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Ethnomathematics: Mathematics de TODOS

Ethnomathematics: Mathematics de TODOS

Carlos LópezLeiva, Kyndall Brown, and Silvia Llamas-Flores

Mathematics and daily life activities are connected. For many cultures and societies mathematics is not an isolated field or subject, it is part of an encompassing knowledge or science that helps us understand and work with the world (Cajete, 2000). Mathematics is often taught and practiced at school in ways that are rarely linked to the learners’ experiences and interests, their community, their culture, their histories, and real-life applications. However, we have learned in mathematics education that mathematics is a human endeavor (Jacobs, 1970) present across human civilizations and cultural practices such as, playing, locating, measuring, counting, explaining, and designing and building (Bishop, 1988).

Ethnomathematics is a term introduced by Ubiratàn D’Ambrosio (1991) from Brazil to describe the techniques used to explain, understand, and cope with reality in order to survive across diverse communities. Ethno relates to the members of distinct groups identified by cultural traditions, codes, symbols, myths, and specific ways of reasoning and inferring (D’Ambrosio, 1985). So, ethnomathematics refers to the way that members of various cultural groups mathematize their own reality because it examines how both mathematical ideas and practices are processed and used in daily activities (D’Ambrosio and Rosa, 2017, p. 288). In fact, this approach highlights mathematics as a cultural practice existent in human activity and challenges perspectives that present mathematics mainly as a Western—Roman, Greek—knowledge commonly taught at school. An ethnomathematical approach helps us understand mathematics from a perspective wider than traditional school mathematics, of seeing mathematics as a human act. As a result, such vision can helps renovate how we teach mathematics (Lange,1996; Rosa & D’Ambrosio, 2018).

In mathematics teaching, this approach helps us expand, affirm and redistribute mathematical authorship and empowerment; draw from and expand resources to teach and learn mathematics; recognize and challenge spaces of marginality of knowledges of many communities; and strengthen the relationship between learners and mathematics (Aguirre, Mayfield-Ingram, & Martin, 2013; Kokka, 2015). Such an approach should “perpetuate and foster—to sustain—linguistic, literate, and cultural pluralism that are part of schools” (Paris, 2012, p. 93). Thus, when students and teachers use the real world as a starting point for conceptual development, mathematics teaching and learning become more complex (De Lange, 1996) as they also become doers of mathematics (NCTM, 2000) by engaging in problem solving, multi-modal representations, and communication to develop mathematical meaning making and mathematize through their own perspectives (CCSS-M, 2010; Freudenthal, 1973).

These notes and blog were developed with the goal of sharing available resources around ethnomathematics. Our hope is that mathematics teachers and educators can access and use them as needed. This blog includes three main sections:
1. How is ethnomathematics relevant and critical?
2. What has been learned and done in ethnomathematics?
3. What can be done in the classroom?

We hope you enjoy it, and if you experience some of these or new ideas in your classroom, please share with us here, so more teachers and researchers can learn about what of ethnomathematical approaches can be implemented in the mathematics classroom.

How Is Ethnomathematics Relevant and Critical?

Ethnomathematics presents implications for classroom teachers by asking us to re-examine our beliefs and practices about what counts as legitimate mathematics, how mathematical concepts are to be taught, and how to assess children’s knowledge of mathematics. With these ideas in mind, let’s listen to a conversation between Ubiratàn D’Ambrosio and Paulo Freire as they discuss the relevance of ethnomathematics by its connection with the community thus mediating a culturally-responsive approach of teaching mathematics.

What Has Been Learned and Done in Ethnomathematics?

