Deck 2: Principles of Mathematics Education

Question 1

Which of the following is a false assumption that is commonly held by new teachers of mathematics?

A)Technology is helpful to learning mathematics.
B)Students will benefit from exposure to the same learning environment that was experienced by the teacher.
C)Mathematics is perceived as being very difficult by many of their students.
D)Teaching methods can and do make a difference in student success.
E)All students are capable of learning mathematics.

Answer 1

Students will benefit from exposure to the same learning environment that was experienced by the teacher.

Question 2

In which year did the National Council of Teachers of Mathematics (NCTM)publish Principles to Actions: Ensuring Mathematical Success for All, from which the 6 principles were described?

A)1980.
B)1989.
C)2000.
D)2010.
E)2014.

Answer 2

2014.

Question 3

Which of the following refers to the essential elements that are needed to create an exemplary mathematics program for students?

A)Principles.
B)Indicators.
C)Standards.
D)Goals.
E)Focal Points.

Answer 3

Principles.

Question 4

Which of the following is NOT one of the six NCTM principles?

A)Teaching and Learning.
B)Tools and Technology.
C)Assessment.
D)Environment.
E)Professionalism.

Question 5

Which of the following principles refers to "high expectations and strong support for all students"?

A)Curriculum.
B)Access and Equity.
C)Teaching and Learning.
D)Assessment.
E)Tools and Technology.

Question 6

Which of the following principles states that students should be engaged in "meaningful learning through individual and collaborative experiences"?

A)Tools and Technology.
B)Curriculum.
C)Teaching and Learning.
D)Access and Equity.
E)Assessment.

Question 7

The analogy of learning to play guitar, as explained in Chapter 2, illustrates which of the following?

A)Music, like mathematics, can be difficult to master.
B)A student might be skilled at playing guitar but not the piano, just as one student might feel comfortable with the use of technology while another does not.
C)The focus in a mathematics classroom should go beyond skill-based procedures.
D)Students need to learn the basics in mathematics, just as they do in music.
E)Mathematics lessons, like music lessons, must be challenging.

Question 8

Problem solving can best be described as which of the following?

A)The opportunity to put skills to use in a real-life situation.
B)The best way to wrap up a mathematics unit on a given topic.
C)The opportunity to practice routine skills.
D)Showing students an approach that can be used anytime a similar situation occurs.
E)Assigning homework from the book that is clearly marked as "problems."

Question 9

Which of these can be described as the "flexible use of procedures in the problem- solving process"?

A)Productive Disposition.
B)Fluency.
C)Conceptual Understanding.
D)Strategic Competence.
E)Adaptive Reasoning.

Question 10

An example of relating procedural knowledge to conceptual ideas that is presented in Chapter 2 involves which of the following?

A)Proving the congruence of triangles.
B)Using the distributive property.
C)Finding the percentage of a number.
D)Combining similar terms.
E)Determining the volume of a solid.

Question 11

The inter-relating of mathematical ideas is referred to as which of the following?

A)Applying mathematics.
B)Reasoning mathematically.
C)Making connections.
D)Using procedures.
E)Finding solutions.

Question 12

Which of the following is the most important factor in the learning of mathematics?

A)Textbooks used.
B)Technology used.
C)Skill of the teacher.
D)Strength of the curriculum.
E)Support of the community.

Question 13

Which of the following is NOT necessarily associated with effective mathematics teaching?

A)High level of competence in mathematics.
B)Strict adherence to lesson plans and textbooks.
C)A well designed set of teaching strategies.
D)Knowledge about which teaching approaches work best in a given situation.
E)Understanding of how students learn.

Question 14

Which of the following is a decision that a teacher must make almost every day?

A)Selection of content and processes to emphasize.
B)Determining how much time to spend on a given topic.
C)Selecting appropriate problems to solve.
D)Determining how to measure student understanding.
E)All of these.

Question 15

Which of the following is NOT considered a high-leverage teaching practice?

A)Establish mathematics goals to focus learning.
B)Pose purposeful questions.
C)Build procedural fluency from conceptual understanding.
D)Research and use an extensive variety of web resources.
E)Facilitate meaningful mathematical discourse.

Question 16

The Mathematical Teaching Practices are for teachers as which of the follow is for students?

A)Standards for Mathematical Practice.
B)Principles of Assessment.
C)Disposition Checklist.
D)Professional Teaching Standards.
E)None of these.

Question 17

Which course is often referred to as a "gatekeeper" for the study of higher mathematics?

A)Geometry.
B)Pre-Algebra.
C)Algebra I.
D)Trigonometry.
E)Algebra II.

Question 18

Which is the determining factor on which teachers are ordinarily given the assignment to teach the higher-level mathematics courses in secondary and middle schools?

A)Mathematics the teacher studied in college.
B)Years of teaching experience in the district.
C)Preference of the teacher.
D)Requests made by potential students.
E)Reputation of the teacher.

Question 19

Which of the following most accurately defines equity in mathematics education?

