Deck 3: Learning Theories and Psychology in Mathematics Education

Question 1

What term does the National Council of Teachers of Mathematics use for the attitudinal side of teaching mathematics?

A)Mathematical view.
B)Mathematical concern.
C)Mathematical attention.
D)Mathematical disposition.
E)Mathematical overview.

Answer 1

Mathematical disposition.

Question 2

The type of research that deals with gathering numerical data and analyzing it is called which of the following?

A)Formative research.
B)Qualitative research.
C)Quantitative research.
D)Questionnaire research.
E)Descriptive research.

Answer 2

Quantitative research.

Question 3

Which type of research method was used first in education?

A)Interview research.
B)Recording research.
C)Qualitative research.
D)Quantitative research.
E)Descriptive research.

Answer 3

Quantitative research.

Question 4

Which of the following is NOT generally considered a method of collecting qualitative research?

A)Tape recording teacher/student conversations.
B)Videotaping a class period.
C)Filling out a checksheet on observed student behavior.
D)Summarizing student journal entries.
E)Recording student test scores.

Question 5

The type of research that deals with the collection and analysis of non-numerical data is called which of the following?

A)Formative research.
B)Qualitative research.
C)Quantitative research.
D)Reflective research.
E)Experimental research.

Question 6

A school district decided to look at the effects of a new teaching method.They had one teacher teach in a "traditional" manner, while another taught using a "new"
approach.Which research method would involve comparing student test results of each group to determine which method was more effective?

A)Descriptive research.
B)Experimental research.
C)Historical research.
D)Informative research.
E)Qualitative research.

Question 7

Dr.Jones reported that 67% of the students at Lieb High School and 43% of the students at Hoehn High School continued their education at a post-secondary
institution.Because he obtained this information to generate a discussion, which type of research would this be considered?

A)Descriptive research.
B)Experimental research.
C)Historical research.
D)Informative research.
E)Summative research.

Question 8

Some of the most powerful research conclusions have been drawn from studies that have included both quantitative and qualitative elements.Which of the following contains both elements?

A)Collecting pre-test and post-test data.
B)Collecting data from an achievement test and an aptitude test.
C)Collecting student grades and teacher comments.
D)Collecting student comments and teacher comments.
E)Collecting data from video recordings and written summaries of student journal entries.

Question 9

Which of the following would be typical in a classroom in which a teacher embraced a behaviorist philosophy?

A)Students actively explore mathematical ideas with manipulatives.
B)Students practice a skill over and over, after having been shown a procedure by the teacher.
C)Students work at a computer and make conjectures based on their research.
D)Students work in teams on a limited number of "rich" problems.
E)Students examine examples and counterexamples and develop their own generalizations.

Question 10

Which educational theorists were responsible for research on the "zone of proximal development" and "multiple intelligences", respectively?

A)Bruner and Gardner.
B)Van Hiele and Piaget.
C)Gardner and Piaget.
D)Vygotsky and Bruner.
E)Vygotsky and Gardner.

Question 11

Which three elements are required for a "community of practice"?

A)Domain, Community, Shared Practice.
B)Model, Domain, Community.
C)Experiment, Community, Discourse.
D)Model, Discourse, Shared Practice.
E)Interaction, Community, Discourse.

Question 12

Which educational theorist is known for work on the topic of "mindsets"?

A)Dweck.
B)Bruner.
C)van Hiele.
D)Vygotsky.
E)Bruner

Question 13

An individual who believes that intelligence is static and avoids challenges is said to possess which of the following mindsets?

A)Habitual.
B)Growth.
C)Avoidance.
D)Fixed.
E)Implicit.

Question 14

Jerome Bruner theorized that learning generally proceeds in order through which of the following three phases?

A)Active, enactive, and iconic.
B)Active, enactive, and symbolic.
C)Active, reactive, and iconic.
D)Enactive, iconic, and symbolic.
E)Enactive, reactive, and symbolic.

Question 15

Jerome Bruner's theory led to extensive use of which of the following materials in the mathematics classrooms?

A)Calculators.
B)Manipulatives.
C)Movies and other media.
D)Textbooks.
E)Workbooks.

Question 16

Select the correct way for a student to represent the number 2.53 by using base ten blocks.

A)Two flats, five longs, and three units.
B)Five units, two longs, and three flats.
C)Two units, five flats, and three longs.
D)Three longs, two flats, and five units.
E)Two longs, five flats, and three units.

Question 17

Select the correct representation of the solution to simplifying the expression $2 x ^ { 2 } + x + 4 + 3 x ^ { 2 } + 5 x + 7$ using algebra tiles.

A)Five longs, five flats, and eleven units.
B)Five longs, nine flats, and eleven units.
C)Five flats, eight longs, and eleven units.
D)Six longs, five flats, and eleven units.
E)Five flats, nine units, and six longs.

