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Midterm
Midterm
Midterm
Midterm
Midterm
100
Differentiate between procedural & conceptual knowledge. Give examples.
Procedural- skillful use of math rules/algorithms (ex: knowing the steps to complete long division). Conceptual- understanding math concepts (ex: understanding that division is forming equal groups)
100
What is Summative Assessment? What is Formative Assessment? What are the primary purposes of each?
Summative Assessment is the assessment OF learning, ex: EOGs. Formative Assessment is the assessment FOR learning, ex: homework.
100
Why is a mental computation important?
Mental computations encourages flexible thinking, promotes number sense, & encourages creativity & exploration.
100
This is a definition of what? "Describes the range of activities a child can do at a certain level of thinking"...
Vygotsky's Zone of Proximal Development
100
Think about the Marilyn Burns introduction into fraction LP; "CCSSM: The Big Picture" article; and write the instructions to solve Problem Solver Four's Task 2 problem (most likely that problem)**
You're going to do GREAT!!
200
What are the contributions of these psychologists? Skinner; Piaget; Brownell; Dienes; Vygotsky
Skinner- Behaviorist Approach Piaget- came up with Constructivism Brownell- forerunner of Constructivism Dienes- characterized children's levels of development through Constructivism Vygotsky- developed the notion of the zone of children's proximal development
200
Identify 6 different assessment techniques. What kind of information would you gather with each techniques? (OQIPSP)
Observation- how students tackle problems Questioning- know what they're thinking Interviewing- learn about students' thinking Performance Tasks- observe "real life" skills Self/Peer Assessment- eliminate weakness & find ways to improve Portfolio- assess progress
200
Summarize the guidelines for developing mental computations. (9)
- Encourage students to do computations mentally. - Learn which computations students prefer to do mentally. - Find out if students are applying written algorithms mentally. - Plan to include mental computations regularly in instruction. - Keep practice sessions short. - Develop children's confidence. - Encourage inventiveness. - Mental computations or estimation?
200
Observation; Questioning; Interviewing; Performance Tasks; Self/Peer Assessment; Portfolio- are all examples of what?
What is 6 different assessment techniques. **Know the information they each gather also!
200
Part-Whole- the whole has been split into equal parts Quotient- fraction means division Ratio- fractions mean "to" and "of" also.
What are the three meanings of fractions.
300
What did Vygotsky mean by "zone of proximal development"?
Vygotsky means to describe the range of activities & experiences a child can do at a certain level of thinking.
300
What are some specific items you would include in a student's mathematics portfolio?
3 homework assignments 3 writing samples 2 quizzes 2 class notes 1 example of specific project work 1 example of cooperative group work
300
What are the 5 estimation strategies & give examples.
- Front-End Estimation- using only the first number - Adjusting- evaluating if it would be over or under the next round number - Compatible Numbers- changing fractions to be more easily recognizable. - Flexible Rounding- rounding numbers to make them easier to work with. - Clustering- averaging to estimate a sum
300
3 homework assignments 3 writing samples 2 quizzes 2 class notes 1 example of specific project work 1 example of group work ... Are all examples of what?
What is Specific items you would include in a student's mathematics portfolio.
300
Region- special version of the area model, region is the whole & the parts are congruent. Length- any unit of length can be partitioned into fractional parts of equal length. Set- uses a set of objects as a whole. Area- more general version of the Region model, but these parts are equal in area, but not congruent.
What are the 4 models of the Part-Whole Concept and how the region & area models are different.
400
What is the principle of Multiple Embodiment?
Multiple Embodiment is the use of perceptually different models. ex: using a plate, coin, or ring to represent the shape of a circle.
400
When should a calculator be used as a COMPUTATIONAL tool?
Facilitates problem solving Eases burden of doing tedious computations Focuses attention on meaning Removes anxiety about incorrectly doing computations Provides motivation & confidence
400
What are the 3 meanings of fractions?
- Part-Whole: the whole has been split into equal parts - Quotient: fractions mean division (3/5= 3 divided by 5) - Ratio: fractions means "to" or "of" (3/5= 3 of 5)
400
Using a calculator to: Search for patterns Supports concept development Promotes number sense Encourages creativity & exploration... Is what kind of tool?
What is INSTRUCTIONAL tool.
400
Using a calculator to: Facilitate problem solving Eases burden of doing tedious computations Focuses attention on meaning Removes anxiety about doing computations incorrectly Provides motivation & confidence
What is using a calculator as a COMPUTATIONAL tool.
500
What is Metacognition?
Metacognition is thinking about one's own thoughts.
500
When should a calculator be used as an INSTRUCTIONAL tool?
Search for patterns Supports concept development Promotes number sense Encourages creativity & exploration
500
What are the 4 models of the part-whole concept? How are the region & area models different?
- Region: special version of the area model, region is the whole & the parts are congruent. - Length: any unit of length can be split into fractional parts of equal length - Set: uses a set of objects as a whole. - Area: more general version of the regional model, in which the parts must be equal in area but not congruent.
500
- Encourage students to do computations mentally. - Learn which computations students prefer to do mentally. - Find out if students are applying written algorithms mentally. - Plan to include mental computations regularly in instruction. - Keep practice sessions short - Develop children's confidence - Encourage inventiveness - Mental computations or estimation?
What are the guidelines for developing mental computations.
500
How would you use benchmarks to order fractions?
By understanding where friendly fractions lie on the number line (benchmarks) they will be able to more easily identify where more difficult fractions reside between 0 & 1. So using the placement of 1/2, 1/4, 1/3, 3/4 & 2/3 helps as benchmarks to determine where other more difficult fractions would be placed.