GCI Chapters 7-9

GCI Chapters 7-9

--> Chapter 7: Children's Strategies for Solving Multidigit Problems

     Chapter 7 discusses strategies that children use when solving multidigit problems. When adding and subtracting, students can directly model with ones or tens. When modeling with tens, students are using their previous base ten knowledge. Students also invent algorithms to solve problems. When adding students add tens and then ones and then add them together. When subtracting, students subtract tens place and then remaining ones place. Algorithms can include incrementing, combining same units, or compensating. Allowing students to invent their own algorithms allows them to connect to what they are learning and often times avoid misconceptions.
     When multiplying and dividing, students may directly model with tens, use addition strategies to multiply and divide, invent multiplication and division algorithms, and use base 10 strategies with manipulatives.

--> Chapter 8: Problem Solving as Modeling

     Chapter 8 explains that children naturally want to model what they are doing. This helps them understand the problems they are solving on a deeper level. This is also encouraging students to be problem solvers.

--> Chapter 9: Develop Classroom Practice: Posing Problems and Eliciting Thinking

     When posing problems, teachers need to consider their goal and the complexity they want to target. Posing problems and asking questions should allow for student engagement. Students should unpack the problem into smaller questions and concepts. Students should share their ideas and discuss where they got those ideas from. Lastly, students should make sense of what they did to solve the problem.
     Eliciting student thinking can involve asking questions that force students to think about what they have done and how they have done it. Teachers need to consider the questions they are asking and follow-up questions that may come next. Teachers need to be prepared to ask questions to students who have the wrong answers. These questions should help students develop other solutions and a better understanding. When planning instruction, teachers should consider the ways that students think and solve problems.

   
References
Carpenter, T.P., Fennema, E., Franke, M.L., Levi, L., Empson, S.B. (2015). Children’s mathematics: Cognitively guided instruction. [Booklet & Online Video] Porstmouth, NH: Heinemann.

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