CHAPTER 12
Problem Solving and Mathematics
AUTHENTIC ASSESSMENTS
1. Students will think of 10 additional problem-solving activities for early childhood years and grades.
2. Students will write and submit 10 age-appropriate early childhood activities for mathematics concepts
including number, shape, and size.
3. Complete a project plan or lesson plan for one of the topics from this chapter.
SUGGESTED TEST QUESTIONS
1. As teachers, we should be more concerned about getting the right answer than the process of
arriving at an answer.
2. Memorizing mathematical facts is not the same as understanding the process.
3. Spatial relationships refer to the mathematical study of astronomy and space.
4. A great way to teach math is through children‘s everyday experiences.
5. There are excellent workbook pages and ditto sheets for math that should be used daily in early
childhood.
6. Classification relies on the ability to recognize likenesses and differences.
7. It is unlikely that children will seek out math-related activities in early childhood.
8. Problem-solving skills relate only to the math area of the curriculum.
9. Rote counting comes before one–to-one correspondence in young children.
10. Early childhood teachers should use play money instead of real money because the children may
lose the real money.
11. Time is an especially difficult concept for young children because it involves measuring
Fill–in-the-Blank Questions
1. Four basic steps to problem solving generally include:
2. Classification refers to objects, and seriation refers to objects.
3. An example of a spatial relationship is ; and an example of a temporal
relationship is .
4. If two sets are compared and found to be equal even when they are arranged to look unequal, this
skill is called .
5. An empty set is called .
Multiple-Choice Questions
1. The focus in teaching math in the early childhood years should be on
I. producing the correct answer.
II. teaching the thinking skills.
III. the analyzing involved.
IV. making math fun.
V. the reasoning involved.
a. All of the above b. I, II, III, V
c. I, II, IV d. II, III, IV, V
2. Math during early childhood must be
a. cognitively oriented.
b. knowledge producing.
c. manipulative.
d. abstract.
3. During early childhood, number concepts that children will explore include
I. classification.
II. comparison.
III. ordering.
IV. ordinal number.
V. one–to-one correspondence.
VI. cardinal number.
VII. addition and subtraction.
VIII. money.
IX. time.
a. All of the above b. I, III, IV, V
c. II, IV, V, VII, IX d. I, II, III, V, VI
4. Conservation can relate to
I. number.
II. amount.
III. volume.
IV. shape.
V. weight.
a. All of the above b. I, II, V
c. I, II, IV, V d. I, II, III, V
5. By what age can most children differentiate geometric shapes?
a. 2–3 years
b. 3–4 years
c. 5–6 years
d. 7–8 years
6. Skill in which of the following concept areas has the most influence on a child’s reading
readiness?
a. Shape and form
b. Number
c. Size
d. Weight and balance
e. Color
. 7. Which of the following concepts related to size are appropriate for early childhood?
I. Some of the children in the class are big, and some are little.
II. The farther away one goes from an object, the smaller it looks.
III. Certain experiences we have may make us feel larger or smaller, even though our
physical size does not change.
IV. People change size.
a. All of the above b. I, III, IV
c. II, III, IV d. I, II, III
Matching
1. Piaget has defined three basic kinds of knowledge. Match the kind of knowledge in the right
column to the correct definitions in the left column.
Observation and manipulation of objects. a. Logico-mathematical
Rules, customs, acceptable behaviors. b. Physical
Classification, seriation, number. c. Social
1. What are some of the math concepts children will learn in early childhood?
2. Describe some of the incidental ways children use numbers in their daily experiences.
3. What is the difference between number and numeral?
4. Describe three of the concepts relating to time that are appropriate for early childhood.
5. List some of the vocabulary words relating to time that children in early childhood will come to
understand.
Chapter 12
