Consider the following for items 64-66.

In her mathematics class, Melanie is provided a number of strategies to use to help her solve word problems.  One of those strategies is to draw a picture or diagram of the problem.  In her science class, recently, a different teacher provided her with a problem to solve, and she immediately drew a picture of the problem.  Last night, Melanie was asked to arrange the seating for her sister’s wedding reception, and she started by drawing a picture of all of the tables in the room.

64.Drawing a picture is best described as:

a.an algorithm.

b.a rule.

c.a component skill.

d.a strategy.

65.Drawing a picture best fits into which of the following phases of the general problem-solving model?

a.Identify and define the problem

b.Represent the problem

c.Evaluate the results

d.Attend to opportunities for transfer

66.How is the problem of setting the seating arrangement best described?

a.A reasoning task

b.A well-defined problem

c.An ill-defined problem

d.A meta-problem

Items 67-70 are related.

67.All things being equal, which of the following is the best predictor of ability to solve a given problem successfully?

a.Metacognitive regulation

b.Problem-solving strategies

c.Domain-specific knowledge

d.Ample time to solve the problem

68.Jesse is teaching his students how to solve Sudoku problems.  He tells them how to solve them and then provides several examples that are completed.  The strategy Jesse is using best illustrates:

a.teaching metacognitive strategies.

b.providing worked examples.

c.modeling critical thinking.

d.illustrating elaborative questioning.

69.If the learners successfully solve new problems by comparing them with those presented in class, which of the following heuristics will they be using?

a.Means-ends analysis

b.Hill climbing

c.Working backward

d.Drawing analogies

Use the following example to answer items 70–72.

Mr. Wilson has presented his students with the following problem:

We have a quart of pure alcohol.  If we add a cup of water to the alcohol, what percent of the new mixture is alcohol?

He then says, “Let’s look at what we’re given and what we want.”

“We want the total amount of the mixture we have together,” Robert suggests.

“I think we should first find the fraction of the total that is alcohol,” Eva suggests.

After some discussion, the class decides that the mixture is 75% alcohol.  “I don’t think that’s right,” Kathy observes.  “We have 5 cups of mixture altogether, and only one of those cups is water.”

70.Mr. Wilson’s statement: “Let’s look at what we’re given and what we want,” best illustrates his attempt to help his students with which step in the problem-solving process?

a.Identifying the problem

b.Selecting a strategy

c.Implementing the strategy

d.Evaluating the results

71.  Eva’s comment is most closely related to which step in the problem-solving process?

a.Identifying the problem

b.Selecting a strategy

c.Implementing the strategy

d.Evaluating the results

72.Kathy’s comment is most closely related to which step in the problem-solving process?

a.Identifying the problem

b.Devising a plan

c.Implementing the plan

d.Evaluating the results

73.Susan, Jabar, and Saroja were working on an algebra problem.  Saroja said, “Well, maybe we could draw a picture of the problem.”

“But I don’t know how to draw trains!” Susan replies.

“Maybe if we tried different numbers, we could see what works,” Jabar suggests.

Which of the following is the best description of this discussion?

a.They are not attending to the problem they were assigned.

b.They are using social interaction to help them determine how to solve the problem.

c.They have more background knowledge than they need to solve the problem.

d.They are preparing to use an algorithm to further their understanding.