Despite important advances in primary prevention,atheroscl.docx

D
espite important advances in primary prevention,
atherosclerosis remains the leading cause of death in
developed societies.1 In addition to risk factors such
as hypertension, diabetes mellitus, tobacco use and dyslipi-
demia, less traditional risk factors have also been sought.
Many markers, including C-reactive protein and interleukins,
highlight inflammation as a key mediator in both the pro-
gression and activation of atherosclerotic lesions.2–4 Some
medications that are used to prevent cardiovascular diseases,
such as statins, also appear to reduce inflammation.5
Animal experiments have shown that pneumococcal vacci-
nation reduces the extent of atherosclerotic lesions.6 We
hypothesized that antibodies directed against Streptococcus
pneumoniae also recognize oxidized low-density lipoprotein
(LDL) and impede the formation of foam cells. Interestingly,
a retrospective cohort study involving World War II veterans
who had undergone splenectomy documented excess mortal-
ity rates from both pneumonia and ischemic heart disease.7
More recent data have suggested that acute pneumococcal
infections, but not vaccinations, increase the risk of vascular
events;8 however, the duration of vaccination exposure con-
sidered in that study was limited.
Our primary objective was to evaluate the association be-
tween pneumococcal vaccination and the risk of myocardial
infarction. We also explored whether any effect of vaccina-
tion on the risk of infarction waned over time.

Methods
Design and ethics approval
We conducted a case–control study of patients who were con-
sidered at risk for myocardial infarction and who had been
admitted to a tertiary care hospital. We obtained approval for
this study from the research ethics board of the Centre hospi-
talier universitaire de Sherbrooke and Quebec’s Commission
d’accès à l’information.
Data sources
We used 2 databases for this study. The first was the
research-purpose database9 of the Centre informatisé de
recherche évaluative en services et soins de santé of the Cen-
tre hospitalier universitaire de Sherbrooke, a tertiary care
teaching hospital in the province of Quebec. Along with de-
mographic data, this database included, for each hospital ad-
mission since 1996, detailed information on all primary and
secondary diagnoses, coded according to the International
Classification of Diseases, 9th revision (ICD-9). This data-
base also contained all biochemical and pharmaceutical data
recorded during the admission, including, for each medication
prescribed, the name, dosage, formulation, quantity dis-
François Lamontagne MD MSc, Marie-Pierre Garant PhD,
Jean-Christophe Carvalho MD,
Luc Lanthier MD MSc, Marek Smieja MD PhD, Danielle Pilon
MD MSc
@@ See related commentary by Madjid, page 749
Pneumococcal vaccination and risk of myocardial infarction
From the Department of Medicine (Lamontagne, Garant,
Carvalho, Lan-
thier, Pilon), Université de Sherbrooke, Sherbrooke, Que.; and

the Depart-
ment of Clinical Epidemiology and Biostatistics (Lamontagne,
Smieja), Mc-
Master University, Hamilton, Ont.
CMAJ Research
Background: Based on promising results from laboratory
studies, we hypothesized that pneumococcal vaccination
would protect patients from myocardial infarction.
Methods: We conducted a hospital-based case–control
study that included patients considered to be at risk of
myocardial infarction. We used health databases to obtain
hospital diagnoses and vaccination status. We compared
patients who had been admitted for treatment of myocar-
dial infarction with patients admitted to a surgical depart-
ment in the same hospital for a reason other than myocar-
dial infarction between 1997 and 2003.
Results: We found a total of 43 209 patients who were at
risk; of these, we matched 999 cases and 3996 controls ac-
cording to age, sex and year of hospital admission. Cases
were less likely than controls to have been vaccinated (ad-
justed odds ratio [OR] 0.53, 95% confidence interval [CI]
0.40–0.70). This putative protective role of the vaccine was
not observed for patients who had received the vaccine up
to 1 year before myocardial infarction (adjusted OR 0.85,
95% CI 0.54–1.33). In contrast, if vaccination had occurred
2 years or more before the hospital admission, the associa-
tion was stronger (adjusted OR 0.33, 95% CI 0.20–0.46).
Interpretation: Pneumococcal vaccination was associated
with a decrease of more than 50% in the rate myocardial
infarction 2 years after exposure. If confirmed, this associa-
tion should generate interest in exploring the putative

mechanisms and may offer another reason to promote
pneumococcal vaccination.
Abstract
CMAJ 2008;179(8):773-7
Une version française de ce résumé est disponible à l’adresse
www.cmaj.ca/cgi/content/full/179/8/773/DC1
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CMAJ • OCTOBER 7, 2008 • 179(8)
© 2008 Canadian Medical Association or its licensors
773

