What's Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success (30 page)

16
. Sian L. Beilock, Lauren E. Holt, Catherine A. Kulp, and Thomas H. Carr, “More on the Fragility of Performance: Choking Under Pressure in Mathematical Problem Solving,”
Journal of Experimental Psychology
133, no. 4 (2004): 584–600.

17
. Gray and Tall, “Duality, Ambiguity, and Flexibility.”

9/Moving to a More Positive Future

1
. See for example: Jeffrey E. Froyd, “Evidence for the Efficacy of Student-active Learning Pedagogies,” April 22, 2007, http://trc.virginia.edu/wp-content/uploads/2013/07/Evidence-for-Efficacy-Froyd.pdf.

2
. Carol S. Dweck, “The Perils and Promises of Praise,”
Educational Leadership
65, no. 2 (2007): 34–39.

3
. Lisa S. Blackwell, Kali H. Trzesniewski, and Carol S. Dweck, “Implicit Theories of Intelligence Predict Achievement Across an Adolescent Transition: A Longitudinal Study and an Intervention,”
Child Development
78, no. 1 (2007): 246–63.

4
. Eccles and Jacobs, “ Social Forces.”

5
. Joseph J. Williams, Tania Lombrozo, and Bob Rehder, “Why Does Explaining Help Learning? Insight from an Explanation Impairment Effect,” in
Proceedings of the 32nd Annual Conference of the Cognitive Science Society
(2010): 2906–11.

6
. Moser et al., “Mind Your Errors.”

7
. http://online.stanford.edu/course/how-to-learn-math-for-students-s14.

8
. Carol S. Dweck, “Is Math a Gift?: Beliefs That Put Females at Risk,” in Stephen J. Ceci and Wendy M. Williams, eds.,
Why Aren’t More Women in Science?: Top Researchers Debate the Evidence
(Washington, DC: American Psychological Association, 2007).

9
. Jo Boaler, “Changing the Conversation About Girls and STEM,” paper presented to the Council on Women and Girls at the White House, April 28, 2014. Available for download at www.youcubed.stanford.edu.

10
. Alina Tugend, “The Problem with Praise,”
Worth,
http://www.worth.com/index.php/component/content/article/4-live/2908-the-problem-with-praise.

11
. Boaler and Humphreys,
Connecting Mathematical Ideas.

12
. http://scpd.stanford.edu/instanford/how-to-learn-math.jsp.

13
. Ibid.

14
. Gray and Tall, “Duality, Ambiguity, and Flexibility.”

15
. Silva and White,
Pathways to Improvement
.

16
. Boaler, “Fluency Without Fear.”

17
. Boaler, “Research Suggests.”

18
. http://online.stanford.edu/course/how-to-learn-math-for-students-s14.

19
. Flannery,
In Code
.

Note: Page numbers in
italics
indicate photographs and illustrations. Additionally, the page numbers in this index refer to the printed version of this book. To find the corresponding locations in the text of this digital version, please use the “search” function on your e-reader. Note that not all terms may be searchable.

