Math Methods Final Exam

Which of the following is an example of a poorly worded question?

"Does everyone understand the homework now?"

If students use graph paper to explore decimals and a 10 x 10 grid represents 1, then what would a single square represent?

.01

Which of the following statements most accurately represents NCTM's view of the teaching of algebra?

Algebra should be integrated into the curriculum so that all students have access to the topic

Which of the following statements is specifically included in the NCTM Standards for the teaching of algebra?

All students should be able to analyze change in the contexts

Which of the following is NOT a reason why a mathematics teacher should give a homework assignment?

An assignment should be given on a previously mastered skill to keep students into the routine of doing homework

Which of the following most accurately describes the assess principle in Principles and Standards for School Mathematics?

Assessment should provide useful information that supports the learning of mathematics

Some teachers check homework by having students keep a notebook of the week's assignments and hand it in on Fridays for checking. According to the author in Chapter 11, what is the most significant ADvantage to using this technique?

students are given the opportunity to revise solutions before handing them in

According to the NCTM, which of the following groups of students have NOT historically been "victims of low expectations"?

students from rural communities

Which of the following practices for the teaching of probability is supported by research as an effective way to develop student thinking?

students should explore data sets and suggest their own probability questions

The exploration of geometry without using coordinates is referred to as which of the following?

synthetic

Which of the following is a paradox of Koch's Snowflake?

the perimeter is infinite, but the area is bounded

For some teachers, the majority of assessment data is collected through an end-of-the-unit test. What is the greatest error that the teacher is making in doing this?

the teacher finds out too late that students need intervention

Some teachers check homework by reading the correct solutions from an answer book, and having the students ask questions, when necessary. According to the author in Chapter 11, what is the most significant disadvantage to using this technique?

this technique promotes the image of the teacher as the authority

Generally, standardized tests are administered for which of the following purposes?

to determine the effectiveness of a mathematics program

If a special education student is on an IEP, then regular assessments are conducted by the teacher primarily for what purpose?

to track the progress of the student in meeting goals

Which of the following does NOT comprise a type of algebraic reasoning?

using tools, such as a straightedge

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

writing the equation of a line

What term is used for assessment procedures that involve the collection of data for the purpose of giving feedback to students throughout the learning cycle?

formative assessment

Which of the following describes a geometric shape that is generated by starting with an initial image and then applying successive iterations of a rule?

fractal

Which of the following is a property of all fractal images?

fractals are self-similar

Which of the following is NOT a rationale for using games in the mathematics classroom?

games require relatively little preparation time

Which of these is generally the LEAST likely to be associated with the term "assessment" even by other educators?

gathering information

Which of the following ethnic groups do Caucasian students tend to outperform?

hispanic and african american students

Which of the these represents a traditional but important way for teacher to collect formative assessment data of students progress?

homework

The sample lesson in Chapter 9 in which students explore an episode involving drinking a pitcher of tea leads them to the exploration of which concept?

iteration and recursion

Which of the following is an assessment tool that includes writing which reflects daily student thinking, problem-solving approaches, and opinions?

journal

In addition to not addressing the cultural needs of african american students, which of the following is also a cited in Chapter 12 as a major contributing factor to failure in inner city schools?

lack of financial resources

What is the possible explanation for why males have historically outperformed females on mathematics achievement tests?

males have tended to take more upper level mathematics courses

Which of these most accurately describes the roles of "number sense" and "algebra" in the mathematics curriculum, according to Principles and Standards for School Mathematics?

Content Strands

The PSAT, SAT, and ACT examinations result in scores that tell students how they compare to the performances of other students across the country. These tests are referred to as which of the following?

norm-referenced assessment

What is important for a teacher to do to make mathematics teaching tools become worthwhile?

Effectively generate classroom discussion or discourse

The assumption that "all students have a right to equally accessing all areas of the curriculum as well as access high-quality instructional materials and reaching" is the definition of which term?

Equity

The assumption that all students have the right to access quality mathematics curriculum and teaching is referred to as which of the following?

Equity

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

Factoring trinomials

Which of the following is NOT considered an area of the study of discrete mathematics?

Functions

What should be the order in distribution materials for use in hands-on activities?

Give directions, then hand out the materials

Determining the path that a snowplow should follow to clear all of the roads, while minimizing how many roads have to be traversed twice, is typical of which type of discrete mathematics problem?

Graph Theory

When teaching a lesson on adding decimals in the middle school, which of the following are considered the "best" tools for a teacher to use?

It depends on the situation

According to the author in Chapter 8, which of the following represents a common flaw in the structure and order of traditional textbooks in mathematics?

Mathematics topics may appear to be disconnected

Which homework checking strategy is recommended in Chapter 11 as being the best choice?

One is not necessarily better than the other; teachers should choose a strategy that is consistent with their values and beliefs

One suggestion for promoting equity through assessment is to ensure that assessment goals are made clear to the students. Which assessment standard is illustrated in this suggestion?

Openness standard

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

Reasoning

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

Reasoning and sense making should work together when solving problems

Which of the following refers to the ability to look back on a lesson or teaching episode and analyze it from every angle, thinking about what worked and what didn't?

Reflection

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

Sense Making

Which of the following words describes the regular collection of formative assessment data to inform instruction?

Short-cycle assessment

What is the main reason that specific rules for the use of manipulatives should be established?

Students are tempted to exhibit off-task behavior

Which of the following is an implication of achieving equity through assessment?

Students should be able to demonstrate understanding in ways that are consistent with their learning styles

Which of the following statements most accurately describes classroom assessment?

Students should be able to predict their final grades

If a teacher intends to use observation and checklists as part of the assessment of a unit in a class, what "rule of thumb" should be followed?

