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135 Cards in this Set
- Front
- Back
Students must experience mathematics that what?
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makes sense
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Students must come to believe what?
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That they are capable of making sense of mathematics
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What should teachers stop doing?
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teaching by telling
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Name some of the verbs of "DOING" mathematics. (not to be confused with the daily objective verbs)
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use
explain predict investigate formulate justify verify explore represent |
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In a productive classroom culture, what is the currency of the classroom?
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ideas
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In a productive classroom culture, students have autonomy with what?
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respect to the methods used to solve problems
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In a productive classroom culture, how are mistakes viewed?
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as an opportunity to learn
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In a productive classroom culture, reasonability lies in what?
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The logic and structure of the subject, not the person or social status of the participants.
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Which principle includes high expectations and is shown through words, actions, and parental involvement?
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Equity principle
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Which principle states that one should know the content and know how students learn?
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Teaching princple
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The ___________ principle is coherent, focused, and well articulated across grade levels.
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curriculum principle
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In the ________ principle, new knowledge is built through connections with prior knowledge and experiences.
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learning principle
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The _________ principle enhances students learning, allows for more/deeper mathematics to be taught.
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technology
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What are the 5 content strands
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number and operations
algebra geometry measurement data and analysis |
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What are the 5 process standards?
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problem solving
reasoning and proof representations communication connections |
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The ____________ process standard is how students learn mathematics.
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problem solving
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The ________ process standard states that logical thinking should determine if and why answers are correct; providing a rationale should be part of every answer.
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Reasoning and proof
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The __________ process standard includes talking about, writing about, explaining, and describing mathematical ideas.
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communication
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In the connections process standard, there are two ways to make connections. What are they?
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within and among mathematics ideas
to the real world and other disciplines |
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Using symbols, charts, diagrams, graphs, and manipulatives is part of what process standard?
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representation
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When "doing" mathematics, you do what?
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devise a plan
apply the plan to see if it leads to a solution check to see if solution makes sense |
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What should the act of doing mathematics in the classroom closely model?
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the act of doing mathematics in the real world
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What does Piaget believe about children?
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that they create their own learning
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Piaget believes that people construct their own knowledge according to what?
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their previous knowledge, which gives them meaning to things they think about
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What is understanding?
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a measure of the quantity and quality of the connections that an idea has with existing ideas
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What does understanding exist on?
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a continuum
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________________ understanding is when ideas are highly connected and the person knows what to do and why.
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relational understanding
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_______ understanding takes a lot of work and effort.
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relational understanding
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___________ understanding is when concepts and connections develop over time, and not in a day.
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relational understanding
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_____________ understanding is when ideas are isolated completely. It involves doing with understanding.
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instrumental understanding
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Effective learning of new concepts and procedures is a benefit of what?
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relational understanding
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With ______________ understanding, there is less to remember, increased retention and recall, enhanced problem solving abilities, and improved attitudes and beliefs.
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relational understanding
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__________ understanding is knowledge about the relationships or foundational ideas of a topic.
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conceptual understanding
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___________ understanding is knowledge of the rules and procedures used in carrying out mathematical processes and of the symbolism that is used to represent mathematics.
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procedural understanding
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Is conceptual or procedural understanding taught first?
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conceptual
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Pictures, written symbols, manipulative models, real world situations, and oral language are what?
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Ways of representing mathematical ideas
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When should written symbols be used during a lesson?
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at the end
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How many ways of representing mathematical ideas should be used?
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at least 3
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Which three ways of representing mathematical ideas should be used at all times?
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manipulative models
pictures real world situations |
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Which way of representing a mathematical idea should be used in groups?
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oral language
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A ____________ is a task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific correct solution or method.
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problem
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When solving a problem, student should do what?
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work through it on their own.
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There are 3 features of a problem for learning math. The first feature states that it should begin where?
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Where the students are
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Students should have the appropriate ideas to engage and solve the problem, yet still find it what?