ability grouping,
103
–19

advantage of mixed-ability classes,
112
–13,
113
–17

and borderline casualties,
111

damage caused by tracking,
109
–14

and fixed mind-sets,
110

and learning opportunities,
109
–10

and problem-solving skills,
118
–19

research on impact of,
103
–8

and student respect,
113
–17

abstraction,
28
, 51,
74
,
82
,
129
,
150

achievement gaps,
88
,
97
,
99

active learning

and assessment for learning approach,
98
–99,
101
–2

described, 3

and math use after school years,
83

and the math wars,
38

and problem-solving skills,
40
–41

research supporting,
185

addition skills,
139
–40,
143
–45,
179

adolescents,
1
, 9, 49,
115

adults and math,
4
.
See also
parents

advanced classes,
66

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

algebra

and communicative approach,
59
–66

fostering algebraic thinking,
146
,
156

and math wars, 35–37

and number sense,
192

and shortcomings of passive learning, 47

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

and student tracking,
107

and summer school program,
151

and varied learning styles,
162
–63

Alonzo’s staircase problem,
159
–63,
160
–61,
203
–5

Amber Hill School

and ability grouping,
117
–18

Amber Hill Question,
75
,
202
–3

and comparison of classroom styles,
77
–80

and gender issues,
120
,
124
–25

and math use after school years,
80
–82

and traditional math instruction,
69
,
74
–77

anonymous surveys,
152

antireform activists, 33–35,
38
, 39,
185

anxiety about math, 3, 13,
86
,
188
,
192

application of math concepts,
151

architecture,
18
,
79

area problems,
71
–74,
162
–63,
205
–6

art and mathematics,
18

assessment of math skills

and ability grouping,
104
–6

assessment for learning approach,
95
–102

and borderline students,
111
–12

and detracking,
107
–8

expansion of standardized testing,
84
–85

and summer school program,
151
–52

and use of pseudocontexts,
52
–53

See also
testing

Associated Press–America Online (AOL) news poll, 5

Australia,
18
, 55

Barbie, 5

Beans and Bowls Puzzle,
182
,
213
–14

A
Beautiful Mind
(2001),
27

Belenky, Mary,
129

Bennett, John,
134

biases,
81
,
86

binomials,
121

Black, Paul,
98

borderline students,
111
–12

boredom,
152

Bracey, Gerald,
104
–5

brain physiology,
129

Brinkmann, Heinrich,
176

Brown, Dan,
16

Buddhist Monk Puzzle,
173
–74,
208

building blocks,
170

Burris, Carol,
107

Burton, Leone,
26
–27

Bush, George W.,
88

Businessweek,
7

Butler, Ruth,
99

Cabana, Carlos,
176

calculation and computation,
19
,
24
,
27
.
See also
equations and formulas

calculators,
72
–73,
90

calculus, 43,
58
,
66
,
107
–8,
126

California

and communicative approach,
58

and gender issues,
135

innovative math classes in,
1

and the math wars,
31
–32,
36
,
38

and mixed-ability classes,
108

and summer school program,
145
–54

and testing standards,
87
–91

California Dreaming
(Wilson),
38

Cambridge University,
22
–23,
133

Carnegie Corporation,
115

categorizing students.
See
ability grouping

Chessboard problem,
12
, 55,
199
–201

choice in math education,
71
,
74

Church of England,
134

circles,
18
–19

citizenship skills,
115

class divisions,
80
–81,
134

classroom behaviors,
157
,
159

classroom strategies

and assessment of math skills,
100
–101

communicative approach,
58
–68

importance of,
57
–58

and lifetime math skills,
80
–83

project-based approach,
68
–74,
78
–80

traditional approach,
74
–77,
78
–80

Clinchy, Blythe,
129

Coalition for Essential Schools,
115

Cohen, Michele,
134

collaboration

and communicative approach,
58
–59,
62
,
65
,
67
–68

and group education,
105
–6

and high-level mathematics,
129
–30

and learning styles,
163
–66

and the mathematical process,
26
–27

and mixed-ability classes,
112
–13,
116
–17

and project-based approach,
74

and shortcomings of passive learning, 47

and summer school program,
152

college admissions, 33–35

college performance,
86

Columbia University,
95
,
107

comment-based feedback,
99
–100

Commission for Women and Girls,
136

Common Core,
89

common sense, 51.
See also
number sense

communications and learning style,
163
–66.
See also
discussions in classrooms

communicative approach,
58
–68

comparison of math students,
93
,
94
.
See also
research on math teaching methods

competition,
122

complex instruction,
65
,
117
–18

complex problems

and ability grouping,
104

and compression of math concepts,
142
–43

and conceptual understanding,
156

and learning styles,
158

and mixed-ability classes,
108

and parental involvement in education,
172

and problem-solving skills, 11

and shortcomings of passive learning,
48

and standardized testing,
86
–88

and varieties of math strategies,
141
–42

comprehension

and conceptual understanding,
143
–45

and learning styles,
155
–56

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

stages of knowing,
129

compression of math strategies,
143
–45

conceptual understanding,
143
–45,
190
–91

confidence of students

and ability grouping,
114

and asking questions,
176

and learning styles,
166

puzzles and problems to foster math skills,
172
–75

and standardized testing,
89
–91,
91
–92

conjecture,
25

connected thinkers,
128
–29

Connecting Mathematical Ideas
(Humphreys),
190

constructive feedback,
93
–94

context in mathematics education, 51–56,
75

conversing.
See
active learning; collaboration; discussions in classrooms

core skills assessment,
101

Cornell University,
142
–43

Corno, Lyn,
99

Council for Adolescent Development,
115

Count Down
(Olson),
116

“counting all” strategy,
139
–41

“counting on” strategy,
140

course of work assessments,
101

Cowpens & Bullpens problem,
162
–63,
205
–6

creativity

and communicative approach,
67
–68

and gender issues,
128
–29

importance to learning,
194

and the mathematical process,
25
–26,
27
,
28
,
30

and opportunities to learn,
159

and parental involvement in education,
171
,
180
,
193

and problem-solving skills,
25
–26

and quantitative literacy,
8

and settings for math learning,
172

and shortcomings of passive learning, 43

and varied learning styles,
159
–63

cubes,
21

cues,
76
–77

Cuisenaire rods,
168

curiosity about math, 43,
159
,
160

curricula

focus on computation,
8

and the math wars,
31
–38, 39

recommended curricula by grade,
217
–18

and research on teaching methods,
83

and testing standards,
89
,
93
,
94

data interpretation,
73

The
Da Vinci Code
(Brown),
16

debates,
2

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

Deevers, M.,
93
–94

definitions of math,
15
,
16
,
19
–20,
59
–60

demographics of school populations,
69

derived facts,
140

detracking,
59
,
107
–8,
115
–16

Devlin, Keith,
19
,
29

diagnostic feedback,
100

dice,
170

dieting, 9

differences among students,
110
–11

discussions in classrooms

and learning styles,
154
–56,
157
–59,
163
–66

and shortcomings of passive learning, 49–51

and summer school program,
150
–51

diversity,
65
,
145

drawing,
54
,
67
,
71
–72,
122
,
189
–91,
198
,
201

drilling,
144
–45

Duckworth, Eleanor,
171
–72

Dweck, Carol,
110
,
188
–89

ego feedback,
93

Elawar, Maria,
99

elementary school,
19

employment issues,
6
–7,
79
–80

encouragement,
188
.
See also
enjoyment of math

engagement of students

curiosity about math, 43,
159

and future of math education,
185

and importance of creativity,
194

and mixed-ability classes,
116

and Moskam’s class,
1
–3

and open work,
116

and research on teaching methods,
83

and shortcomings of passive learning, 49

See also
active learning; explaining math work

engineering, 7–8,
161

England, math education in

and ability grouping,
106

and comparison of classroom styles,
108

and complex math problems,
28

and gender issues,
131

and national examinations,
77

and variety in math work strategies,
139