pensed, date dispensed and duration of prescription. Other re-
searchers have used this database in previous pharmacoepi-
demiologic studies.10–12
We also used the Logivac database, a government-
maintained database that records each pneumococcal vaccina-
tion administered in the province of Quebec. Since 1988, the
Agence de la santé et des services sociaux de l’Estrie, the
public health agency of the Estrie area, has recorded all such
data for the region in this database.
Study population
We considered for inclusion all patients who were at risk for
myocardial infarction and who were admitted to the Centre
hospitalier universitaire de Sherbrooke between Jan. 1,
1997, and Dec. 31, 2003. We defined risk for myocardial in-
farction as the presence of at least one of the following risk
factors, as recorded in the patients’ medical records: high
blood pressure, diabetes mellitus or dyslipidemia in men
older than 45 years and in women older than 50 years. We
included only patients who had a permanent address in the
same administrative area as the Centre hospitalier universi-
taire de Sherbrooke, where this hospital is the sole dispenser
of specialized care.
We defined cases as patients with one or more of the
specified cardiovascular risk factors, as documented in the
medical record, and no previously diagnosed atherosclerotic
disease (i.e., coronary, cerebral or peripheral vascular disease,
vascular dementia or any revascularisation) who had experi-
enced a new (i.e., incident) myocardial infarction within the
study period. We identified myocardial infarction with or
without ST-segment elevation on the basis of ICD-9 code
410. The hospital’s research database did not provide data on

deaths from myocardial infarction; thus, we did not differenti-
ate between episodes that resulted in death and those that did
not. For cases, we deemed the date of hospital admission for
myocardial infarction to be the index date.
We defined controls as patients with one or more of the
specified cardiovascular risk factors, as documented in the
medical record, and no previously diagnosed atherosclerotic
disease (i.e., coronary, cerebral or peripheral vascular disease,
vascular dementia or any revascularisation), who did not ex-
perience a new myocardial infarction during the study period.
We included only patients who had been
admitted to one of the hospital’s surgical
departments (orthopedics, gynecology,
urology, general surgery, plastic surgery
or otorhinolaryngology). For controls, we
considered the date of admission into one
of these departments as the index date. We
matched 4 controls to each case on the
basis of age (within 2 years), sex and
index date (within 1 year).
Definition of exposure
We considered patients to have been ex-
posed to the pneumococcal polysaccharide
vaccine if they had received this vaccine
in the 10 years before the index date, as
recorded in the Logivac database. We
stratified exposure by the interval between
vaccination and index date: up to and in-
cluding 1 year before the index date, more
than 1 year but less than 2 years before the
index date, and 2 years or more before the
index date. We were unable to perform
further stratification because too few pa-

tients had received the vaccine between 3
and 10 years before the index date. These
cut-offs were arbitrary, as there are no
clinical data to support this classification.
Definition of other important risk
factors
We included the following variables in our
models (as recorded in the patients’ med-
ical records between 1997, when the com-
puterized database was implemented, and
the index date): chronic obstructive pul-
monary disease, chronic renal failure, his-
Research
CMAJ • OCTOBER 7, 2008 • 179(8)774
Residents of the selected
administrative region
n = 43 185
Patients at risk for
myocardial infarction
n = 43 209
Excluded
• No health insurance card n = 24
Patients who met
all criteria
n = 20 480
Cases

n = 1 000
Controls
n = 19 480
Not selected
for analysis
n = 15 484
Matched for
analysis
n = 3 996
Excluded
• Not admitted to a selected surgical
department or had previous athero-
sclerotic disease n = 21 503 controls
• Had predefined exclusion criteria
as secondary diagnosis before the
date of myocardial infarction
n = 1 202 cases
Excluded
• Could not be
matched for age
n = 1
Cases
included
n = 999
Figure 1: Flow diagram showing the selection of cases and
controls for inclusion in a

study of the relation between pneumococcal vaccination and
myocardial infarction.
tory of splenectomy, history of S. pneumoniae infection, dia-
betes mellitus, hypertension and dyslipidemia. We selected
these covariables because we considered them a priori as
likely confounders; that is, associated with both myocardial
infarction and pneumococcal vaccination. We based our
choices on biological rationales, rather than statistically sig-
nificant associations.
Statistical analysis
On the basis of the findings from a pilot study, we estimated
baseline exposure to the pneumococcal polysaccharide vac-
cine at 20%. Given a type 1 error of 0.05, a type 2 error of
0.2, a correlation coefficient for exposure of 0.9 and an odds
ratio (OR) of 0.5, representing a moderate to large effect size,
we needed a sample size of 4610 patients: 922 cases and 3688
controls. An OR of less than 1 implies that the odds of being
exposed to the vaccine were lower for cases than for controls,
suggesting a protective effect of the vaccine.
We used conditional logistic regression to estimate ad-
justed OR and 95% confidence interval (CI) for new myocar-
dial infarctions in relation to receipt of the pneumococcal
polysaccharide vaccine. We conducted both univariable and
multivariable analyses, incorporating the covariables stated
above. We first ran a multivariable model entering in a single
step the following covariates: pneumococcal vaccination
status, chronic obstructive pulmonary disease, chronic renal
failure, previous S. pneumoniae infection, splenectomy and
diabetes. In our second model, we included in a single step
the same covariables along with hypertension and dyslipid-
emia. For all analyses, we matched cases and controls by

