What's Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success (31 page)

English Inside the Black Box
(booklet),
85

English language learners (ELL),
88
,
89
–90

enjoyment of math

and artificiality of math, 55

and asking questions,
175
,
177
,
178

and children’s self-esteem,
10
–11

and difficult problems,
24
, 33

fostering, 13,
82

and gender issues,
123

impact of teaching style on,
138

and number talks,
149

outside school settings, 5

and puzzles,
172
,
192

and Railside students,
66

and student engagement,
28
,
30

and summer school program,
151
–54,
155
–56,
158
,
164
–66

and traditional teaching methods,
48

equality issues,
185

equations and formulas

and communicative approach,
62

and comparison of classroom styles,
78

and engineering, 7

and Fermat’s last theorem,
20

and gender issues,
122
,
125
–27

and math wars,
40

and parental involvement in education,
173

and physical representations,
204
–5

and shortcomings of passive learning,
44
–46

and traditional math instruction,
75
,
75
–76

estimation skills,
25

ethnicity,
86
,
114

European Young Scientist of the Year Award,
46
,
168

expectations,
109
–10,
177

Experiencing School Mathematics
(Boaler),
82

explaining math work

in active learning settings,
48
–50

and advantages of mixed-ability classes,
112
–13

and collaborative learning,
163

and communicative approach,
59
,
67

and gender issues,
121
–22,
124
–25

and Moskam’s class,
1
–2

and parental involvement in education,
175
–76,
177
,
187

and project-based approach,
71
–72

and questioning skills for parents,
189
–90

and standardized testing,
89

and summer school program,
147

in traditional settings, 11,
46
–47,
76
–77

extremism in curriculum debates, 35

factoring,
59

fear of math, 3, 13,
178
.
See also
anxiety about math

feedback,
95
–102.
See also
discussions in classrooms

Fennema, Elizabeth,
130

Fermat, Pierre de,
20
–21

Fermat’s Enigma
(Singh),
22

Fermat’s last theorem,
20
–23

Fibonacci sequence,
16
–18

Fields Medal,
29
,
142
–43

films about math,
27
,
184

Finland,
103
,
110

Fiori, Nick,
169

fixed-ability messages,
186

fixed mind-sets,
110
,
187
–88

Flannery, Sarah,
46
, 47,
168
,
172
–75

flexibility

and conceptual understanding,
144
–45,
191

and math skills in the workplace,
6
–7

and number sense,
141
–42

and number talks,
148
–49

and opportunities to learn,
159

and parental involvement in education,
178
–83

and project-based approach,
74

and summer school program,
146
,
149
–50

and technological advance,
56

FOIL pneumonic,
121

Four
4
s Puzzle,
180
,
210
–11

fractions,
44
–45,
171

Frederiksen, John,
97

freedom in math education,
71
,
74

Gainsburg, Julie, 7–8

games,
169
,
193

gender issues in math instruction

and achievement gaps,
99

and asking questions,
177

and creativity,
128

current state of,
130
–32

and learning styles,
120
–30,
154
–56

parental impact on,
187

and praise of math skills,
189

rates of women math majors, 3–4

and respect among students,
114

and SAT scores,
135
–36

and settings for math learning,
170

and shortcomings of passive learning, 43

and standardized testing,
86

and stereotypes, 5,
133
–37

and testing standards,
91

and university math departments,
132
–33

General Certificate of Secondary Education (GCSE) examination,
131

geometry

and communicative approach,
64
–66

and Fermat’s last theorem,
21

and Moskam’s class,
2

and student tracking,
107

Thirty-six Fences problem,
71
–74

George Mason University,
104
–5

Gilligan, Carol,
128
–29

girls.
See
gender issues in math instruction

Goldberger, Nancy,
129

golden ratio,
16
–18

grading systems,
99
–100.
See also
testing

Graduate Record Examination (GRE),
86

graphs,
60
,
60
,
63

Gray, Eddie,
139
,
149
,
178

group work

and ability grouping,
105

advantages of mixed-ability classes,
116
–17

and learning styles,
158
,
215

and Moskam’s class,
1
–2

and project-based approach,
74

and summer school program,
150

and traditional math instruction,
75

The
Guardian,
78

guessing,
25
,
190

