Chapter 5
Instructional DecisionMaking, Objectives, and
Activities
MATHEMATICS
Teachers’
Perceptions of
Their DecisionMaking Autonomy
Original Data for Slides 5–7
(not for presentation)
Table 5.2
Mathematics Classes in Which Teachers Report Having Strong Control
Over Various Curriculum and Instruction Decisions, by Grade Range
Elementary
Determining the amount of homework to be assigned
Selecting teaching techniques
Choosing criteria for grading student performance
Determining course goals and objectives
Selecting content, topics, and skills to be taught
Selecting textbooks/programs
56
44
29
12
8
3
(2.6)
(2.5)
(2.4)
(1.5)
(1.1)
(0.8)
Percent of Classes
Middle
77
70
56
24
23
13
(2.4)
(2.6)
(2.7)
(2.1)
(2.2)
(2.3)
High
75
72
55
28
24
20
(2.0)
(1.8)
(2.1)
(2.1)
(1.9)
(2.1)
Elementary School Mathematics Classes in Which Teachers
Report Having Strong Control Over Various Decisions
Determining the amount of homework to be
assigned
56
Selecting teaching techniques
44
Choosing criteria for grading student
performance
29
Determining course goals and objectives
12
Selecting content, topics, and skills to be
taught
8
Selecting textbooks/programs
3
0
20
40
60
80
Percent of Classes
100
Middle School Mathematics Classes in Which Teachers
Report Having Strong Control Over Various Decisions
Determining the amount of homework to be
assigned
77
Selecting teaching techniques
70
Choosing criteria for grading student
performance
56
Determining course goals and objectives
24
Selecting content, topics, and skills to be
taught
23
Selecting textbooks/programs
13
0
20
40
60
80
Percent of Classes
100
High School Mathematics Classes in Which Teachers
Report Having Strong Control Over Various Decisions
Determining the amount of homework to
be assigned
75
Selecting teaching techniques
72
Choosing criteria for grading student
performance
55
Determining course goals and objectives
28
Selecting content, topics, and skills to be
taught
24
Selecting textbooks/programs
20
0
20
40
60
80
Percent of Classes
100
Original Data for Slide 9
(not for presentation)
Table 5.3
Class Mean Scores for Curriculum Control and
Pedagogical Control Composites, by Subject and Grade Range
Mean Score
Curriculum
Pedagogical
Mathematics Classes
Elementary
Middle
High
29
45
52
(1.2)
(1.5)
(1.4)
74
87
88
(1.1)
(1.4)
(0.7)
Mathematics Class Mean Scores for Curriculum and
Pedagogical Control Composites, by Grade Range
Class Mean Score
100
74
80
60
52
45
40
88
87
29
20
0
Elementary
Curriculum
Middle
Pedagogical
High
Objectives of
Mathematics
Instruction
Original Data for Slides 12–14
(not for presentation)
Table 5.8
Mathematics Classes with Heavy Emphasis on
Various Instructional Objectives, by Grade Range
Elementary
Percent of Classes
Middle
High
Understanding mathematical ideas
Preparing for further study in mathematics
Learning mathematical practices (e.g., considering how to
approach a problem, justifying solutions)
Learning mathematical procedures and/or algorithms
69
47
(1.4)
(1.8)
70
57
(2.0)
(2.2)
69
55
(1.4)
(1.6)
51
44
(1.5)
(1.9)
54
49
(2.3)
(2.2)
55
48
(1.3)
(1.5)
Learning about real-life applications of mathematics
Learning test taking skills/strategies
Increasing students’ interest in mathematics
Learning to perform computations with speed and accuracy
45
37
50
36
(1.7)
(1.5)
(1.7)
(1.9)
42
36
37
24
(1.9)
(2.5)
(1.9)
(1.8)
29
28
27
18
(1.3)
(1.3)
(1.4)
(1.2)
Elementary School Mathematics Classes with Heavy
Emphasis on Various Instructional Objectives
Understanding math ideas
69
Learning math practices
51
Increasing students’ interest in math
50
Preparing for further study in math
47
Learning about real-life applications of math
45
Learning math procedures and/or algorithms
44
Learning test taking skills/strategies
37
Learning to perform computations with
speed/accuracy
36
0
20
40
60
Percent of Classes
80
100
Middle School Mathematics Classes with Heavy
Emphasis on Various Instructional Objectives
Understanding math ideas
70
Preparing for further study in math
57
Learning math practices
54
Learning math procedures and/or algorithms
49
Learning about real-life applications of math
42
Increasing students’ interest in math
37
Learning test taking skills/strategies
36
Learning to perform computations with
speed/accuracy
24
0
20
40
60
Percent of Classes
80
100
High School Mathematics Classes with Heavy
