PostLecture Quiz, Chapter 2
William O. Lacefield III 
Chapter 2
PostLecture Quiz
True or False
1. Students with strong procedural knowledge really have no need to develop strong conceptual knowledge.
Answer
Page Ref: Page 20
2. Dienes was an advocate of free play, which gives young learners opportunities to interact with physical objects in the environment.
Answer
Page Ref: Page 23
3. According to Piaget, when a person is operating in the formal operational stage, his/her thinking is limited to physical reality.
Answer
Page Ref: Page 23
4. According to Bruner, learning is influenced by discussions with oneself and others.
Answer
Page Ref: Page 24
5. In order to facilitate learning of mathematics concepts, it is a good idea to have students use models only for short periods of time.
Answer
Page Ref: Page 29
Multiple Choice
6. While research suggests that a mathematics learning environment should not reflect a pure behaviorist approach, one benefit of infusing some behaviorist beliefs into a mathematics classroom is
A. Strengthened development of procedural knowledge in learners
B. Increased focus on students’ thinking
C. Recognition that learning depends only on what the teacher does
D. Recognition that learners construct new knowledge based on their prior knowledge
Answer
Page Ref: Pages 2122
7. Vygotsky’s research on the zone of proximal development has led mathematics educators to believe that students may develop higher level skills
A. By repeatedly reciting mathematical definitions
B. By visualizing mathematical equations in the mind
C. Through the support of someone more skillful or knowledgable
D. When working independently
Answer
Page Ref: Page 24
8. All of the following theorists contributed to the constructivist view of learning except
A. Piaget
B. Dienes
C. Bruner
D. Skinner
Answer
Page Ref: Page 23
9. In a learning task where students explore the concept of volume by building boxes from blocks, the learners are involved in all of the following except:
A. Using models
B. Methodically applying a formula
C. Making decisions
D. Thinking about mathematics
Answer
Page Ref: Page 27
10. When using an object to illustrate a mathematical concept, the teacher should keep in mind that
A. A student may focus on irrelevant attributes of the object
B. The object may illustrate numerous mathematics concepts at once
C. A student may fail to identify relevant attributes
D. All of the above
Answer
Page Ref: Page 28
11. For young children still developing the ability to write,

Writing in the mathematics classroom should be discouraged, so as not to cause confusion

The teacher should display statements for students to copy to the best of their abilities

The teacher should encourage communication through drawing or through dictating thoughts to a more skillful writer

The teacher should assign extra homework assignments
Answer
Page Ref: Page 30
Short Answer
12. What are some strategies for creating a positive mathematics learning environment?
Suggested Answer
Page Ref: Page 16
13. What are some ways that teachers might help students to cope with mathematics anxiety?
Suggested Answer
Page Ref: Pages 1718
14. What are some actions that a teacher might take to nurture equity in the mathematics classroom?
Suggested Answer
Page Ref: Pages 1819
15. What are some of the basic tenets of the constructivist viewpoint of learning mathematics?
Suggested Answer
Page Ref: Page 24
Answers
1. False
2. True
3. False
4. True
5. False
6. A
7. C
8. D
9. B
10. D
11. C
12. Make sure the classroom arrangement is safe and comfortable and that it supports the lesson’s learning activities. Make sure the classroom environment is intellectually stimulating for learning mathematics. Communicate the fact that confusion, partial understanding, and some frustration are a natural part of the process of learning mathematics. Reward students for critical thinking and creative problem solving so that students learn to value and respect those approaches.
13. Emphasize meaning and understanding rather than memorization. Model problemsolving strategies rather than presenting finished solutions. Show a positive attitude toward mathematics. Give students mathematical experiences that they will enjoy and that will interest them and challenge them while allowing them to be successful. Show a positive attitude toward students at all times. Encourage students to tell you how they feel about mathematics. Be careful not to overemphasize speed tests or drills.
14. Dispel myths (such as “mathematicians work in complete isolation” or “only white males do mathematics”) that discourage women and some minorities from pursuing careers in mathematics. Have equally high expectations for all students, and clearly communicate those expectations to both students and their parents. Engage both boys and girls in solving difficult problems, raising questions, and communicating their mathematical thinking. Make relevant connections between mathematics and students’ lives. Call attention to role models of both genders and the widest range of racial, cultural, and ethnic backgrounds, in both mathematics and science. Help students increase their awareness of career opportunities for people with strong mathematics backgrounds. Communicate to parents the importance of encouraging all their children—both girls and boys—to aspire to success in mathematics. Discuss learned helplessness with students having problems and develop ways to prevent learned helplessness or to remedy it. Use a variety of ways to assess student performance (e.g., a range of test formats, interviews, and portfolios).
15. Knowledge is not passively received; rather, knowledge is actively created or invented (constructed) by learners. Students create (construct) new mathematical knowledge by reflecting on their physical and mental actions. Learning reflects a social process in which children engage in dialogue and discussion with themselves as well as others (including teachers) as they develop intellectually.
To accompany Helping Children Learn Math9e , Reys et al.
©2009 John Wiley & Sons