A)All students have a right to equally access all areas of the curriculum.
B)All students should be taught the same.
C)All students should obtain high grades in mathematics.
D)All students should be exposed to both the best and the weakest teachers in their schooling experience.
E)All students should use the same books and materials in their mathematics classes.

Question 20

Which of the following can contribute significantly to helping every student learn mathematics?

A)Cooperative group work.
B)Hands-on teaching strategies.
C)Use of computers.
D)Individual tutoring.
E)All of these.

Question 21

Which of the following is often used interchangeably with the word "curriculum" in the community?

A)Lesson plans.
B)Activities.
C)Units.
D)Textbooks.
E)Principles.

Question 22

Which of the following terms refers to "all of the experiences that a student has throughout his or her educational career"?

A)Mathematics education.
B)Student learning.
C)Curriculum.
D)Standards.
E)Assessment.

Question 23

What is the name of the educational theorist who developed the term implicit curriculum?

A)Gardner.
B)Eisner.
C)Dussan.
D)Vygotsky.
E)Annenberg.

Question 24

Which of the following is NOT recognized as part of the implicit curriculum?

A)The seating arrangement in the classroom.
B)The psychological environment established by the teacher.
C)The courses taken by a student.
D)The way that lessons are conducted.
E)The manner in which technology is incorporated in teaching.

Question 25

Which of the following is a way that a student can verify that a trinomial has been factored properly?

A)Examine the graphs of the trinomial and product of the binomials.
B)Substitute a value for the variable and simplify the trinomial and the product of the binomials.
C)Examine a table of values for the trinomial and for the product of the binomials.
D)Re-multiply the binomial solution to compare the product to the original trinomial.
E)All of these.

Question 26

What is the most important reason for why a teacher should consider using a graphing calculator in graphing and tabular modes to verify the solutions to polynomial
simplifying problems?

A)The strategy promotes equity.
B)The strategy is always enjoyable to students.
C)The strategy is easier than using pencil and paper approaches.
D)The strategy prepares the students for real-life problems involving polynomials.
E)The strategy requires the use of less class time.

Question 27

Which of the following is LEAST associated with curriculum?

A)What material is taught.
B)How the material is taught.
C)The sequence in which the material is taught.
D)Which concepts are emphasized.
E)Why the material is included in a course.

Question 28

Sequencing mathematical topics in a reasonable order is most likely to result in which of the following benefits?

A)Covering topics more quickly and studying more mathematics.
B)Avoiding duplication of topics and building on student knowledge.
C)Using technology and providing more visuals for students.
D)Appealing to the interests of students and increasing achievement.
E)Increasing course-taking and raising awareness of the usefulness of mathematics.

Question 29

Which of the following describes a transversal?

A)A line that intersects two other lines.
B)A ray that bisects an angle.
C)A segment that joins the endpoint of a longer segment to its midpoint.
D)A line that serves as the base for a triangle.
E)A line that is perpendicular to another given line.

Question 30

According to the author in Chapter 2, the use of technology to explore a problem, rather than simply drawing a picture with pencil-and-paper, is more likely to produce which
result?

A)Accuracy of the figure drawn.
B)Success in teaching the concept.
C)Motivation of the students.
D)Attention of the class.
E)Acceptable behavior by the students.

Question 31

A common misuse of technology in teaching mathematics is which of the following?

A)Using technology in all units throughout a school year.
B)Using graphing calculators with students before they are ready.
C)Restricting the use of technology to checking answers.
D)Playing mathematical games.
E)Solving problems that should have been worked by hand.

Question 32

Which of the following is an important technological tool that is appropriate for use in secondary and middle school mathematics classrooms?

A)Graphing calculators.
B)Computers.
C)Personal Electronic Devices.
D)Interactive whiteboards.
E)All of these.

Question 33

Which groups of students often benefit the most from the use of technology when learning mathematics, according to the author in Chapter 2?

A)Middle school students.
B)Students in high-level mathematics courses.
C)Students who are frequently absent from school.
D)Students with learning disabilities and visual learners.
E)Students with negative attitudes toward mathematics.

Question 34

Which statement most accurately characterizes the NCTM's vision of mathematical assessment?

A)Gathering information about students.
B)Determining student grades.
C)Evaluating student progress.
D)Giving tests to students.
E)Viewing student work at the end of a unit.

Question 35

Which of the following would be considered a formal means of assessing student progress?

A)Observing students working on a team project.
B)Observing students as they make a presentation to the class.
C)Reading student journal entries.
D)Interviewing a student while doing seatwork.
E)Administering a test.

Question 36

Which statement best describes the ideal role of assessment in mathematics?

A)End-of-unit measurement of progress.
B)Somewhat of an interruption to the teaching process.
C)Something that is done more "to" the student than "for" the student.
D)An ongoing process.
E)The best measure of a teacher's effectiveness.

Question 37

Which of the following is considered an "essential component" of effective assessment in a mathematics classroom?

