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Using Productive Classroom Talk in Mathematics Content Courses for Elementary and Special Education Teachers. Suzanne H. Chapin Boston University Framingham State College April 3, 2008. The Essential Questions??. What content should be in each course? What methods do we want to emphasize?
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Using Productive Classroom Talk in Mathematics Content Courses for Elementary and Special Education Teachers Suzanne H. Chapin Boston University Framingham State College April 3, 2008
The Essential Questions?? • What content should be in each course? • What methods do we want to emphasize? • How do we balance content and methods?
BU Course Offerings • MA 107 Elementary Math I • Number and Operations • 4 credits • MA 108 Elementary Math II • Geometry and Algebra • 4 credits
To Little Time ……. • How do we fit methods into content courses? • Model the desired methodology • Require students to practice the methodology • Focus on teaching and learning with understanding • Use assignments that connect content to the classroom
Extensive Use of Discourse • Discussions • Partner talk • Presentations • Written explanations
What is Productive Talk? • Productive talk is classroom talk by students and teachers that supports the development of students’ reasoning and students’ abilities to express their thoughts clearly. • All academically productive talk is talk about academically important content.
Why Use Productive Talk? To learn mathematics content
Why Use Productive Talk? • To strengthen and expand students’ reasoning in all subject areas “I think there are an infinite number of degrees possible [in a circle], because you can think of the degrees like wedges that get smaller and smaller, so more and more fit in.”
Improve Reasoning Skills Logical reasoning can be strengthened and taught. Claim Evidence or Counterexample
Self Reflection About Knowledge Getting students to talk about academic ideas or procedures can bring to the surface their gaps in understanding: they may realize that they don’t understand. “I’m really confused by what you just said. Could you repeat it?”
Address Misconceptions Talk allows teachers to hear students’ misconceptions and identify what students do and don’t understand. Teacher: “So you are saying that one-sixth is larger than one-third because six is bigger than 3?” Student 1: “Yes, I just look at the bottom number in a fraction and I can decide right away.”
Create a Community of Learners Talking about ideas and procedures exposes students to what other students think about these same concepts. Student 2: “I think that one-sixth is smaller than one-third. One-sixth means you cut a pizza into six pieces. One of those pieces is smaller than if you cut the pizza into three pieces.” Student 1: “What if it isn’t pizza? Isn’t pizza special? It seems like one-sixth should be more.”
Enhance Student Engagement Allowing students to talk about academic thinking and problem solving gives them more to observe, more to listen to, and more chances to participate.
Develop Students’ Language Skills • the ability to produce precise and full descriptions; • the ability to understand and analyze complex texts and problem situations; • the ability to clearly externalize their thinking; and • the ability to acquire and use new vocabulary.
Provide Motivation to Learn It is hard work to communicate clearly. Knowing that others are listening and trying to make sense of what you say is a source of motivation to make the effort.
Normative Practices • Respectful discourse • Students set the rules • Consistency • Equitable participation • Call on everyone • Students practice with a partner or group
What do we talk about? • Concepts and relationships • Procedures • Representations • Strategies • Types of reasoning • Vocabulary, symbols, conventions
How Do We Talk —Productive Talk Moves • Revoicing • Repeating • Reasoning • Do you agree or disagree? Why? • Further participation • Who would like to add to this discussion? • Wait time
Talk Moves: Revoicing Revoicing is a talk move that enables teachers to deal with the inevitable lack of clarity of many student contributions. “So you’re saying …….? Is that right?”
Talk Moves: Repeating Repeating is a talk move where students repeat or paraphrase what others havesaid. Repeating slows down the pace of the conversation, providing more time to process the information. Repeating provides evidence that other students heard the contribution and can participate. Repeating provides a student with evidence that his or her thinking is taken seriously.
Talk Moves: Agree or Disagree? This talk move focuses on students’ reasoning about another’s claim. It is critical that the teacher ask for justification. “Do you agree or disagree with Carlos? Why?”
Talk Moves: Further Participation This talk move is used to bring students into a discussion. It reinforces the idea that everyone’s contribution is important and valued. Students often state the same information as their peers, illustrating the need for each individual to make sense of the ideas and procedures.
Fall Semester • Introduce productive talk methodology including talk moves • Read and discuss “Teaching and Learning with Understanding” • Tasks • Tools • Structuring and applying knowledge • Reflection and articulation • Making mathematical knowledge one’s own
Fall Semester — Students • Complete small math projects • Watch and discuss short video clips of students solving problems (in class) • Students read and discuss articles about learning with understanding • Solve problems and exercises
Spring Semester • Students study mathematics curriculum materials to see if they support learning with understanding • Students analyze video clips of student thinking • Students continue talking about mathematics and solving problems
Examples of Talk Topics • Which fractions can be represented as terminating decimals? Why? • Is the sum of two odd numbers even or odd? Why? • Explain why the standard algorithm for multiplication of 2-digit by 2-digit numbers works. • Examine three different definitions of the term, “function.” What do the definitions mean? Define a function in your own words.
Examples of Methodology • Explain the mathematics that a child is using when she solves 9 + 4 by changing the problem to 10 + 3. How might you support this strategy? • What concrete models are used to teach base 10 concepts? What are the advantages and disadvantages of each model? • What will you do when a child states that there are no numbers between 5.7 and 5.8? Reflect on activities you did in class and for homework.
Required Textbooks • A Problem Solving Approach to Mathematics for Elementary School Teachers Billstein, Libeskind, and Lott • Math Matters: Understanding the Math You Teach Chapin and Johnson • Classroom Discussions: Using Math Talk to Help Students Learn Chapin, O’Connor, and Anderson • Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School Carpenter, Franke, and Levi
For More Information • Contact Suzanne Chapin at schapin@bu.edu • Resources: • How Students Learn: Mathematics in the Classroom (2005). Donovan & Bransford (Eds.). National Academy Press. • Making Sense: Teaching and Learning Mathematics with Understanding (1997). Hiebert et.al. Heinemann. • Adding It Up: Helping Children Learn Mathematics. (2001).Kilpatrick, Swafford & Findell (Eds.). National Academy Press. • Mathematics Classrooms that Promote Understanding. (1999). Fennema & Romberg (Eds). Erlbaum.
