Question 1

Viewing mathematics as "a coherent whole" refers most closely to which of the following?
A)Problem Solving.
B)Reasoning.
C)Constructing Viable Arguments.
D)Connections.
E)Modeling.

Accepted Answer

Viewing mathematics as "a coherent whole" aligns with making connections within mathematics, which involves understanding how mathematical ideas interrelate and build upon one another across different concepts and representations.

Question 2

Which Standard for Mathematical Practice is involved when a student recognizes that (x+3)(x-5)=(x-5)(x+3)for the same reason that 7 ×3=3 ×7?
A)SMP #1: Make sense of problems.
B)SMP #3: Reason abstractly.
C)SMP #4: Model with mathematics.
D)SMP #6: Attend to precision.
E)SMP #7: Make use of structure.

Accepted Answer

This involves SMP #7: Make use of structure, as the student is recognizing the commutative property of multiplication, which is a structural property of arithmetic and algebra.

Question 3

The connections Standard stresses which of the following processes?
A)Connecting among different mathematical ideas and connecting mathematics to other subject areas.
B)Connecting with peers to determine a "strategy" and connecting among different mathematical ideas.
C)Connecting with the teacher to determine a "goal" and connecting mathematics to other subject areas.
D)Connecting with the teacher to determine a "goal" and connecting among different mathematical ideas.
E)Connecting with the teacher to determine a "goal" and connecting with peers to determine a "strategy".

Accepted Answer

The Connections Standard emphasizes the importance of students making connections among different mathematical ideas and between mathematics and other disciplines, to apply mathematics in various contexts and integrate knowledge.

Question 4

Problems that bring together several mathematical topics into a single investigation emphasize which mathematical process?
A)Problem Solving.
B)Reasoning.
C)Communication.
D)Connections.
E)Tools.

Accepted Answer

Problems that integrate multiple mathematical topics into a single investigation highlight the importance of making connections between different areas of mathematics, emphasizing the mathematical process of "Connections." This process involves recognizing and applying the interrelations among mathematical concepts across various topics.

Question 5

Which of the following is a typical middle school practice that promotes mathematical connections?
A)Use of block scheduling.
B)Common planning time for teachers in the school.
C)Use of common textbooks among teachers in the school.
D)Bi-weekly faculty meetings after school.
E)Use of technology in all classes.

Accepted Answer

Common planning time for teachers allows them to collaborate and integrate different subjects, promoting mathematical connections across the curriculum.

Question 6

Some students prefer to solve a given problem by drawing a graph; whereas, other students would rather write an equation or use hands-on materials.Which of the
 following mathematical processes emphasizes the importance of students viewing the
 same problem with multiple approaches?
A)Problem Solving.
B)Reasoning.
C)Communication.
D)Connections.
E)Representation.

Accepted Answer

Representation emphasizes the importance of students viewing the same problem through multiple approaches, such as graphs, equations, or hands-on materials, to understand and solve mathematical problems.

Question 7

The Standards for Mathematical Practice address the use of tools in the classroom. Which of the following would NOT necessarily be considered a tool?
A)Worksheets.
B)Calculators.
C)Protractors.
D)Graphs.
E)Rulers.

Accepted Answer

Worksheets are generally considered as resources or materials for practice and instruction rather than tools for mathematical exploration or computation. Tools in mathematics typically refer to physical or digital items used to perform calculations, measurements, or to visualize concepts, such as calculators, protractors, graphs, and rulers.

Question 8

Which of the following words describes the use of "tools" in the mathematics classroom?
A)Required.
B)Technological.
C)Appropriate.
D)Daily.
E)Optional.

Accepted Answer

The use of "tools" in the mathematics classroom is considered "appropriate" because it depends on the context of the lesson and the objectives of the learning activity. Tools can enhance understanding and engagement, but their use should be based on their educational value and relevance to the material being taught.

Question 9

Which of the following factors tends to most significantly impact a teacher's ability to incorporate the mathematical processes and practices in the classroom?
A)The teacher's mathematics content background.
B)The ability level of students in the class.
C)The textbook used to teach the class.
D)The type of homework problems assigned to students.
E)The teacher's understanding of child psychology.

Accepted Answer

The teacher's mathematics content background is crucial for incorporating mathematical processes and practices in the classroom because it directly influences their ability to understand, interpret, and teach complex mathematical concepts effectively.

Question 10

Mr.James had his class select an authentic example of a linear function that they have encountered in their lives.By having students submit written papers about their
 functions he was stressing which mathematical process?
A)Problem Solving
B)Reasoning.
C)Communication.
D)Connection.
E)Representation.

Accepted Answer

By having students write papers about linear functions they've encountered, Mr. James is emphasizing the mathematical process of communication. This process involves expressing mathematical ideas and reasoning in written form.