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challenging and interesting
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The problematic or engaging aspect of the problem must be due to what?
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the mathematics that the students are about to learn
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Students should be primarily concerned with making sense of mathematical ideas and then doing what?
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developing an understanding of those ideas
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In a problem for learning math, it must require what?
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explanations and justifications for answers
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What is the value of teaching through problem solving?
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A teacher changes her philosophy of how she thinks children learn. and how she can best help them learn.
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Models can be thought of as what?
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thinker toys
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___________ are used to help students develop new concepts or relationships.
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models
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___________ are used to help students make connections between concepts and symbols.
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models
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__________ are use to assess students' understanding.
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models
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Good problems will integrate what?
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multiple topics
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Teaching with problems focuses students' attention on what?
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ideas and sense making
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Teaching with problems allows _____________ for a wide range of students.
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an entry point for a wide range of students
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Teaching with problems provides what?
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ongoing assessment data
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Teaching with problems allows for what?
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extensions and elaborations
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What are the 3 types of information teachers should provide for students?
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mathematical conventions
alternative methods clarification of student methods |
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Symbols, terminology, definitions, and labels are what?
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mathematical conventions
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Student writing is important because it is a ________ process.
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reflective
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In the three-part lesson format, the before phase has the teacher doing what three things?
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activating prior knowledge
making sure the task is understood establishing clear expectations |
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In the three-part lesson format, the during phase says that teachers should do what?
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let the students do it on their own
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In the during phase of the three-part lesson plan, the teacher should provide appropriate what?
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hints
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For students who finish quickly, the teacher should provide what?
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worthwhile extension ideas
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In the three-part lesson format, the after phase says to promote what?
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a mathematical community of learners
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Teacher should encourage student-student what?
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dialogue
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What should be requested to accompany all answers?
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explanations
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Teachers should listen actively without what?
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evaluation
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Teachers should summarize main ideas and identify what?
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future problems
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Problems that can be approached in several different ways depending on the ability and learning style of the student is what?
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a multiple point entry problem
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_______________ is a provision of a different environment or circumstance made with particular students in mind.
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accommodation
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___________ refers to a change in the problem or task itself.
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modification
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____________ refers to different problem based tasks or experiences, spread over numerous class periods, each addressing the same basic ideas.
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practice
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__________ refers to repetitive, non-problem-based exercises designed to improve skills or already acquired skills.
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drill
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___________ can provide an increased facility with a strategy but only with a strategy already learned.
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drill
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With ___________, there is a review of facts or procedures so they are not forgotten.
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drill
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With __________, there is a focus on a singular method and an exclusion of flexible alternatives.
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drill
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With ___________, there can be a false appearance of understanding.
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drill
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_______ only focuses on what is known.
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drill
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____________ provides an increased opportunity to develop conceptual ideas and more elaborate and useful connections.
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practice
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___________ provides an opportunity to develop alternative and flexible strategies.
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practice
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___________ provides a greater chance for all students to understand, particularly students with special needs.
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practice
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_____________ provides a clear message that mathematics is about figuring things out and making sense.
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practice
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When doing practice, you should practice the use of what?
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flexible conceptual approaches, not isolated meaningless procedures learned by rote
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How long should practice be?
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15 minutes, 3 to 4 times per week
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What are the reasons you have students practice?
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To help them become quick, yet flexible
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What does homework communicate to parents and students?
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the importance of conceptual understanding
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When home work is drill, it should be what?
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kept short
have an answer key not be graded on correctness not gone over in class |
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When teaching with a textbook, the goal is to teach what?
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the big ideas, not the pages
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When using a textbook, the pace of the lessons should be determined by what?
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student performance and understanding
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__________ is the process of gathering evidence about a students' knowledge of, ability to use, and disposition toward mathematics and of making inferences from that evidence for a variety of purposes.
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assessment
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The purpose of _________ is to monitor student progress.
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assessment
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The purpose of ___________ is to make instructional decisions.
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assessment
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The purpose of ________ is to evaluate student achievement.
