Deck 4: Standards, Objectives, and Resources

Question 1

The authority to set standards, by virtue of the U.S.Constitution, is delegated to which "group"?

A)The federal government.
B)The states.
C)The counties.
D)The school districts.
E)The teachers.

Answer 1

The states.

Question 2

Which of the following is a term standing for a benchmarks that establish what students should know or be able to do at the end of each grade level?

A)National core.
B)National curriculum.
C)Model.
D)Standard.
E)Strand.

Answer 2

Standard.

Question 3

The NCTM's Principles and Standards for School Mathematics document was published in which year?

A)1980.
B)1984.
C)1989.
D)1995.
E)2000.

Answer 3

2000.

Question 4

According to research, which of the following skills is NOT a skill that is highly valued by employers?

A)Participate as a member of a team.
B)Solve problems.
C)Communicate effectively.
D)Compute without calculators.
E)Learn new skills.

Question 5

Which of the following is NOT listed by NCTM as a primary reason why students need to possess mathematical competence?

A)Thinking and problem solving are needed in the workplace.
B)The scientific and technical communities use mathematics frequently.
C)Algebra and geometry skills are required in every profession.
D)Knowledge of mathematics can be personally satisfying.
E)Mathematics should be recognized as a part of cultural heritage.

Question 6

Which of the following statements most closely reflects the purpose of NCTM publishing the Standards documents?

A)The Standards provided recommendations for states and school districts but were not mandatory.
B)The Standards provided recommendations for states and mandatory frameworks for school districts.
C)The Standards provided mandatory curricular benchmarks for states but recommendations for districts.
D)The Standards provided mandatory curricular benchmarks for states and for districts but recommendations for teachers.
E)The Standards provided mandatory curricular benchmarks for states, districts, and teachers.

Question 7

Which of the following accurately describes the curriculum Standards of Principles and Standards for School Mathematics?

A)The Standards were to be addressed by every child, every year.
B)Standards prescribed a mathematics course for each grade level.
C)The Standards mandated a curriculum to be followed by all schools.
D)The Standards were written by a small committee consisting of 10 members.
E)The Standards are written so that different students would address different topics, depending on their ability levels.

Question 8

Which of the following documents was released in 2006 "as a starting point in a dialogue on what is important at particular levels of instruction"?

A)Curriculum and Evaluation Standards for School Mathematics.
B)Principles and Standards for School Mathematics.
C)Curriculum Focal Points.
D)Professional Teaching Standards.
E)The College Board Standards for College Success.

Question 9

Which of the following organizations publishes a syllabus for Advanced Placement Calculus?

A)The College Board.
B)The National Council of Teachers of Mathematics.
C)Each state's Department of Education.
D)Project Achieve.
E)TIMSS researchers.

Question 10

Which of the following topics is NOT included in the syllabus for calculus, according to the Advanced Placement document?

A)Series.
B)Matrix operations.
C)Derivatives.
D)Limits.
E)Integrals.

Question 11

In which year were the Common Core State Standards released?

A)1989.
B)1991.
C)2000.
D)2010.
E)2014.

Question 12

Which of the following describes a significant emphasis of the Common Core State Standards?

A)Inquiry-based learning.
B)Use of technology.
C)Big ideas of mathematics.
D)Integrated curriculum at the secondary and middle school levels.
E)All of the above.

Question 13

Which of the following is NOT one of the conceptual categories for high school in the Common Core State Standards?

A)Algebra.
B)Discrete Mathematics.
C)Statistics and Probability.
D)Modeling.
E)Functions.

Question 14

Which of the following describes a group of related Standards in the Common Core State Standards for Mathematics?

A)Grouping.
B)Conceptual Category.
C)Domain.
D)Cluster.
E)Core.

Question 15

Appendix A of the Common Core State Standards for Mathematics outlines ideas for specific courses in high school and is often referred to as which of the following?

A)Core.
B)Model.
C)Domain.
D)Options.
E)Pathways.

