Deck 4: Learning Mathematics

Question 1

The zone of proximal development and scaffolding are ideas about learning put forth by:

A)Jean Piaget.
B)Lev Vygotsky.
C)Jerome Bruner.
D)Richard Skemp.

Answer 1

Lev Vygotsky.

Question 2

Chip trading, unifix cubes, place ten blocks, and bean sticks are "multiple embodiments" associated with the ideas of:

A)Jerome Bruner.
B)Zoltan Dienes.
C)Edward Thorndike.
D)Howard Gardner.

Answer 2

Zoltan Dienes.

Question 3

The concrete operational stage is one of the developmental stages described by:

A)Jean Piaget.
B)Jerome Bruner.
C)Edward Thorndike.
D)Howard Gardner.

Answer 3

Jean Piaget.

Question 4

Recommendations based on research for improving student achievement in mathematics include all of the following except :

A)teachers' salaries bear directly on the achievement of students.
B)students can learn both concepts and skills through solving problems.
C)giving students both an opportunity to discover and invent new knowledge and an opportunity to practice what they have learned improves student achievement.
D)using small groups of students to work on activities, problems, and assignments can increase student mathematics achievement.

Question 5

The theory that suggests that children must understand what they are learning if learning is to be permanent was put forth by:

A)Jerome Bruner.
B)Jean Piaget.
C)William Brownell.
D)Lev Vygotsky.

Question 6

According to research by LeFrancois, the memories that are stored and retrieved by the brain are apparently controlled by all of the following except :

A)the learner's learning style.
B)the learner's emotions.
C)the learner's motivations.
D)the learner's intentions.

Question 7

The theory of multiple intelligences is the idea put forth by:

A)Jean Piaget.
B)Jerome Bruner.
C)Zoltan Dienes.
D)Howard Gardner.

Question 8

The enactive, ikonic, and symbolic levels of representation are associated with:

A)Jean Piaget.
B)Edward Thorndike.
C)Jerome Bruner.
D)Howard Gardner.

Question 9

Cognitive theories of learning:

A)are very similar to behaviorist theories of learning.
B)emphasize thinking and reasoning in creation of meaning.
C)apply to all human activities.
D)reflect experiments done by Pavlov with animals.

Question 10

Which of the following is not a theme of teaching in a constructivist manner?

A)Mathematics is viewed as invented by human beings; it is not an independent body of abstract and necessary set of rules.
B)Mathematics learning occurs most effectively through guided discovery.
C)Study and assessment of learners must occur through primarily procedurally based assessments.
D)Effective teaching occurs through the creation of classroom learning environments that encourage the development of diverse and creative problem-solving processes in students.

Question 11

Which of the following is an example of concrete representation?

A)base-10 blocks showing 321
B)pictures of base-10 blocks showing 321
C)written number 321
D)number sentence 99 + 222 = 321

Question 12

A cognitive theory known as information processing uses all the following metaphors for learning except :

A)instinctual behavior is similar to preprogrammed read-only memory in a computer.
B)random access memory is similar to short-term memory.
C)learning becomes permanent when new ideas are transferred from long-term memory to short-term memory, similar to the process in a computer.
D)information stored in a computer's memory is available based on the needs and choices of the computer user, similar to the process that a person's brain performs.

Question 13

Stimulus and response bonds are most closely associated with the theory of behaviorism of:

A)Jean Piaget.
B)Jerome Bruner.
C)Edward Thorndike.
D)Howard Gardner.

Question 14

The following are ideas or theorists associated with behaviorism except for :

A)discovering predictable relationships between stimuli and responses.
B)Jerome Bruner and Jean Piaget.
C)Ivan Pavlov and B. F. Skinner.
D)machinelike qualities of human functioning.

Question 15

Learning at two levels, experience and abstraction, is proposed by:

A)Lev Vygotsky.
B)Jerome Bruner.
C)Richard Skemp.
D)Edward Thorndike.