age, sex and index date.
Results
Using information from the Centre informatisé de recherche
évaluative en services et soins de santé database, we initially
identified 43 209 patients at risk for myocardial infarction
during the study period. Of these, we selected 999 cases and
3996 controls, matched for age, sex and index date, for analy-
sis (Figure 1).
Overall, cases were significantly less likely than controls
to have been vaccinated (7.1% v. 11.6%), and cases were sig-
nificantly more likely to have chronic renal failure (10.1% v.
3.0%) and diabetes (15.4% v. 5.0%) (Table 1).
The mean time between the administration of the pneumo-
coccal polysaccharide vaccine and the index date was 1.81
years (standard deviation [SD] 1.02) for patients who had
been exposed to the vaccine. The mean interval since expos-
ure to the vaccine was 1.50 (SD 0.95) years before the index
date for cases and 1.86 (SD 1.03) years before the index date
for controls (p < 0.001).
After adjustment for potential confounding variables,
cases were significantly less likely than controls to have re-
ceived pneumococcal vaccine (OR 0.53, 95% CI 0.40–0.70).
With stratification by time since vaccination, this difference
was evident for vaccinations given more than 1 year before
the index date (Table 2).
Two additional variables (hypertension and dyslipidemia),
for which data are not presented in Table 1 or Table 2, were
independently associated with the outcome both before and
after adjustment. However, including them in the multivari-
able analysis did not alter the direction or the size of the vac-

cine effect (OR 0.43, 95% CI 0.31–0.59).
Research
CMAJ • OCTOBER 7, 2008 • 179(8) 775
Table 1: Sociodemographic and health characteristics of cases
(n = 999) and controls (n = 3996) in a study of the relation
between
pneumococcal vaccine and myocardial infarction
No. (%) of patients*
Characteristic
Cases
n = 999
Controls
n = 3996
Odds ratio
(95% CI)†
Age, yr, mean (SD) 59.2 (12.7) 58.8 (13.0) NA
Sex, male 684 (68.5) 2736 (68.5) NA
Pneumococcal vaccination 71 (7.1) 465 (11.6 ) 0.55 (0.42–
0.72)
Timing of vaccination in relation to index date, yr
≤ 1 25 (2.5) 112 (2.8) 0.89 (0.57–1.38)
1–2 46 (4.6) 353 (8.8) 0.47 (0.34–0.65)

≥ 2 20 (2.0) 208 (5.2) 0.36 (0.22–0.57)
Concurrent conditions
Chronic obstructive pulmonary disease 41 (4.1) 66 (1.7) 1.70
(0.77–3.75)
Chronic renal failure 101 (10.1) 119 (3.0) 3.97 (2.97–5.31)
History of Streptococcus pneumoniae infection 7 (0.7) 21
(0.5) 1.33 (0.57–3.14)
Splenectomy 8 (0.8) 7 (0.2) 4.57 (1.66–12.61)
Diabetes mellitus 154 (15.4) 200 (5.0) 3.59 (2.85–4.52)
Note: CI = confidence interval, NA = not applicable, SD =
standard deviation.
*Unless indicated otherwise.
†Odds ratios for myocardial infarction were estimated from
univariable conditional logistic regression models (for matched
analyses) between risk of myocardial
infarction and each of the independent variables (total n =
4995).
Interpretation
Inferences from our study lend support to the hypothesis
that vaccination against S. pneumoniae is associated with a
lower risk of myocardial infarction. Our results suggest that,
after a number of confounding and modifying variables
were taken into account, the odds of having received a vac-
cination against S. pneumoniae in the group who had experi-
enced myocardial infarction was about half that in the con-

trol group. Moreover, this association appeared stronger and
the benefit appeared to increase with time since exposure to
the vaccine.
Several studies have examined the effect of infections on
atherosclerosis. Specific antibiotic regimens targeting a single
microbe and given as secondary prevention did not reduce the
incidence of acute coronary syndromes.13–16 Some authors
have suggested that it is the total burden of infection at vari-
ous sites and the associated inflammatory cascade that affect
the progression of atherosclerosis and elicit clinical manifest-
ations.4,17,18 A recent study8 showed a greater risk of myocar-
dial infarction and stroke after acute respiratory and urinary
tract infection and a lower risk after influenza vaccination. In
that study, in contrast to our study, pneumococcal vaccination
was not associated with a lower risk of myocardial infarction;
however, the vaccination history was limited to 91 days be-
fore the vascular episode.
In addition to preventing acute S. pneumoniae infections,
the pneumococcal vaccine is thought to alter the natural his-
tory of atherosclerosis in another way. In pathogen-free
mice without the LDL receptor, vaccination against S. pneu-
moniae decreased the extent of atherosclerotic lesions in the
aorta by 30 weeks.6 This phenomenon appeared to result
from molecular mimicry between the recognized epitopes
on S. pneumoniae and oxidized LDL. IgM antibodies
directed against S. pneumoniae also impeded the uptake of
oxidized LDL by macrophages, thereby interrupting an
early and crucial step leading to atherosclerosis. The fact
that this protective effect of the vaccine appeared after
1 year also concurs with results obtained by Smeeth and col-
leagues,8 who found that pneumococcal vaccination did not
alter the risk of a vascular event when it had been given
within 3 months before the diagnosis.