Question 16

What was the main reason, stated in Chapter 4, for the curriculum Standards documents to include the challenge of making mathematics accessible to all students?

A)Minority students were being discriminated against.
B)The world had moved into an information age.
C)The U.S.and other countries jointly made the decision.
D)There was a discrepancy in achievement tests.
E)Universities wanted more consistency in student background.

Question 17

According to U.S.Bureau of Labor, how many different jobs will the average worker hold between ages 18 and 48?

A)3)
B)5)
C)8)
D)12.
E)16.

Question 18

According to the U.S.Department of Labor, approximately what percentage of all jobs being created today require a post-secondary education?

A)10%.
B)33%.
C)50%.
D)67%.
E)75%.

Question 19

What does the Common Core State Standards for Mathematics consider a "core curriculum"?

A)Pre-K to 12 curriculum for all students.
B)Pre-K to 8 curriculum for all students.
C)Middle school curriculum for all students.
D)Three years of high school curriculum for all students.
E)Four years of high school curriculum for all students.

Question 20

Select the list that represents three possible core curriculum models for schools.

A)Crossover, Enrichment, and Differentiated.
B)Crossover, Enrichment, and Integrated.
C)Enrichment, Differentiated, and Linear.
D)Enrichment, Differentiated, and Integrated.
E)Differentiated, Integrated, and Linear.

Question 21

Which core curriculum model is probably the easiest to adopt if the school is in a traditional tracking system?

A)Differentiated.
B)Enrichment.
C)Crossover.
D)Integrated.
E)Linear.

Question 22

Which core curriculum model has the students homogeneously grouped?

A)Differentiated.
B)Enrichment.
C)Crossover.
D)Integrated.
E)Linear.

Question 23

Which of the following is NOT a characteristic of the crossover model?

A)There is a fourth year level for college bound students only.
B)All students visit the same core objectives.
C)Students can move from non-college bound to college bound.
D)Students can move from college bound to non-college bound.
E)Students are grouped by ability in teams within individual classes.

Question 24

Which core curriculum models have students arranged into small groups at the beginning of each unit throughout the three-year common core?

A)Crossover and Enrichment.
B)Enrichment and Differentiated.
C)Differentiated and Integrated.
D)Integrated and Linear.
E)Linear and Differentiated.

Question 25

If a group of students in the enrichment model completes the core content, what would the teacher typically have them do?

A)More review problems are assigned for practice.
B)Students complete a teacher-selected "challenge" problem.
C)Students take an in-depth look at one or more of the concepts from the unit.
D)Students move on to the next unit.
E)Students read or study and wait for the others to catch up.

Question 26

In a school, one group in a class of geometry students is cutting paper with scissors to generate area formulas; another group uses computers to draw polygons and create
area formulas, and a third group uses area formulas "on paper" to solve complex
problems.Which core curriculum model is probably at work in this school?

A)Crossover Model.
B)Integrated Model.
C)Differentiated Model.
D)Enrichment Model.
E)Linear Model.

Question 27

Which core curriculum model has classes heterogeneously grouped and has all students explore the same topics but at a variety of levels?

A)Crossover.
B)Enrichment.
C)Differentiated.
D)Integrated.
E)Linear.

Question 28

Which of the following is NOT a characteristic of the differentiated model for the core curriculum?

A)There is a fourth year level available for all students.
B)Groups explore topics at a variety of levels.
C)Students are heterogeneously grouped.
D)All students explore the same topics.
E)All students complete a core of objectives, and some move on to additional topics.

Question 29

Which of the following is the name for a teaching model that involves putting gifted students together, while others are in mixed groups, used particularly at middle school
level?

A)Differentiating.
B)Clustering.
C)Accelerating.
D)Enriching.
E)Modeling.

Question 30

In a core curriculum, what mathematics topics are given equal weight in terms of importance?

A)Arithmetic, algebra, and geometry.
B)Algebra, geometry, statistics, and topics from discrete mathematics.
C)Algebra, geometry, and statistics.
D)Algebra, geometry, and trigonometry.
E)Algebra, geometry, and pre-calculus.

