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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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The artifact chosen for this teaching practice is the diagnostic interview. The diagnostic interview elicits student think by having them recall what they have learned and share their responses with you. To further this, the teacher could use this evidence to further teach the student. If I notice a student struggling on a concept in the diagnostic interview, I would compile another diagnostic interview based solely on what the student was struggling on and then create an embedded lesson.

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Support productive struggle in learning mathematics

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Support productive struggle in learning mathematics

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Intentional Talk talks about "Troubleshoot and Revise". Troubleshoot and Revise is a mathematic teaching method used to support productive struggle. The book says, "They find answers to be a "catalyst" for discussions and point out that the discussion is more than an opportunity to just correct the wrong answer." Instead of telling a student they are wrong, the teacher should identify that the student might have partial understanding. The partial understanding a student has is something a teacher should use to scaffold the rest of their understanding from.

Citation:
Hintz, A. & Kazemi, E. (2014). Intentional talk: How to structure and lead a mathematical discussion. Stenhouse Publishers.

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Build procedural fluency from conceptual understanding

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Build procedural fluency from conceptual understanding

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Elementary and Middle School Mathematics Chapter 10 discusses developing early number concepts and number sense. In the book it mentions a basic skills game called "Ten-Frame Flash". In this basic skills game, students are shown ten frame cards and they have to identify the number of dots shown on the card. This game is fast paced and engaging for the students. The book says, "Ten-frame flash is surprisingly challenging for children, as there is a lot to keep in their working memory. Children must reflect on the two rows of five, the spaces remaining, how a particular number is more or less than 5 and how far away it is from 10." This game is geared for students first understanding number sense, but basic skills games constantly build procedural fluency because the teacher can consistently do basic skills. Basic skills builds conceptual understanding because it is building on skills that the students have previously learned. Basic skills is not teaching the students a new concept, it is scaffolding off of the concepts the child has already learned.

Citation:
Bay-Williams, J.M., Karp, K.S., & Van De Walle, J.A. (2016). Elementary and middle school mathematics: Teaching developmentally. Pearson.

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"What works best and why?" is a great way to pose purposeful questions because students can determine their own way of mathematically solving a problem and describing why they believe it works best. During What's Best and Why, students have to choose for themselves which strategy they like best. As a teacher, you could ask questions such as, "Why did you choose this strategy?" or "Why is this strategy better than the other one?" These questions get the students thinking about why they like a particular strategy over the other.  Intentional Talk say, "With What's Best and Why? discussions, we're asking students to analyze situations and decide on the effectiveness of particular strategies." This method is one I'd like to use in my future classroom.

Citation:
Hintz, A. & Kazemi, E. (2014). Intentional talk: How to structure and lead a mathematical discussion. Stenhouse Publishers.

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The artifact used for this teaching practice is my number talk. Mathematical discourse involves whole class discussion and students displaying their understanding of mathematical concepts. For my number talk, I chose to do "What does not belong" because the students were learning about shapes. The number talk facilitates meaningful mathematical discourse because students are required to think of more than one way to solve the problem. The students are also required to explain their answer. When teaching mathematics, teachers are more worried about if the student got the correct answer, instead of worrying about how the student got the answer.

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Use and connect mathematical representtions

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Use and connect mathematical representtions

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Intentional Talk discusses "Compare and Connect". This artifact works for this teaching practice because Compare and Connect uses multiple strategies and compares them to one another. During compare and connect students look at two strategies for a problem and must decide for themselves which strategy works best for them. The book says, "It can be tempting to pursue other interesting ideas that may emerge; however, a Compare and Connect discussion is all about delving into the connections between the strategies of focus." I believe this artifact works because the students are using two strategies and connecting them to one another in a mathematical sense.

Citation:
Hintz, A. & Kazemi, E. (2014). Intentional talk: How to structure and lead a mathematical discussion. Stenhouse Publishers.

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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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The artifact chosen for this teaching practice is a worthwhile task. I found a worthwhile task called $100 word challenge. Each letter gets a number. The student must add up the "letters" to get to $100. This game can be altered and made more challenging. There are many versions that a teacher can use of this. This promotes reasoning and problem solving because the students must use their own ways to solve a problem. Ideally, the students must find their own way to get to $100. This activity also promotes reasoning because it is integrating language arts, therefore the students must correctly spell words or sentences.

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Watch as teachers learn how to properly develop math problems and tasks to give their students. Many problems with allow students to solve using multiple approaches.

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Establish mathematics goals to focus learning

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Establish mathematics goals to focus learning

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The artifact attached to the NCTM teaching practices is my community based lesson plan. The lesson plan had clear objectives that directly aligned to the standards and the assessment piece at the end. The objectives were "TSWBAT compare two dimensional shapes" and "TSWBAT create their own pizza and identify the shapes and number of shapes on their pizza with 100% accuracy." The assessment connected to it was the pizza worksheet that asked the students to identify the shapes.