Embedding sustainable
development educa3on inmathema3cs educa3on texts
David Wagner
University of New Brunswick
Canadadwagner@unb.ca

Antonius Warmeling

Masami Isoda

Parvin Sinclair

Sustainable Development Goals (SDGs)

hKps://sustainabledevelopment.un.org/sdgs

Poten3al contribu3ons of mathema3cs
Philosophies of mathema3cs:• formalism• platonism• humanism• etc.
To teach mathema3cs for sustainable development ahumanist understanding of mathema3cs is most relevant.
Mathema3cs is a human ac3vity,
a way of addressing challenges inpar3cular human contexts.
(or a set of ways)

Poten3al contribu3ons of mathema3cs
Six ac3vi3es of mathema3cs (Bishop):• coun3ng• measuring• loca3ng• designing• explaining• playing
When people design, explain, or play with coun3ng,
measuring or loca3ng, they are doing mathema3cs.

Poten3al contribu3ons of mathema3cs
Six ac3vi3es of mathema3cs (Bishop):• coun3ng• measuring• loca3ng• designing• explaining• playing
When people design, explain, or play with coun3ng,
measuring or loca3ng, they are doing mathema3cs.

Poten3al contribu3ons of mathema3cs
Six ac3vi3es of mathema3cs (Bishop):• coun3ng• measuring• loca3ng• designing• explaining• playing
When people design, explain, or play with coun3ng,
measuring or loca3ng, they are doing mathema3cs.

Poten3al contribu3ons of mathema3cs
Six ac3vi3es of mathema3cs (Bishop):• coun3ng• measuring• loca3ng• designing• explaining• playing
When people design, explain, or play with coun3ng,
measuring or loca3ng, they are doing mathema3cs.

Poten3al contribu3ons of mathema3cs
Six ac3vi3es of mathema3cs (Bishop):• coun3ng• measuring• loca3ng• designing• explaining• playing
When people design, explain, or play with coun3ng,
measuring or loca3ng, they are doing mathema3cs.

Poten3al contribu3ons of mathema3cs
Six ac3vi3es of mathema3cs (Bishop):• coun3ng• measuring• loca3ng• designing• explaining• playing
When people design, explain, or play with coun3ng,
measuring or loca3ng, they are doing mathema3cs.

Poten3al contribu3ons of mathema3cs
Six ac3vi3es of mathema3cs (Bishop):• coun3ng• measuring• loca3ng• designing• explaining• playing
When people design, explain, or play with coun3ng,
measuring or loca3ng, they are doing mathema3cs.

Poten3al contribu3ons of mathema3cs
We can communicate with• precision• accuracy
Necessary for agreements(trea3es, contracts,…)

Nego3a3ngmathema&cs
complex systems
individual current needs

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provides toolsforbalancing
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needs for everyone

needs for the future

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systems thinking

Poten3al contribu3ons of mathema3cs
To balance conﬂic3ng needs we:• consider measures that indicate iden3ﬁed goals,• assign numeric values to things that are not easy to measure,• weight these indicators to align with our values.
These indicators can• measure various policy scenarios to iden3fy an op3mum decision,• compare regions to see who/what needs aKen3on.
This depends on the quality of our choices about:• what to measure• which measures to value the most, and• the mathema3cal model for predic3ng results
It may seem arbitrary, but it is less arbitrary than the alterna3ve.

Poten3al contribu3ons of mathema3cs
p op u lar p
To balanceneeds we:ress
(uncle conﬂic3ng
ar me measures that indicate iden3ﬁed goals,• consider
thod)• assign numericvalues to things that are not easy to measure,• weight these indicators to align with our values.

These indicators can• measure various policy scenarios to iden3fy an op3mum decision,• compare regions to see who/what needs aKen3on.
This depends on the quality of our choices about:• what to measure• which measures to value the most, and• the mathema3cal model for predic3ng results
It may seem arbitrary, but it is less arbitrary than the alterna3ve.

Poten3al contribu3ons of mathema3cs
p op u lar p
To balanceneeds we:ress
(uncle conﬂic3ng
ar me measures that indicate iden3ﬁed goals,• consider
thod)• assign numericvalues to things that are not easy to measure,• weight these indicators to align with our values.