Question 18

According to the author, in Chapter 3, why does addition using algebra tiles make sense to the student?

A)The tiles are the same shape and size.
B)The tiles are the same color and texture.
C)The tiles are the same thickness and shape.
D)The tiles are the same shape and color.
E)The tiles are the same size and thickness.

Question 19

Using algebra tiles to model equation solving would be a typical activity at which of Bruner's stages of representation?

A)Iconic.
B)Reactive.
C)Symbolic.
D)Representational.
E)Enactive.

Question 20

The pictorial phase of Bruner's theory is called which of the following stages?

A)Active.
B)Enactive.
C)Iconic.
D)Reactive.
E)Symbolic.

Question 21

If a student goes from manipulating pattern blocks to drawing a picture for representing multiplication of fractions, which stages of Bruner's theory have been
involved?

A)Active to enactive.
B)Active to iconic.
C)Enactive to iconic.
D)Enactive to symbolic.
E)Iconic to symbolic.

Question 22

If a student found the area of the yard by using a formula, in which of Bruner's stages is that person operating?

A)Active.
B)Enactive.
C)Iconic.
D)Reactive.
E)Symbolic.

Question 23

Many students find mathematics to be nothing more than a set of rules and procedures because they have been taught almost entirely on which level of Bruner's theory?

A)Symbolic.
B)Enactive.
C)Iconic.
D)Reactive.
E)Active.

Question 24

The van Hiele Model is a theory that addresses the development of children's learning of which area of mathematical content?

A)Algebra.
B)Geometry.
C)Measurement.
D)Number Relations.
E)Probability.

Question 25

When given different shapes, Jenny can recognize which are triangles, squares, rectangles, and trapezoids, but she cannot put into words each shape's characteristics.Jenny is most likely functioning at which van Hiele level?

A)Analysis.
B)Deduction.
C)Informal Deduction.
D)Rigor.
E)Visualization.

Question 26

Suppose that a student was able to state that a parallelogram has two pairs of opposite parallel sides, but is still unable to compare it to a rectangle.At which van Hiele level
is this student most likely functioning?

A)Analysis.
B)Deduction.
C)Informal Deduction.
D)Rigor.
E)Visualization.

Question 27

During which level of the van Hiele model would the student begin to compare geometric shapes and construct simple proofs?

A)Analysis.
B)Deduction.
C)Informal Deduction.
D)Rigor.
E)Visualization.

Question 28

Historically, high school geometry has included the study of theorems and postulates and the process of writing two-column and paragraph proofs.At which van Hiele
level does the student have these abilities?

A)Analysis.
B)Deduction.
C)Informal Deduction.
D)Rigor.
E)Visualization.

Question 29

If a student states that the sum of the angles of a triangle is not always 180° because it is greater than 180° in the study of spherical geometry, the student is probably
operating at which van Hiele level?

A)Analysis.
B)Deduction.
C)Informal Deduction.
D)Rigor.
E)Visualization.

Question 30

Research by Shaughnessy and Burger in 1985 showed that about the following percent of students entering high school geometry functioned below level 2 of the Van Hiele model.

A)10%.
B)30%.
C)50%.
D)70%.
E)90%.

Question 31

For students to advance from one level of development to another, the van Hieles found that it is not simply the chronological age of the student but also which of the
following factors?

A)Heterogeneous student grouping.
B)Use of technology.
C)Maturity level of the student.
D)Quality of mathematics instruction.
E)Number of mathematics courses taken.

Question 32

Which of the following terms refers to a type of computer software that is designed so that students can interact with images on the screen, such as stretching or shrinking a
geometric shape?

A)Deductive Software.
B)Inquiry Software.
C)Tutorial Software.
D)Sensory Software.
E)Dynamic Software.

Question 33

The activity in Chapter 3 involving folding paper in half numerous times is an example where students discover properties and invent their own mathematical rules.Which term best describes this type of lesson?

A)Behaviorist.
B)Piagetian.
C)Inquiry.
D)Invention.
E)Traditional.

Question 34

Which of the following techniques would NOT ordinarily be used in an inquiry based classroom?

A)Hands-on lessons.
B)Active lessons.
C)Cooperative learning.
D)Student-centered lessons.
E)Teacher-centered lessons.

Question 35

Which of the following is NOT considered a central component of constructivism?

A)Knowledge is constructed from within.
B)There is not one, true reality.
C)Knowledge is created through reflection.
D)Concepts should build from part to whole.
E)Learning is a social process.

Question 36

Which of the following would be typical of a constructivist classroom?

A)Correct answers validate student learning.
B)Assessment is separate from teaching.
C)Information is "etched" into the students.
D)Adherence to a fixed curriculum is highly valued.
E)Teachers seek the students' point of view.

Question 37

In a constructivist classroom, the teacher can and should include which of the following?

