SN ESM3 TASK 1 PROFESSIONAL MATHEMATICS STANDARDS

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ESM3 TASK 1: PROFESSIONAL MATHEMATICS STANDARDS - A. Identify two NCTM process standards in the attached “Executive Summary: Principles and Standards for School Mathematics,” that you observed in the lesson from the “Teaching Math: Staircase Problem” video. Support each standard with a specific, relevant example from the lesson. 1. Problem Solving: The students in the video are engaged in problem-solving activities as they explore the staircase problem. They are trying to determine how many blocks are needed to construct staircases of different heights, such as 50 steps, 100 steps, and N steps. They are using their mathematical thinking skills to analyze the patterns and come up with strategies for finding the number of blocks required for different staircase heights. They discuss different approaches, make conjectures, and test their ideas through calculations and observations. Throughout the video, the students were actively involved in problem-solving by identifying patterns, making observations, and developing rules or strategies to determine the number of blocks needed for different staircase heights. 2. Communication: The students in the video are engaged in communication as they discuss and exchange ideas with their teacher and peers. They ask questions, share their observations, explain their reasoning, and seek clarification. They communicate their thoughts and strategies to their group members and the teacher, facilitating the sharing of ideas and collaboration. The students ask questions to clarify their understanding of the problem, propose different approaches to solving it, and explain their reasoning to their peers and the teacher. They engage in discussions, share their observations, and seek feedback from others. The teacher also encourages communication by asking students to share their progress and thoughts with the class. B. Explain how the activity in the “Teaching Math: Staircase Problem” video is a high-level cognitive demand task. Support your claims using a specific, relevant example from the lesson. The activity in the video is a high-level cognitive demand task because it requires students to engage in critical thinking, problem-solving, and abstraction. They are tasked with finding a rule or pattern that relates the number of steps in a staircase to the number of blocks needed to build it. By generalizing the pattern, they need to determine the number of blocks required for staircases of different heights, such as 50 steps, 100 steps, and an arbitrary number of steps denoted as N. One example from the video that demonstrates the high-level cognitive demand is when the students discuss their approach to finding the rule. At one point, they consider adding the number of steps and the number of blocks together to get the next number of blocks. However, they realize that this method would require calculating all the previous steps, which is

ESM3 TASK 1: PROFESSIONAL MATHEMATICS STANDARDS - labor-intensive. They understand that they need a more efficient approach and talk about alternative strategies. The students' engagement in discussing different possibilities and testing their ideas demonstrates the high-level cognitive demand of the task. They are required to analyze patterns, formulate hypotheses, and refine their thinking based on evidence. Throughout the activity, the students are encouraged to think deeply, reason abstractly, and develop mathematical reasoning skills. C. Explain how the activity in the “Teaching Math: Staircase Problem” video provides multiple entry and exit points. Support your claims using a specific, relevant example from the lesson. The activity in the video allows students to enter and exit at different points, engaging in problem-solving and exploration at varying levels of understanding. They begin by observing and analyzing the given staircases, considering the relationship between the number of steps and blocks. Discussions arise, such as one student suggesting that each step increases the number of blocks by one, while another student raises concerns about the time-consuming nature of this method. These interactions highlight the multiple entry and exit points within the activity. As students progress, they explore alternative approaches, such as adding the number of blocks and steps, to find patterns and generalize the relationship between steps and blocks. However, they recognize the limitations of these strategies, as they require knowledge of all previous steps. Throughout the activity, students engage in collaborative discussions, test and revise ideas, and deepen their understanding. By accommodating different entry and exit points, the activity promotes critical thinking and collaborative problem-solving, allowing students to develop a comprehensive understanding of the patterns and rules involved. D. Explain the importance of using tasks that involve a relevant context. Include a specific, relevant example from the lesson to support your claims. Using tasks that involve a relevant context is important because it helps students connect the mathematical concepts to real-world situations, making the learning experience more meaningful and engaging. The staircase problem allows students to explore the relationship between the number of steps in a staircase and the number of blocks needed to build it. By working with concrete examples and visualizing the staircases, students can develop an understanding of patterns and generalization. In the lesson, students initially make arithmetic mistakes but gradually grasp the idea of finding a rule to generalize the relationship. They discuss different approaches, such as adding the number of steps and blocks or multiplying the number of steps by a specific factor. Through hands-on exploration and collaborative discussions, students begin to notice patterns and make

ESM3 TASK 1: PROFESSIONAL MATHEMATICS STANDARDS - connections. The teacher encourages them to focus on gathering data and understanding the relationship between the height of the staircase and the number of blocks, rather than immediately seeking a rule. This approach allows students to build a solid foundation of understanding before moving on to more abstract concepts. Using relevant tasks, like the staircase problem, enables students to actively engage in the learning process, make connections between math and the real world, and develop a deeper understanding of mathematical concepts.

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