Essay math vidoe

1 What are the fingers in each problem being used to keep track of?
In the first video, the math problem was 5+9= . The student used fingers to track 5 numbers from 10-14, and got the answer14.
In the second video, the math problem was 7+ =11. The student used fingers count from 8 to the target number 11, and figured out that 4 fingers were needed, so the student got the answer 4.
2. Are the fingers being used to track the same information? If yes, why do you think that? If no, how are they different?
No, they are different. The first student used the fingers to track the resulting number, so he counts from 10, and stops until he gets the fifth number 14. This was a result unknown. But the second student used the fingers to track the changing number. The student counted from 8 to the target number, and then got the changing number from the fingers and figured out 4. This was a change unknown.

Shulman concludes three categories of content knowledge, “subject matter content knowledge, pedagogical content knowledge, and curricular knowledge.” (Shulman, 1986)
Content knowledge is about “the amount and organization of knowledge in the mind of the teacher” (Shulman, 1986). Shulman believes that teachers must grasp as much knowledge as people who are in the major. Teachers should not only excel in knowledge but also think about the questions behind the knowledge and the reasons of learning the knowledge. Pedagogical content knowledge is “the dimension of subject matter knowledge for teaching”. Shulman considers that teachers should understand how to represent the subject content, and how to make learners easy to comprehend. He also mentions an important element “research-based knowledge”. He believes it’s so crucial for teachers to gather students misconceptions and overcome the instructional conditions. Curricular knowledge is the knowledge of understanding materials. Shulman divides it into three parts: 1. Looking for “alternative curriculum materials”; 2. “Be familiar with the curriculum materials under study by his or her students in other subjects”; 3. Be familiar with the materials of the same subject “during the preceding and later years in school” (Shulman, 1986). Shulman also concludes three forms of knowledge: “propositional knowledge, case knowledge, and strategic knowledge” (Shulman, 1986). Propositional knowledge is about rules and disciplines, and it includes “principles, maxims, and norms”. Shulman found people are hard to remember those rules, and no details are with the rules. Case knowledge is “knowledge of specific, well-documented, and richly described events” (Shulman,

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