Question 11

Surveys from industry indicate that employers are looking for a workforce that has skills in which of the following?
A)Arithmetic and problem solving.
B)Basic algebra and communication.
C)Problem solving and communication.
D)Independent thinking and arithmetic.
E)Independent thinking and basic algebra.

Accepted Answer

Employers often prioritize employees who can effectively solve problems and communicate. These skills are essential for teamwork, innovation, and adapting to new challenges in the workplace.

Question 12

Which of the following might be considered the most accurate description of what it means to "do," to "teach," and to "learn" mathematics?
A)Mathematics is all about memorizing rules and procedures.
B)Mathematics primarily involves students learning to manipulate symbols, such as numbers and variables.
C)Mathematics is a process with very little content to be learned.
D)Mathematics is a verb - something that one does - as well as a large body of content to be learned.
E)Mathematics only exists inasmuch as it connects to other subjects, such as biology or social studies.

Accepted Answer

Mathematics is indeed both an active process (something one does through problem-solving, reasoning, and applying concepts) and a substantial body of knowledge comprising theories, principles, and facts. This description acknowledges the dynamic nature of engaging with mathematics as well as the depth and breadth of content it encompasses.

Question 13

Describe some of the most significant results of the TIMSS, NAEP, and PISA reports.
 Based on the findings, state some suggestions for improving our mathematics education
 system.

Accepted Answer

The answer of Describe some of the most significant results...

Question 14

Compare and contrast the overriding mathematics education views of the New Math
 movement, back-to-basics movement, and the current reform efforts, which use the
 Principles and Standards for School Mathematics, and Common Core State Standards for Mathematics as a guide.

Accepted Answer

The answer of Compare and contrast the overriding mathematics education...

Question 15

Give an example of a question you could pose to a group of secondary or middle school
 mathematics students and explain why it could be considered a "problem" to some
 students but an "exercise" to others.

Accepted Answer

The answer of Give an example of a question you...

Question 16

Give an example of a "rich" problem that could be given to a group of students at the
 grade level of your choice.Demonstrate at least three ways of solving the problem using the strategies stated in Chapter 1.

Accepted Answer

The answer of Give an example of a "rich" problem...

Question 17

Pick two of the eight mathematical practices from the Common Core State Standards for
 Mathematics and describe their importance in the secondary or middle school
 mathematics curriculum.

Accepted Answer

The answer of Pick two of the eight mathematical practices...

Question 18

Describe three uses for Pascal's triangle and explain why it is important to make these
 types of connections in the mathematics curriculum.

Accepted Answer

The answer of Describe three uses for Pascal's triangle and...

Quiz 1: Mathematics As a Process

Viewing mathematics as "a coherent whole" refers most closely to which of the following?

Which Standard for Mathematical Practice is involved when a student recognizes that (x+3) (x-5) =(x-5) (x+3) for the same reason that 7 ×3=3 ×7?

The connections Standard stresses which of the following processes?

Problems that bring together several mathematical topics into a single investigation emphasize which mathematical process?

Which of the following is a typical middle school practice that promotes mathematical connections?

Some students prefer to solve a given problem by drawing a graph; whereas, other students would rather write an equation or use hands-on materials.Which of the following mathematical processes emphasizes the importance of students viewing the same problem with multiple approaches?

The Standards for Mathematical Practice address the use of tools in the classroom. Which of the following would NOT necessarily be considered a tool?

Which of the following words describes the use of "tools" in the mathematics classroom?

Which of the following factors tends to most significantly impact a teacher's ability to incorporate the mathematical processes and practices in the classroom?

Mr.James had his class select an authentic example of a linear function that they have encountered in their lives.By having students submit written papers about their functions he was stressing which mathematical process?

Surveys from industry indicate that employers are looking for a workforce that has skills in which of the following?

Which of the following might be considered the most accurate description of what it means to "do," to "teach," and to "learn" mathematics?

Describe some of the most significant results of the TIMSS, NAEP, and PISA reports. Based on the findings, state some suggestions for improving our mathematics education system.

Compare and contrast the overriding mathematics education views of the New Math movement, back-to-basics movement, and the current reform efforts, which use the Principles and Standards for School Mathematics, and Common Core State Standards for Mathematics as a guide.

Give an example of a question you could pose to a group of secondary or middle school mathematics students and explain why it could be considered a "problem" to some students but an "exercise" to others.

Give an example of a "rich" problem that could be given to a group of students at the grade level of your choice.Demonstrate at least three ways of solving the problem using the strategies stated in Chapter 1.

Pick two of the eight mathematical practices from the Common Core State Standards for Mathematics and describe their importance in the secondary or middle school mathematics curriculum.

Describe three uses for Pascal's triangle and explain why it is important to make these types of connections in the mathematics curriculum.