Question 31

As discussed in Chapter 4, what is the main reason why schools choose to teach an "integrated" high school mathematics program instead of a traditional sequence of
algebra and geometry courses?

A)They are following the NCTM requirements.
B)They are following the mandate of the CCSSM.
C)They want to involve real-world application problems.
D)They want to connect a variety of mathematical topics.
E)They want to integrate students into the same classroom.

Question 32

Which of the following represents a Pythagorean Triple?

A)2-3-4.
B)3-4-7.
C)5-12-13.
D)7-21-23.
E)9-15-16.

Question 33

Which of the following is the sequence of triangular numbers?

A)1, 3, 6, 9, 12, ...
B)1, 3, 6, 10, 15, ...
C)3, 6, 9, 12, ...
D)3, 6, 10, 15, ...
E)3, 9, 27, 81, ...

Question 34

Which of the following can generally be done on a "hand-held computer" that cannot be done with a "graphing calculator?"

A)Manipulate algebraic symbols.
B)Sketch graphs of trigonometric functions.
C)Perform computation with matrices.
D)Determine maxima and minima for quadratic functions.
E)Find combinations and permutations.

Question 35

If you multiply a matrix representing a polygon by a 2 x 2 matrix having rows of 0, 1 and -1, 0, what is the result?

A)A translation of 1 unit to the right.
B)A reflection over the x-axis.
C)A reflection over the y-axis.
D)A clockwise rotation of 90°.
E)A counter clockwise rotation of 90°.

Question 36

If you add a matrix representing a triangle to a 2 x 3 matrix having rows of 2, 2, 2 and 0, 0, 0, what is the result?

A)A translation of 2 units to the right.
B)A translation of 2 units up.
C)A dilation with a scale factor of 2.
D)A reflection over the line y = 2.
E)A reflection over the line x = 2.

Question 37

Which of the following is a significant benefit to using an integrated approach to teaching mathematics?

A)Research strongly suggests that an integrated approach results in greater long-term retention of material than traditional sequences.
B)Less time needs to be spent each year on reviewing material from the previous course.
C)Most colleges and universities now expect their undergraduates to have some experience with having taken integrated mathematics courses.
D)Many topics from the traditional curriculum can be omitted, making it easier to explore all required outcomes.
E)The cost of implementing an integrated sequence of courses is considerably less than using a traditional sequence.

Question 38

Which of the following educational practices often results in students experiencing different mathematical content?

A)Differentiating.
B)Tracking.
C)Integrating.
D)Modeling.
E)Clustering.

Question 39

Some schools or districts choose not to use an integrated approach.Which of the following is NOT a reason discussed in Chapter 4?

A)Availability of resource materials.
B)Difficulty level of teaching.
C)Lack of research.
D)Teachers would rather continue with the same textbook series.
E)Tradition.

Question 40

Why did the integrated approach fall to the wayside in past history, according to the author in Chapter 4?

A)Teachers were uncomfortable with teaching the material.
B)Students were not retaining knowledge.
C)The integrated approach became a track that was deemed more appropriate for vocational students.
D)The Back to the Basics reform movement occurred.
E)The New Math reform movement occurred.

Question 41

According to a study published in 2001, which of the following is true about the achievement of students enrolled in the integrated verses the traditional sequence of mathematics courses?

A)Students continue to be successful on the SAT but are less likely to complete upper-level mathematics classes.
B)Students tend to be less successful on tests such as the SAT but tend to complete more upper-level mathematics classes.
C)Students tend to score about the same on SAT tests but are more likely to complete upper-level mathematics classes.
D)Students tend to score higher on AP exams but are less likely to complete upper- level mathematics classes.
E)Students tend to score about the same on SAT and AP exams but are less likely to complete upper-level mathematics classes.

Question 42

Which of these refers to broad statements of what a student should be able to achieve as a result of participating in the district's program?

A)Beliefs.
B)Objectives.
C)Goals.
D)Guidelines.
E)Philosophy.

