Question 1

Explain how the philosophy of how "number sense" and "algebra" should be taught in schools has evolved from a traditional to a more contemporary view.

Accepted Answer

The traditional view of teaching "number sense" and "algebra" in schools focused on rote memorization of formulas and procedures. Students were expected to memorize multiplication tables, algorithms for solving equations, and rules for manipulating numbers and variables. This approach often led to a lack of understanding and a fear of math, as students struggled to see the connections between different mathematical concepts.

In more contemporary views, there has been a shift towards a more conceptual understanding of "number sense" and "algebra". Educators now emphasize the importance of developing a deep understanding of the underlying principles and relationships in mathematics. This includes a focus on real-world applications, problem-solving, and critical thinking skills. Students are encouraged to explore and make connections between different mathematical concepts, rather than simply memorizing procedures.

Additionally, there is a greater emphasis on the use of manipulatives, visual representations, and technology to help students develop a concrete understanding of mathematical concepts. This hands-on approach allows students to see and interact with mathematical ideas in a more tangible way, leading to a deeper understanding and appreciation for the subject.

Overall, the evolution of the philosophy of teaching "number sense" and "algebra" in schools has shifted from a focus on memorization and procedures to a more conceptual and hands-on approach that emphasizes understanding, problem-solving, and real-world applications. This contemporary view aims to help students develop a strong foundation in mathematics and a positive attitude towards the subject.

Question 2

Approximately what percentage of high schools in the United States follow anintegrated sequence of courses?

Accepted Answer

A) 5%. 
B) 10%. 
C) 25%. 
D) 40%. 
E) 60%. 
A) 5%. 
B) 10%. 
C) 25%. 
D) 40%. 
E) 60%. B

Question 3

According to NCTM (2011), which of the following should be emphasized as earlyalgebra skills for Grades 3-5?

Accepted Answer

A) Generalize, express, and justify relationships. 
B) Simplify algebraic expressions. 
C) Graph linear functions. 
D) Identify types of functions. 
E) Perform operations on fractions. 
A) Generalize, express, and justify relationships. 
B) Simplify algebraic expressions. 
C) Graph linear functions. 
D) Identify types of functions. 
E) Perform operations on fractions. A

Question 4

Which of the following is NOT listed as a topic of the Functions domain at Grade 8 inthe Common Core State Standards for Mathematics?

Accepted Answer

A) Defining functions. 
B) Evaluating functions. 
C) Graphing functions. 
D) Using functions to describe real-world situations. 
E) Comparing functions to one another. 
A) Defining functions. 
B) Evaluating functions. 
C) Graphing functions. 
D) Using functions to describe real-world situations. 
E) Comparing functions to one another.

Question 5

When a student draws conclusions based on evidence that has been presented, whichof the following is being developed in the mathematics classroom?

Accepted Answer

A) Reasoning. 
B) Mathematical Practice. 
C) Problem Solving. 
D) Sense Making. 
E) Representation. 
A) Reasoning. 
B) Mathematical Practice. 
C) Problem Solving. 
D) Sense Making. 
E) Representation.

Question 6

In Chapter 10, the example of the students exploring a burning candle addressedwhich of the following content strands?

Accepted Answer

A) Algebra. 
B) Geometry. 
C) Number. 
D) Discrete Mathematics.ier 2020.For instructor use only. 
E) Probability. 
A) Algebra. 
B) Geometry. 
C) Number. 
D) Discrete Mathematics.ier 2020.For instructor use only. 
E) Probability.

Question 7

Explain what it means for schools to emphasize the study of algebra and geometry as "content strands," rather than as courses to be taken in middle and high school.What is the vision of school mathematics in the Common Core State Standards for Mathematics, Catalyzing Change, and related state-level Standards documents.

Accepted Answer

Emphasizing the study of algebra and geo

Question 8

The sample lesson in Chapter 10 that uses a "how well do you know yourself" data setleads students to the exploration of which algebraic concept?

Accepted Answer

A) Graphing linear functions. 
B) Solving linear equations. 
C) Calculating slopes of lines. 
D) Simplifying algebraic expressions. 
E) Graphing inequalities. 
A) Graphing linear functions. 
B) Solving linear equations. 
C) Calculating slopes of lines. 
D) Simplifying algebraic expressions. 
E) Graphing inequalities.

Question 9

Which key algebra concept can be explored and discussed by recording data about theheight of a burning candle over a particular period of time?

Accepted Answer

A) Solving quadratic equations. 
B) Factoring trinomials. 
C) Writing the equation of a line. 
D) Simplifying a rational expression. 
E) Estimating the value of a square root. 
A) Solving quadratic equations. 
B) Factoring trinomials. 
C) Writing the equation of a line. 
D) Simplifying a rational expression. 
E) Estimating the value of a square root.