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assessment
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The purpose of __________ is to evaluate programs.
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assessment
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What three things should be assessed in mathematics?
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concepts and procedures
mathematical processes productive dispositions |
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True/false questions should be limited to what?
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10
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How many matching should there be on a test?
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between 5-15
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What kinds of lists should be used with matching?
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homogeneous
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Where should the main idea be stated in a multiple choice question?
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in the stem
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_________ is comparing students' work to correct answers or specific criteria that describes what we expect the work to be
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scoring
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________ is the result of accumulating scores and other information about a student's work for the purpose of summarizing and communicating to others.
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grading
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________ are frameworks that can be designed or adjusted by the teacher for a particular group of students or a particular mathematics task; used to"score the task".
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rubric
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_____________ are task specific statements that describe what performance looks like at each level of the rubric and in doing so establish criteria for acceptable performance.
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performance indicators
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____________ are brief write-ups about certain students, kept on individual note cards or on large peel-off labels.
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anecdotal records
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___________ are useful for planning purposes.
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observational rubrics
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__________ is one checklist per student, but each contains the same set of specific processes to be observed.
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individual checklists
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______________ are one page charts with places for checks when certain "behaviors" have been observed or not.
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checklists for full classes
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What are the advantages of writing in the math classroom?
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it's private
it can be revised or edited it can be re-read at a later time includes pictures, graphs, and symbols |
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What are the 4 types of writing in the math classroom?
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journal writing
problem solving explaining the idea reflective writing |
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Give an example of a math writing prompt.
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If math were a color, what would it be?
I need help with _________ because.............. |
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A ______ is a statistic that is used to communicate to others the achievement level that a student has attained in a particular area of study.
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grade
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When looking at the grade at the end of a period, it should reflect what?
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all areas of grading, not just tests
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Grades assigned should reflect all of what?
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objectives
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What are the 6 assessment standards?
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Openness
Learning Mathematics inferences coherent equity |
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Using the frameworks to determine what the students should know and do and basing assessments on those essential concepts and processes is which standard?
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mathematical standard
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Incorporating assessment as an important part of instruction and not an interruption or at the end of the unit is part of what standard?
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learning standard
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In the _______ standard, the teacher should determine students' misunderstanding of the material and go deeper.
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learning standard
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In the __________ standard, the teacher should respect the unique qualities, experiences, and expertise of all students.
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equity
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In the __________ standard, the teacher should maintain high expectations for students, while recognizing their individual needs.
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equity
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In the _________ standard, the teacher should look at how the students can demonstrate what they know.
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openness
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In the ___________ standard, the teacher should avoid looking at the answers and give attention to the examination of the thinking processes students used.
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openness
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In the ____________ standard, the teacher should provide students with examples of responses that meet expectations and those that don't meet expectations.
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openness
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In the _________ standard, the teacher should reflect seriously and honestly on what students are revealing about what they know.
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inferences
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In the _______ standard, the teacher should use multiple assessments and avoid bias by establishing a rubric that describes the evidence needed and the value of each component used for scoring.
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inferences
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In the _______ standard, the teacher should match his/her assessment techniques with both objectives of the instruction and the methods of the instruction,
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coherence standard
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In the ___________ standard, the teacher should ensure that assessments are a reflection of the content the teacher wants the student to learn, and develop a system of assessment that allows the teacher to use the results to inform the teachers instruction in a feedback loop.
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coherence standard
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In _________, students must be actively participants in the development of their own understanding.
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constructivism
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In ___________, students make connections between old ideas and the new ones.
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constructivism
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Students are not _______, they do not absorb new ideas.
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blank slates
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In the teaching principle, the teacher should use what?
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appropriate instructional tasks
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In the teaching principle, the teacher should use a journal for what?
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to reflect on lessons
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In the teaching principle, the teacher should share ideas and what?
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plan ahead
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____________ principle is used to guide instructional decision.
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assessment
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Assessments should be done ____ students.
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for
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