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Chapter 1: Teaching Mathematics in the 21st Century
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
1) 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
2) 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
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
3) The person who will play the greatest role in shaping how the mathematics students will learn is
_____________.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
4) 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.
5) 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.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
6) 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.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
7) 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.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
8) 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.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
9) 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.
10) The Five Process Standards are the mathematical processes through which students should acquire
knowledge and should not be thought of as separate content in the curriculum.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
11) The Five Process Standards are 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.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
12) What statement best reflects the Connections standard of the Five Process Standards from 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.
13) Which of the following represents a true statement about the Curriculum Focal 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.
14) 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.
15) The Standards for Mathematical Practice are
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.
16) 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.
17) 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.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
18) 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.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
19) Analysis of 81 videotaped lessons from U.S. classrooms showed not one example of high-level
mathematics content.
20) 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.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
21) 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.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
22) 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.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
23) There are certain characteristics that one needs to succeed as a teacher of mathematics. Name two of them,
and explain why they are essential.
Chapter 1