Question 10

By which grade level do the Common Core State Standards for Mathematics expectstudents to perform operations on positive and negative integers?

Accepted Answer

A) Grade 5. 
B) Grade 6. 
C) Grade 7. 
D) Grade 8. 
E) Grade 9. 
A) Grade 5. 
B) Grade 6. 
C) Grade 7. 
D) Grade 8. 
E) Grade 9.

Question 11

Which term(s)apply to the number "12"?

Accepted Answer

A) Abundant and Prime. 
B) Composite and Perfect. 
C) Deficient and Prime. 
D) Abundant and Composite. 
E) Composite and Deficient. 
A) Abundant and Prime. 
B) Composite and Perfect. 
C) Deficient and Prime. 
D) Abundant and Composite. 
E) Composite and Deficient.

Question 12

Which of the following is considered an "essential component" of algebra in highschool, according to Catalyzing Change?

Accepted Answer

A) Using CAS technology. 
B) Examining problems with manipulatives. 
C) Making predictions based on algebraic models. 
D) Using algebraic properties. 
E) Graphing non-linear equations. 
A) Using CAS technology. 
B) Examining problems with manipulatives. 
C) Making predictions based on algebraic models. 
D) Using algebraic properties. 
E) Graphing non-linear equations.

Question 13

Which of the following is considered a high school number topic, according to theCommon Core State Standards for Mathematics?

Accepted Answer

A) Negative Numbers. 
B) Integer Operations. 
C) Imaginary Numbers. 
D) Irrational Numbers. 
E) Percentages. 
A) Negative Numbers. 
B) Integer Operations. 
C) Imaginary Numbers. 
D) Irrational Numbers. 
E) Percentages.

Question 14

Which of the following most accurately describes the relationship between theprocesses of reasoning and sense making?

Accepted Answer

A) Reasoning skills should be taught prior to students developing sense making. 
B) Sense making is necessary to develop reasoning skills. 
C) Reasoning and sense making should work together when solving problems. 
D) Reasoning and sense making are developed best in informal situations. 
E) Reasoning and sense making are developed best in formal situations. 
A) Reasoning skills should be taught prior to students developing sense making. 
B) Sense making is necessary to develop reasoning skills. 
C) Reasoning and sense making should work together when solving problems. 
D) Reasoning and sense making are developed best in informal situations. 
E) Reasoning and sense making are developed best in formal situations.

Question 15

Which of the following is a typical memory of most people when they think of thestudy of geometry?

Accepted Answer

A) Exploring shapes with technology. 
B) Creating geometric designs as projects. 
C) Studying the history of geometry. 
D) Writing two-column proofs. 
E) Conducting hands-on activities. 
A) Exploring shapes with technology. 
B) Creating geometric designs as projects. 
C) Studying the history of geometry. 
D) Writing two-column proofs. 
E) Conducting hands-on activities.

Question 16

Which of the following is a typical memory of most people when they think of thestudy of algebra?

Accepted Answer

A) Conducting hands-on activities. 
B) Participating in long-term projects. 
C) Factoring trinomials. 
D) Exploring functions with technology. 
E) Solving problems in teams. 
A) Conducting hands-on activities. 
B) Participating in long-term projects. 
C) Factoring trinomials. 
D) Exploring functions with technology. 
E) Solving problems in teams.

Question 17

The example in Chapter 10 with students changing the scale on a graphing calculatoremphasizes which mathematical idea? For instructor use only.

Accepted Answer

A) Graphing absolute value functions. 
B) Labeling axes. 
C) Using a straightedge. 
D) Plotting points. 
E) None of these. 
A) Graphing absolute value functions. 
B) Labeling axes. 
C) Using a straightedge. 
D) Plotting points. 
E) None of these.

Question 18

When a student develops understanding by connecting ideas with pre-existingknowledge, which of the following is being developed in the mathematics classroom?

Accepted Answer

A) Reasoning. 
B) Mathematical Practice. 
C) Problem Solving. 
D) Sense Making. 
E) Representation. 
A) Reasoning. 
B) Mathematical Practice. 
C) Problem Solving. 
D) Sense Making. 
E) Representation.

Question 19

Which of the following LEAST accurately describes the ideal contemporary view ofthe study of algebra?

Accepted Answer

A) Algebra is a course. 
B) Algebra is a language. 
C) Algebra is a content strand. 
D) Algebra is a K-12 experience. 
E) Algebra is a responsibility for all teachers. 
A) Algebra is a course. 
B) Algebra is a language. 
C) Algebra is a content strand. 
D) Algebra is a K-12 experience. 
E) Algebra is a responsibility for all teachers.

Question 20

Which term refers to a number whose sum of its factors equals the number itself?

