Question 1

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.

Accepted Answer

Enactive to iconic. Bruner's theory outlines three stages of cognitive representation: enactive (learning through actions), iconic (learning through images and visual aids), and symbolic (learning through symbols, such as language). Moving from manipulating physical objects (pattern blocks) to drawing pictures represents a transition from the enactive stage, where learning is through direct manipulation and action, to the iconic stage, where learning is through visual representations and images.

Question 2

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.

Accepted Answer

The student is operating in the Symbolic stage according to Bruner's stages of cognitive representation. In this stage, individuals use abstract symbols, such as numbers and words, to represent concepts, which is what the student is doing by using a formula to find the area.

Question 3

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.

Accepted Answer

Bruner's theory posits that learning occurs in three stages: enactive (learning through actions), iconic (learning through images and visual aids), and symbolic (learning through symbols, such as language and mathematical symbols). When students perceive mathematics as merely a set of rules and procedures, it indicates that their learning has been focused on the symbolic stage, where abstract symbols and notations are heavily emphasized without necessarily grounding them in concrete or visual representations.

Question 4

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.

Accepted Answer

The van Hiele Model specifically addresses the development of children's understanding in geometry. It outlines levels of geometric thought through which students progress, enhancing their ability to understand and reason about geometric concepts.

Question 5

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.

Accepted Answer

Jenny's ability to recognize different shapes by their appearance without being able to articulate their properties suggests she is operating at the Visualization level. This is the first level of the van Hiele model, where individuals recognize shapes based on their overall appearance and not by understanding their properties or definitions.

Question 6

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.

Accepted Answer

The student is at the Analysis level, where they can identify properties of shapes but cannot yet relate different shapes or understand the hierarchical relationships between them.

Question 7

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.

Accepted Answer

At the Informal Deduction level of the van Hiele model, students start to understand the properties of geometric shapes and how they relate to each other, which allows them to compare shapes and construct simple proofs.

Question 8

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.

Accepted Answer

The van Hiele level of Deduction is where students are able to understand the process of logical deduction, including the study of theorems and postulates and the ability to write two-column and paragraph proofs. This level typically aligns with high school geometry education.

Question 9

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.

Accepted Answer

The answer of If a student states that the sum...

Question 10

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%.

Accepted Answer

Research by Shaughnessy and Burger in 1985 indicated that approximately 70% of students entering high school geometry functioned below level 2 of the Van Hiele model, highlighting a significant gap in geometric understanding at that educational stage.

Question 11

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.

Accepted Answer

The van Hieles emphasized that the quality of mathematics instruction is crucial for students to progress through different levels of geometric understanding, rather than just their age or the number of courses taken.

Question 12

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.

Accepted Answer

Dynamic Software is designed to allow users to interact with visual representations, such as geometric shapes, by manipulating them directly on the screen. This type of software is particularly useful in educational settings for teaching concepts that benefit from visual and interactive exploration.

Question 13

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.

Accepted Answer

Inquiry-based learning involves students in the process of exploring the natural or material world in a way that leads to asking questions, making discoveries, and rigorously testing those discoveries in the search for new understanding. The activity described fits this model as it encourages students to explore, ask questions, and discover mathematical properties on their own.

Question 14

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.

Accepted Answer

Inquiry-based classrooms focus on student engagement and active participation in learning. This approach emphasizes hands-on, active, cooperative, and student-centered lessons, contrasting with teacher-centered lessons, where the teacher is the primary source of information and students are passive recipients.

Question 15

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.

Accepted Answer

Constructivism emphasizes that learners construct knowledge through their experiences rather than absorbing information directly. It suggests that knowledge is subjective and constructed, not discovered in a pre-existing, objective form. The idea that concepts should build from part to whole is more aligned with traditional, incremental learning theories rather than constructivism, which values the integration of experiences and the contextual understanding of knowledge.

Question 16

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.

Accepted Answer

Constructivist classrooms focus on understanding students' perspectives and building knowledge through experiences, rather than just delivering content or sticking strictly to a fixed curriculum.

Question 17

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.

Accepted Answer

In a constructivist classroom, the teacher can incorporate a variety of teaching methods including direct instruction, assessments like pencil-paper tests, individual work, and group work. This approach supports the idea that learning is constructed through active engagement and the integration of new information with existing knowledge, allowing for a diverse range of activities to facilitate learning.

Question 18

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.

Accepted Answer

Inductive teaching involves students observing, identifying patterns, and making generalizations about what they have learned, which leads them to understand and formulate the rule or concept being taught.

Question 19

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.

Accepted Answer

Deductive teaching involves stating a rule or principle at the beginning and then applying it to specific examples. This approach moves from the general to the specific.

Question 20

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.

Accepted Answer

The concept attainment method is an instructional strategy designed around the idea of teaching concepts through the presentation of examples and non-examples, leading students to induce or figure out the concept being taught. This aligns with induction as a teaching technique, where learners are guided to derive general principles from specific examples.

Quiz 3: Learning Theories and Psychology in Mathematics Education

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?

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

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?

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

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?

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?

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

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?

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?

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.

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?

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?

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?

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

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

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

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

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

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

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