Question 1

Learning for problem solving refers to developing skills to apply to real-life problems.

Accepted Answer

A) True 
 B)False  True

Question 2

Presented with a problem such as "Which is larger, 230 or 320?" which of the following strategies would be the most effective strategy for solving the problem?

Accepted Answer

A) acting it out 
B) solving a simpler problem 
C) building a model 
D) guess and check 
A) acting it out 
B) solving a simpler problem 
C) building a model 
D) guess and check B

Question 3

Patterning is a thinking process in which humans find:

Accepted Answer

A) regularity and repetition in seemingly unconnected events and objects. 
B) cause and effect relationships. 
C) similarities among many events and objects. 
D) differences between many events and objects. 
A) regularity and repetition in seemingly unconnected events and objects. 
B) cause and effect relationships. 
C) similarities among many events and objects. 
D) differences between many events and objects. C

Question 4

Explain what Schroeder and Lester (1989)meant by their three approaches to problem-solving instruction (teaching about problem solving, teaching for problem solving, and teaching via problem solving).

Accepted Answer

Schroeder and Lester (1989) proposed thr

Question 5

Describe a school activity or event that a teacher might use as an opportunity for students in grades 3-6 to have an open-ended problem solving experience.

Accepted Answer

One school activity or event that a teac

Question 6

You will throw 5 darts in a game. The bull's-eye has a value of 5. The middle circle has a value of 3, and the outer circle has a value of 1. In your game, each dart hits and sticks to the board. 
   
(a)What is the highest score you could have in your game? 
(b)The lowest score? 
(c)What other scores could you have? 
(d)Is there anything unique about scores for this 5-dart board? 
(e)Identify your strategy or strategies and explain how you used them. 
This rubric will be used to evaluate your work on this task. Credit will be awarded on a 4-point scale.

Accepted Answer

The answer of You will throw 5 darts in a...

Question 7

What is the greatest strength of the strategy "solving a simpler problem"?

Accepted Answer

The greatest strength of the strategy "s

Question 8

Learning about problem solving refers to learning different strategies.

Accepted Answer

A) True 
 B)False

Question 9

Eleven strategies are all the strategies needed for solving problems.

Accepted Answer

A) True 
 B)False

Question 10

In this number sequence, which are the next numbers? 
4, 8, 3, 9, 2, ____

Accepted Answer

A) 1, 10, 0 
B) 10, 0, 1 
C) 10, 1, 11 
D) 7, 4, 11 
A) 1, 10, 0 
B) 10, 0, 1 
C) 10, 1, 11 
D) 7, 4, 11

Question 11

As estimation skills are developed, students need referents, or ____________, to help them make reasonable estimates.

Accepted Answer

A) hints 
B) small numbers 
C) heuristics 
D) comparisons 
A) hints 
B) small numbers 
C) heuristics 
D) comparisons

Question 12

Give an example of a problem that could use the "working backward" strategy, then explain why you think this is a useful strategy.

Accepted Answer

An example of a problem that could benef

Question 13

A balanced approach to mathematics means that students learn:

Accepted Answer

A) concepts and skills as they learn how to apply the skills in problems. 
B) speed and accuracy in computation. 
C) how to use calculators and computers at the same time they are learning math facts. 
D) about geometry and number systems. 
A) concepts and skills as they learn how to apply the skills in problems. 
B) speed and accuracy in computation. 
C) how to use calculators and computers at the same time they are learning math facts. 
D) about geometry and number systems.

Question 14

The strategy break set:

Accepted Answer

A) is a strategy that should be tried when working on breaking sets of objects like base ten blocks into smaller sets of objects when solving a problem. 
B) should be tried last after all other strategies have been tried to solve a problem. 
C) suggests that persistence and perseverance are highly valued when solving problems. 
D) suggests that having flexibility and being able to change points of view are highly regarded problem solving strategies. 
A) is a strategy that should be tried when working on breaking sets of objects like base ten blocks into smaller sets of objects when solving a problem. 
B) should be tried last after all other strategies have been tried to solve a problem. 
C) suggests that persistence and perseverance are highly valued when solving problems. 
D) suggests that having flexibility and being able to change points of view are highly regarded problem solving strategies.

Question 15

Learning through problem solving means that students learn the four-step Polya method and apply it in all situations.

Accepted Answer

A) True 
 B)False

Question 16

Explain how the strategy "finding and using a pattern" progresses from kindergarten into algebra in middle school. Give an example to help you explain.

Accepted Answer

The strategy of "finding and using a pat

Question 17

Building a model is a problem-solving strategy which:

Accepted Answer

A) is used by teachers to allow children to play during class. 
B) allows children to use objects to represent the problem concretely. 
C) keep children from feeling like failures in learning mathematics. 
D) girls have more difficulty understanding spatial relationships. 
A) is used by teachers to allow children to play during class. 
B) allows children to use objects to represent the problem concretely. 
C) keep children from feeling like failures in learning mathematics. 
D) girls have more difficulty understanding spatial relationships.

Question 18

What is the area of the shaded region of the figure below? 
   
a. 24 
b. 30 
c. 36 
d. 42

Accepted Answer

The answer of What is the area of the shaded...