Accepted Answer

A) Deficient. 
B) Prime. 
C) Abundant. 
D) Composite. 
E) Perfect. 
A) Deficient. 
B) Prime. 
C) Abundant. 
D) Composite. 
E) Perfect.

Explain how the philosophy of how "number sense" and "algebra" should be taught in schools has evolved from a traditional to a more contemporary view.

Approximately what percentage of high schools in the United States follow anintegrated sequence of courses?

According to NCTM (2011), which of the following should be emphasized as earlyalgebra skills for Grades 3-5?

Which of the following is NOT listed as a topic of the Functions domain at Grade 8 inthe Common Core State Standards for Mathematics?

When a student draws conclusions based on evidence that has been presented, whichof the following is being developed in the mathematics classroom?

In Chapter 10, the example of the students exploring a burning candle addressedwhich of the following content strands?

The sample lesson in Chapter 10 that uses a "how well do you know yourself" data setleads students to the exploration of which algebraic concept?

Which key algebra concept can be explored and discussed by recording data about theheight of a burning candle over a particular period of time?

By which grade level do the Common Core State Standards for Mathematics expectstudents to perform operations on positive and negative integers?

Which term(s)apply to the number "12"?

Which of the following is considered an "essential component" of algebra in highschool, according to Catalyzing Change?

Which of the following is considered a high school number topic, according to theCommon Core State Standards for Mathematics?

Which of the following most accurately describes the relationship between theprocesses of reasoning and sense making?

Which of the following is a typical memory of most people when they think of thestudy of geometry?

Which of the following is a typical memory of most people when they think of thestudy of algebra?

The example in Chapter 10 with students changing the scale on a graphing calculatoremphasizes which mathematical idea? For instructor use only.

When a student develops understanding by connecting ideas with pre-existingknowledge, which of the following is being developed in the mathematics classroom?

Which of the following LEAST accurately describes the ideal contemporary view ofthe study of algebra?

Which term refers to a number whose sum of its factors equals the number itself?

Mathematics As a Process

Principles of Mathematics Education

Learning Theories and Psychology in Mathematics Education

Standards, Objectives, and Resources

Planning for Instruct

Assessment: Purposes and Strategies

Principles of Assessment Practices

Teaching and Learning

Teaching and Learning: Tools and Technology

Teaching Geometry, Statisticsprobability, and Discrete Mathematics

Managing a Mathematics Classroom

The Teacher of Mathematics in the School Community

Filters

Exam 10: Teaching Number Sense and Algebra

Explain how the philosophy of how "number sense" and "algebra" should be taught in schools has evolved from a traditional to a more contemporary view.

Approximately what percentage of high schools in the United States follow anintegrated sequence of courses?

According to NCTM (2011), which of the following should be emphasized as earlyalgebra skills for Grades 3-5?

Which of the following is NOT listed as a topic of the Functions domain at Grade 8 inthe Common Core State Standards for Mathematics?

When a student draws conclusions based on evidence that has been presented, whichof the following is being developed in the mathematics classroom?

In Chapter 10, the example of the students exploring a burning candle addressedwhich of the following content strands?

The sample lesson in Chapter 10 that uses a "how well do you know yourself" data setleads students to the exploration of which algebraic concept?

Which key algebra concept can be explored and discussed by recording data about theheight of a burning candle over a particular period of time?

By which grade level do the Common Core State Standards for Mathematics expectstudents to perform operations on positive and negative integers?

Which term(s)apply to the number "12"?

Which of the following is considered an "essential component" of algebra in highschool, according to Catalyzing Change?

Which of the following is considered a high school number topic, according to theCommon Core State Standards for Mathematics?

Which of the following most accurately describes the relationship between theprocesses of reasoning and sense making?

Which of the following is a typical memory of most people when they think of thestudy of geometry?

Which of the following is a typical memory of most people when they think of thestudy of algebra?

The example in Chapter 10 with students changing the scale on a graphing calculatoremphasizes which mathematical idea? For instructor use only.

When a student develops understanding by connecting ideas with pre-existingknowledge, which of the following is being developed in the mathematics classroom?

Which of the following LEAST accurately describes the ideal contemporary view ofthe study of algebra?

Which term refers to a number whose sum of its factors equals the number itself?

Mathematics As a Process

Principles of Mathematics Education

Learning Theories and Psychology in Mathematics Education

Standards, Objectives, and Resources

Planning for Instruct

Assessment: Purposes and Strategies

Principles of Assessment Practices

Teaching and Learning

Teaching and Learning: Tools and Technology

Teaching Geometry, Statisticsprobability, and Discrete Mathematics

Managing a Mathematics Classroom

The Teacher of Mathematics in the School Community

Filters