Chapter 16 Test Bank:
Helping All Students Succeed in Mathematics
16.1 Students in the United States, across all achievement groups, are not faring well in mathematics
when compared with students in other countries. Many researchers believe the reason for this is:
a. In other societies parents regard education as their responsibility. In the U.S. parents
relinquish this responsibility to the schools.
b. In other countries mathematics is taught with a greater emphasis on rote facts with plenty
of drill and practice. In the U. S. the emphasis is on conceptual problem solving.
c. Mathematics instruction is a continuous state of change. School districts modify the
curriculum every few years without using research as a basis for their decisions.
d. Mathematic performance in the United States is related to the way mathematics is taught.
16.2 The current trend in mathematics instruction is the emphases on teaching students to effectively
problem solve and to spend less time on skill and drill. What implication do many researchers
believe the current trend will have on students with learning problems?
a. The performance of students with learning problems will dramatically improve.
b. Students with learning problems will learn neither math computation nor higher order
mathematics.
c. Students performance on higher order mathematics will improve, but their performance
on computation skills will dramatically worsen.
d. The performance of these students will remain the same, because the essential issue is
still not being addressed. Students with learning problems must be taught strategies and
accommodations in order to succeed in mathematics.
16.3 When teaching facts and mathematics computations, it will be important for you to monitor the
progress of students with learning problems because they are less likely to learn these skills
incidentally. In other words, they have difficulty learning these skills:
a. through lectures
b. through the process of problem solving
c. by reading the text
d. with a buddy
16.4 Michael hates math. Whenever he is assigned a page full of problems for homework, he
completes the first three or four problems and then gives up. He already knows he’s going to get
them all wrong anyway. What type of factor is influencing Michael’s behavior?
a. cognitive factors
b. educational factors
c. personality factors
d. neuropsychological patterns
16.5 Katie, a first grader, has been given an assortment of different size blocks to arrange from
smallest to largest. Even though Katie is able to arrange some of the blocks correctly, she has
difficulty with those that are closest to each other in size. What type of factor is influencing her
behavior?
a. cognitive factors
b. educational factors
c. personality factors
d. neuropsychological patterns
16.6 Paul, an eleventh grader, has a developmental arithmetic disorder. Which of the following is most
likely true about Paul?
a. Good teaching will assure grade level performance.
b. Paul has probably had problems with mathematics during his entire school life.
c. Paul’s overall cognitive functioning is low.
d. Paul is probably failing all other subjects as well.
16.7 All of the following are problems associated with students who display nonverbal mathematics
problems, EXCEPT:
a. reading below grade level
b. social immaturity
c. deficits in visual, motor and self-help skills
d. problems with estimating distance and time
16.8 There are several reasons why students display poor math performance, which one can be most
readily corrected?
a. parent involvement
b. computer accessibility
c. inappropriate or inadequate instruction
d. textbook modifications
16.9 There is considerable concern that poor math content is the result of the spiral curriculum. The
spiral curriculum occurs when:
a. the pages and organizational format if the text vary considerable and make learning from
text difficult.
b. students do not master the necessary prerequisite skills that are assumed by the text and
this the next level is too difficult.
c. there are insufficient problems covering any one concept or operation and there are too
few opportunities for application of knowledge learned
d. the same skills are woven into every year of school and students continually repeat
knowledge acquisition in the same area.
16.10 Which of the following programs stresses direct instruction through a highly sequenced format
that provides immediate feedback to students?
a. Structural Arithmetic
b. Touch Math
c. Key Math and Practice
d. DISTAR Arithmetic Program
16.11 Peter is a fourth grader who has difficulty writing clearly. Even though he knows how to add and
subtract well, he often makes mistakes because he cannot read the numbers he has copied from
the board. What type of problem is Peter having?
a. motoric
b. visual detail
c. procedural
d. spatial organization
16.12 Leon and Pepe suggest a strategy designed to teach students to self-instruct and monitor their own
progress. Which of the following is in the correct sequence of steps for this strategy?
a. The student verbalizes the procedure independently with the teacher monitoring, the
teacher guides the student through verbalization, the teacher verbalizes the procedure for
the students, and the student whispers the procedure to himself.
b. The teacher guides the student through the verbalization of the problem, the student
verbalizes the procedure to himself, the student whispers the procedure to himself, and
then the teacher verbalizes the procedure to himself.
c. The teacher verbalizes the procedure for the student, the teacher guides the student
through the verbalization, the student whispers the procedure to himself, and then the
student verbalizes the procedure independently with the teacher monitoring.
d. The teacher verbalizes the procedure for the student, the teacher guides the student
through the verbalization, the student verbalizes the procedure independently with the
teacher monitoring, and the student whispers the procedure to himself.
16.13 What are the three major types of interventions for mathematics instruction identifies by
Mastropieri, Scruggs, and Shiah?
a. behavioral, cognitive, and alternative instructional delivery
b. compensatory, strategic, and cognitive
c. academic, behavioral, and interdisciplinary
d. emotional, compensatory, and strategic
16.14 Jose, a first-grade teacher, draws stick figures on the board as he explains some basic addition
facts. In which stage are his students?
a. concrete
b. semi-concrete
c. semi-abstract
d. abstract
16.15 Michelle, a sixth-grade mathematics teacher, always asks her students to explain to their buddy
what she just said. Why does Michelle do this?
a. to increase the students math vocabulary
b. to ensure students go through the abstract stage
c. because she knows it is important to use alternative instructional delivery systems
d. to teach for comprehension.