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TODOS Blog on Voting

TODOS Blog on Voting

The Mathematics of Voting and its Consequences: Ideas for Mathematics Lessons

By Silvia Llamas-Flores, Carlos LópezLeiva, & Kyndall Brown

As the 2018 midterm election approaches, there are many opportunities to engage students in critical issues through mathematics. This blog focuses on specific social justice issues related to voting. We are sharing resources that teachers can use to create lessons. If you are inspired by the information below and develop a lesson, we encourage you to share it with us through the TODOS BLOG, so that other teachers can also implement/adapt your lesson.
The blog starts by focusing on the historic link between democracy and voting and challenges that have emerged over time. The second section of the blog provides resources around a number of currentissues related to policies that tend to restrict voting rights, such as: Inequitable voting requirements across states and people’s status, closure of voting polls, felony disenfranchisement, and gerrymandering. The third section of the blog is dedicated to mathematics lessons on voting. There are some examples with links to previous mathematics lessons on voting. The use of Modeling in a lesson as a mathematical practice is presented as a link between issues of voting and the Common Core State Standards for Mathematics.
1.     Voting, Democracy, & People’s Voices
2.     Mathematics, Policy, & Voting
3.     Mathematics Lessons & Voting
1.     Voting, Democracy, & People’s Voices
The idea of voting comes from a democratic perspective and practice in which peace is maintained and collective social and political issues are resolved through collective input. What people voice becomes the guide of steps and actions to be implemented. Despite these equity-oriented goals, processes in promoting and sustaining democratic processes are not always equitable thus undermining the integrity of a process called ‘democratic’. The links provided below elaborate on elections, democracy, and and connections between democracy and voting.
1. a. Why elections and voting are important?
-Video on voting and democracy:
1.b. History of Elections
-What are the Presidential elections?
-Forecast for 2020 elections
2.    Mathematics, Policy and Voting
Mathematics is a tool that can help us assess not only the results of voting in an election process. Mathematics can also help us assess the entire process even before elections take place.  For example, who can or is allowed to vote? Where can you vote? Is accessible?
2.a. Inequitable Voting requirements across states and people’s status
There has been a resurgence of state and local measures to disenfranchise voters of color.  Inequitable voting requirements, such as requiring identification at voting polls, is only one form of voter suppression.  Thirty-four states have introduced legislations that would require voters to show some form of photo identification in order to vote.  The purpose and effect of these restrictive voting laws is to suppress the vote of certain groups of people, including people of color, making voting rights a social justice issue.
-Background Information - voter ID laws, variations of ID laws, breakdown by state:
-Voter ID as a form of Suppression - effects of voter ID requirements, challenges of voter ID laws:
2.b. Closure of voting polls 
The Voting Rights Act was established 53 years ago aimed to protect voters against discrimination. In 2013, Shelby County v. Holder put into jeopardy voter protections by eliminating Section 5, which required jurisdictions with a history of voter discrimination to demonstrate that cost savings from polling site closures wouldn’t disadvantage voters of color.  As a result, there has been a widespread effort to close polling sites, many located in areas primarily serving people of color.  A national study reported that out of the 381 counties studied, 165 of them - 43% have reduced voting locations.  For example, in Arizona alone, there have been 212 poll closures since Shelby.  In general, there has been a shift to close polling places on a massive scale across the nation, indicating a movement to suppress people’s right to vote. 
