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Elementary Education
Q:
Decimal concepts are good for developing number sense, but don"t have connections to many real-life situations.
Q:
Teacher directions spoken in the language of doing mathematics center around verbs that require lower-level thinking, such as listenand memorize.
Q:
The 10 to 1 relationship of place value extends infinitely in both the whole number and decimal directions.
Q:
Which of the following is an example of a statement spoken in the language of doing mathematics?
a) "Memorize these steps."
b) "Compute this answer."
c) "Explain how you solved the problem."
d) "Copy down these steps into your notebooks."
Q:
The role of the decimal point is to designate the _____________position by sitting just to the right of it.
Q:
Which statement below best describes the idea of mathematics as engaging in the science of pattern and order?
a) Mathematical processes and concepts follow logical patterns and have a logical order. Students are capable of and should be allowed to explore this regularity and make their own sense of mathematics.
b) Students develop conceptual understanding and become less confused when they are given a specific set of logical, orderly steps to solve each type of math problem.
c) Students best acquire efficient methods for computing with timed drills.
d) To avoid confusion and be successful in all mathematics, students must develop conceptual understanding of topics in a very specific order.
Q:
The base-ten system and place value
a) Are not at all related to decimal numbers.
b) Of whole numbers should be reviewed with students as a way to connect previous knowledge to the decimal place values.
c) Of whole numbers frequently involves regrouping, which is not needed in the decimal place value system.
d) Of decimal numbers is not easily shown with models like that for whole numbers is.
Q:
There are certain characteristics that one needs to succeed as a teacher of mathematics. Name two of them, and explain why they are essential.
Q:
Which of the following is NOT a common misconception about fraction computation?
a) Multiplying always results in a bigger number, while dividing always make a number smaller.
b) Fractions have to have a common denominator for all computation.
c) Procedures developed from conceptual understanding are usually easier than the standard algorithms.
d) Estimation is not important.
Q:
Negative preconceived notions that students and their families may have about mathematics are so hard to overcome that there is nothing the teacher can do to reverse them.
Q:
A common, but frequently misunderstood, method of teaching faction division is to tell students, "____________________ the second fraction and multiply."
Q:
In this ever-changing world, those who love mathematics will likely survive the ups and downs of the economy. Which of the following is NOT a contributing factor to this fact?
a) Society is becoming more reliant on technology and the data it produces.
b) There are countless jobs in which people do simple computation.
c) Teachers are currently preparing students for jobs that don"t yet exist, and they will likely need to be skilled at approaching problems in different ways.
d) The world is surrounded by algorithms that help make predictions.
Q:
The _______________________ interpretation of division is seen in this example: "Melissa has 2-1/2 yards of fabric and wants to make shirts that use yard each. How many shirts can she make?"
Q:
Analysis of videotaped lessons from countries outside of the United States showed, in contrast to those from the United States, an emphasis on conceptual understanding and problem-solving.
Q:
A mixed number must be turned into an improper fraction before one can use it in a multiplication problem.
Q:
Analysis of 81 videotaped lessons from U.S. classrooms showed not one example of high-level mathematics content.
Q:
The algorithm for fraction multiplication
a) Can be discovered by students when they see patterns emerge from the problems they solve with models.
b) Should be discovered after only a few days of working with contextual examples and models.
c) Does not need to be connected to a real-life context because it's the easiest of all fraction computation algorithms.
d) Requires common denominators.
Q:
The original Trends in International Mathematics and Science Study (TIMSS) labeled the U.S. mathematics curriculum ___________________________________________________, meaning that it was very unfocused, required coverage of many more topics than other countries, had a great deal of repetition, and, consequently, frequently failed to provide opportunities to learn topics with depth.
Q:
Although an area model is very useful for modeling whole number multiplication, it is not easily applied to fraction multiplication.
Q:
The National Assessment of Educational Progress
a) Consists of data collected by individual school districts so they may assess their teachers.
b) Reported in 2009 that less than half of all fourth- and eighth-graders performed on a standardized mathematics test at the desirable levels of "proficient" or "advanced."
c) Showed dramatic decreases in U.S. mathematics scores over the last 30 years.
d) Produced results in 2009 that indicated U.S. students would likely reach the goal required by No Child Left Behind legislation that all students perform at or above a proficient level by 2014.