A)Frequent testing or quizzing of student knowledge.
B)Timely feedback on assessments given to students.
C)"Curving" of grades to promote positive student attitudes.
D)Ensuring that assessments are always objective.
E)Fairness, promoted by ensuring that all students are assessed the same way.

Question 38

Assessment should serve to improve which of the following?

A)The teaching and learning of mathematics.
B)The design of the curriculum.
C)The accuracy of final grades.
D)The evaluation of a teacher.
E)The use of tools and technology.

Question 39

Which of the following most accurately characterizes the process of becoming a teacher?

A)An undergraduate education degree program.
B)A graduate education degree program.
C)Ten years of teaching experience.
D)A lifelong endeavor.
E)An impossible goal to achieve.

Question 40

A learning community of teachers often focuses on which of the following?

A)Examining lesson plans.
B)Examining teaching practices.
C)Examining assessments.
D)Working together for mutual improvement.
E)All of these.

Question 41

Which of the following professional development activities best lends itself to addressing self-directed plans for improvement?

A)Exploring websites.
B)Attending workshops.
C)Taking college courses.
D)Attending conferences.
E)Participating in teacher meetings.

Question 42

Learner.org is a popular professional development site because it provides the teacher with hundreds of which of the following?

A)Examples of student work.
B)Lesson plans.
C)Classroom activities.
D)Streaming video clips.
E)Problems to pose to students.

Question 43

According to the author in Chapter 2, perhaps the most important task of the teacher is to develop his or her skills to do which of the following?

A)To make mathematics fun for students.
B)To challenge the students to perform to their potential.
C)To use technology in the classroom.
D)To write effective lesson plans.
E)To motivate and engage the learners.

Question 44

Which of the following most accurately characterizes the six NCTM principles?

A)Each principle should be considered separate from the others, as they represent very different aspects of the mathematics teaching profession.
B)The most important is the learning principle, since the ultimate measure of success is what the students have learned.
C)The equity and technology principles are the most closely related, as one promotes the other, yet both are different from the other four principles.
D)The six principles are all interwoven, as each connects in some way with the others.
E)Three of the principles relate primarily to the teacher, while the other three are directed at the students.

Question 45

Which of the following can be considered the major components of the mathematics teaching profession?

A)Equity, teaching, and learning.
B)Curriculum, assessment, and teaching and learning.
C)Technology, teaching and learning, and equity.
D)Teaching, learning, and assessment.
E)Assessment, technology, and equity.

Question 46

Curricular changes in a school district are most likely to directly bring about changes in which of the following?

A)Equity.
B)Teaching.
C)Learning.
D)Technology.
E)Problem solving.

Question 47

When a teacher decides to assign a quarterly project in mathematics, which of the principles is being directly addressed?

A)Assessment.
B)Teaching.
C)Learning.
D)Equity.
E)Curriculum.

Question 48

Which of the following does research suggest may be one of the best ways to bring about reform in mathematics teaching practices in a school district?

A)Rewriting the curriculum.
B)Purchasing interactive whiteboards for each classroom.
C)Adoption of different assessment strategies.
D)Purchase of new textbooks.
E)Involvement of the community in decision-making.

Question 49

NCTM's Principles and Standards for School Mathematics describes teaching mathematics in which of the following ways?

A)A profession that lends itself to "recipes" for success.
B)A profession in which it is fairly easy to help teachers become effective.
C)A complex profession with no universal approaches that work for all.
D)A profession with enough research to know what works with virtually all students, most of the time.
E)A profession with little valid research to drive day-to-day decisions.

Question 50

Which of the following is NOT a characteristic of the teaching profession?

A)Making the best of current research.
B)Putting research to practice in the classroom.
C)Believing that every student can learn.
D)Reflecting on practice to improve over time.
E)Acknowledging that teachers who are relatively new to the profession are the least likely to be successful.

Question 51

Becoming an effective teacher of mathematics can be best described by which of the following?

A)Success in the field depends on a high level of success in college.
B)The development of a teacher is a career-long process.
C)Most teachers are not successful until they have at least 10 years of experience.
D)It is more difficult to teach mathematics than any other subject area.
E)Most teachers of mathematics will never feel truly successful in their entire career.

Question 52

Discuss how a teacher's personal success in doing mathematics, together with his/her experiences as a student, influence the way that the teacher runs his/her own classroom.

Question 53

List and provide a brief description of each of the six NCTM principles of an effective mathematics program.

Question 54

Explain how a teacher's view on the question, "Do you believe that all students are capable of learning mathematics?" will affect his/her teaching practices.

Question 55

A broad use of the term "curriculum" implies more than simply the textbook used in teaching mathematics.Explain a more comprehensive view of the meaning of curriculum, as described in the NCTM principles.

Question 56

Give an example of a mathematics lesson that illustrates the teaching and learning principle at work.(You can either discuss the example presented in Chapter 2 or describe a situation of your own.)

Question 57

Explain how the three major components of mathematics education - curriculum, teaching and learning, and assessment - connect and influence one another.