16.16 Feedback is essential to the success of students with math difficulties. Which of the following is
an example of appropriate feedback?
a. “Garth you did a great job with the addition problems, but you still have some trouble
with subtraction. Please do five through ten over again.”
b. “Garth, please remind me to go over those subtraction problems with you next week.”
c. “Garth, let’s look at number five again. What do you do first?”
d. “Garth, I see you had some trouble with numbers five through ten. I know you tried very
hard so don’t worry. I’ll only grade half of your assignment.”
16.17 “Hannah, please go and get a piece of candy for each student in your group. How many more do
you need?” What is Mrs. Lopez having Hannah practice by asking her to distribute candy?
a. the concept of zero
b. one-to-one correspondence
c. operation shifting
d. classification
16.18 Desiree Black tells Tina to arrange the pieces of chalk from smallest to largest. What skill is
being taught?
a. numeration
b. constant time delay
c. classification
d. seriation
16.19 Which sequence should students follow to learn fractions?
a. manipulates concrete models, points to fractional models when name is stated by another,
names fractional units when selected by another, draws diagrams to represent fractional
units, matches fractional units, writes fractional names when given fractions to solve
problems.
b. manipulates concrete models, matches fractional models, points to fractional models
when name is stated by another, names fractional units when selected by another, draws
diagrams to represent fractional units, writes fractional names when given fractional
drawings, uses fractions to solve problems
c. manipulates concrete models, points to fractional models when name is stated by another,
matches fractional models, draws diagrams to represent fractional units, names fractional
units when selected by another, writes fractional names when given fractional drawings,
and uses fractions to solve problems
d. manipulates concrete models, matches fractional models, draws diagrams to represent
fractional units, points to fractional models when name is stated by another, names
fractional units when selected by another, writes fractional names when given fractional
drawings, and uses fractions to solve problems
16.20 Which of the following errors is an example of a spatial organization mistake?
a. 38
+58
816
b. 25 – 17 = 12
c. 146
+ 2311
3777
d. 12 x 2 = 14
Fill-in-the-Blank Questions:
16.21 The National Council of Teachers of Mathematics believes that _________________________ is
the “essential goal of instruction. Some of the areas you will need to address to document
whether students are making progress might include integrating conceptual understanding,
procedural fluency, strategic competence, ____________________, and
_____________________ into your math instruction.
16.22 If you have a student in your class whose overall cognitive functioning and academic
performance in subject areas other than mathematics are at or above grade level he/she may be
experiencing a ___________________________________________.
16.23 In your fifth-grade math class you have a student who does well in language arts but when it
comes to math you have been noticing so issues. The student seems to have deficits in visual,
motor, and self-help skills, tends to have problems when it comes to estimating distance and/ or
time. This student may have a __________________________________________.
16.24 In your classroom of middle school students you have found that several students have difficulty
with traditional math strategies. You have found that if you use real-world problems and present
those in a _______________________ that students tend to perform much better.
16.25 One mathematics approach that has taken hold due to work at the University of Chicago is the use
of a __________________________ where the same skills literally entwined into each year of
school and the students “relearn” those skills in the same area.
16.26 Another approach to instruction that teachers may use with their students who experience
problems in math and to build their proficiency in mathematics is instructional design principles.
The design principles included would be ____________________, ____________________,
____________________, ____________________, and ____________________.
16.27 You have several students in your class who is having difficult in math. They seems, based on
their scores on homework and tests, to be lacking in some of the basic skills needed to be
successful in mathematics. One program you are considering to use with these students is the
________________________ by Englemann and Carnie because it uses direct instruction to
provide explicit practice on skills that are at a deficit for students.
16.28 The use of response to intervention (RTI) in mathematics instruction can be just as important as it
is for reading instruction. There are several principles of RTI that can be used in math and
include ____________________, ____________________, ____________________, and
___________________.
16.29 There are a few students in your classroom who have difficulty with counting. You feel you need
to assess their “number sense” to see what skills are at a deficit and whether the students are
performing at or above grade level. In order to assess number sense you have decided to use
_______________________, _____________________, and _____________________ in order
to complete the screening with these students.
16.30 Understanding the skill of one-to-one correspondence is essential for all students to learn in order
to move forward to other math skills. In order to help ensure your students are mastering this
skill, you could use activities like _____________________________,
_____________________________, and _____________________________ to help students
practice and apply the skill.
16.31 Discuss the current trend in mathematics instruction. What is mathematical power? How will the
current trend in mathematics affect students with learning problems?
16.32 Describe the four factors that influence the mathematic ability of students with learning problems,
and describe a possible classroom implication for each.
16.33 Compare developmental arithmetic disorders to nonverbal math difficulties. What are the
characteristics of students in each of these groups?
16.34 Why have traditional math curricula not worked very well for students with learning problems?
What modifications can teachers make to assist students with learning problems with each of
these difficulties with math curricula?
16.35 What should you take into consideration when adapting basal materials for students with special
needs? Your author lists nine resources that are helpful for students who have difficulty learning
math. Choose three and briefly describe what types of difficulties are they designed to address.
16.36 Discuss the importance of establishing goals. How can you assist students to set realistic goals
and teach them to monitor their progress?
16.37 Describe cooperative instructional practices you can use to assist students with learning problems
succeed in mathematics.
16.38 Discuss how to provide appropriate instruction in mathematics. Which elements contribute to
systematic and explicit instruction in mathematics? How should you use manipulatives to teach
mathematical concepts? How should you provide correction and feedback to students with
learning difficulties?
16.39 Basic prenumbering skills are necessary for initial success in mathematics. Define one-to-one
correspondence, classification, and seriation. Give examples of the difficulties students with
learning problems have with these concepts and describe the strategies teachers can use to assist
students to master them.
16.40 There are patterns of computation errors that students make. Choose four of the common types of
mechanical arithmetic errors, briefly describe each, and provide strategies to assist students to
overcome them.
CHAPTER 16
