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26 Cards in this Set
- Front
- Back
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What is the primary purpose of drill of basic facts?
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*No drill until understanding is attained.
*the intent is to MEMORIZE *should be 5-10 minutes almost every day. |
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Addition strategies
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*Commutativity-changing the order of the addends does not affect the sum
*strategies for 0,1 and doubles *Counting on-start from the larger addend and count on (easy when one is a 1,2, or 3) *Adding to ten |
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Subtraction strategies
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*Using 0 and 1 - same as addition
*Doubles - rests on the assumption that children know the doubles for addition *Counting back *Counting on |
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Multiplication strategies
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*Commutativity
*Using 0 and 1 *Skip counting *Repeated addition *Splitting the product into known parts *Patterns |
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Division Strategies
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*Find missing factor in the multiplication problem
*Fact families *Find missing factor in the multiplication problem *Repeated subtraction |
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How is the calculator a valuable computational tool?
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*facilitates problem solving
*Relieves tedious computation *focuses attention on meaning *removes anxiety about computational failures *provides motivation & confidence |
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Why emphasize mental computation?
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*It's useful. three-fourths of all calculations done by adults are done mentally.
*It provides a direct and efficient way of doing many calculations. *It is an excellent way to develop critical thinking and number sense and to reward creative problem solving. *Contributes to increased skill in estimation. |
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Strategies in teaching mental computation
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*Encourage students to do computations mentally.
*Check to learn what computations students prefer to do mentally *Include mental computation systematically and regularly as an integral part of your instruction *Keep practice sessions short - perhaps 10 minutes at a time *Develop children's confidence *Encourage inventiveness - there is no one right way to do any mental computation *Make sure children are aware of the differences between estimation and mental computation |
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4 phases for the classroom assessment process (in sequential order)
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1. plan assessment
2. gather evidence 3. interpret evidence 4. use results |
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The most common type of assessment is
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observation
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What are the 4 prerequisites to numerical operations
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*Counting expertise: count forward, backward, by 2's, 3's, etc.
*Experience with concrete situations *Familiarity with problem-solving situations - "I don't know the answer, but I can work it out!" *Experience in Using Language to Communicate Math Ideas |
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What is the most difficult computational algorithm?
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Division
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Why is division so hard for kids?
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*It works from left to right (opposite of the way they are accustomed)
*It jumps around the page *It uses multiplication, division, and subtraction *It requires guess and check (multiply to see if the number fits) |
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Differences and similarities of problem, exercise, routine problem, and non-routine problem.
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*Problem: involves a situation in which the solution route is not immediately obvious
*Exercise: a situation in which the solution route is obvious *Routine Problem: the application of a mathematical procedure in the same way it was learned. *Non-routine problem: the choice of mathematical procedures is not obvious. WHICH TERMS ARE SYNONYMS? Problem <--> non-routine problem Exercise <--> Routine problem |
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Polya's Model of Problem Solving
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1. Understand the problem
2. devise a plan for solving it 3. carry out your plan 4. look back to examine your solution |
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Problem-Solving strategies
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(1) act it out (2) made a drawing/diagram (3) look for a pattern (4) construct a table (5) guess and check (6) work backward (7) write an open sentence -> equation (8) solve a simpler or similar problem (9) change your point of view
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Change your point of view problem solving strategy
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If the teacher holds up a checkerboard, how many squares are there?
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Calculator myths
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*calculator use does not require thinking
* use of calculators will harm student's math achievement * computation with calculators are always faster * calculators are useful for computation |
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What are the 2 types of math assessments?
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*Summative: this is an assessment OF learning. Provides evidence of student achievement for purposes of public reporting and accountability (tests, exams, standardized tests)
*Formative: Assessment FOR learning. Documents students' achievement as well as guides instructional decisions and helps students learn. (Homework, in-class assignments, performance assessments, teacher observations, classroom tests) |
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4 purposes of assessment
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*Make instructional decisions
*Monitoring Students' progress *Evaluating students' achievement *Evaluating programs |
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Major Shifts in Assessing to MAKE INSTRUCTIONAL DECISIONS
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Toward: (1) integrating assessment w instruction (2) Using evidence from a variety of assessment formats and contexts (3) Using evidence of every student's progress toward long-range planning goals.
Away From: (1) Depending primarily on scheduled testing (2) relying on any one source of information (3) planning primarily for content coverage. |
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Major Shifts in Assessing to MONITOR STUDENTS' PROGRESS
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Toward: (1) assessing progress toward mathematical power (2) communicating w/ students about performance in a continuous, comprehensive manner (3) using multiple and complex assessment tools (4) Students learning to assess their own progress
Away From: (1) Assessing knowledge of specific facts and isolated skills (2) simply indicating right or wrong answers (3) Primary reliance on answers to brief questions of quizzes and tests (4) teachers and external agencies as the sole judges of progress |
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Shifts in Assessing to EVALUATE STUDENTS' ACHIEVEMENT
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Toward: (1) Comparing students' performance w/ performance criteria (2) Assessing progress toward mathematical power (3) Certification based on balanced, multiple sources of information (4) Profiles of achievement based on public criteria
Away From: (1) Comparing student w/ student (2) Assessing knowledge of specific facts and isolated skills (3) Relying on only a few narrowly conceived sources of evidence (4) Single letter grades based on variable or nonpublic criteria |
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Assessment Methods
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(1) Observation (2) Questioning (3) interviewing (4) Performance Tasks [usually applicable to real life. Best to pair students to hear conversation and reasoning] (5) Self-Assessment and Peer Assessment
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Front end estimation
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3242 + 748
3200 + 700 = 3900 |
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Compatible numbers in estimating
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23,562 / 13 compatible numbers are
24,000 / 12 12 goes into 24 answer is 2,000 _____________________ 30,916 / 972 compatible #s are 32,000 / 800 b/c 8 goes in 32 answers = 40 |
