategis for different problems, recognize the strategies when you see students use them, and use the strategy to help you to determine problem difficulty.
Homework: Read: Making Sense, chapter 1
Children’s Thinking, chapters 1, 2
Complete: Problem type chart
Day 2: Friday 9-1, Focus: Strategies for Addition and Subtraction, Place Value
During the module on place value we will work specifically on what it means for students to understand place value at the different grade levels. Again you will be expected to understand the research literature on the development of children’s place value understanding and what that means for classroom practice. Place value is a difficult and critical concept throughout elementary school. We want to make sure that each of you understands the content, what is expected based on the standards at each grade level, and how to support the development of students’ place value understanding in the classroom.
Homework: Read: Making Sense,chapter 7
Children’s Thinking, chapters 3, 6
Complete: Strategy worksheet
Day 3: Monday 9-1 Assessing student thinking, Fractions (we will meet at UES at 8:45)
We will start the third day assessing students at UES. We will provide the assessment. You will assess in pairs and each pair will assess two students. We will debrief in our classrooms. The goal here is to focus on using what you learned about the development of student thinking to listen to students. And then begin to use what you hear to think about instructional decisions. We expect that you will be able to classify the student strategies and talk about what the students know about the mathematical ideas. We will then turn to a focus on fractions and fair sharing. Again we will focus on developmental trajectory and the strategies you might expect to see students use as they solve problems. We expect that you will be able to detail fair sharing strategies and strategies for problems using common dominators.
Follow up: We will meet week 3, 6, and 9 during the regularly scheduled class time (Tuesday 6-8).
We will use this time to continue to address student thinking and connect that to classroom practice. We will use your student teaching experiences as a focus for conversation.
During these three meetings we will also continue to address the content of algebra, geometry and those we began the first three days. You will have one assessment to complete. You will have a reading and reflective writing exercise due for each follow up session.
Follow up 1: Algebraic Thinking
During this session we will focus on the development of mathematical norms – what they are, what some afford and do not afford. You will be expected to consider the norms you want to establish and why. We will also investigate the development of students’ algebraic thinking. We will discuss how the development of these algebraic ideas build on the work of addition and subtraction. We will examine student work, video of individual student development and classrooms engaged in algebraic thinking. You will be expected to document the development of students’ algebraic thinking and ways to support that development within the regular curricula.
Homework: Read Making Sense – Equity chapter
Complete the norms reflection sheet
Solve the fraction garden plot problem
Follow up 2: Fractions and Tools