Our study had some limitations. First, there may have
been residual confounding. Other cardiovascular risk fac-
tors, such as smoking, medication use, obesity and lifestyle
factors, including exercise and diet, could not be incorpor-
ated in the model because these characteristics are not
recorded in the research database. It is plausible that pa-
tients who are more concerned about their health are less
likely to smoke and are more likely to seek vaccination.
Another limitation of our study was the potential for mis-
classification of exposure; specifically, some patients
might have received the pneumococcal vaccine outside of
the administrative region and their exposure would not
have been recorded in the government database. We at-
tempted to minimize this potential problem by selecting
only patients who resided in the administrative area. Fur-
thermore, it is unlikely that cases and controls would differ
in terms of this factor. Finally, the study population was
limited to one centre and consisted mostly of white males,
which limits the external validity of our results. Despite
these limitations, the strength and precision of the associa-
tion, as well as the apparent dose–response by time of ex-
posure favour the conclusion that true causality exists.
Validation through a larger prospective study is required to
help resolve these issues.
In conclusion, the results of this study of patients at risk
for vascular disease suggest an effect of pneumococcal vac-
cination in reducing episodes of new myocardial infarction.
Future projects should aim to confirm the association and
better characterize the immune and inflammatory responses
to the vaccine.
Research
CMAJ • OCTOBER 7, 2008 • 179(8)776

Table 2: Adjusted odds ratios for myocardial infarction
associated with pneumococcal vaccination among patients at
risk for
cardiovascular diseases (n = 4995)
Comparison; adjusted odds ratio* (95% CI)
Risk factor
Vaccine
(v. no vaccine)
Vaccine ≤ 1 yr before index
date (v. no vaccine
or vaccine > 1 yr before
index date)
Vaccine > 1 yr before index
date (v. no vaccine
or vaccine ≤ 1 yr before
index date)
Vaccine ≥ 2 yr before index
date (v. no vaccine
or vaccine < 2 yr before
index date)
Pneumococcal vaccination 0.53 (0.40–0.70) 0.85 (0.54–1.33)
0.46 (0.32–0.64) 0.33 (0.20–0.46)
Chronic obstructive
pulmonary disease

2.21 (1.44–3.39) 2.23 (1.46–3.42) 2.21 (1.44–3.39) 2.24 (1.45–
3.44)
Chronic renal failure 3.17 (2.33–4.31) 3.19 (2.35–4.33) 3.13
(2.30–4.25) 3.08 (2.27–4.18)
History of Streptococcus
pneumoniae infection
0.67 (0.26–1.73) 0.65 (0.25–1.69) 0.67 (0.26–1.73) 0.68 (0.27–
1.75)
Splenectomy 2.61 (0.84–8.17) 2.85 (0.91–8.88) 2.62 (0.84–
8.21) 2.62 (0.83–8.23)
Diabetes mellitus 3.36 (2.65–4.27) 3.26 (2.57–4.13) 3.38 (2.66–
4.29) 3.43 (2.70–4.36)
Note: CI = confidence interval.
*In each of the 4 models, each odds ratio was adjusted for the
other risk factors in the model.
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10. Brophy JM, Brassard P, Bourgault C. The benefit of
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15. Grayston JT, Kronmal RA, Jackson LA, et al. Azithromycin
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16. O’Connor CM, Dunne MW, Pfeffer MA, et al. Azithromycin

for the secondary
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17. Zhu J, Nieto FJ, Horne BD, et al. Prospective study of
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CMAJ • OCTOBER 7, 2008 • 179(8) 777
This article has been peer reviewed.
Competing interests: None declared.
Contributors: François Lamontagne was responsible for
initiating the project
and contributed to the conception and design of the study and
the acquisition
and interpretation of the data; he wrote the initial and
subsequent versions of
the article. Marie-Pierre Garant contributed to the data analysis
and interpreta-
tion. Jean-Christophe Carvalho contributed to the acquisition
and interpreta-
tion of the data. Luc Lanthier and Marek Smieja contributed to
the design of
the study and edited the manuscript. Danielle Pilon supervised
the design and

