Helping Children Learn Mathematics
Mid-Term
The following questions are from chapters 1-4 in the textbook Helping
Children Learn Mathematics.
1.
All of the following are topics that should be covered in a mathematics
classroom, except:
A.
B.
C.
D.
E.
2.
algebra
geometry
measurement
geography
probability
Which of the following groups was responsible for establishing mathematics
standards?
A.
B.
C.
D.
E.
The National Math Council
The Math Association of America
The National Council of Teachers of Mathematics
The North American Math Council
None of the above
3.
T or F The three needs that should be taken into consideration when thinking
about the mathematics curriculum are the needs of society, the needs of
teachers, and the needs of the child.
4.
When a teacher believes that students will need to be able to solve problems
and communicate so we can advance our technological world, he or she is
considering the needs of the:
A.
B.
C.
D.
E.
subject
child
government
parent
society
5.
Explain what is meant by each of the following principles:
Technology Curriculum Teaching Learning Assessment Equity -
6.
What does the word equity mean? Is it synonymous with equality? Give
examples to support your answer.
7.
T or F According to a research mentioned in the text, most states have the
same grade-level expectations in the specificity and in the grade in which a skill
was targeted.
8.
T or F According to the 2003 TIMSS, U.S. fourth graders were below the
international average.
9.
As you prepare to teach mathematics, what three challenges should you take
into consideration?
10. T or F Creating a positive learning environment and establishing clear
expectations are two strategies for supporting all students without having to
individualize instruction.
11. As a classroom teacher, discuss five strategies that you could employ to alleviate
children’s math anxieties.
12. A student who has procedural knowledge without conceptual knowledge will
have difficulty:
A.
B.
C.
D.
E.
knowing when to use it.
remembering how to do it.
applying it in new situations.
judging if results are reasonable.
all of the above
13. Behaviorism has some drawbacks. One of them is that it tends to not focus on
learning and understanding but rules and procedures. If you were to teach from
a behaviorist perspective, how would you defend your choice?
14. T or F Suppose you walked into Mrs. Andrews’ classroom and saw that she was
showing students the rules and procedures for multiplying two fractions. After
the lesson, she gives students lots of practice problems using the rules and
procedures. This is an example of constructivist teaching.
15. T or F Suppose you walked into Mrs. Andrews’ classroom and saw that she was
showing students the rules and procedures for multiplying two fractions. After
the lesson, she gives students lots of practice problems using the rules and
procedures. This is an example of constructivist teaching.
16. Explain what is meant by the zone of proximal development.
17. T or F Children from low SES backgrounds tend to favor problem
solving in mathematics as opposed to rote memorization.
18. T or F Teacher with strong content knowledge are better able to develop their
students’ conceptual knowledge.
19. After correcting her students’ tests, Mrs. Wang discovers that most of her
students got the problem involving fraction multiplication wrong. This is an
example of which of the following functions of an instructor?
A.
B.
C.
D.
E.
planning
teaching
assessing
analyzing
none of the above
20. A teacher planning a first-grade lesson on addition realizes that his students
need to manipulate concrete objects to solve addition problems and are just
beginning to use symbols to represent those objects. Which of the following
questions is this teacher mainly concerned with?
A.
B.
C.
D.
E.
Do I understand the mathematics I am teaching?
What are the developmental characteristics of my students?
What do my students already know?
What kinds of tasks will I give my students?
None of the above
21. During the first week of third-grade math class, Mr. Martin gives his class a pretest. In doing this, Mr. Martin is mainly concerned with which of the following
questions?
A.
B.
C.
D.
E.
Do I understand the mathematics I am teaching?
What are the developmental characteristics of my students?
What do my students already know?
What kinds of tasks will I give my students?
None of the above
22. In Mrs. Hoffman’s second-grade class, the children work with the place values
tens and ones. In third grade, they work with hundreds, tens, and ones. This is
an example of:
A.
B.
C.
D.
E.
the spiral approach
scaffolding
multiple embodiment
mathematical complexity
none of the above
23. T or F According to research, drill and practice should follow, not precede, the
development of mathematical meaning.
24. After having Alexa share her response with the class, the teacher asks the
following question, “What do you think will happen to the measure of each
interior angle of a polygon if we were to increase the number of angles?” This
type of question is a question that is primarily aimed at:
A.
B.
C.
D.
E.
helping students work together to make sense of mathematics
helping students to learn to reason mathematically
helping students learn to conjecture
helping students connect mathematics to other areas
none of the above
25. T or F According to the text, it is better to place low-achieving students together
because then they can proceed at their own pace and help each other learn.
26. Discuss three reasons why technology should be incorporated into the
mathematics classroom.
27. A fifth-grader is using a piece of computer software. The software teaches her
how to add and subtract fractions. This is an example of what kind of software?
A.
B.
C.
D.
E.
Drill-and-practice
Tutorial
Educational game
Simulation
None of the above
28. T or F Japanese teachers typically follow the review-teach-practice format for
mathematics lessons.
29. In Mrs. Jones’ lesson plan, she grabs the students’ attention by posing an
interesting problem. This is an example of which lesson plan component?
A.
B.
C.
D.
E.
introduction
launch
instruct
summarize
none of the above
30. T or F Investigative lessons are better than direct instruction ones because
students get to actually do things.
31. You want to adapt a lesson on division of whole numbers by two-digit divisors
by using the level of support adaptation. Which of the following does NOT
illustrate this adaptation?
A.
B.
C.
D.
E.
Provide base-ten blocks.
Pair up students.
Assign a paraprofessional to assist particular students.
Have some students divide by one-digit divisors.
None of the above.
32. T or F At the end of the year, Mrs. Meyers gives students a standardized math
test to determine what students have learned during the school year. This is an
example of assessment for learning.
33. Compare and contrast formative and summative assessments and also give one
example of each.
34. What does the phrase, “alignment of standards with assessments” mean?
35. Which of the following acts mandates that states must develop content
standards in mathematics, create annual assessments, and administer those
tests to nearly all students annually in grades 3-8, and at least once in grades 1012?
A.
B.
C.
D.
E.
Elementary and Secondary Education Act
Civil Rights Act
No Child Left Behind Act
All of the above
None of the above
36. In order to assess students’ understanding of operations involving decimals,
Mr. Ramirez has his students demonstrate using base-ten blocks. This is an
example of which phase of the classroom assessment process?
A.
B.
C.
D.
E.
planning
gathering
interpreting
using
all of the above
37. Which of the following are things that a student may want to put into his
portfolio?
A.
B.
C.
D.
E.
problem solving tasks
writings
reports
none of the above
all of the above
38. Your text states that writing can be an invaluable tool in mathematics. Describe
some ways in which you can incorporate writing into your classroom and some
of its benefits.
39. What are three strategies for keeping student records.
40. Name the three groups with whom you will have to communicate assessment
information. Also, for each group, include a recommendation for making the
communication a positive experience.