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36 Cards in this Set
- Front
- Back
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NCTM |
National Council of Teachers of Mathematics |
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Why do the NCTM Principles and Standards exist? What motivated them, and what purpose do they serve? |
Math reform in the early 1980s introduced problem solving as an important strand of math curriculum. The standards provide guidance and direction for teachers and other leaders in math. |
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What does NCTM do? |
Share research based findings that influence standards |
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What are the six NCTM Principles? |
Equity, curriculum, teaching, learning, assessment, and technology |
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Describe the equity principle |
High expectations for all students. All students have the opportunity and adequate support to learn math. |
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What are the five NCTM Process Standards? |
Problem solving, reasoning and proof, communication, connections, and representation |
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Describe the connection standard |
Use connections among mathematical ideas, understand how math ideas interconnect and build on one another to produce a coherent whole, recognize and apply math in contexts outside of math. |
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What are standards for mathematical practice? |
1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning |
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Describe the standard "Make sense of problems and persevere in solving them" |
students should start by explaining the meaning of a problem and looking for entry points. Students check their answers, and continually ask "does this make sense" EX: Changing the viewing window on graphing calculator |
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What is mathematics? |
Generating strategies for solving problems, applying those approaches, seeing if they lead to solutions, and checking to see whether your answer makes sense |
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List several verbs that could be used to describe the doing of math |
Compare, explain, predict, explore, represent, solve, and verify |
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Explain constructivist learning |
Learners are not blank slates, but rather creators of their own knowledge. Networks and cognitive schemas are the product of constructing knowledge. As learning occurs, networks are rearranged, added to, or modified. This can happen with assimilation and accommodation. |
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Explain Sociocultural learning |
Mental processes exist between and among people in social learning settings, and from these social settings the learner moves ideas into his or her own psychological realm. Information is internalized depending on whether it was withing the learners ZPD and the child's level of assisted performance. |
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What do constructivist and sociocultural perspectives have in common? |
Both ideas are based on students' own ideas and solutions to problems. These aren't teaching strategies, but rather they inform teaching. Both ideas can be thought of as tools |
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What is productive disposition? Why is it important? |
A "can do" attitude. Ex: If you were committed to making sense of and solving tasks, knowing that if you kept at it, you would get the solution, then you have a productive disposition. |
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How does Van De Walle define a problem? |
A problem is a task for which students have no prescribed or memorized rules or methods (procedure-less). |
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What are the features of a problem? |
Must begin where students are, problematic aspect of the problem must be due to the mathematics that the students are to learn, and must require justifications and explanations for answers and methods. |
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Give an example of a problem-based task. |
Place an X on the number line about where 11/8 would be. Explain why you put your X where you did. It fits the features of a problem Van De Walle describes. |
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Describe three different possible approaches to the fraction problem. Why is it important for teachers to anticipate different approaches when lesson planning? |
1. Use a ruler or by folding strips of paper. 2. Draw a picture or area model 3. Guess and check 4. It is important because of scaffolding and all students learn differently |
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Why is it important to teach through problem solving? |
the more problem solving students do, the more willing and confident they are to solve problems and the more methods they develop for attacking future problems. |
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What do the teacher/students do in the Before phase? |
Before phase is about activating prior knowledge, making sure the problem is understood, and establishing clear expectations |
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What do the teacher/students do in the During phase? |
Students are given the change to work without guidance, the teacher takes notes on students' mathematical thinking, and giving appropriate support |
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What do the teacher/students do in the After phase? |
Promote a math community of learners through productive discussion, listen actively without evaluation, and summarize main ideas and identify future problems |
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What concerns do teachers often have about problem-based teaching? |
How can I teach all the basic skills I have to teach? Why is it better for students to explain than for me to do so? Is it okay to help students who have difficulty solving a problem? |
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How could you respond to these concerns? |
1. (Teach basic skills) It may be tempting to resort to rote drill, but evidence strongly suggests problem-based approaches are most successful 2. (Students explain) Students' explanations are grounded in their own understanding and as they communicate their ideas they solidify their own understanding. Also, think about the implications for creating a community of learners. |
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What doe the NCTM Assessment Principle say about assessment? |
Assessment should support the learning of math. Assessment should be a major factor in making instructional decisions |
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What does Van de Walle mean by performance-based assessment? |
Tasks that permit every student in the class to demonstrate knowledge, skills, or understanding. Also include real-world contexts that interest students or relate to recent classroom events. |
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Give an example of a performance based task |
Mary counted 15 cupcakes left. She noted that she already at two-fifths. How many cupcakes were there? It is performance based because every student has a chance to figure it out, and the teacher can draw conclusions about children's understandings from their answers |
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What is the difference between evaluating a students and learning about that student's mathematical thinking? |
Evaluating a students is testing them on the goals of the instruction. Learning about a student's thinking means getting a closer look at the way that student understands math. |
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How can you help prepare your students for high-stakes tests? |
Teach the big ideas in the mathematics curriculum that are aligned with your state and local standards. Students who have learned conceptual ideas in a relational manner and who have learned the processes and practices of doing mathematics will perform well on tests. |
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What challenges do different groups of students experience in learning math? |
Students identified as struggling may not be able to keep the same pace, students who are ELLs may not understand the "real-life" examples, and students who are gifted may not be challenged enough |
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What are specific strategies that you can use to teach math to students with special needs? |
Some strategies are explicit strategy instruction, concrete, semi-concrete, and abstract sequence, peer assisted learning, and think alouds. |
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What are specific strategies that you can use to help ELLs learn math? |
Honor use of native language, write and state content and language objectives, build background knowledge, and explicitly teach vocabulary |
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What is one piece of advice regarding teaching gifted students? |
Don't wait for students to demonstrate their mathematical talent; we need to develop it through a challenging set of tasks |
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What does the NCTM principle say about technology? |
Technology is essential in teaching and learning math; it influences the math that is taught and enhances student learning. |
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Argument for calculator use in classrooms |
Calculators can be used to develop concepts and enhance problem solving, practicing basic facts, and improve student attitudes and motivation. Also, the use of calculators does not threaten the development of basic skills and can actually enhance conceptual understanding. |