interpretation of the data. All of the authors made substantial
revisions to the
intellectual content of the manuscript and approved the final
version.
Acknowledgements: Dr. Sophie Michaud contributed to the
design of the
study. Hassan Diab was responsible for the management of the
Centre infor-
matisé de recherche evaluative en soins et systèmes de la santé
database.
Danielle Pilon has received funding from the Fonds de la
recherche en
santé du Quebec.
Funding: The Quebec Ministère de la santé et des services
sociaux and the
Agence de la santé et des services sociaux de l’Estrie provided
funding for
this study.
Correspondence to: Dr. Danielle Pilon, Faculty of Medicine,
Université de Sherbrooke, 3001, 12e Avenue N, Sherbrooke QC
J1H 5N4; fax 819 820-6406; Danielle.P[email protected]
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The Mathematics Educator
2005, Vol. 15, No. 1, 2–6
2 Building a Socially Just and Diverse Democracy
Guest Editorial…
The Role of Mathematics Instruction in Building
a Socially Just and Diverse Democracy
Deborah Loewenberg Ball
Imani Masters Goffney
Hyman Bass
As elementary school teachers, Deborah and Imani
did not just teach academic subjects. They taught their
pupils skills and knowledge to help develop them as
individuals and as members of a collective. Subject
matters offered important resources for these social
goals: they and their students read literature in the
voices of a wide range of people, about experiences
both similar to and different from theirs. They studied
other cultures and learned about work, life, and
practice in a variety of societies and settings. And they
learned that issues of voice, experience, culture, and
setting were important threads in the tapestry of what it
means to be human. The work they did with their
pupils across these academic subjects was, of course,
also aimed at developing the children’s skills and
knowledge, their capacity to interpret texts and

artifacts, to reason in disciplined ways, and to solve
problems within and beyond these domains.
Their young students were also resources for the
goals toward which Deborah and Imani worked as
teachers. From a variety of cultural backgrounds, and a
wide range of communities, their students thought
differently from one another, and they brought ideas
and experiences to offer to the collective work in their
classes. They were children — they made friends,
argued and fought, and were generously caring. What
they did, said, and felt comprised their classroom’s
working environment and offered a myriad of
opportunities for learning. Over time, Deborah and
Imani each learned to listen to and notice what the
children brought and to use and mediate their
differences.
All this was well and good — in reading, social
studies, art, music, and even science. But mathematics
seemed isolated from the rest. There seemed little to
discuss, little opportunity to notice and use the
diversity of their students. Deborah and Imani
explained ideas and procedures, the students practiced,
and they all reviewed. Although the two teachers
thought the students were capable mathematically, the
students did not think so. Some viewed themselves as
“good at math,” while others disparaged their own
abilities. Deborah and Imani saw differences in
accomplishment produced from their instruction, and
they worried. They grew concerned about which
students were coming to see themselves as “bad at
math,” and were quite sure that the source lay not with
these students, but in their teaching.

Now, when the three of us discuss these teaching
experiences, we understand a different landscape than
Deborah and Imani knew to see then. We recognize
that mathematics — and the ways in which teachers
teach it — is a key resource for building a socially just
and diverse democracy. While other school subjects,
too, offer resources for democratic education and
social justice, mathematics makes its own unique
contributions to these goals. Instead of seeing
mathematics as culturally neutral, politically irrelevant,
and mainly a matter of innate ability, we see it as a
critical lever for social and educational progress
(Moses & Cobb Jr., 2001) if taught in ways that make
Deborah Loewenberg Ball is the William H. Payne Collegiate
Professor of Mathematics Education and Teacher Education, and
Director of Teacher Education, at the University of Michigan.
Ball's work focuses on studies of instruction and the processes
of
learning to teach. She also directs several research projects that
investigate efforts to improve teaching through policy, reform
initiatives, and teacher education..
Imani Masters Goffney is a doctoral student in mathematics and
teacher education at the University of Michigan. She earned her
bachelor's degree from Spelman College in 2000 and her
Masters' degree in Curriculum Development from the University
of Michigan in April 2002. Her research interests include
innovations in teacher education and mathematics education,
both at the pre-service level and in professional development,
and issues of equity.
Hyman Bass is the Roger Lyndon Collegiate Professor of
Mathematics and Mathematics Education at the University of
Michigan. He is President of the International Commission on
Mathematics Instruction. During the past seven years he has
been collaborating with Deborah Ball and her research group at
the University of Michigan on the mathematical knowledge and

resources entailed in the teaching of mathematics at the
elementary level.
Deborah Loewenberg Ball, Imani Masters Goffney, & Hymann
Bass 3
use of its special resources. Three main points structure
the perspective that we take in this essay.
First, in order to enable all students to be
successful with mathematics, we see that some
elements of “good teaching” of mathematics —
listening closely to students’ ideas, for example, or
being sensitively careful at the interface between
mathematical and everyday language — are especially
important. They are important in order to recruit
students into mathematics, as well as to help them
succeed there. Consider the imperative to listen closely
to students, and to be sensitive to the boundaries
between mathematical and everyday language:
Students who are working on mathematics in an
English that they are just learning1 express
mathematical ideas in ways that seemed to us unusual
or hard to understand at times; but when Deborah and
Imani focused carefully, they heard significant
mathematical insights they had previously missed, or
misunderstood. The many varieties of English spoken
in the classroom make it especially important to notice
the ambiguities between technical and everyday uses of
English: For example, what does it mean for a number
to be “odd,” or “big”? What is a “right” angle? What
about “similar” figures, or “equivalent” fractions? Why
are some numbers “rational” and others not, and still
others “radicals?” Is there a synonym for “regular,”

