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Elicit and use evidence of student thinking 

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Elicit and use evidence of student thinking 

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In the textbook Elementary and Middle School Mathematics there is an example of a diagnostic interview. A diagnostic interview can be used to elicit and use evidence of student thinking. The process of a diagnostic interview is to evaluate and collect evidence of the student's thinking. After, the interview has been completed, the next step to address is how this evidence can help instruction and math understanding in the future. In conclusion, the diagnostic interview uses the evidence of student thinking to help progress and support extended mathematical learning.

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Support productive struggle in learning mathematics 

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Support productive struggle in learning mathematics 

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In the Intentional Talk book there is a chapter of the book that discusses students' partial understandings, confusion, and misconceptions. One way to address these issues is through troubleshooting and revising. This teaching strategy displays productive struggle for the students. In this situation below, the teacher wants to address a student's confusion on why the answer is false. The teacher creates objectives for the class and then provides techniques that might be beneficial to the students to understand the solution. The teacher is using turn-and-talk and diagrams as tools to allow the students to have different opportunities to grapple with the problem.

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Implement tasks that promote reasoning and problem solving

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Implement tasks that promote reasoning and problem solving

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An example for this standard is the teaching strategy "What's Best and Why?" from the Intentional Talk book. This strategy entails students determining and reasoning what the best strategy to use to approach a problem.  Determining, which strategy to use elicits problem solving because the students have to evaluate multiple strategies and choose what is the best or efficient way of solving the problem.

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Establish mathematics goals to focus learning

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Establish mathematics goals to focus learning

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A lesson plan exhibits this NCTM standard because mathematical goals are established in a lesson plan. Objectives, standards, and essential questions are all examples of mathematical goals for the students. For example, the objectives the teacher lists are measurable goals for the students. The teacher provides an expectation of the students to obtain a certain fraction or percentage of knowledge.

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math discussion for practicum lesson plan

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Build procedural fluency from conceptual understanding

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Build procedural fluency from conceptual understanding

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I believe Ten Frames can be used as an example for this standard. Ten Frames originate as a foundation for conceptual understanding. The students first need to understand that there are ten squares and to count how many squares are filled or not filled. The students should understand the number can never proceed ten. Then, over time the procedure of counting using the ten frame can become more fluent. The students will be able to recognize that if only one row is filled then that must mean that there are five dots; instead of the students counting each individual dot. In conclusion, Ten Frames can also help with counting on. Once, the foundation has been established with how to count inside the Ten Frames, the students can move on to placing dots outside of the Ten Frame. As conceptual understanding develops the students will be able to recognize that a dot outside the Ten Frame means there are eleven dots.

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A principle that aligns with this NCTM standard is a Talk Moves discussion. Talk Moves has a list of strategies to promote discussion. For example, a Talk Moves strategy may be to have a student repeat another student's answer in their own words. In addition, another Talk Moves strategy is adding on, where the student creates their own a idea based off of another student. These strategies help promote purposeful questions because they allow the teacher to assess the students' reasoning skills. Furthermore, it allows the students to make sense of other students' ideas. Finally, the Talk Moves helps the students build connection and relationships through students sharing ideas and adding on to those ideas.

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Use and connect mathematical representations 

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Use and connect mathematical representations 

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This article example represents this standard because it provides a demonstration of how this standard could be utilized in class. In this example, the teacher has instructed the students to provide a representation of having seven rows with twenty chairs in each row. Then, the students found a partner with a different representation and shared. The students are connecting math representations by comparing and contrasting their answers.

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A Number Talk can be used to demonstrate mathematical discourse. During, Number Talks students are able to share ideas, understandings, analyze, and compare and contrast how they were able to solve a problem. In addition, Number Talks provide students with the opportunity to argue or support their answers. Finally, Number Talks allow mathematical discourse to be verbal and written. The students are able to share their approaches out loud while the teacher writes down their responses so others can observe and analyze the answers.