Q:
Students should be introduced to fraction multiplication with problems that require finding fractions of whole numbers.
Q:
Mathematics Teaching Today lists six major components of the mathematics classroom that are necessary to allow students to develop mathematical understanding. Which of the following below is NOT a true statement about these components?
a) Teachers should maintain a balance between focusing on conceptual understanding and procedural fluency.
b) The learning environment should allow all students an equal opportunity to learn.
c) Students should use their own mental abilities, rather than technology, to enhance their understanding.
d) Teachers should use multiple assessments aligned with instructional goals.
Q:
Talking explicitly about common misconceptions only causes students to develop them.
Q:
The Standards for Mathematical Practiceare
a) A component of the Common Core State Standards that outlines a series of important mathematical processes all students should be able to do regularly.
b) Important for students to be able to do, but are not actually a part of the Common Core State Standards.
c) A set of basic computation skills that students should have to enhance their problem-solving ability.
d) A series of common summative assessments to help teachers better understand their students' individual needs.
Q:
When subtracting mixed number fractions, it is helpful to
a) Deal with the whole numbers first and then work with the fractions.
b) Always trade one of the whole number parts into equivalent parts.
c) Avoid this method until the student fully understands subtraction of numbers less than one.
d) Teach only the algorithm that keeps the whole number separate from the fractional part.
Q:
The Common Core State Standards
a) Provide a framework of essential big ideas and mathematics concepts for preschool-aged children.
b) Have been adopted by less than half of the states so far.
c) Provide a focused set of mathematical content standards and practices for use across states that adopt them.
d) Was developed by a highly selective group of teachers.
Q:
Adding and subtracting with unlike denominators
a) Should be introduced at first with tasks that require both fractions to be changed.
b) Is sometimes possible for students, especially if they have a good conceptual understanding of the relationships between certain fractional parts and a visual tool, such as a number line.
c) Is a concept understood especially well by students if the teacher compares different denominators to "apples and oranges."
d) Should initially be introduced without a model or drawing.
Q:
Which of the following represents a true statement about the CurriculumFocal Points?
a) They were developed by the National Council of Teachers of Mathematics and specify the big ideas of the most significant concepts and skills for each grade level.
b) They are a selected group of sample tests from large urban school districts.
c) Many school districts have avoided adopting them, and they will likely disappear soon.
d) They were designed to assess traditional mathematics content and are not good for assessing students' conceptual understanding.
Q:
Which of the following is NOT an example of a linear model for adding and subtracting factions?
a)Mary needs 3-1/3 feet of wood to build her fence. She only has 2-3/4 feet. How much more wood does she need?
b) Milly is at mile marker 2-1/2. Rob is at mile marker 1. How far behind is Rob?
c)Half a pizza is left from the 2 pizzas Molly ordered. How much pizza was eaten?
d)What is the total length of these two Cuisenaire rods placed end to end?
Q:
What statement best reflects the Connectionsstandard of the Five Process Standardsfrom Principles and Standards for School Mathematics?
a) Students should be able to interpret and create various symbolic representations of mathematical ideas.
b) Students should be able to connect personally to their fellow classmates in order to fully enjoy the learning process.
c) Students should be able to explain and justify the thought process behind their arguments.
d) Students should be given opportunities to see how various mathematical ideas relate to one another and to a variety of real-life experiences.
Q:
To help students develop strategies for fraction addition and subtraction
a) They should be given lots of practice with just plain computation before they are confused by the addition of word problems.
b) They should be provided with problems that always use the same kind of model, to promote a deeper understanding.
c) Mixed numbers and fractions should be taught separately.
d) Addition and subtraction situations should be mixed.
Q:
The Five Process Standardsare the mathematical processes through which students should acquire knowledge. The big idea of the ___________ standard is that students should be able to use a variety of representations, such as symbols, charts, graphs, manipulatives, and diagrams to express mathematical ideas and relationships.
Q:
Students traditionally perform better at computing with fractions than they do at estimating with them.
Q:
The Five Process Standardsare the mathematical processes through which students should acquire knowledge and should not be thought of as separate content in the curriculum.
Q:
Estimation of fractions can result in estimates that are not close to the actual computed answer and should be avoided.
