Task 1- Mathematics Learning and Teaching
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Western Governors University *
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C284
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Communications
Date
Apr 3, 2024
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docx
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3
Uploaded by ChiefRain13624
Courtney Brewer
Task 1
Mathematics Teaching and Learning
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.
Problem Solving: Within the video, students are given consistent opportunities to formulate, tackle, and (hopefully, eventually) resolve an intricate problem that demanded substantial effort. In the video, students were given a staircase problem where they were asked to find a pattern in the data formulated from the about of blocks needed for an undetermined height of a staircase. Problem Solving continues throughout the video as students work in groups—
engaging in the challenge by using critical thinking skills and perseverance. Groups are continually shown using a data chart to track their work and ideas; as well as any questions that may arise during their thinking process. As the video progresses, the instructor, Jesse Solomon, is seen encouraging them to contemplate their thought processes. At 5:45, you can specifically hear him encouraging two female students on their two different approaches. He did not claim that one idea is better than the other, and further encouraged their thinking progress by having the students contemplate an easier/faster way than working out each individual step. At 12:20, we see Solomon continuing to allow students to reflect on their learning by having them expand
on their thought process of the staircase resembling a square or triangle. This encouraged the students to continue from their stuck place to further their exploration. Communication: In groups of 3, students were expressing mathematical concepts through communication by sharing their different ideas for a possible pattern of the staircase. A particular communication between two students that really stood out to me was beginning at 4:25 when two students were discussing the possible pattern. These two students were both focused on breaking down each step, but you can tell that one of the students was focused on the overall pattern while the other student was focused on calculating for a specific number. You
can hear one say at 5:05 “What would you do? Would you do all of these out to 99?” showing that this method would be involve a surplus of work. The same student was seen in the next scene explaining this to the teacher. The greatest part of this communication was the part where she said “it was a good idea, but the way she got it, it wasn’t” meaning that she agreed but also understood that it wasn’t the best solution to the overall problem at hand. It showed a level of communication where there was mutual appreciation and understanding of different viewpoints. 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.
This lesson is a high-level cognitive demand task by incorporating mathematical communication as a central element. Students were tasked with articulating and sharing the outcomes of their critical thinking through both oral means (communication between their group peers and the instructor) as well as written (shown in a data chart completed by the group). The instructor and
the activity challenged students to be not only clear but also convincing and precise in their use of mathematical language. Solomon was continually asking clarifying questions to students to further broadening their explanations and thinking. Students were pushed to delve into the reasoning behind their solutions. You can hear frustration from students at 14:20 where students are pushing the boundaries of their thinking—followed by the instructor acknowledging it. In the following scene, you hear the students’ appreciation of the high-level demand that the teacher has for his students—“he gives us this desire to want to learn.. he motivates us to learn more and that’s what’s special”. 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 staircase problem has a variety of ways for students to approach the problem, as well as demonstrate their understanding.
For their entry points, you see multiple different strategies throughout the video of solving the challenge given. One group of students is seen using manipulatives (2:31, 3:14) to manually create staircases (conducting their problem-solving kinesthetically and visually). You see others drawing out their individual staircases on a poster, while another group going straight into their data chart (2:42). Within the actual calculations, students are approaching the problem in multiple ways: by working on each individual step (repeated addition), by thinking about the staircase as perfect squares or triangles, or by working on a ‘master rule’ directly that would solve for any given variable (3:10).
For their exit points, students demonstrate their learning through communication with their teacher, Jesse Solomon, where they are able to carry on a conversation in which they are explaining their approach (5:15), the reasoning behind it (8:10), defending the strategy (6:20; 8:10), and gathering critiques (8:30) in order to learn new tactics in order to reapproach (9:45; 12:25) or further their exploration.
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 helps students understand the practical application of their learning. It is crucial for contexts in your classroom to mirror the cultures and interests of your students, as emphasized in Chapter 3 on Teaching through Problem Solving. Incorporating everyday situations not only boosts student engagement but also encourages the use of diverse problem-solving strategies, fostering the development of a positive attitude towards learning. Within the staircase lesson, Solomon and his students are heard relating the figures to their prior knowledge of patterns within one step and two step functions (1:46, 2:06) and of perfect squares (12:51). Solomon also makes it relevant by relating the lesson to a real-
life situation of building a staircase needing to know the materials needed to complete the task (1:36, 9:15).
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