-Suppressing the Black Vote
-Poll Closures - The Effects of Shelby County v. Holder
-Voter Suppression Across the Nation
2.c. Felony disenfranchisement
Felony disenfranchisement refers to the eligibility to of the exclusion of people from voting. This status relates to conviction of a criminal offense, such as: crimes of incarceration for a duration of more than a year, or felony. This status can be permanent or restored after completing a sentence, or probation (Wikipedia).
-Data and statistics on felony disenfranchisement
-Impact of felony disenfranchisement
-Collection of articles about felony disenfranchisement
2.d. Gerrymandering
Gerrymandering is a political practice that establishes an advantage to a particular party or group by manipulating the boundaries of a district. The defined district is known as a gerrymander. According to Wikipedia, Gerrymandering uses: "cracking" (i.e. diluting the voting power of the opposing party's supporters across many districts) and "packing" (concentrating the opposing party's voting power in one district to reduce their voting power in other districts).
3.     Mathematics Lessons & Voting
Mathematical modeling provides students with opportunities to analyze and understand the world around them by providing insight into real-world phenomena.  The practice of mathematical modeling provides students with opportunities to mathematize the world around them, a practice supported and encouraged by the Common Core Standards.  Modeling can be used as a powerful tool in identifying and finding solutions to practical issues such as those related to social justice, including the many issues surrounding voting and marginalized groups. Such approach has been called, Critical Mathematics Education. For example, a mathematical model can help students mathematize poll closures across the nation while simultaneously looking at the effects these poll closures have on specific groups’ voting rights.  While we provide some resources below that touch on modeling and work in mathematics education related to voting, at the end we invite you to share your lessons and resources with us!
3.a. Modeling
Modeling is of the mathematical practices promoted by the Common
Core State Standards for Mathematics and NCTM. This mathematics education approach helps students understand the relevance and applications of mathematical ideas as well as how many everyday activities are mathematical in nature. Links below describe in more details what modelling is and some examples of how this relates to the mathematics standards in education. 
-Video on what is math modeling
-Common Core State Standards Modeling
-California State Board of Education - What is Modeling?
-Think Math - What is modeling with mathematics? 
3.b. Mathematical modeling and some examples
This section provides some resources useful for teachers interested in promoting the mathematics practice of modeling. These resources include examples of modeling and how this approach can be implemented in the classroom.
Engaging students in the mathematical modeling process 
Mathematical modeling, sense making, and the Common Core State Standards
3.c. Previous work in mathematics education related to voting
Finally, this section describes previous work in mathematics education specifically related to voting.  While not all lessons are specific to mathematics, the ideas relate to teaching and they can be used to mathematize aspects related to voting.  
-Video about voting from University of Wisconsin
3.d. Your Turn!!
NOW, it is your turn. We encourage you to get inspired and develop your own lesson plans and activities and share it with us. We will later on include a blog on lessons related to this blog. Please contact and send us  what you develop at: [email protected] 