Emphasis on Various Instructional Objectives
Understanding math ideas
69
Learning math practices
55
Preparing for further study in math
55
Learning math procedures and/or algorithms
48
Learning about real-life applications of math
29
Learning test taking skills/strategies
28
Increasing students’ interest in math
27
Learning to perform computations with
speed/accuracy
18
0
20
40
60
Percent of Classes
80
100
Class Activities
Original Data for Slides 17–25
(not for presentation)
Table 5.20
Mathematics Classes in Which Teachers Report Using
Various Activities at Least Once a Week, by Grade Range
Elementary
Explain mathematical ideas to the whole class
Engage the whole class in discussions
Have students explain and justify their method for solving a problem
Have students work in small groups
Have students consider multiple representations in solving a problem
(e.g., numbers, tables, graphs, pictures)
Give tests and/or quizzes that include constructed-response/openended items
Have students compare and contrast different methods for solving a
problem
Have students present their solution strategies to the rest of the class
Give tests and/or quizzes that are predominantly short-answer (e.g.,
multiple choice, true/false, fill in the blank)
Have students practice for standardized tests
Have students read from a mathematics textbook/program or other
mathematics-related material in class, either aloud or to
themselves
Focus on literacy skills (e.g., informational reading or writing
strategies)
Have students write their reflections (e.g., in their journals) in class
or for homework
Provide manipulatives for students to use in problemsolving/investigations
Have students attend presentations by guest speakers focused on
mathematics in the workplace
Percent of Classes
Middle
High
97
96
88
85
(0.5)
(0.8)
(1.0)
(1.2)
98
93
85
70
(0.5)
(1.1)
(1.5)
(2.1)
95
84
79
63
(0.7)
(1.1)
(1.3)
(1.7)
78
(1.3)
75
(1.5)
65
(1.4)
39
(1.9)
50
(2.3)
56
(1.6)
66
64
(1.6)
(1.5)
63
60
(2.1)
(2.0)
56
46
(1.6)
(1.4)
47
31
(1.8)
(1.6)
39
40
(2.1)
(2.4)
36
32
(1.2)
(1.5)
41
(1.8)
34
(2.3)
25
(1.4)
40
(2.0)
23
(1.9)
14
(1.0)
26
(1.7)
21
(1.6)
11
(1.0)
82
(1.2)
33
(1.9)
18
(1.0)
3
(0.7)
2
(0.6)
1
(0.3)
Elementary School Mathematics Classes
Using Various Activities at Least Once a Week
Explain math ideas to the whole class
97
Engage the whole class in discussions
96
Have students explain/justify how they
solved a problem
88
Have students work in small groups
85
Provide manipulatives for students to
use in investigations
82
0
20
40
60
80
Percent of Classes
100
Elementary School Mathematics Classes
Using Various Activities at Least Once a Week
Have students consider multiple
representations in solving a problem
78
Have students compare/contrast
different methods for solving a problem
66
Have students present their solution
strategies to the rest of the class
64
Give tests/quizzes that are
predominantly short-answer
47
Have students read from a textbook
41
0
20
40
60
80
Percent of Classes
100
Elementary School Mathematics Classes
Using Various Activities at Least Once a Week
Focus on literacy skills
40
Give tests/quizzes that include
constructed/open-ended items
39
Have students practice for standardized
tests
31
Have students write their reflections
26
Have students attend presentations by
guest speakers
3
0
20
40
60
80
Percent of Classes
100
Middle School Mathematics Classes Using
Various Activities at Least Once a Week
Explain math ideas to the whole class
98
Engage the whole class in discussions
93
Have students explain/justify how they
solved a problem
85
Have students consider multiple
representations in solving a problem
75
Have students work in small groups
70
0
20
40
60
80
Percent of Classes
100
Middle School Mathematics Classes Using
Various Activities at Least Once a Week
Have students compare/contrast
different methods for solving a problem
63
Have students present their solution
strategies to the rest of the class
60
Give tests/quizzes that include
constructed/open-ended items
50
Have students practice for standardized
tests
40
Give tests/quizzes that are
predominantly short-answer
39
0
20
40
60
80
Percent of Classes
100
Middle School Mathematics Classes Using
Various Activities at Least Once a Week
Have students read from a textbook
34
Provide manipulatives for students to
use in investigations
33