These indicators can
GDP per capita (or PPP)• measure various policy scenarios to iden3fy an op3mum decision,• compare regions to see who/what needs aKen3on.
This depends on the quality of our choices about:• what to measure• which measures to value the most, and• the mathema3cal model for predic3ng results
It may seem arbitrary, but it is less arbitrary than the alterna3ve.

Poten3al contribu3ons of mathema3cs

p op u lar p
To balanceneeds we:ress
(uncle conﬂic3ng
ar me measures that indicate iden3ﬁed goals,• consider
thod)•
assignnumeric
values to things that are not easy to measure,
GINI c•oeweightthese indicators to align with our values.
ﬃ
c
i
ent
(gene
ralizedinequcan
These indicators
ality in GDP per capita (or PPP)ex)
• measure various policydscenarios
to iden3fy an op3mum decision,• compare regions to see who/what needs aKen3on.
This depends on the quality of our choices about:• what to measure• which measures to value the most, and• the mathema3cal model for predic3ng results
It may seem arbitrary, but it is less arbitrary than the alterna3ve.

Poten3al contribu3ons of mathema3cs

p op u lar p
To balanceneeds we:ress
(uncle conﬂic3ng
ar me measures that indicate iden3ﬁed goals,• consider
thodgrowthGDP •growth,
HDI)
assignnumeric
values to things that are not easy to measure,
GINI c(humandevelopment•oeweightthese indicators to align with our values.
ﬃ
c
i
ent
(gene
ralizIWI
index),
ed igrowthnequcanThese
indicators
lity indGDP per capita (or PPP)
(inclusive wealthaindex)
ex)• measure various policy scenarios
to iden3fy an op3mum decision,• compare regions to see who/what needs aKen3on.
This depends on the quality of our choices about:• what to measure• which measures to value the most, and• the mathema3cal model for predic3ng results
It may seem arbitrary, but it is less arbitrary than the alterna3ve.

Poten3al contribu3ons of mathema3cs

p op u lar p
To balanceneeds we:ress
(uncle conﬂic3ng
ar me measures that indicate iden3ﬁed goals,
Gros•s nconsider
thodgrowtha3onnumericGDP •growth,
HDI
)
a
l
assignto things that are not easy to measure,happvaluesin
GvIsNGI Dess (GNHc•oPeweightaﬃdevelopments cguithese(humanindicators
to align with our values.
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ent
ecisions)(gene
ralizIWI
index),
ed igrowthnequcanThese
indicators
lity indGDP per capita (or PPP)
(inclusive wealthaindex)
ex)• measure various policy scenarios
to iden3fy an op3mum decision,• compare regions to see who/what needs aKen3on.
This depends on the quality of our choices about:• what to measure• which measures to value the most, and• the mathema3cal model for predic3ng results
It may seem arbitrary, but it is less arbitrary than the alterna3ve.

Poten3al contribu3ons of mathema3cs
We can measure:• pollu3on• income• law breaking• educa3on aKainment• reading• cri3cal thinking• ...

We can compare across:• regions• gender• age• ethnicity• immigra3on status• sexual iden3ty• socio-economics• ...

This supports• local and global decision making• engaged ci3zens

Poten3al contribu3ons of mathema3cs
We can measure:• pollu3on• income• law breaking• educa3on aKainment• reading• cri3cal thinking• ...

We can compare across:• regions• gender• age• ethnicity• immigra3on status• sexual iden3ty• socio-economics• ...

This supports• local and global decision making• engaged ci3zens

hKp://aqicn.org/map/japan

Poten3al contribu3ons of mathema3cs
Limita&ons:• When is it appropriate to measure love, fear, pain,
hunger, …?
• Mathema3cs can support good mo3ves and bad.
(bombs, eugenics, ...)• Abstrac3on ignores local knowledge.
When doing human mathema3cs,
students should discuss the limita3ons.

Poten3al contribu3ons of mathema3cs
Limita&ons:• When is it appropriate to measure love, fear, pain,
hunger, …?
• Mathema3cs can support good mo3ves and bad.
(bombs, eugenics, ...)• Abstrac3on ignores local knowledge.

Poten3al contribu3ons of mathema3cs
Limita&ons:• When is it appropriate to measure love, fear, pain,
hunger, …?
• Mathema3cs can support good mo3ves and bad.
(bombs, eugenics, ...)• Abstrac3on ignores local knowledge.