Students, Teachers, Mathematics and DACA

Students, Teachers, Mathematics and DACA: What are some issues and opportunities?
Silvia Llamas-Flores, Kyndall Brown, and Carlos LópezLeiva
This blog provides information and resources for teachers, students, and the public in general, who are interested in understanding more about DACA and the students under this program. This information could be used to develop lessons to teach students about DACA, who are DACA students. This information can help deconstruct stereotypes on DACA students and immigrants in general. The information itself challenges readers and teachers to take action and advocate for TODOS/ALL students.  We ask some discussion questions throughout the blog and at the end. Please, participate in the discussion and share with us what you think. Gracias.  
What is DACA?
In 2012, the Deferred Action for Childhood Arrival (DACA) program was put into place by the Obama administration to “lift the shadow of deportation” for children that were brought to the United States undocumented.  In order to request consideration for DACA, children must meet the following guidelines. 
·     Came to the United States when you were under 16
·     Are in school, have a high school diploma or GED
·     No criminal record
In addition to protecting young children from being deported, it allowed young adults to work legally in the United States.  Approximately 800,000 children and young adults received protection from deportation under DACA.
Discussion Questions / Resources
Supreme Court Decision on DACA:
In September of 2017, the Trump administration announced that it was rescinding the DACA program, putting at risk some 700,000 young undocumented immigrants for deportation.  Since then, several judges have ruled that the Trump administration had abused its discretion, and issued nationwide injunctions ordering the administration to keep key elements of the program.  As a result, the Trump administration appealed to the Supreme Court in hopes of rescinding the DACA program in its entirety.
In early 2018, the Supreme Court declined the Trump administration’s appeal, thereby shielding “Dreamers” from immediate deportation.  So what does this mean for “Dreamers” already signed up for the DACA program?  For the time being, they are allowed to remain in the DACA program, which protects them from deportation, as well as allows them to keep working legally in the United States, although it is unclear what that timeframe looks like.   
The reality is that unless Congress takes meaningful action to address this issue, and the broader issue of immigration in the United States, this victory for Dreamers will be short-lived.  
Discussion Questions / Resources
Ways to Support Students and Teachers:
The uncertainty surrounding DACA during a time of racial tensions and can be daunting and frightening for many DACA students and their teachers.  While the recent Supreme Court decision to not hear arguments by the Trump administration about the constitutionality of DACA has provided a temporary victory for Dreamers, it has left Dreamers’ fate in limbo.  
As educators and advocates of ALL our students, it is important we provide support in as many ways possible.  This can range from mentoring to connecting students with various organizations that specialize in offering legal and other forms of support for Dreamers.  Below are some resources for teachers and students.
Discussion Questions / Resources
DACA/Immigration Fact Sheet:
Center for American Progress Survey of 3,063 DACA recipients in 46 states and D.C.
  • 72% of top 25 Fortune 500 companies employ DACA recipients
  • 97% of respondents are currently employed or enrolled in school
  • 8% of DACA recipients have started their own business
  • Respondents average hourly wage has increased 84% since receiving DACA
  • Of the 45% of respondents who are currently in school, 72% are pursuing a bachelor’s degree or higher
Discussion Questions / Resources
  • UCSD, United We Dream, National Immigration Law Center
Immigrant Contributions to Counteract Stereotypes:
  • In 2014, immigrants earned $1.3 trillion and contributed $105 billion in local and nearly $224 billion in federal taxes
  • In 2014 immigrants had almost $927 billion in consumer spending
  • Undocumented immigrants contributed more than $11.6 billion in state and local taxes each year.
  • If the estimated 11 million undocumented immigrants were given a pathway to citizenship or legal resident status, those tax contributions could rise by nearly $2 billion.
Discussion Questions / Resources
  • What are DACA students’ contributions to the U.S., and how can you use this information to develop a culturally responsive and socially just math lesson?
Looking Beyond DACA:
We need to see beyond the Supreme Court’s decision on DACA to be fair. This supportive decision is just a step up onto a more humane and fair way in the acknowledgement of human rights of DACA students and their families. It is because many other issues are still at stake. Below, we present some resources that address three major topics that often misguide audiences on who DACA students are.
Many fixed ideas about DACA students is that they are criminals. In fact, one of the main prerequisites to become a DACA student is to have no criminal record. Rather than criminals, we need to let ourselves learn about who DACA students are, so that limited understandings and perspectives on these students do not become the only way we see them.
  • Seeing DACA students as exclusively Latinx
Part of the limited perspective about understanding DACA students is thinking of this as a specific racial group (e.g., Latinx), when in fact, while this group of students shares similar experiences about displacement, immigration, and living in U.S. territory and society as home, they all come from diverse backgrounds.  
  • Viewing DACA students (and families) as an economic burden/challenge.
Recently, the Center on Budget and Policy Priorities informed that 22 states faced revenue shortfall. At the same time, TIMES magazine informed that states with the highest shares of immigrant populations include: CA, TX, and NV. Interestingly, none of these states was near the breakdown of the 22 states listed with revenue shortfalls. These patterns confirm previous arguments on how immigrant populations nurture and support the economic growth. In fact, the slow rates of revenue shortfalls were linked to energy prices, and tax cuts, and tax collection growth. While these links need further exploration, DACA students represent a hard-working population that actively contributes to the betterment and growth of the U.S. society and economy. These levels of hard-work promote greater activation of growth, rather than simply “stealing” jobs away, as NPR reports, from U.S. citizens.
Discussion Questions / Resources
  • Click on blue text to access resources linked to the information on “Looking Beyond DACA”
  • How can mathematics help us deconstruct the misleading topics about DACA students presented in this section?
Critical Discussion Questions:
1 What can we do in our teaching practices to promote greater understanding of DACA students and the assets they bring to the classroom?
2 How can mathematics help us understand this issue better?
3 What else should we know about DACA students?


January Blog:

Mathematics & Diversity:

Why? What do you think?