and what is the distinctive technical meaning of a
“group” — in elementary school or higher level math?
All these are words used one way in everyday talk, and
in other ways in mathematics. Mathematics often uses
and specializes everyday language, sometimes
metaphorically, rather than coining a separate technical
vocabulary (Halliday, 1978), thus both enabling and
complicating entry to its register (Pimm, 1987).
Teachers also coin expressions to support students’
learning, saying that a number “goes into” another, or
that one “borrows” from the tens. So although listening
closely and being careful about the differences between
technical and everyday uses of mathematical language
are important aspects of “good teaching,” they demand
emphasis in order to make mathematical success both
common and expected.
Second, the disparities in mathematics
achievement are tightly coupled with social class and
race, and have not narrowed over the last decade
despite a rhetoric of “mathematics for all.” Some have
come to suspect that some aspects of “good teaching”
may unwittingly create, reproduce, or extend inequities
among students, differences deeply rooted in the
inequalities of our society (Ball, Hoover, Lewis, Bass,
& Wall, 2003). Take an example: A glance at
mathematics textbooks, even those newly designed or
revised, reveals the settings for many mathematics
problems to be most familiar to middle class white
students. Plans for garden plots, mileage covered on
family vacations, stereotypical images of “family,”
allowance plans — these and other “meaningful” and
“real world” contexts may be more familiar and
engaging to some students than to others. The effort to
wade through an unfamiliar context in order to get to

the mathematics can impede students’ learning
(Lubienski, 2002). The enthusiasm for “real world”
problems, left unchecked, may disadvantage students
for whom the chosen settings are not understood or
valued. This is not to say that problems or contexts
may not be useful to students, only that contexts are
often social or cultural and depend for their usefulness
on students’ experiences. Attentive to this, some
educators work to design contexts that are rooted in
broader and more diverse experience and culture. They
might use African designs as a site for studying
geometric patterns, or urban street games as settings
for using complex numerical strategies. Still, the
difficulties that can arise from uneven familiarity with
particular “contexts” require vigilance. We return
below to the rich possibilities inherent in the use of
cultural contexts.
Other practices of teaching thought to be “good”
also deserve closer scrutiny — reluctance to “tell”
students or to be explicit, for example. Letting students
figure out crucial mathematical practices — how to
compare representations, or how to build a
mathematical argument — for themselves may well
mean that only some students figure them out. This is
not benign: Past evidence suggests that white or Asian
middle class students, often male, tend to learn these
implicitly, while many others do not (RAND
Mathematics Study Panel, 2003). The contemporary
enthusiasm for instructional approaches in which the
teacher “facilitates” and refrains from being direct may
be more congruent with some students’ experiences
and practices than others, thus inadvertently
advantaging those students if participation in such
discourse is not explicitly taught (Delpit, 1988; Heath,
19xx; Heath, 1983; Lubienski, 2002). And, moreover,

explicit guidance for learning complex skills or ideas is
essential if all students are to develop such capacities.
Leaving the construction of these skills to chance can
make student success susceptible to cultural
differences in discursive norms.
Affirming students’ accomplishments, rewarding
success, and praise are all ways in which good teachers
encourage and inspire students to work hard and to see
themselves as mathematically capable (Boaler &
NetLibrary Inc., 2000; Cohen, Lotan, Abram, Scarloss,
& Schultz, 2002). But these also signal to students
what it means to be “good at math.” Unexamined,
these messages may communicate a narrow
perspective on what mathematical ability is, and thus
assign competence unevenly and without attention to a
full range of mathematical skill and practice, and their
diverse forms of expression.
So far we have discussed what may underlie
significant and persistent disparities in mathematics
achievement, efficacy, and success. Although many
important societal factors shape these disparities,
instructional practices also matter. Instruction can take
aim at pervasive inequality, or it can reinforce or even
create it. Too often, unexamined, it may do the latter.
Thus, learning to examine who and what is being
valued and developed in math class is essential.
Still, our argument would be incomplete if we did

