What's Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success (32 page)

objectivity,
101

Olson, Steve,
116

online courses,
177
–78

open work,
116
,
117
–18,
161
,
165
.
See also
group work

opportunity to learn,
109
–10

opposition to change.
See
antireform activists

Organisation for Economic Co-operation and Development (OECD), 41

pace of learning,
158
,
192

pacing guides,
185
–86

Painted Cubes Puzzle,
181
,
212
–13

panic,
178

parents

activities for parents,
167
,
168
,
170

and asking questions,
175
–76,
177

fear of mixed-ability classes,
108

and future of math education,
185

and mathematical flexibility,
178
–83

puzzles and problems to foster math skills,
172
–75

Parker, Ruth,
44
,
148

participation,
152
.
See also
engagement of students

Partitions Puzzle,
182
,
215

Partnership for Assessment of Readiness for College and Careers (PARCC),
89

passive learning,
40
–42, 43–46,
46
–51,
98
–99.
See also
traditional math instruction

pattern blocks,
168

patterns and pattern recognition

and ability grouping,
105

and artificiality of mathematics, 55

and collaborative learning,
164

and communicative approach,
59
–62,
64

and conceptual understanding,
156

and definitions of math,
15
,
16
,
19
–20

and Fermat’s last theorem,
23

and gender issues,
124

lasting impact on math skills,
154

and opportunities to learn,
158

and parental involvement in education,
167
,
168
,
170

and project-based approach,
73

and puzzles,
201
–2,
206
,
215

and summer school program,
146
,
151

Peacock, Ray,
6

peer-assessment,
96
–98

peer discussions, 49–50.
See also
collaboration; discussions in classrooms

performative element of math,
29

phi,
16
–17

Phillips Laboratories,
6

Phoenix Park School

and ability grouping,
117
–18

and comparison of classroom styles,
76
–77,
79
–80

and gender issues,
125

and math use after school years,
80
–82

and project-based approach,
68
–74

physics,
97
,
127

pi,
18
–19

PISA (Programme for International Student Assessment), 41

Pisano, Leonardo (Fibonacci),
16

policy issues,
136
–37

polls on opinions of math, 5

Pólya, George,
26

polynomials,
59

popular culture, 5

population growth problems, 53

positive feedback,
93
–94

practicality of math skills, 51–56,
74
,
79
,
80
–83

practice,
191
–92

praise of achievements,
186
–87,
187
–88,
188
–89

precalculus,
66
,
107
–8

Prelude to Mathematics
(Sawyer),
19
–20

prescriptive curricula,
186

Presidential Award, 11

pressure on math students,
87

prior attainment,
103

probability,
73
,
74

problem-solving skills

and engineering, 7–8

and informal math methods, 9–10

and learning styles,
161

and the mathematical process,
27
–28

and mathematical proofs,
25

and math use after school years,
6
–7,
82

and mixed-ability classes,
118
–19

and practicality of math skills,
80
–81

and puzzles,
166
,
172
–75

and shortcomings of passive learning,
40
, 43

See also
puzzles

productive struggles,
188
,
191
–92

professional development, 33

professionalism,
80
–81

Programme for International Student Assessment (PISA), 41,
138

project-based approach,
68
–74,
77
–79,
78

promoting change in math education,
185

prompts,
180

proofs, mathematical,
21
–22,
24
, 49

pseudocontexts, 53

psychology of math instruction,
118
–19,
134

public opinion and awareness,
4
–5,
130
,
184
.
See also
antireform activists

puzzles

Beans and Bowls Puzzle,
182
,
213
–14

Buddhist Monk Puzzle,
173
–74,
208

Fermat’s last theorem,
20
–23

Four
4
s Puzzle,
180
,
210
–11

and math use after school years, 5,
82

and Moskam’s class,
2

Painted Cubes Puzzle,
181
,
212
–13

and parental involvement in education,
167
–68,
170
,
172
–75,
183
,
192
–93

Partitions Puzzle,
182
,
215

Rabbit Puzzle,
173
–74,
207
–8

and shortcomings of passive learning,
46

Two Jars Puzzle,
173
,
206
–7

and varied learning styles,
12

See also
games

Pythagorean formula,
20
–21

quantitative literacy,
8
.
See also
number sense

Queensland, Australia,
101

questioning skills,
