#kcmcpowerfulproblemsolving search results
Problem-solving is the creative process one takes to tackle mathematical problems. One tries different techniques/heuristics to figure out a possible solution pathway. It is also a process to deal with ambiguities. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Some effective routines and actions to help students concretize and abstract is the use of manipulatives, noticing & wondering, multiple representations, metacognition & reflection, and comparing & contrasting strategies #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
@maxrayriek has a great point here. Number sense is an important tool to help us make an original guess to start a problem. We can use this guess to test some of the constraints & quantities. We can revise it as needed. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Noticing and Wondering can be useful as students decompose a problem, to compare and contrast different representations, to brainstorm possible solution pathways, and as @maxrayriek shares, as a tool to "get unstuck." #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
As students engage in problem-solving, it is important that we take the moment to reflect on what worked and what did not work. It is important to have them reflect on the math practices that they used. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
I agree with @maxrayriek. The context really helps to make sense of the quantities & tentative solutions of a problem. Abstraction is what happens as we make decisions in problem solving & generalize results via a model. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
I totally agree with @maxrayriek for one can use the answer as a starting point for other higher-order thinking tasks which include generalizing, deriving, and proving formulas, methods, and algorithms. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
@maxrayriek is absolutely right. Organization is fundamental to be able to see patterns that lead to the use of structure and repeated reasoning. In this sense, being organized relates directly to math practices 7 and 8. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
As @maxrayriek states, communication in math helps to push our thinking. So, some purposes are clarifying, comparing, & contrasting. We can ensure students feel heard when we create a classroom where discourse is the norm. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Dot talks, number talks, and comparing and contrasting activities such as Which One Does Not Belong are great ways to help students develop effective listening skills in math class. Problem-Solving also helps with these! #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
I agree with @maxrayriek, changing representations can provide perspective into new possible solution pathways. Multiple representations also help us to identify other aspects of the problem that were previously unnoticed. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
As we reflect on our metacognition as we engage in problem-solving, we can determine the habits of minds that are more effective and efficient to solve other problems. We engage in tasks in the zone of proximal development. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
I plan to continue promoting an environment that fosters productive struggle by using the activities I learned via this book study. I also plan on continuing using low-floor-high-ceiling tasks and promoting math discourse! #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Math modeling allows us to see the connections between the maths & the world. It also gives us the opportunity to get creative and encounter multiple perspectives. Mathematical modeling is a low-floor high-ceiling endeavor #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
This pathway is definitely not linear. Mathematicians continuously move back and forth across stages to reaffirm or disprove conjectures and to test extra information they gather as they play with the problem/task at hand. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
I definitely agree with @maxrayriek on this statement. Productive struggle allows us to see the math as the aspirin and not the headache (like @ddmeyer would say). In that sense, students can become more inclined to learn! #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
I plan to continue promoting an environment that fosters productive struggle by using the activities I learned via this book study. I also plan on continuing using low-floor-high-ceiling tasks and promoting math discourse! #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
I totally agree with @maxrayriek for one can use the answer as a starting point for other higher-order thinking tasks which include generalizing, deriving, and proving formulas, methods, and algorithms. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
As we reflect on our metacognition as we engage in problem-solving, we can determine the habits of minds that are more effective and efficient to solve other problems. We engage in tasks in the zone of proximal development. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
This pathway is definitely not linear. Mathematicians continuously move back and forth across stages to reaffirm or disprove conjectures and to test extra information they gather as they play with the problem/task at hand. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Q4: As a conclusion, @maxrayriek reminds us about the importance of fostering productive struggle, using and discovering methods, and valuing students’ ideas. How do you plan to start or continue promoting problem-solving? #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Q3: According to @maxrayriek, obtaining the solution to a problem is not the last step. The problem solver can still reflect, revise, justify, and extend the results. Do you agree? Why or why not? #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Q2: @maxrayriek explains that the process of problem solving & metacognition are related. What is the role of metacognition in mathematics? How does this connect to Vygotsky's zone of proximal development and independence? #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Q1: @maxrayriek shares that expert mathematicians move through different stages (read, analyze, explore, plan, implement, and verify) when solving a problem. Is the movement across stages linear? Why or why not #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Welcome to our fourth and last sequence of posts for our book study of Powerful Problem Solving by @maxrayriek. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
I definitely agree with @maxrayriek on this statement. Productive struggle allows us to see the math as the aspirin and not the headache (like @ddmeyer would say). In that sense, students can become more inclined to learn! #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Math modeling allows us to see the connections between the maths & the world. It also gives us the opportunity to get creative and encounter multiple perspectives. Mathematical modeling is a low-floor high-ceiling endeavor #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Some effective routines and actions to help students concretize and abstract is the use of manipulatives, noticing & wondering, multiple representations, metacognition & reflection, and comparing & contrasting strategies #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
@maxrayriek is absolutely right. Organization is fundamental to be able to see patterns that lead to the use of structure and repeated reasoning. In this sense, being organized relates directly to math practices 7 and 8. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Q4: @maxrayriek shares that having students experience productive struggle can be a great structure and motivator for students to hear instruction and learn. Do you agree? Why or why not? #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Q3: @maxrayriek expresses “a mathematical model is a representation of a mathematical idea” (p. 112). Modeling is explicit as a mathematical practice. What are the benefits of mathematical models and mathematical modeling? #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Q2: Abstracting and concretizing are two terms @maxrayriek uses in chapter 8. What are effective routines or actions to help students abstract and concretize in the mathematics classroom? #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
Q1: @maxrayriek highlights the importance of being organized in mathematics. Why is organization key in math? How does this skill relate to the math practices? #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
We welcome you to our third discussion of Powerful Problem Solving by @maxrayriek. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
@maxrayriek has a great point here. Number sense is an important tool to help us make an original guess to start a problem. We can use this guess to test some of the constraints & quantities. We can revise it as needed. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
I agree with @maxrayriek. The context really helps to make sense of the quantities & tentative solutions of a problem. Abstraction is what happens as we make decisions in problem solving & generalize results via a model. #KernCMC #KernProblemSolving #KCMCPowerfulProblemSolving
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