Mathema&cs is known for abstrac&on,
but it has both processes:• abstrac3on (moving to the abstract)• par3culariza3on (moving from the general to the par3cular)Poten3al contribu3ons of mathema3cs
Moving away from context can help us see a system at work.

Incarcera3on Rates by Race 2010 (USA)Race/ethnicity
White
HispanicBlack% of US
Na3onal% of US popula3on incarcera3on rate
popula3on in prison(per 100,000)
64%
39%
450
16%
19%
831
13%
40%
2,306

Mathema&cs is known for abstrac&on,
but it has both processes:• abstrac3on (moving to the abstract)• par3culariza3on (moving from the general to the par3cular)Poten3al contribu3ons of mathema3cs
Beauty• apprecia3ng diverse ingenuity• standing beside each other to appreciate common
experiencePoten3al contribu3ons of mathema3cs
Beauty• apprecia3ng diverse ingenuity• standing beside each other to appreciate common
experience

4

5

3

Tools for embedding sustainability/peace
Real contexts
AKen3on to context
AKen3on to human choices
Current issues
Complexity (avoid simplicity)
Acknowledging values
Access to data
Interdisciplinarity
sensi3vity to marginaliza3onOpen dialogue
Collabora3on
Access to everyone
Technology
Courage
TrustTools for embedding sustainability/peace
Real contexts• contexts real to thestudent with real data
• shows that mathema3cs
is usefule.g. Isoda

Tools for embedding sustainability/peace
A<en&on to context• Draw on students’ context knowledge• Structure textbooks around context instead of procedures• Chapters and topics organized around procedures tells
students that the procedure is more important thanthe context.
• Chapters and topics organized around contexts tells
students that the mathema3cs responds to context.

Tools for embedding sustainability/peace
A<en&on to context• Draw on students’ context knowledge• Structure textbooks around context instead of procedures•Word
Chapters
and topics organized around procedures tells
Problems
that the procedure is more important than• Astudents
long tradi3onthecontext.
• thushard to change• “throw-away
Chapters andcontexts”
topics organized around contexts tells
students that the mathema3cs responds to context.

Children aged 14, 15, and 16 go to the store. Candy bars areon sale for 43¢ each. They buy a total of 12 candy bars. How
much do they spend, not including tax? (Peterson & Gutstein)Tools for embedding sustainability/peace
A<en&on to human choices• Ques3ons that have mul3ple possible responses• Language that iden3ﬁes human choice. (“I chose to”)
• People from diverse demographic groups so that students
can visualize themselves using mathema3cs powerfully

Wagner and Herbel-Eisenmann

Tools for embedding sustainability/peace
A<en&on to human choices• Ques3ons that have mul3ple possible responses• Language that iden3ﬁes human choice. (“I chose to”)
• People from diverse demographic groups so that students
can visualize themselves using mathema3cs powerfully
If we think about the
choices in ourmathema3cs, it helps us

STOP

to think about the
choices behind themath others do
Wagner and Herbel-Eisenmann

Tools for embedding sustainability/peace
Complexity (avoid simplicity)• Simplifying context gives the idea that the procedure ismore important that the contexts it is designed to addressor that math is
not able tohandlecomplexity• Systems thinking

Tools for embedding sustainability/peace
Complexity (avoid simplicity)• Simplifying context gives the idea that the procedure ismore important that the contexts it is designed to addressor that math is
not able tohandlecomplexity• Systems thinking

Tools for embedding sustainability/peace
Complexity (avoid simplicity)• Simplifying context gives the idea that the procedure ismore important that the contexts it is designed to addressor that math is
not able tohandlecomplexity• Systems thinking

Tools for embedding sustainability/peace
Acknowledge values• Doing a problem requires decisions about what is mostimportant• Any choice of context suggests that the topic is an
important one for students.
For example:
A problem about running a business or responding toclimate change.
• If it is about running a business, can a student choose
to value proﬁt, sustainability, or … ?
• If it is about climate change, can a student choose
how to balance current needs with future needs?

Tools for embedding sustainability/peace
Access to data
• Cite sources for data used.
• Point to other possible sources for further inves3ga3on.
When students access publicly available data, they develop
the skills and conﬁdence for doing this when they facesustainability challenges outside school.

Tools for embedding sustainability/peaceInterdisciplinarity• Peace and sustainable development problems areespecially good for interdisciplinary connec3ons.
• Making interdisciplinary connec3ons values complexity ofcontexts, and invites discussion about how mathema3cs
can help with decisions in such complex situa3ons.