Question 16

The theory of social constructivism that emphasizes the social context of learning is associated with:

A)Jerome Bruner.
B)Richard Skemp.
C)Edward Thorndike.
D)Lev Vygotsky.

Question 17

LeFrancois concludes that the information processing model of human learning:

A)involves memory chips in the brain.
B)shows how human knowledge is instinctual in nature.
C)suggests the development of neural networks.
D)eliminates the role of emotion in learning.

Question 18

Behaviorist theories emphasize learning: ​

A)through construction of meaning.
B)motor skills rather than cognitive skills.
C)in stages.
D)through reactions to stimulus.

Question 19

The brain model of human learning suggested by Hart emphasizes:

A)the importance of finding and using patterns.
B)learning through repetition.
C)storage and retrieval mechanisms in learning.
D)developmental stages of learning.

Question 20

Seeing learning as a continual process of assimilation and accommodation was advocated by:

A)Jean Piaget.
B)Jerome Bruner.
C)William Brownell.
D)Lev Vygotsky.

Question 21

Contrast behaviorist and cognitivist theories of learning.

Question 22

Teachers can keep current about research in mathematics through:

A)reading educational journals.
B)ERIC.
C)conducting action research in their classrooms.
D)all of these options are correct.

Question 23

Discuss the metaphor implied in the term "constructivism."

Question 24

Memorizing the steps in long division is:

A)an example of procedural learning.
B)an example of conceptual learning.
C)a learning objective for second grade.
D)an indication of mathematical understanding.

Question 25

One cognitive theory called information processing uses a computer as a metaphor for how children learn. Explain the basic concepts of this metaphor as it relates to computers and children's learning processes.

Question 26

Explain how the common theme in the theories put forth by Skemp, Dienes, and Bruner affect children's learning of mathematics.

Question 27

Explain why it is important for teachers to know about learning theorists when teaching elementary mathematics.

Question 28

Thinking proportionally is one example of:

A)concrete thinking.
B)abstract thinking.
C)psychomotor understanding.
D)concrete and abstract thinking and psychomotor understanding.

Question 29

ERIC is:

A)a searchable database of educational articles, research, and teaching ideas.
B)expensive to join and use.
C)available only at university libraries.
D)all of these options are correct.

Question 30

Which of the following statements is true regarding procedural and conceptual learning?

A)"Learning how" is most important.
B)"Learning why" is most important.
C)Connecting "learning why" and "learning how" is most important.
D)Procedural learning comes before conceptual learning.

Question 31

Based on research, Grouws and Cebulla recommend classroom practices such as:

A)learning mathematics through solving problems.
B)active student learning engagement with conversations about learning.
C)emphasizing number sense, mental calculations, and estimation.
D)all of these options are correct.

Question 32

Finding patterns in real-life people and events:

A)is a good game for young children.
B)is an early example of algebraic thinking.
C)is an example of how the brain organizes experience.
D)all of these options are correct

Question 33

Hart puts forth six premises about how the brain is built to learn. Give two of his premises with accompanying examples to illustrate how you would use this information in teaching children mathematics.

Question 34

Disequilibrium during learning:

A)should be avoided.
B)refers to too much accommodation.
C)refers to the balance of assimilation and accommodation.
D)is a natural part of learning.

Question 35

Contrast procedural learning with attaining conceptual knowledge.

Question 36

Explain why drawing conclusions based on a single research study is inherently incorrect.

Question 37

Classification of objects helps students develop:

A)concepts of size such as big and small.
B)concept of colors.
C)common characteristics of different objects.
D)concepts of size and colors, and common characteristics of different objects.

Question 38

Research shows that whole-class discussions following individual and group work improve student achievement. Explain why you think this is true.

Question 39

Piaget suggested that cognitive development progresses through four stages (sensorimotor, preoperational, concrete operational, and abstract). Choose two of these stages and explain what he meant by them. Give examples to help you explain.