Focus on literacy skills
23
Have students write their reflections
21
Have students attend presentations by
guest speakers
2
0
20
40
60
80
Percent of Classes
100
High School Mathematics Classes Using
Various Activities at Least Once a Week
Explain math ideas to the whole class
95
Engage the whole class in discussions
84
Have students explain/justify how they
solved a problem
79
Have students consider multiple
representations in solving a problem
65
Have students work in small groups
63
0
20
40
60
80
Percent of Classes
100
High School Mathematics Classes Using
Various Activities at Least Once a Week
Have students compare/contrast
different methods for solving a problem
56
Give tests/quizzes that include
constructed/open-ended items
56
Have students present their solution
strategies to the rest of the class
46
Give tests/quizzes that are
predominantly short-answer
36
Have students practice for standardized
tests
32
0
20
40
60
80
Percent of Classes
100
High School Mathematics Classes Using
Various Activities at Least Once a Week
Have students read from a textbook
25
Provide manipulatives for students to
use in investigations
18
Focus on literacy skills
14
Have students write their reflections
11
Have students attend presentations by
guest speakers
1
0
20
40
60
80
Percent of Classes
100
Original Data for Slides 27–29
(not for presentation)
Table 5.22
Mathematics Classes in Which Teachers Report that Students Use
Various Instructional Technologies at Least Once a Week, by Grade Range
Elementary
Percent of Classes
Middle
High
Graphing calculators
Scientific calculators
Four-function calculators
Internet
0
4
13
43
(0.0)
(1.3)
(1.7)
(2.4)
13
40
40
26
(2.2)
(2.8)
(2.5)
(2.6)
64
53
33
11
(2.0)
(2.1)
(2.2)
(1.2)
Personal computers, including laptops
Classroom response system or “Clickers”
Hand-held computers
Probes for collecting data
36
4
5
0
(2.5)
(1.3)
(1.1)
(0.3)
22
11
5
1
(2.8)
(1.6)
(1.5)
(0.7)
10
4
4
1
(1.2)
(0.7)
(0.8)
(0.4)
Elementary School Mathematics Classes in Which Students
Use Various Technologies at Least Once a Week
Internet
43
Personal computers, including laptops
36
Four-function calculators
13
Hand-held computers
5
Classroom response system or “Clickers”
4
Scientific calculators
4
Probes for collecting data
0
Graphing calculators
0
0
20
40
60
Percent of Classes
80
100
Middle School Mathematics Classes in Which Students
Use Various Technologies at Least Once a Week
Four-function calculators
40
Scientific calculators
40
Internet
26
Personal computers, including laptops
22
Graphing calculators
13
Classroom response system or “Clickers”
11
Hand-held computers
5
Probes for collecting data
1
0
20
40
60
Percent of Classes
80
100
High School Mathematics Classes in Which Students
Use Various Technologies at Least Once a Week
Graphing calculators
64
Scientific calculators
53
Four-function calculators
33
Internet
11
Personal computers, including laptops
10
Hand-held computers
4
Classroom response system or “Clickers”
4
Probes for collecting data
1
0
20
40
60
Percent of Classes
80
100
Original Data for Slides 31–33
(not for presentation)
Table 5.25
Mathematics Classes Participating in Various
Activities in the Most Recent Lesson, by Grade Range
Elementary
Percent of Classes
Middle
High
Teacher explaining a mathematical idea to the whole class
Students completing textbook/worksheet problems
Whole class discussion
Teacher conducting a demonstration while students watched
93
80
89
74
(0.9)
(1.5)
(1.1)
(1.5)
93
78
85
71
(1.0)
(1.8)
(1.4)
(2.0)
95
83
75
65
(0.7)
(1.0)
(1.3)
(1.2)
Students using instructional technology
Students doing hands-on/manipulative activities
Test or quiz
Students reading about mathematics
Practicing for standardized tests
29
77
19
19
14
(1.7)
(1.4)
(1.3)
(1.3)
(1.3)
31
37
19
23
23
(1.8)
(1.6)
(1.6)
(1.7)
(1.9)
43
21
20
17
16
(1.3)
(1.3)
(1.3)
(1.2)
(1.1)
Elementary School Mathematics Classes Participating in
Various Activities in the Most Recent Lesson
Teacher explaining an idea to the whole class
93
Whole class discussion
89
Students completing worksheets
80
Students doing hands-on activities
77
Teacher conducting a demonstration
74
Students using instructional technology
29
Students reading about mathematics
19
Test or quiz
19
Practicing for standardized tests
14
0
20
40
60
Percent of Classes
80
100
Middle School Mathematics Classes Participating
