What's Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success (30 page)
Authors: Jo Boaler
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
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
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
and comparison of classroom styles,
77
–80
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
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
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
California
and communicative approach,
58
and gender issues,
135
innovative math classes in,
1
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
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
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 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
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
drawing,
54
,
67
,
71
–72,
122
,
189
–91,
198
,
201
drilling,
144
–45
Duckworth, Eleanor,
171
–72
ego feedback,
93
Elawar, Maria,
99
elementary school,
19
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