146
–48,
175
–78,
189
,
191
,
192

Rabbit Puzzle,
173
–74,
207
–8

race issues,
91
,
145

Race to
20
Game,
181
,
211
–12

Railside High School,
58
–68,
89
,
108
,
113
,
114

ranking math students,
90

real-world application of math skills, 51–56,
74
,
79
,
80
–83

reasoning skills

and asking questions,
175
–78

and math skills in the workplace,
6
–7

puzzles and problems to foster math skills,
172
–75

and shortcomings of passive learning,
48
–49

and summer school program,
146

See also
active learning; problem-solving skills

recomposing numbers,
140
–41,
146
,
149
,
178
–80

reconstruction,
50

rectangles,
72

reform in mathematics, 39–46

remedial math courses,
4

repetition,
24
,
144
–45,
160
.
See also
traditional math instruction

reporting of assessments,
91
–92,
93

representation of ideas,
146
–48

research on math teaching methods

on classroom styles,
77
–79,
78

on effect of mistakes,
187

and future of math education,
185

and gender issues,
125
–26,
130

resources for,
194

and summer school program,
145
–54

and testing standards,
91

See also
longitudinal studies

respect among students,
113
–17

Ribet, Ken,
24

role models,
132

Romero, Carissa,
110

Rose, Hillary, 55

Rosenthal, Robert,
109

Rubik’s Cubes,
170

rules of math

and communicative approach,
59

and compression of math concepts,
144

and definitions of math,
15
,
19

and gender issues,
123
,
129

and the mathematical process,
28

and parental involvement in education,
178
,
190

and shortcomings of passive learning,
42
–44, 49

and traditional math instruction,
75
–76

See also
equations and formulas

Sadler, Royce,
100

SAT tests,
86
,
89
,
90
,
92
,
130
–31

Sawyer, W. W.,
19
–20

Schoenfeld, Alan,
38

school-based work assessment,
101

Second International Mathematics and Science Study (SIMMS),
104

Sela, David,
127

self-image

and ability grouping,
113
–17

and asking questions,
177

and assessment for learning,
96
–99

and mistakes,
187
–88

and opportunity to learn,
109
–10

and pride in accomplishments,
159

and test scores,
93

self-regulation,
95

separate thinkers,
128
–29

settings for math learning,
168
–72,
193
–94

sexism,
132
,
134
.
See also
gender issues in math instruction

shopping, 9

silent learning approaches, 47–49.
See also
passive learning

The
Simpsons,
5

Singh, Simon,
22
–23,
24

Skateboard Problem,
2
,
197
–99

“slow” learners,
141

Smarter Balanced Assessment Consortium,
89

snap cubes,
170

social class,
80
–81,
114

socialization and social skills,
67
,
129
.
See also
discussions in classrooms

societal stereotypes,
133

socioeconomic status (SES),
104
,
146

South Side High School,
107

speed contests,
148

spending on education, 3–4

spirals,
16
–18,
17

Staircase problem,
159
–63,
160
–61,
203
–5

standard deviation,
125

standardized testing,
84
–85,
85
–94

Stanford University,
12
,
34
,
125
–26

state assessment,
102

statistics,
73

Steele, Clause,
91

STEM (science, technology, engineering, and mathematics) subjects,
128
–29,
132
,
136
–37

stereotypes, 5,
91
,
132
.
See also
gender issues in math instruction

strategies,
138
–39

structural engineering, 7–8

student resources,
112
–13

subtraction skills,
140
,
141

Sudoku, 5

summer school programs,
145
–54,
154
–56,
157
–59,
159
–63,
163
–66

supplemental curricula,
217
–18

symbolic reasoning,
28
.
See also
abstraction

tables,
63

Tall, David,
139
,
149
,
178

tangent ratio,
72
–73

tangrams,
170

Tarule, Jill,
129

technology,
56
,
57
,
184

TED talks,
8

Telegraph,
29

television, 5,
134
,
135

testing,
84
–102

Advanced Placement classes and exams,
94
,
107
–8,
113
,
126
,
131

assessment for learning approach,
95
–102

and borderline students,
111
–12

frequency of,
84
,
92

Graduate Record Examination (GRE),
86

national examinations,
77
–79,
124

problems with current system,
85
–94

SAT tests,
86
,
89
,
90
,
92
,
130
–31

standardized,
84
–85,
87
–89,
92
,
94

testing movement,
85

and traditional math instruction,
76
–79