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Mathematical Processes. What We are Learning Today. Mathematical Processes What are they? How do we teach through these processes? How do students learn the content through these processes? Effective Instruction: Scaffolding Instruction
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What We are Learning Today Mathematical Processes • What are they? • How do we teach through these processes? • How do students learn the content through these processes? Effective Instruction: Scaffolding Instruction • Content, Task, and Material… linking to the mathematical processes Exemplars • Rubrics and Performance Indicators Benchmarking • Practice Marking
Traffic Light Communication Connections Mental Math and Estimation Visualization Reasoning and Proof Problem Solving Use of Technology
Jigsaw 1. Problem Solving 2. Reasoning and Proof 3. Communication 4. Connections/Representation 20 min in Expert Group 20 min in Home Group
Effective Instruction What are Students Doing? • Actively engaging in the learning process • Using existing mathematical knowledge to make sense of the task • Making connections among mathematical concepts • Reasoning and making conjectures about the problem • Communicating their mathematical thinking orally and in writing • Listening and reacting to others’ thinking and solutions to problems • Using a variety of representations, such as pictures, tables, graphs and words for their mathematical thinking • Using mathematical and technological tools, such as physical materials, calculators and computers, along with textbooks, and other instructional materials • Building new mathematical knowledge through problem solving
Effective Instruction What is the Teacher Doing? • Choosing “good” problems – ones that invite exploration of an important mathematical concepts and allow students the chance to solidify and extend their knowledge • Assessing students’ understanding by listening to discussions and asking students to justify their responses • Using questioning techniques to facilitate learning • Encouraging students to explore multiple solutions • Challenging students to think more deeply about the problems they are solving and to make connections with other ideas within mathematics • Creating a variety of opportunities, such as group work and class discussions, for students to communicate mathematically • Modeling appropriate mathematical language and a disposition for solving challenging mathematical problems
Your Turn… • In your groups: • Rewrite the problem using content scaffolding • Using this new rewritten math statement fill in the task scaffolding chart. • As you and your partner discuss this process through Think Aloud- make notes how this discussion supports growth in each of the 5 mathematical processes
Reflection…How does task Scaffolding teach content through the mathematical processes?
Building Assessment into Instruction Assessment should enhance students’ learning Assessment is a valuable tool for making instructional decisions
Benchmarking The WNCP 2006 states that assessment in the classroom should be designed to help students learn and to help teachers teach. Benchmarking is a way for us to gather data about what the students in our class and within the whole division know, understand and are able to do at any given time during a school year. Benchmarking can help us understand what students need to continue their learning and what the teacher needs to do to assist students with their continued learning.
Benchmarking • Work with a partner. • Score each problem using the rubric and performance indicators. (Long sheet of paper.) Score each area of the rubric separately. • Attach the recorded scored rubric (small piece of paper) to the problem and continue with the next problem. • When all your problems have been marked, transfer the information from each scored rubric to the Final Recording Sheet.
Benchmarking • How can the information gathered on the Final Recording Sheet help to inform instruction? • Discuss with your partner (table group) the kinds of experiences/modeling/opportunities/activities that the teacher should provide to take the students to the next level. • (IE. What are the strengths of this group of students? What areas are these students having more difficulties with?)
