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
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