not also consider what mathematics — and
mathematics instruction — can contribute to education
for democracy. As Malloy (2002) argues, mathematics
education that is oriented to promote democratic goals
can “provide students with an avenue through which
they can learn substantial mathematics and can
[develop into] productive and active citizens” (p. 21,
emphasis added). Clearly, we need vigorous efforts to
improve every student’s access to and development of
usable mathematical literacy, including the skills for
everyday life, preparation for the increasing
mathematical demands of even relatively non-technical
workplaces, and for continued mathematical study.
The need for collective commitment to this goal has
never been greater. In addition, however, we claim that
mathematics has a special role to play in educating
young people for participation in a pluralistic
democratic society. Making that possible depends on
instruction that uses the special resources that
mathematics holds for realizing these broader societal
aims.
One way in which mathematics teaching can help
to build the resources for a pluralistic society is
through the development of tools for analysis and
social change. Mathematics offers tools to examine and
analyze critically the deep economic, political, and
social inequalities in our society, for studying crucial
societal problems, and for considering a host of issues
that can be understood and critiqued using quantitative
tools. For example, who voted in the last election and
why? How does the Electoral College shape whose
votes count most in a presidential election? How do
our income and inheritance tax laws shape the
distribution of wealth and access to fundamental

resources, as well as what is valued? How does our
system of school funding, for example through real
estate taxes, shape the quality of education that
different children in our country receive? Developing
and using the mathematical skills that enable young
people to engage in social analysis and improvement is
one way in which mathematics can contribute to the
development of a diverse democracy.
A second way in which mathematics teaching can
play a role in education for democracy is as a setting
for developing cultural knowledge and appreciation,
important resources for constructive participation in a
diverse society. Mathematics represents an ancient and
remarkable set of cultural achievements and
engagements. As such, the historical development of
mathematical ideas and methods offers a medium for
studying history and culture and their intersections in
domains of human activity as diverse as architecture,
art, music, science, and religion. Mathematics offers
opportunities for young people to learn about their own
cultural heritage and that of others. Such learning is
crucial for developing the understanding and
appreciation of diverse traditions, values, and
contributions, and ways to notice, respond to, and use
them. Such learning is also crucial for developing a
sense of one’s own cultural identity, and sense of self
and membership, both for oneself and also as a
participant in the broader cultural milieu.
But a third way that mathematics teaching can
support the development of democratic goals — the
one on which we focus here — is through the skills and
norms embedded in mathematical practice itself. In
other words, we argue that it is not just the content of
mathematics and its tools that contributes to

democratic goals, but the very nature of mathematical
work. Mathematics instruction, we claim, can offer a
special kind of shared experience with understanding,
respecting, and using difference for productive
collective work. How so? Consider that mathematics is
centrally about problem solving, and about discovering
and proving what is true. Alternative interpretations
and representations of a problem can often serve to
open a path to its solution; sometimes a novel
metaphor, diagram, or context can crack a difficult part
of a problem. At the same time, the use of difference is
structured and supported by common disciplinary
language, norms, and practices. Terms must be
precisely defined and used in common ways.
Disagreements are resolved not by shouting or by
plurality, but by reasoned arguments whose
construction can be taught and learned. Decisions such
Deborah Loewenberg Ball, Imani Masters Goffney, & Hymann
Bass 5
as whether 0 is even or odd, or how to interpret the
meaning of
!
3
4
, whether
!

5
5
is greater or less than
!
4
4
, or
whether a solution to a particular problem is valid are
subject to mathematical reasoning, not governed by
desire or power. Moreover, mathematical reasoning is
a practice to be learned, not an innate talent.
In these ways, mathematics instruction can
deliberately help young people learn the value of
others’ perspectives and ideas, as well as how to
engage in and reconcile disagreements. Mathematics
instruction can be designed to help students learn that
differences can be valuable in joint work, and that
diversity in experience, language, and culture can
enrich and strengthen collective capacity and
effectiveness. Students can also learn that mathematics
is not an arena in which differences are resolved by
voting. Politics is an arena in which differences are
managed in this way, but the study of literature or
mathematics is not. In a democratic society, how
disagreements are reconciled is crucial. But
mathematics offers one set of experiences and norms
for doing so, and other academic studies and
experiences provide others. In literature, differences of
interpretation need not be reconciled, in mathematics
common consensus matters. In this way, mathematics

contributes to young people’s capacity for participation
in a diverse society in which conflicts and are not only
an inescapable part of life, but their resolution, in
disciplined ways, is a major source of growing new
knowledge and practice.
How might instruction be designed to serve both
mathematical and democratic ends? One element
would lie with the mathematical tasks selected. Tasks
that serve to develop common skills, language, and
practices offer ways that can help to build the common
skills needed for class work on mathematics. Also
useful are tasks that yield to alternative representations,
so that students’ understanding of the material is
deepened through the different ways in which their
classmates see the ideas. Although it is valuable to use
mathematical tasks that profit from others’
interpretations, such tasks should not, however, depend
unfairly on unevenly distributed cultural experience or
knowledge.
How mathematical tasks are used is crucial in
determining whether or not their potential is realized in
classrooms. If not carefully structured and guided,
cognitively complex tasks can degrade to simple
routine problems, and problems ripe with opportunity
for reasoning and representation can become
algorithmic (Stein, 1996). Similar vigilance is needed
in order for tasks to serve as contexts for the
development of democratic skills and dispositions.
Such vigilance is centered on cultivating attention to
and respect for others’ mathematical ideas. Students
would need to develop a consistent stance of civility
with one another, a stance based on intellectual interest
and respect, not mere social politeness or “niceness.”

