C284 Task 1
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School
Western Governors University *
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Course
284
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
3
Uploaded by AmbassadorUniverseWasp44
Tyler Phanhthavilay December 11, 2023
C284 Task 1
A. Two NCTM Process Standards: One standard that was identified in the passage was problem solving
. This standard is not just finding the answer but the way they got to that answer and the process to it. It is fundamental for learning mathematics and cultivating key abilities such as persistence, curiosity, and confidence to think critically to solve complex problems. Being able to reflect on hard problems and not being given the answer right away allows for the ability of adaptability for a plethora of different situations. A specific example that was demonstrated in the video lesson was that the teacher had given them a problem. The problem was a one block high staircase would take one block, a 2-block high staircase would equal 3 blocks, and by this he gave them the complex question to find out what the pattern is to find how many blocks it would take for x amount of how high a staircase is. This is a prime example of this NCTM process standard of problem solving because he did not give them a direct answer, but he wanted them to find the relationship from the blocks and find the answer for themselves. He allows the students to work in groups and to have peer collaboration to throw down ideas to help those who are confused and to develop those ideas as well. This fosters for a more positive learning environment where a hard problem is given, and the students use critical thinking skills to persist to find an answer. Another standard that was identified was communication
. This standard is an essential ability for students to learn effectively. Students are not only challenged to think about the correct solution, but they also must be able to articulate their mathematical ideas in writing and in discussion. Also, this can be produced by listening and talking with other people’s ideas and considering it to their own, this would help develop one’s understanding and to explore mathematical ideas from multiple perspectives. A specific example that was shown within the video was when the teacher had split the students into groups to find the pattern or equation for the block staircase problem. The students would talk to each other and find solutions and then another student would give their input and prove that one way is wrong. One specific example is that one student would just count each step as it went up, then another student intervened and said that it would take too long and doesn’t provide
an exact equation. Then the teacher came up and said that they were both right, and that her way was a great starting point and that they should identify more patterns to find the equation. The teacher would also not give them the answer directly to foster more communication with one another. Although, he did ask questions to make sure that the students were on track and understood the concept.
B. High-Level Cognitive Task The “Teaching Math: Staircase Problem” demonstrated a high-level cognitive task to the students
because it fostered critical thinking, problem solving, conceptual understanding, and visual representations. The students in the lesson were asked to find a pattern for a block arrangement that would increase by one step, this had them think about the process and the pattern to find the
Tyler Phanhthavilay December 11, 2023
C284 Task 1
systematic equation to solve it. Instead of just giving the students the equation and follow it up with questions that pertain to it, he wanted the students to think about how they got that equation before providing it to them, this gave the students a high effort thinking task. In the video the teacher would also ask the students questions of where they were at and what they found out so far. This was an example of how the teacher would guide the students and encourage them to think conceptually to understand the relationship of blocks to pattern, this is a high cognitive task
as it is does not promote memorized procedure but develops complex thinking. Then the teacher also gave them visual representation to have them think about it not just conceptually but also visually as they could build the blocks to form a relationship between them. C.
Multiple Entry Points:
The students would engage with this complex problem at different levels of understanding based on how they think and prior knowledge. For example, one student who may have 0 understanding would go straight to the blocks to visualize it better to identify the pattern of the blocks. Then by step by step they would gradually gain a better understanding of the concept. Although, the more experienced students or those who had a better grasp may go straight to writing concepts on paper with formulas using variables. As these students may enter at a different point where they grasp the pattern easier and would create algebraic expressions before those who are building the blocks visually. Some students may start by asking questions to the teacher and thinking about it to themselves instead of doing the blocks or going straight into making equations. This is an example of different entry points to this lesson as it was portrayed in the video as a lot of students used the visual blocks, one girl would ask a bunch of questions to proceed her thinking, and some students would write equations that were somewhat correct. D.
Incorporating relevant contexts within math lessons is essential as it encourages students understanding, motivation, and their mathematical concepts that pertain to the real world. In the lesson the staircase problem gives students viable context to real world life because it gives them
a connection from math to building real staircases in life. Understanding the connection between the two would help foster critical thinking when thinking about construction or design of such things. It also cultivates motivation because it gives the students meaningful context because it makes the learning experience more fun and interesting if it has something the students could see
in real life. Learning math equations with no context to what it could relate to in real life may have students bored and wondering why they are even learning it. Solving authentic problems like the staircase one helps the students reinforce their ability to use mathematical concepts in a practical scenario as they worked collaboratively with blocks to figure it out. Transforming abstract ideas and patterns into something tangible that you see all around you in life, motives and creates a learning environment that is meaningful which this teacher had formed. E. Sources
Tyler Phanhthavilay December 11, 2023
C284 Task 1
Used the video given and the passage given by WGU.
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