Guthrie, Francis,
54

Harvard University,
171

Hebrew University of Jerusalem,
99
,
127

Hersch, Reuben,
15
,
27
, 47

Herzig, Abbe,
132

Heubert, Jay,
107

hexagons,
71
–72

high-achieving students,
104

high-level mathematics,
129
–30.
See also
complex problems

Hilton, Peter,
27

home environments,
153
–54.
See also
parents

Humphreys, Cathy,
176

Hyde, Janet,
130

In a Different Voice
(Gilligan),
128
–29

In Code: A Mathematical Journey
(Flannery),
172
–75

The
Independent,
78

inequalities, mathematical,
59
,
131

inequality, social,
88

informal math methods, 9–10

inspiring teachers,
176

Interactive Mathematics Program (IMP) curriculum, 33, 35–36, 37

international rankings of math competency, 3–4,
10

Interpreting the World activities,
73

intervention curricula,
217
–18

intuition,
128
–29

IQ tests,
109

Isaac Newton Institute,
23

Israel,
111
,
127

Jacobson, Lenore,
109

Japan,
103
,
104
–5,
116
–17

Kenschaft, Pat,
176
–77

King, Martin Luther,
86

knowing, stages of,
129

known facts strategy,
140
–41

Kohn, Alfie,
84
–85,
87
–88

Korea,
104

labels,
91
.
See also
stereotypes

Lakatos, Imre,
25

Lamon, Susan,
130

language of math,
59

language skills,
88

large-scale assessments,
101
–2

Lave, Jean, 9

LEGO blocks,
170

life skills and mathematics,
80
–83

linear patterns,
64

listening, 47.
See also
passive learning

logic, 5,
67
,
172
–75

longitudinal studies

author’s research, 11–12

on impact of ability grouping,
105
–6

on mixed-ability classes,
113

on project-based approach,
69

on shortcomings of passive learning, 41

long-term impact of teaching methods,
153
–54

low-income students,
68
–74,
88

Maclagan, Diane,
24

manipulation of data, 33

manipulatives (teaching tools),
148

map problems,
54
,
54

masters degrees,
130

materials for math learning,
168
–72,
169
–70,
171

Mathematica,
8

Mathematically Correct,
38
, 39

The
Math Gene
(Devlin),
19

math majors,
130

Math Power: How to Help Your Child Love Math, Even If You Don’t
(Kenschaft),
176

math wars,
31
–38, 39

“The Math Wars” (Schoenfeld),
38

Mazur, Barry,
23

media,
130

memorization

contrasted with comprehension,
27
–28,
29
,
40
–42,
75
–76,
121
–23

and gender issues,
121
–24,
126

and learning styles,
155

and shortcomings of passive learning,
40
–42

and traditional math instruction,
75

and variety in math work strategies,
138
–39

mental math abilities,
179
.
See also
number sense

meta-analysis of research,
130

Michigan State University,
38

middle school settings,
57
,
67
,
152
–53

Mirzakhani, Maryam,
29

misrepresentations of math,
15

mistakes

and asking questions,
178

and damage caused by tracking,
110

and parental involvement in education,
187
–88,
192

and shortcomings of passive learning,
42

and varieties of math strategies,
141

mixed-ability classes

advantages of,
106
–8,
111
,
112
–13,
114
,
116
–17

and detracking initiatives,
115
–16

lasting impact of,
118

and project-based approach,
70

and summer school program,
145
–54

modeling,
8

Moskam, Emily,
1
–3, 11,
32
, 47

multiple-choice tests,
85
–86,
89
–90,
94

multiple representations approach,
59

multiplication skills

and compression of math strategies,
143
–45

and gender issues,
121

and number sense,
179
,
180

and number talks,
148
–49

and parental involvement in education,
179

and summer school program,
148
–49

music,
29

myths about math skills,
186

narrowing of math curricula,
87

Nash, John,
27

national assessment,
101
–2

National Council of Teachers of Mathematics (NCTM), 39

national examinations,
77
–79,
124

natural ability view of math skill,
186

nature, mathematics in,
16
–18,
17
,
18
–19

news media,
77
–79,
78

New York Times,
18
,
135

No Child Left Behind Act,
88
,
94

nonlinear patterns,
64

notation, mathematical,
28
–29

“Numbers Don’t Lie: Men Do Better than Women,”
135
–36

number sense

and conceptual understanding,
143
–45,
191

described,
140
–41

and number talks,
179

and parental involvement in education,
179
,
191
–92

number talks,
148
–49,
164
–65,
178
–80