A)Direct instruction and mini-lectures.
B)Pencil-paper tests.
C)Individual work.
D)Group work.
E)All of these.

Question 38

Which type of teaching involves having students thinking through several examples and then generalizing a rule?

A)Behaviorist.
B)Deductive.
C)Formative.
D)Inductive.
E)Summative.

Question 39

Which type of teaching involves having a rule stated and then applying the rule to specific examples?

A)Constructivist.
B)Deductive.
C)Formative.
D)Inductive.
E)Summative.

Question 40

The concept attainment method can be used to promote which type of classroom teaching technique?

A)Behaviorism.
B)Deduction.
C)Formation.
D)Induction.
E)Summation.

Question 41

Which educational theorists are primarily responsible for the constructivist model and the concept attainment method, respectively?

A)Piaget and Bruner.
B)van Hiele and Piaget.
C)Skinner and Piaget.
D)Bruner and Gagne.
E)Piaget developed both of these.

Question 42

In Geometry class, the teacher gave the students the Pythagorean Theorem as $a ^ { 2 } + b ^ { 2 } = c ^ { 2 }$ , and students used it to solve fifteen practice exercises.Which type of approach did the teacher us?

A)Constructivist.
B)Deductive.
C)Formative.
D)Inductive.
E)Summative.

Question 43

According to Ford's theory, what are the three interacting components that constitute the psychological construct called motivation?

A)Determination, goals, and self-confidence.
B)Determination, emotions, and self-confidence.
C)Goals, emotions, and self-confidence.
D)Goals, attitudes, and emotions.
E)Emotions, attitudes, and self-confidence.

Question 44

Which of the following characteristics is NOT emphasized in students with a mastery goal orientation?

A)Grades.
B)Intrinsic value of learning.
C)Effort.
D)Self-improvement.
E)Hard work.

Question 45

A student has which type of orientation if success is based upon performance in relationship to others in the class?

A)Self-efficacy.
B)Ego goal.
C)Mastery goal.
D)Concept goal.
E)Mathematical disposition.

Question 46

As stated in the text, which two emotions should teachers most frequently attempt to appeal to in their students?

A)Caring and curiosity.
B)Caring and enjoyment.
C)Curiosity and enjoyment.
D)Curiosity and interest.
E)Interest and happiness.

Question 47

When a student is given a set of manipulatives, such as algebra tiles, which type of curiosity is often evoked in the student?

A)Intuitive.
B)Cognitive.
C)Sensory.
D)Personal.
E)Motivational.

Question 48

Find the term below that means essentially the same as self-efficacy.

A)Curiosity.
B)Desire.
C)Self-confidence.
D)Self-motivation.
E)Self-sufficiency.

Question 49

A tendency to act in positive ways, as well as the attitude of students in a mathematics class, refers to which of the following?

A)Mathematical curiosity.
B)Mathematical disposition.
C)Mathematical interest.
D)Mathematical orientation.
E)Mathematical success.

Question 50

Which of the following is NOT listed in the 1989 evaluation Standards of the NCTM as a characteristic of mathematical disposition?

A)Flexibility when mathematical problems.
B)Willingness to reflect on thinking.
C)Valuing the use of mathematics in other disciplines.
D)Recognizing the importance of obtaining high grades in mathematics.
E)Recognizing the role of mathematics in the culture.

Question 51

Research supports that the best way to cultivate positive dispositions toward mathematics in students is which of the following?

A)Have frequent discussions with students about the importance of viewing mathematics positively.
B)Feature regular guest speakers to address the need for mathematics in our society.
C)Use cooperative learning strategies in the classroom to boost morale and help students to view mathematics positively.
D)Model positive dispositions while teaching, since students will pick up on the ways that teachers act.
E)All of these are strongly supported by research.

Question 52

Which is a recommended in Chapter 3 as a strategy to reduce mathematics anxiety?

A)Assign less homework.
B)Help students develop a growth mindset.
C)Make use of additional manipulatives.
D)Eliminate testing.
E)Reduce class period lengths.

Question 53

Explain the difference between qualitative and quantitative research.Provide an example of a situation in which a qualitative study may be more appropriate and a situation in which a quantitative study may be better.

Question 54

If the principal walked into a mathematics classroom where the teacher was using a constructivist approach, what types of teaching strategies should the principal expect to see? How would this differ from a traditional classroom setting?

Question 55

What are the three components of "motivation," according to Ford's theory.Briefly explain each of these components.

Question 56

Describe the difference between a student having an ego-goal and a mastery-goal orientation.Give a specific example of something teachers can do to promote intrinsic motivation in their students.

Question 57

Discuss the stages of Jerome Bruner's theory.Provide an example of a concept and how it might be taught with these stages in mind.

Question 58

Explain the levels of the van Hiele Model.For each level, provide an example of something the student can do and something the student may not be ready to do.