NCTM has identified eight Mathematics Teaching Practices that research indicates are consistent components of every mathematics lesson. Learners should have experiences that enable them to engage with challenging tasks. . . connect new learning with prior knowledge and informal reasoning. . . acquire conceptual as well as procedural knowledge. . . construct knowledge through discourse, activity, and interaction with meaningful problems. . . receive descriptive and timely feedback. . . develop metacognitive awareness of themselves as learners, thinkers, and problem solvers” (NCTM, 2014, p. 9).
Based on these principles, Wayne RESA has created a Framework for Ambitious Instruction.
The Thinking Through a Lesson Plan Protocol (TTLP) is used to guide teachers to think deeply about a specific lesson that will be taught. The goal is to move beyond a basic lesson plan to a deeper consideration of how to advance students’ mathematical understanding during the lesson.
Part 1 of the TTLP lays the groundwork for planning before the implementation of the rich math tasks in the classroom. First, identify the learning targets of the lesson. Then, select a high cognitive demand math task aligned to the learning targets from the district’s textbook resource. Next, determine how to launch the task to help students make sense of problem. For example, determine how to activate prior knowledge, make sense of the task and decide which instructional tools will be made available to the students.
Part 2 of the TTLP helps monitor students as they engage in the task during the Explore Phase. Prior to implementing the math task, anticipate strategies and misconceptions students may encounter while solving the task. Based on anticipated strategies, formulate questions ahead of time to clarify and assess student thinking. The rest of the monitoring tool can be completed during the Explore Phase while monitoring and recording the names of students using the anticipated strategies. The monitoring tool will help in selecting and sequencing the students who will share their thinking in the Summarize Phase.
Part 3 of the TTLP focuses on how to orchestrate a whole-group discussion of the task. This discussion uses the different solution strategies produced by students to highlight the mathematical ideas that are the focus of the lesson. Strategically plan the order in which solutions are presented to help develop students’ understanding of the mathematical ideas. In addition, develop questions to ask to make connections between students’ strategies. Read Thinking Through a Lesson Protocol: Successfully Implementing High-Level Tasks to dig deeper.
“Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and argument.” (Huinker & Bill, 2017).
Teachers need to establish norms for discourse to create a safe environment and ensure equitable participation. Productive talk moves can be used by teachers to engage all students in discussion. Teachers need to think about the goal they are trying to reach based on student responses. Think about the following goals and you determine which talk move to use during discussion.
Helping Individual Students Clarify and Share their Own Strategies
Helping Students Orient to the Thinking of Other Students
Helping Students Deepen their Reasoning
Helping Students to Engage with the Reasoning of Other
Taking Action: Implementing Effective Mathematics Teaching Practices (K-5) ISBN-13: 978-0873539692
Taking Action: Implementing Effective Mathematics Teaching Practices (6-8) ISBN-13: 978-0873539753
Taking Action: Implementing Effective Mathematics Teaching Practices (9-12) ISBN-978- 0-875353-976-0
Children's Mathematics: Cognitively Guided Instruction (Whole Number Operations) ISBN-13: 978-0325052878
Extending Children's Mathematics: Innovations in Cognitively Guided Instruction (Fractions and Decimals) ISBN-13: 978-0325030531