Students should be provided with the criteria that will be used when observing them

Which of the following statements about scoring items on a test is most accurate?

Students should receive credit for demonstrating mathematical thinking on a test

Suppose that several students in a mathematics class choose an alternative to taking a paper-pencil test. Which of the following is NOT a reasonable way for those students to spend class time while their peers are taking tests?

Students spend the class time running errands for the teacher

When students are involved in developing their own scoring rubric for a project, which of the following is most likely to result?

Students take ownership in the project

What term is used for assessment procedures that represent a final evaluation of a student's performance at the end of a course or grading period?

Summative assessment

Why are problems drawn from the area of discrete mathematics often motivating to students in a mathematics class?

The problems tend to be applied to the real world

What does it mean if a question is considered "closed"?

The question has only one expected and correct response

Which of these is a fundamental responsibility of the teacher?

The teacher should seek ways to engage all students in the learning process

What does it mean if a question is considered "open-ended"?

There is not always necessarily one, correct answer

Some teaches check homework by having the students put all of the assigned problems on the board. According to the author in Chapter 11, what is the most significant disadvantage to using this technique?

This strategy does not make good use of class time for most students

What is the purpose of "free play" with manipulatives?

To have students explore and experiment

Bulletin boards are recommended for what purpose?

Utilitarian, showcasing students work, publishing a "problem of the week", and promoting understanding through interactive problems

Which of the following educational theorists studied the way that children learn geometry?

VanHiele

Which of the following questions is likely to help students reason mathematically?

What do others think about what John said?

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

Writing two-column proofs

Which of the following is generally not included in an IEP?

a description of the student's medical history

Which of the following would be considered teaching tools in a geometry class?

pattern blocks, algebra tiles, paper folding, geoboards

Which of the following does NOT comprise the language of algebra?

polygons

What is purposeful collection of work, assembled by a student, to show what the students knows and is able to do?

portfolio

Which of these is NOT an accurate statement about the use of portfolios as an assessment strategy in mathematics?

portfolio assessment has a long history in mathematics education, so many models are available to teachers

Which of the following is NOT considered a possible representation of a function?

problem whose solution is a function

Which of the following factors does the NCTM view as the most important component for achieving equity?

professional development of teachers

What is suggested as a way to make journals manageable for a secondary or middle school teacher who might teach 150 students?

rotate classes so that all journals are not read on the same day

Which of the following refers to the initial image on which a fractal image is generated?

seed

Which of the following represents a definition of "statistics," as determined by a conference on the teaching of statistics?

statistics is the science of learning from data

Which of the following content areas is LEAST likely to have been part of most people's mathematical experiences?

Discrete Mathematics

If a teacher has the class use metric measurements to explore decimals with a decimeter representing a unit, then how would 6.93 be represented?

6 decimeters, 9 centimeters, and 3 millimeters

Which term(s) apply to the number 12?

Abundant and Composite

Which of the following is NOT associated with Pedagogical Content Knowledge?

Access to appropriate teaching tools

The sample lesson in Chapter 9 in which students take a phony True-False quiz leads them to the exploration of which concept?

Determining the probability of an event

The exchange of ideas in the mathematics classroom is referred to in Mathematics Teaching Today as which of the following?

Discourse

Which of the following is recommended in Chapter 11 as a way to teach secondary or middle school students about the value of pi?

Have the student measure the circumference and diameters of several objects and calculate the ratios to approximate the value of pi

Which of the following questions is referred to in Chapter 11 as the most important issue to consider when devising a grading system?

How well will I get to know the development of each of my students by using this system?

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

Imaginary Numbers

What is it called when students with speical needs remain in a classroom with peers, with support services made available?

Inclusion

In a cooperative learning environment, the work is done as a team, but in the end, each student is required to demonstrate an understanding of the concepts through an interview, a written test, or some other means. What term describes this concept?

Individual accountability

What does IEP mean?

Individualized educational program

When a student asks "Is this going to be on the test?" what is the studen really saying to the teacher?

Is this concept important?

Determining how much money would be in a bank account at the end of a period of time is typical of which type of discrete mathematics problem?

Iteration and recursion

Which of the following if NOT one of the Tips on Manipulative Use that is mentioned in the text?

Keep in mind that students "inherently" learn when they use manipulatives, so materials should be a regular part of the classroom

According to the author in Chapter 8, equally important to adding and subtracting decimals is a student's ability to do which of the following?

Look for structures in the numbers

Which statement most accurately describes homework assignments typically given by mathematics teachers in the US?

Teacher is the US generally assign more homework than in other countries and place a higher value on the homework in grading

When assisting students with simple mental arithmetic such as 6 x 13, a teacher can lead the students into thinking of the problem as 6(10+3) and adding 60+80. Which property is being reviewed?

The Distributive Property

Suppose that a teacher regularly uses mathematical projects to asses student progress as an alternative to paper-pencil tests, but is often unclear about how the projects will be scored. Which assessment standard is address, and which standard is being violated?

The equity standard is address, the openness standard is violated

Teachers often assign the even numbered problems at the end of a section in a mathematics book as homework. Which of these is NOT a significant problem with this practice

The even numbered problems generally do not include solutions in the back of the book

The exploration of geometry by using coordinates is referred to as which of the following?

analytic

The inclusion of review items on a test is most likely to promote which of the following mathematical processes?

connections

Proficiency tests are generally aligned with a state's model or curriculum standards and are, therefore, classified as which of the following?

criterion-referenced tests

When a student expresses his/her thinking in a journal, that student becomes more likely to contribute answers in class. Consequently, which of the following is often enhanced by journal writing?

discourse

Ideally, the classroom environment should foster which of the following?

emphasis on discovery and thinking

Which of the following has significantly influenced the collection and analysis of data in society in the recent past?

enhanced technology