Q:
Because each of the five content standards is present across all grade-level bands, teachers should infer that they should all be emphasized equally in every grade.
Q:
Name two of the major guidelines to consider when developing computational strategies for fractions. Describe an instructional sequence that would support each guideline.
Q:
Which of the following is a true statement about the learning principle?
a) As long as students have their basic facts and procedures memorized, they do not have to understand how the mathematics works.
b) Due to technology, it is no longer necessary for students to practice computational skills.
c) To build confidence, students should be taught to not evaluate the mathematical ideas of others.
d) Learning is strongly enhanced when students are encouraged to make and test their own mathematical conjectures.
Q:
When comparing fractions
a) Students' understanding of whole numbers and what makes a "bigger number" can result in erroneous thinking.
b) The usual methods, finding common denominators and cross multiplying, help students develop understanding of various fraction sizes, even when they have not invested a lot of thought into the concept.
c) It is not helpful to compare the fractions to another common benchmark fraction.
d) Teachers should not add complication to students' practice by asking them to compare fractions that are equal.
Q:
The curriculum principle highlights the importance of having instruction built around a series of ______, so that they may see how mathematics is an integrated whole, rather than a collection of isolated bits and pieces.
Q:
The ______________________________________number property is essential to students' understanding of the equivalent fraction algorithm.
Q:
The six Principles and Standards for School Mathematics articulate high-quality mathematics education. What statement below represents the equity principle?
a) Mathematics today requires not only computation skills, but the ability to think and reason.
b) The message of high expectations for all is intertwined with every other principle.
c) Calculators and computers should be seen as essential tools for doing and learning mathematics.
d) Coherence speaks to the importance of building instruction around big ideas.
Q:
Which of the following is NOT an effective model of fraction equivalence?
a) The slope of a line
b) Shapes created on dot paper
c) Plastic, circular area models
d) Clocks
Q:
One of the most important features of the Principles and Standards for School Mathematics is the articulation of six principles that are fundamental to high-quality mathematics education.
Q:
In the case of fraction equivalence, it is best to allow students the extra time to develop a conceptually-based algorithm.
Q:
NCTM emphasized in Principles and Standards for School Mathematics the fact that, as long as students receive high-quality instruction, regular assessment is frequently not a good use of instructional time.
Q:
When estimating with fractions, it is important to keep in mind that students find estimation easier than computation with fractions, so they don"t need a lot of practice. Time should be devoted to computation.
Q:
The person who will play the greatest role in shaping how the mathematics students will learn is _____________.
Q:
Improper fractions
a) Is a clear term, as it helps students realize that there is something unacceptable about the format.
b) Should be taught separately from proper fractions.
c) Are best connected to mixed numbers through the standard algorithm.
d) Should be introduced to students in a relevant context.
Q:
Which of the following is NOT a source of the change that has been occurring in mathematics education within the last 20 years?
a) Cuts to school district budgets
b) Knowledge gained from education research
c) The professional leadership of the National Council of Teachers of Mathematics (NCTM)
d) Less than exemplary performance of U.S. students in national and international studies
Q:
The process of iterating
a) Is not as important to conceptual understanding of factions as partitioning is.
b) Is not consistent with the concept of length.
c) Has a tendency to be more difficult for students when it is used with set models.
d) Is not a good way to help students make a transition from fractions to mixed numbers.
Q:
Which choice reflects two important elements for becoming an effective teacher of mathematics?
a) Manipulatives and an overhead projector
b) Knowledge of mathematics and how students learn
c) Internet sites and computer software
d) Student records and interviews with experienced teachers
Q:
Dividing a shape into equal-sized pieces is called ________________________.
Q:
A common misconception between students is that fractional parts must be the same shape as well as the same size.
Q:
It is important for students to recognize that, regardless of the context, 1/2 is always bigger than 1/3.
Q:
In a __________________________model, the whole is understood to be a collection of objects, and subsets of the collection make up fractional parts.
Q:
A number line is a very useful model for fractions because
a) It does not help build conceptual understanding that a fraction represents one number.
b) It allows comparisons of the fraction's size relative to other numbers.
c) Due to its length, it is hard to connect it a real-life example, measurement.
d) It makes it difficult for students to see how one can find a fraction between any set of two fractions.