Question 43

Broad, open-ended questions that are used to drive a lesson or sequence of lessons are referred to as which of the following?

A)Essential.
B)Affective.
C)Conceptual.
D)Objective.
E)Goal-Oriented.

Question 44

What are specific statements that describe what a student should feel, know, or be able to do at each grade level?

A)Accomplishments.
B)Tasks.
C)Goals.
D)Objectives.
E)Skills.

Question 45

Which of the following describes a current shift in educational practice?

A)More districts are using pupil performance objectives.
B)States are moving away from the use of goals.
C)Educators are moving away from the use of behavioral objectives.
D)Fewer districts are using Standards in lesson planning.
E)Checklists of required skills are becoming more common.

Question 46

Which of the following is NOT a step in the "unpacking" process with regards to Standards?

A)Determining key questions.
B)Creating a sequence and pace for instruction.
C)Identifying a Standard.
D)Generating a list of skills and central concepts to be taught.
E)Comparing content in textbooks and materials to what is stated in the Standards.

Question 47

Which of the following term represents the process of determining performance assessments for students prior to planning for classroom teaching?

A)Backward Design.
B)Formative Assessment.
C)Unpacking.
D)Summative Assessment.
E)Understanding Assessment.

Question 48

Which of the following represent the three categories in which objectives are grouped?

A)Affective, behavioral, and cognitive.
B)Affective, behavioral, and psychomotor.
C)Affective, cognitive, and psychomotor.
D)Behavioral, cognitive, and concept.
E)Behavioral, concept, and psychomotor.

Question 49

Which type of objective refers to attitudes or feelings?

A)Affective.
B)Attitudinal.
C)Behavioral.
D)Cognitive.
E)Psychomotor.

Question 50

Which type of objective refers to skills and concepts the student should be able to understand?

A)Affective.
B)Behavioral.
C)Cognitive.
D)Dispositional.
E)Psychomotor.

Question 51

In which of the following subject areas do we typically find psychomotor objectives?

A)History.
B)Science.
C)Mathematics.
D)The Arts.
E)English.

Question 52

Consider the following objective: "The student will display interest and curiosity in problem solving." Under which classification would this objective be placed?

A)Active.
B)Affective.
C)Cognitive.
D)Concept.
E)Psychomotor.

Question 53

Which type of objective tends to be the most difficult to measure?

A)Active.
B)Performance.
C)Affective.
D)Cognitive.
E)Psychomotor.

Question 54

According to Bloom's original Taxonomy, which of the following represents the highest level of cognition?

A)Application.
B)Evaluation.
C)Knowledge.
D)Analysis.
E)Comprehension.

Question 55

In the revised Bloom's Taxonomy, which of the following is NOT one of the four levels of knowledge?

A)Factual Knowledge.
B)Applied Knowledge.
C)Conceptual Knowledge.
D)Metacognitive Knowledge.
E)Procedural Knowledge.

Question 56

According to Marzano's model of cognition, which verbs describe the highest level, known as knowledge utilization?

A)Integrating and symbolizing.
B)Matching and classifying.
C)Problem solving and investigating.
D)Recognizing and recalling.
E)Summarizing and paraphrasing.

Question 57

Consider the following objective: "Given the length of one side of a right isosceles triangle, the student will determine the lengths of the other two sides without the use
of a calculator." Under which classification would this objective be placed?

A)Affective.
B)Knowledge and skill.
C)Concept.
D)Application.
E)Psychomotor.

Question 58

Consider the following objective: "Given the general equation , the $y = a ( x - h ) ^ { 2 } + k$ student will describe the effects of the parabola as the value of 'a' is changed." Under which classification would this objective be placed?

A)Affective.
B)Knowledge & skill.
C)Psychomotor.
D)Application.
E)Concept.

Question 59

Consider the following objective: "Given a spherical object, a tape measure, and a calculator, the student will determine the diameter, circumference, surface area, and
volume of the object." Under which classification would this objective be placed?