Tools for embedding sustainability/peace
Sensi&vity to marginaliza&on• Directly addressing an equality issue (gender, ethnic, etc.)
is necessary but may draw aKen3on to dispari3es andstereotypes among students.
e.g., We should give problems
that ask about income
distribu3on. Students who arevery rich or very poor might beembarrassed.

Tools for embedding sustainability/peace
Collabora&on• Encourage and expect group work.
• This enables students to hear each other’s ideas and so• they learn to value other ideas• they see that mathema3cs involves choices

What informa3on does each form of representa3on show
especially well?
versus

You are a team of journalists deciding on which
representa3on to include in a news ar3cle. Describe how yourgroup decided which representa3on is the best choice.

Tools for embedding sustainability/peace
Technology• Get students using their technology to gather informa3on.
• More than ﬁnding things on the internet• Smart phones can collect and map data in a community.
• GPS• seismometers• apps that analyze sound• …

e.g., Rubel, Hall-Wieckert, and Lim, 2016

Tools for embedding sustainability/peace
Courage• Sustainable development ques3ons are usually poli3callysensi3ve• These are the most important issues
If we avoid poli3cally sensi3ve issues:• We are saying they are less important.
• We are saying that mathema3cs cannot be used for them.

Tools for embedding sustainability/peace
Trust
When the problem is poli3cally sensi3ve…
• Let students and teachers to make judgments based on
their mathema3cal inves3ga3on and knowledge of therelevant contexts (Do not make the judgments in the text)
Teachers and students may not be completely ready tohandle these diﬃcult issues.
• This is how they learn to handle them.
• No one is completely ready.
A teacher’s guide may be helpful.

Tools for embedding sustainability/peacecommunity
knowledge

classical
knowledge

cri3calknowledge
Gutstein (2007)

Mathema3cs: proof and jus3ﬁca3on

History tells us that quan3ﬁca3on is associated with thedevelopment of democracies and other forms of community
responsibility (Porter, 1995).
When decision makers are not iden3ﬁed through heredity orconnec3on to dei3es, they must prove that their decisions
are made in the interests of the collec3ve good.
• Mathema3cs gives ci3zens tools for this kind of
jus3ﬁca3on.

Embedding sustainable
development educa3on inmathema3cs educa3on texts
David Wagner
University of New Brunswick
Canadadwagner@unb.ca

Photo/chart sources:
hKp://archive.archaeology.org/1111/ar3fact/wiKenberg_germany_tally_s3ck.html
hKps://en.wikipedia.org/wiki/History_of_clothing_and_tex3les
hKps://www.pinterest.com/pin/482588916293971560/
hKp://www.dokdo-takeshima.com/wordpress/wp-content/images/shimane-1907.jpg
hKps://www.wired.com/2014/05/the-world-of-computer-go/
hKp://www.ﬁt.ac.jp/en/undergraduate/info_se
hKp://www.microntesa.co.za/vernier-calipers.htm
hKps://www.researchgate.net/ﬁgure/6766866_ﬁg1_Figure-1-Measure-of-hand-span-05-cm-precision
hKp://globalnews.ca/news/2465526/canada-named-2nd-best-country-in-the-world-report/
hKps://en.wikipedia.org/wiki/List_of_countries_by_income_equality
hKp://www.grossna3onalhappiness.com
hKp://www.unep.org/newscentre/default.aspx?DocumentID=2688&Ar3cleID=9174
hKp://www.japan3mes.co.jp/life/2010/08/26/lifestyle/all-for-the-love-of-tajima-cows/#.WJeDlbGZN3k
hKps://www.youtube.com/watch?v=j1ZFOXVQEvo
hKp://www.abc.net.au/news/2015-08-26/tougher-trucks/6725762
hKp://www.markets500.com/en/markets/stock-and-bonds/2016/05/16/japanese-australian-stocks-recordrise-mondays-trading/
hKp://www.dow.com/en-us/packaging/resources/in-perspec3ve/edi3on-3/japanese-packaging-unraveled
hKp://www.ictdev.org/category/tags/ethnomathema3cs
hKps://www.theguardian.com/environment/blog/2012/nov/26/kyoto-protocol-carbon-emissions
hKps://www.prisonpolicy.org/reports/rates.html