CGI Chapters 10-12

GCI Chapters 10, 11, & 12

--> Ch. 10: Developing Classroom Practice: Engaging Students with Each Others Ideas

This chapter discusses the levels of engagement in mathematics. The first level of engagement is comparing an idea to other ideas. Students should discuss their strategies and see how their strategies are similar or different from other students strategies. The second level of engagement is attending to detail in other students' strategies. This can allow students to get a deeper understanding of what exactly is being done to solve the problem. Lastly students should build on other students ideas to deeper their own understanding. Students should support the ideas of others and share their own. This can increase the amount of understanding for all students.

--> Ch. 11: Mathematical Principles Underlying Children's Mathematics

This chapter discusses the commutative, associative, and distributive properties. The relationship between subtraction and division is also mentioned. Students engage with and use properties before they even know they are properties known to be true. This gives students an understanding of what is happening rather than them memorizing the properties.

--> Ch. 12: The Conceptual Basis for Cognitively Guided Instruction

There are four "interconnected themes" of CGI. The first theme is that knowledge is connected. Simple mathematical concepts can help students understand more complex mathematical concepts. Mathematical concepts can also be used to help students gain understanding in other content areas, such as science. The second theme is that knowledge is generative. This means that students can use ideas to learn new ones and grow their knowledge. The fourth theme is describing, explaining, and justifying mathematical thinking. This explains that students need to understand why the properties and strategies they are working with actually work. It is not enough to simple memorize properties and formulas. The final theme is children's identity as mathematical thinkers. Children need to be pushed to be problem solvers and thinkers. This will help them in all content areas, not just mathematics. Another main point I pulled from this chapter is that teachers should learn from their students and their ways of thinking.

Comments

  1. Dr. NugentOctober 8, 2019 at 9:59 AM

    Great reflection, Darby! You have definitely identified some important key issues...Thanks:)

    ReplyDelete

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