A)Affective.
B)Knowledge & skill.
C)Concept.
D)Application.
E)Psychomotor.

Question 60

Which cognitive objective is the simplest, the most straightforward, and the easiest to measure?

A)Knowledge and skill.
B)Concept.
C)Application.
D)Performance.
E)Psychomotor.

Question 61

Which type of objective is most likely to require a student to explain how or why a problem was solved in a particular way?

A)Affective.
B)Performance.
C)Concept.
D)Psychomotor.
E)Knowledge & skill.

Question 62

Which of the following objectives would be considered vague to most classroom teachers?

A)Given a ruler and a piece of string, the student will be able to measure the length of the string to the nearest centimeter.
B)Given a third-degree polynomial, the student will be able to determine its roots.
C)Given a set of algebra tiles, the student will demonstrate the geometric meaning of the distributive property.
D)Given a geoboard, the student will demonstrate an understanding of triangles.
E)Given a geometric sequence, the student will extend the pattern and generate a formula describing the sequence.

Question 63

Which of the following terms refers to the process of scheduling the sequence and timing for teaching topics in a school year?

A)Application of Standards.
B)Backward Design.
C)Textbook Analysis.
D)Cognitive Structuring.
E)Curriculum Mapping.

Question 64

Which of the following should be the purpose of a textbook and the related teacher's manual?

A)To determine the sequence of topics to be explored in a course.
B)To make it convenient for the instructor to teach all required topics.
C)To provide consistent assessment items.
D)To serve a resource and a guide.
E)To define the curriculum.

Question 65

How do most textbooks and a set of Standards usually compare?

A)The Standards often include considerably more content than would ever be found in a book.
B)Textbooks often include more content than is specified in the Standards.
C)The Standards and textbook generally include the same content.
D)The textbook often serves as the Standards.
E)Most of the content in a typical set of Standards is not included in the textbook at all.

Question 66

Which of the following is LEAST likely to be included in a teacher's resource file?

A)Assignment ideas.
B)Master copies of handouts.
C)Previously-used tests and quizzes.
D)Lesson plans.
E)Classic mathematics problems.

Question 67

Which term is used to represent the tendency to try something for a few years and then abandon it for another trend, only to return to the original plan several years
later?

A)The See-Saw Effect.
B)The Generation Effect.
C)The Pendulum Effect.
D)The Reform Movement.
E)The Boomerang Theory.

Question 68

Which of the following is NOT stated in the 1989 NCTM curriculum Standards as a topic which should have "decreased emphasis"?

A)Multiplication of polynomials.
B)Simplifying complex fractions.
C)Simplifying radicals.
D)Solving quadratic equations by hand.
E)Trinomial factoring.

Question 69

Which of the following most accurately describes the recommendation for high school course sequencing in the Common Core State Standards for Mathematics?

A)High school courses should be integrated.
B)High school courses should follow a sequence of Algebra I, Geometry, Algebra II.
C)High school courses should follow a sequence of Algebra I, Algebra II, Geometry.
D)High school course sequences should be left up to individual states and districts.
E)High schools should offer both an integrated and a traditional course sequence.

Question 70

List the Conceptual Categories of the Common Core State Standards for Mathematics. Then, describe how the Standards are used for curriculum planning and for writing objectives.

Question 71

Discuss the content and format of the Common Core State Standards for Mathematics.Be sure to include a discussion of why the CCSSM were developed and how they are being used.

Question 72

Describe the academic benefits of teaching an integrated mathematics sequence.Then, list some of the reasons why many schools continue to teach a traditional sequence of algebra and geometry courses.

Question 73

Choose any two of the three core curriculum models described in Chapter 4 and explain in detail how students are grouped, how the model operates, and some possible advantages and disadvantages of implementing each of them.

Question 74

State and define each of the levels of cognition as described by Bloom's Taxonomy. Include an example of an objective at each level.Describe how more recent revisions of the Taxonomy have improved upon its design.

Question 75

Explain at least four ways of locating resources that support teaching to a set of Standards beyond the textbook and its related teacher's manual.