This would require learning to listen carefully to
others’ ideas, and checking for understanding before
disagreeing. Other skills, norms, and practices of
collective mathematical work include giving credit to
others’ ideas — referring to ideas by their authors’
names, for example — and critiquing ideas, not people,
using the tools and practices of the discipline. Students
would work to seek agreement on meanings and
solutions, drawing on past shared experiences,
definitions, ideas, and agreements about meaning, and
they would use and contribute to one another’s ideas in
a collective effort to solve and understand the
mathematics and the problems on which they are
working. Important to our argument is that these skills
and practices that are central to mathematical work are
ones that can contribute to the cultivation of skills,
habits, and dispositions for participation in a diverse
democracy.
For mathematics instruction to contribute to the
building of a socially just and diverse democracy will
require more than care with curriculum and teaching. It
will also require more than committed teachers,
sensitive to and skillful in working toward these aims
(Ladson-Billings, 2001). Accomplishing this would
require significant change in teachers’ education and
professional development, no small task. But who
these teachers are matters as well. We need a teaching
force diverse in race, culture and ethnicity, and
linguistic resources. The current teaching population is
disproportionately white, female, and middle-class.
The profession responsible for teaching our nation’s
children should include people of a wider range of
cultural and experiential resources, both because young
learners should have access to more diversity in the
teachers from whom they learn (Irvine, 2003), and

because the collective knowledge, practice, and norms
of the profession would be improved if its members
were more diverse. Responsible for helping prepare
young people for life in society, teachers — and the
mathematics instruction they offer — must collectively
represent and take advantage of the multicultural
nature of that society for individual and common good.
REFERENCES
Adler, J. (2001). Teaching mathematics in multilingual
classrooms.
Boston: Kluwer academic publishers.
Ball, D. L., Hoover, M., Lewis, J., Bass, H., & Wall, E. (2003).
In
attention to equity in teaching elementary school mathematics.
Prepared in Draft form for 2003 annual meeting of the AERA.
Baugh, J. (1999). Out of the mouths of slaves: African american
language and educational malpractice. Austin: The University
of Texas Press.
Boaler, J., & NetLibrary Inc. (2000). Multiple perspectives on
mathematics teaching and learning. Westport, Conn.: Ablex.
Cohen, E. G., Lotan, R. A., Abram, P. L., Scarloss, B. A., &
Schultz, S. E. (2002). Can groups learn? Teachers College
Record 104 (6), 1045–1068.
Delpit, L. D. (1988). The silenced dialogue: Power and

pedagogy
in educating other people's children. Harvard Educational
Review, 58 (3), 280–297.
Halliday, M. A. K. (1978). Language as a social semiotic.
Baltimore, MD: University Park Press.
Heath, S. B. (1983). Ways with words: Language, life and work
in
communities and classrooms. New York: Cambridge
University Press.
Irvine, J. J. (2003). Educating teachers for diversity: Seeing
with a
cultural eye. New York: Teachers College Press.
Ladson-Billings, G. (2001). Crossing over to canaan: The
journey
of new teachers in diverse classrooms (1st ed.). San Francisco:
Jossey-Bass.
Lubienski, S. T. (2002). Research, reform, and equity in U.S.
Mathematics education. Mathematical Thinking and Learning,
4(2–3), 103–125.
Malloy, C. E. (2002). Democratic access to mathematics
through
democratic education. In L. D. English, (Ed.), Handbook of
International Research in Mathematics Education, (pp. 17–
25). Mahwah, NJ: Lawrence Erlbaum Associates.
Moses, R., & Cobb Jr., C. (2001). Radical equations: Math
literacy
and civil rights: Beacon Press.
Pimm, D. (1987). Speaking mathematically: Communication in

mathematics classrooms. London: Routledge.
RAND Mathematics Study Panel, D. L. B., Chair. (2003).
Mathematical proficiency for all students: Toward a strategic
research and developmenet program in mathematics
education. Arlington: RAND.
Schleppegrell, M. J. (2002). Challenges of the science register
for
esl students: Errors and meaning-making. In Developing
advanced literacy in first and second languages (pp. 119–
142). Mahwah, NJ: Lawrence Erlbaum Associates.
Stein, M. K., Grover, B.W., & Henningsen, M. (1996). Building
student capacity for mathematical thinking and reasoning: An
analysis of mathematical tasks used in reform classrooms.
American Educational Research Journal, 33(2), 455–488.
1 We include here those students whose mother language
is another world language as well as those who speak one of
many dialects of the English language (Adler, 2001; Baugh,
1999; Schleppegrell, 2002)

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