Question 19

Problem solving in elementary school is best understood as:

Accepted Answer

A) fun activities such as puzzles and games. 
B) the central focus of mathematics teaching and learning. 
C) challenging problems for the mathematically talented students. 
D) working word problems similar to the rote practice problems in textbooks. 
A) fun activities such as puzzles and games. 
B) the central focus of mathematics teaching and learning. 
C) challenging problems for the mathematically talented students. 
D) working word problems similar to the rote practice problems in textbooks.

Question 20

One value of drawing a picture or diagram as a problem-solving strategy is that it:

Accepted Answer

A) allows children with artistic talent to solve a problem more easily than others. 
B) may obscure the problem if children get too detailed in their drawings. 
C) can be difficult for girls because of their difficulties with spatial situations. 
D) may develop into a solution by making the problem more apparent. 
A) allows children with artistic talent to solve a problem more easily than others. 
B) may obscure the problem if children get too detailed in their drawings. 
C) can be difficult for girls because of their difficulties with spatial situations. 
D) may develop into a solution by making the problem more apparent.

Learning for problem solving refers to developing skills to apply to real-life problems.

Presented with a problem such as "Which is larger, 2³⁰ or 3²⁰?" which of the following strategies would be the most effective strategy for solving the problem?

Patterning is a thinking process in which humans find:

Explain what Schroeder and Lester (1989)meant by their three approaches to problem-solving instruction (teaching about problem solving, teaching for problem solving, and teaching via problem solving).

Describe a school activity or event that a teacher might use as an opportunity for students in grades 3-6 to have an open-ended problem solving experience.

What is the greatest strength of the strategy "solving a simpler problem"?

Learning about problem solving refers to learning different strategies.

Eleven strategies are all the strategies needed for solving problems.

In this number sequence, which are the next numbers? 4, 8, 3, 9, 2, ____

As estimation skills are developed, students need referents, or ____________, to help them make reasonable estimates.

Give an example of a problem that could use the "working backward" strategy, then explain why you think this is a useful strategy.

A balanced approach to mathematics means that students learn:

The strategy break set:

Learning through problem solving means that students learn the four-step Polya method and apply it in all situations.

Explain how the strategy "finding and using a pattern" progresses from kindergarten into algebra in middle school. Give an example to help you explain.

Building a model is a problem-solving strategy which:

What is the area of the shaded region of the figure below? a. 24 b. 30 c. 36 d. 42

Problem solving in elementary school is best understood as:

One value of drawing a picture or diagram as a problem-solving strategy is that it:

Elementary Mathematics for the 21st Century

Defining a Comprehensive Mathematics Program

Mathematics for Every Child

Learning Mathematics

Organizing Effective Instruction

Integrating Assessment

Developing Concepts of Number

Extending Number Concepts and Number Systems

Developing Number Operations With Whole Numbers

Extending Computational Fluency With Larger Numbers

Developing Understanding of Common and Decimal Fractions

Extending Understanding of Common and Decimal Fractions

Developing Aspects of Proportional Reasoning: Ratio, Proportion, and Percent

Thinking Algebraically

Developing and Extending Geometric Concepts and Systems

Developing and Extending Measurement Concepts

Understanding and Representing Concepts of Data

Investigating Probability

Filters

Exam 7: Developing Problem-Solving Strategies

Learning for problem solving refers to developing skills to apply to real-life problems.

Presented with a problem such as "Which is larger, 230 or 320?" which of the following strategies would be the most effective strategy for solving the problem?

Patterning is a thinking process in which humans find:

Explain what Schroeder and Lester (1989)meant by their three approaches to problem-solving instruction (teaching about problem solving, teaching for problem solving, and teaching via problem solving).

Describe a school activity or event that a teacher might use as an opportunity for students in grades 3-6 to have an open-ended problem solving experience.

What is the greatest strength of the strategy "solving a simpler problem"?

Learning about problem solving refers to learning different strategies.

Eleven strategies are all the strategies needed for solving problems.

In this number sequence, which are the next numbers? 4, 8, 3, 9, 2, ____

As estimation skills are developed, students need referents, or ____________, to help them make reasonable estimates.

Give an example of a problem that could use the "working backward" strategy, then explain why you think this is a useful strategy.

A balanced approach to mathematics means that students learn:

The strategy break set:

Learning through problem solving means that students learn the four-step Polya method and apply it in all situations.

Explain how the strategy "finding and using a pattern" progresses from kindergarten into algebra in middle school. Give an example to help you explain.

Building a model is a problem-solving strategy which:

What is the area of the shaded region of the figure below? a. 24 b. 30 c. 36 d. 42

Problem solving in elementary school is best understood as:

One value of drawing a picture or diagram as a problem-solving strategy is that it:

Elementary Mathematics for the 21st Century

Defining a Comprehensive Mathematics Program

Mathematics for Every Child

Learning Mathematics

Organizing Effective Instruction

Integrating Assessment

Developing Concepts of Number

Extending Number Concepts and Number Systems

Developing Number Operations With Whole Numbers

Extending Computational Fluency With Larger Numbers

Developing Understanding of Common and Decimal Fractions

Extending Understanding of Common and Decimal Fractions

Developing Aspects of Proportional Reasoning: Ratio, Proportion, and Percent

Thinking Algebraically

Developing and Extending Geometric Concepts and Systems

Developing and Extending Measurement Concepts

Understanding and Representing Concepts of Data

Investigating Probability

Filters

Presented with a problem such as "Which is larger, 2³⁰ or 3²⁰?" which of the following strategies would be the most effective strategy for solving the problem?