in Various Activities in the Most Recent Lesson
Teacher explaining an idea to the whole class
93
Whole class discussion
85
Students completing worksheet problems
78
Teacher conducting a demonstration
71
Students doing hands-on activities
37
Students using instructional technology
31
Practicing for standardized tests
23
Students reading about mathematics
23
Test or quiz
19
0
20
40
60
Percent of Classes
80
100
High School Mathematics Classes Participating in
Various Activities in the Most Recent Lesson
Teacher explaining an idea to the whole class
95
Students completing worksheet problems
83
Whole class discussion
75
Teacher conducting a demonstration
65
Students using instructional technology
43
Students doing hands-on activities
21
Test or quiz
20
Students reading about mathematics
17
Practicing for standardized tests
16
0
20
40
60
Percent of Classes
80
100
Original Data for Slide 35
(not for presentation)
Table 5.26
Average Percentage of Time Spent on Different Activities
in the Most Recent Mathematics Lesson, by Grade Range
Average Percent of Class Time
Elementary
Middle
High
Whole class activities (e.g., lectures, explanations, discussions)
Small group work
Students working individually (e.g., reading textbooks, completing
worksheets, taking a test or quiz)
Non-instructional activities (e.g., attendance taking, interruptions)
40
29
(0.6)
(0.8)
42
24
(0.8)
(0.9)
48
22
(0.7)
(0.8)
26
6
(0.6)
(0.3)
24
10
(0.7)
(0.2)
22
9
(0.6)
(0.2)
Percentage of Time Spent on Different Activities in the
Most Recent Mathematics Lesson, by Grade Range
Average Percent of Class Time
60
48
40
42
40
29
26
24 24
22 22
20
10
6
9
0
Elementary
Middle
High
Whole class activities
Small group work
Students work individually
Non-instructional activities
Homework and
Assessment
Practices
Original Data for Slide 38
(not for presentation)
Table 5.27
Amount of Homework Assigned in Classes per Week, by Subject and Grade Range
Elementary
Mathematics
Fewer than 15 minutes per week
15–30 minutes per week
31–60 minutes per week
61–90 minutes per week
91–120 minutes per week
More than 120 minutes per week
16
19
35
17
9
4
(1.9)
(2.0)
(2.6)
(1.8)
(1.3)
(0.9)
Percent of Classes
Middle
5
13
28
29
14
10
(0.8)
(2.6)
(2.9)
(2.9)
(1.5)
(1.6)
High
7
8
22
27
13
23
(1.0)
(1.2)
(1.7)
(1.8)
(1.1)
(1.8)
Amount of Homework Assigned in Mathematics
Classes per Week, by Grade Range
Percent of Classes
40
36
35
28 29
27
24
20
19
16
22
17
13
13
7
5
8
0
Elementary
<15 minutes/week
61–90 minutes/week
Middle
15–30 minutes/week
>90 minutes/week
High
31–60 minutes/week
Original Data for Slides 40–45
(not for presentation)
Table 5.29
Mathematics Classes in Which Teachers Report Assessing Students
Using Various Methods in the Most Recent Unit, by Grade Range
Percent of Classes
Elementary
Middle
Questioned individual students during class activities to see if they
were “getting it”
Reviewed student work (e.g., homework, notebooks, journals,
portfolios, projects) to see if they were “getting it”
Administered one or more quizzes and/or tests to assign grades
Went over the correct answers to assignments, quizzes, and/or tests
with the class as a whole
Administered one or more quizzes and/or tests to see if students were
“getting it”
Assigned grades to student work (e.g., homework, notebooks,
journals, portfolios, projects)
Used information from informal assessments of the entire class (e.g.,
asking for a show of hands, thumbs up/thumbs down, clickers,
exit tickets) to see if students were “getting it”
Administered an assessment, task, or probe at the beginning of the unit
to find out what students thought or already knew about the key
mathematical ideas
Had students use rubrics to examine their own or their classmates’
work
High
97
(0.6)
98
(0.6)
97
(0.5)
96
73
(0.7)
(1.6)
95
88
(0.9)
(1.5)
96
94
(0.7)
(0.6)
83
(1.2)
94
(0.9)
92
(0.7)
73
(1.7)
86
(1.5)
86
(1.4)
63
(1.9)
85
(1.6)
85
(0.9)
90
(1.1)
88
(1.3)
83
(1.1)
63
(1.8)
52
(2.2)
42
(1.8)
10
(1.1)
12
(1.3)
8
(0.7)
Elementary School Mathematics Classes in Which
Teachers Report Assessing Students Using Various
Methods in the Most Recent Unit
Questioned students during class activities
97
Reviewed student work
96
Used information from informal assessments of
the entire class
90
Went over the correct answers to
assignments/quizzes/tests
83
Administered quizzes and/or tests to see if