Q:
_______________________________________ rods are a kind of length model that provide lots of flexibility.
Q:
Which is NOT a category of fraction models?
a) Set
b) Area
c) Piecewise
d) Length
Q:
As long as the teacher is using models of fractions, it is not necessary to use a variety of kinds.
Q:
Researchers have described a number of reasons that students have a tendency to struggle with fraction concepts. Name two of these reasons, and describe a method a teacher might use to address each.
Q:
The part-whole construct is the concept most associated with fractions, but other important constructs they represent include all of the following EXCEPT
a) Measure
b) Reciprocity
c) Division
d) Ratio
Q:
Describe three different ways algebra can be connected to other areas of the mathematics curriculum.
Q:
Describe two different ways you could determine whether a function is linear. Describe how these two methods relate to one another, and a possible classroom activity that would help students to see this connection.
Q:
Functions can be represented in five ways: context, table, verbal description, symbolic equation, or____________________.
Q:
The rate of changeof a linear function can be determined from a graph by examining the line's _________.
Q:
A proportional relationship
a) Can only be represented with an equation.
b) Will always have a graph that forms a straight line and passes through the origin.
c) Will always have a positive slope.
d) Is much more challenging for students to generalize than a non-proportional one.
Q:
When students create graphs of functions
a) They are representing them in the manner that makes it the hardest to visualize relationships between patterns.
b) They should place the independent variable (step number) along the vertical axis.
c) It is helpful to provide them with examples within a real-life context.
d) They should always be given specific data, equations, or numbers.
Q:
Students are more likely to describe the explicit formula for a function verbally before they will be able to describe it symbolically.
Q:
Growing patterns
a) Are frequently functions.
b) Are best represented by numbers only.
c) Should not include fractions and decimals.
d) Have either a recursive formula oran explicit formula.
Q:
Which of the following is a true statement about repeating patterns?
a) Children's literature is not a good source of examples.
b) The core of the pattern is the string of elements that repeats.
c) It is overly confusing to show young children the same pattern constructed with different materials.
d) It is difficult, but worthwhile, to find examples from the real world.
Q:
When helping students to develop a conceptual understanding of number properties, it is helpful to
a) Provide students with a list or properties to examine and memorize.
b) Build them into students' explorations with number sentences.
c) Encourage students to only use mathematical symbols to express the properties.
d) Discourage students' conjectures, as they lead to confusion.
Q:
Which of the following is NOT a true statement regarding simplifying expressions and equations?
a) For many students, they have been abstract, meaningless tasks.
b) They are not essential skills to working algebraically.
c) They are specifically mentioned in the NCTM Curriculum Focal Points.
d) Students can gain a better understanding if they examine examples with errors and explain how to fix them.
Q:
The in an open sentence plays the same role as a __________________, which frequently takes the form of a letter.
Q:
The use of true/false and open sentences
a) Can help clarify for students the meaning of the equal sign.
b) Is only appropriate for students of middle school age and up.
c) Is not an effective method of helping students to develop relational thinking.
d) Should only involve textbook and teacher-created problems.
Q:
Which of the following is NOT true regarding students' understanding of the = sign?
a) Because of their early experiences, many students tend to believe the = sign represents "and the answer is."
b) It is important, because the = sign is one of the principle methods of representing important relationships within the number system.
c) The = function can be represented concretely by a number balance scale, which can lead to deeper conceptual understanding.
d) Failure to understand the = sign does not usually cause difficulties understanding the process of solving equations.
Q:
A ___________________________ is a tool, normally thought of as teaching numeration, that can help students to connect number concepts and algebraic thinking.
Q:
Which of the following is NOT one of the five forms of algebraic thinking described by Kaput?
a) Meaningful use of symbols
b) Generalization from arithmetic and from patterns in all of mathematics
c) Number classification
d) Study of patterns and functions
Q:
Of the options below, the earliest form of algebraic thinking demonstrated by a student would most likely be
a) Graphing linear functions.
b) Recognizing and generalizing patterns.
c) Working with expressions that involve variables.
d) Making conjectures about number properties.
Q:
Children typically have no difficulty understanding the meaning of the = symbol.