students were “getting it”
73
0
20
40
60
80
Percent of Classes
100
Elementary School Mathematics Classes in Which
Teachers Report Assessing Students Using Various
Methods in the Most Recent Unit
Administered quizzes and/or tests to assign
grades
73
Administered an assessment, task, or probe at
the beginning of the unit
63
Assigned grades to student work
63
Had students use rubrics to examine work
10
0
20
40
60
Percent of Classes
80
100
Middle School Mathematics Classes in Which Teachers
Report Assessing Students Using Various Methods in
the Most Recent Unit
Questioned students during class activities
98
Reviewed student work
95
Went over the correct answers to
assignments/quizzes/tests
94
Used information from informal assessments of
the entire class
88
Administered quizzes and/or tests to assign
grades
88
0
20
40
60
80
Percent of Classes
100
Middle School Mathematics Classes in Which Teachers
Report Assessing Students Using Various Methods in
the Most Recent Unit
Administered quizzes and/or tests to see if
students were “getting it”
86
Assigned grades to student work
85
Administered an assessment, task, or probe at
the beginning of the unit
52
Had students use rubrics to examine work
12
0
20
40
60
Percent of Classes
80
100
High School Mathematics Classes in Which Teachers
Report Assessing Students Using Various Methods in
the Most Recent Unit
Questioned students during class activities
97
Reviewed student work
96
Administered quizzes and/or tests to assign
grades
94
Went over the correct answers to
assignments/quizzes/tests
92
Administered quizzes and/or tests to see if
students were “getting it”
86
0
20
40
60
Percent of Classes
80
100
High School Mathematics Classes in Which Teachers
Report Assessing Students Using Various Methods in
the Most Recent Unit
Assigned grades to student work
85
Used information from informal assessments of
the entire class
83
Administered an assessment, task, or probe at
the beginning of the unit
42
Had students use rubrics to examine work
8
0
20
40
60
80
Percent of Classes
100
Original Data for Slide 47
(not for presentation)
Table 5.30
Frequency of Required External Testing in Classes, by Subject and Grade Range
Elementary
Mathematics
Never
Once a year
Twice a year
Three or four times a year
Five or more times a year
9
14
7
38
31
(0.9)
(1.3)
(0.9)
(1.7)
(1.7)
Percent of Classes
Middle
2
19
10
38
31
(0.4)
(2.2)
(1.4)
(2.4)
(1.7)
High
21
28
15
22
14
(1.3)
(1.3)
(1.0)
(1.2)
(1.1)
Frequency of Required External Testing in
Mathematics Classes, by Grade Range
38
40
38
Percent of Classes
31
31
28
19
20
15
14
9
22
21
14
10
7
2
0
Elementary
Never
Once a year
Middle
Twice a year
3–4 times a year
High
≥5 times a year
Original Data for Slides 49–51
(not for presentation)
Table 5.31
Classes Required to Take External Assessments Two
or More Times per Year, by Subject and Equity Factors
Percent of Classes
Mathematics
Prior Achievement Level of Class
Mostly High Achievers
Average/Mixed Achievers
Mostly Low Achievers
Percent of Non-Asian Minority Students in Class
Lowest Quartile
Second Quartile
Third Quartile
Highest Quartile
Percent of Students in School Eligible for FRL
Lowest Quartile
Second Quartile
Third Quartile
Highest Quartile
60
71
76
(2.6)
(1.4)
(2.2)
56
65
71
83
(2.4)
(2.0)
(2.1)
(1.5)
66
73
75
81
(2.4)
(1.9)
(1.9)
(1.7)
Mathematics Classes Required to Take External
Assessments Two or More Times per Year, by Prior
Achievement Level of Class
Percent of Classes
100
80
76
71
60
60
40
20
0
Mostly Low Achievers
Average/Mixed
Mostly High Achievers
Achievers
Prior Achievement Level of Class
Mathematics Classes Required to Take External Assessments Two
or More Times per Year, by Percentage of Students in Class from
Historically Underrepresented Race/Ethnicity Groups
100
Percent of Classes
83
80
65
60
71
56
40
20
0
Lowest %
Second Quartile Third Quartile
Highest %
Underrepresented
Underrepresented
Quartiles of Classes Based on Percentage of Historically
Underrepresented Students in Class
Mathematics Classes Required to Take External Assessments Two
or More Times per Year, by Percentage of Students in School
Eligible for Free/Reduced-Price Lunch
Percent of Classes
100
80
66
73
75
81
60
40
20
0
Lowest Poverty Second Quartile Third Quartile
Highest Poverty
Schools
Schools
Quartile of Schools Based on Percentage of Students Eligible for
Free-Reduced Lunch