Why think about diversity in the teaching and learning of mathematics?
Diversity often times is deemed as limiting to what a teacher and students can do in the classroom. In other words, diversity can be seen as an issue.
Have you ever noticed problems with diversity?
For example, sometimes when people have different opinions on an idea trouble is around the corner.
So, is diversity really the issue?
Allan Johnson mentioned:
 “The trouble around diversity, then, isn’t just that people differ from one another. The trouble is produced by a world organized in ways that encourage people to use difference to include or exclude, reward or punish, credit or discredit, elevate or oppress, value or devalue, leave alone or harass” (2006, p. 16).
Then, it seems that diversity itself is not the real problem. The problem is what we do with diversity. In the mathematics classroom diversity could manifest in many ways.
In the November TODOS Live!, Dr. Marta Civil presented on ideas related to this topic. Watch it now

Civil_TL from TODOS Live! on Vimeo.

Please, participate in this TODOS blog by responding to any of the 3 questions on diversity
  1. What to do when the teacher's and the students' backgrounds are different?
  2. What to do when the diversity among students themselves is wide?
  3. What to do in the classroom when students’ experiences with mathematics are diverse?
Resources Question 1 What to do when the teacher's and the students' backgrounds are different?
Resources Question 2 .   What to do when the diversity among students themselves is wide?
Resources Question 3 .   What to do in the classroom when students’ experiences with mathematics are diverse?
Let’s discuss and learn together about diversity and Mathematics.


Mathematics is a cultural activity.  The way in which people engage in mathematics is often determined by who they are, where they are and how they and the people around them think about mathematics.   Ubiratan D’Ambrosio (2001) defines ethnomathematics as a term used to “express the relationship between culture and mathematics” (p. 308). As he explains, “Mathematics is a compilation of progressive discoveries and inventions from cultures around the world during the course of history. Its history and ethnography form a wonderful mosaic of cultural contributions.” (p. 310)
TODOS acknowledges that mathematics is a social construct.  In our cultures, in our homes and in our classrooms we jointly build meaning for what mathematics is. For these constructs to overlap, to agree, to form a common understanding across cultures, is the work of the classroom.
As D’Ambrosio (2001) writes, “An important component of mathematics education today should be to reaffirm, and in some instances to restore, the cultural dignity of children” (p. 308)
TODOS acts to develop tools to build a shared understanding of mathematics that gives each child a place in its definition, each culture recognition for its often unique way of visualizing mathematical ideas and each representation of these ideas thoughtful study.
TODOS holds itself accountable for this work and for advocating for those who provide the research and ideas that grow our understanding of social justice in mathematics.
TODOS stands with Rochelle Gutiérrez and other researchers who provide clarity so we remember what we teach, whom we are teaching and center language, culture and literacy in the mathematics that we teach and in the ways that we teach it.
TODOS 2018 Conference will address this goal through the lens of advocating for equity and social justice. ( Please join us as we further and deepen our understanding of the role of social justice in mathematics education.
Expect to hear from TODOS’ Advocacy Committee.  This group is building the tools we need to proactively support and build on the work of Rochelle and other scholars who are working tirelessly to support us as we advocate for high quality mathematics education for all students.
Please read our joint position statement with NCSM to further acquaint yourself with our stance. (
Take to social media and pass this along:  #IstandwithRochelle
Diane Kinch
President, TODOS:  Mathematics for ALL
D’Ambrosio, U. (2001). What is ethnomathematics and how can it help children in schools. Teaching Children Mathematics,7(6) 308-310.

Taking a Stand for Humanity

TODOS: Mathematics for ALL is an organization that seeks to create a more just, humanizing and equitable mathematics education experience for all. Regardless of your political views, we cannot let our differences overshadow our humanity toward each other. We recognize that the current political climate may affect how we move forward as a people that value democracy and justice for all. We must find strength and resolve to reach out to people hurting, scared and uncertain of their futures. We must find ways to support educators to hold space for listening, emotions, and deeper understanding. We have much work to do.
We reiterate here our TODOS mission and goals. In the present political climate, we interpret these as including the following:
  • Respecting and incorporating into our mathematics programs, the role language and culture play in teaching and learning mathematics.
  • Supporting teachers who need help navigating the political and emotional situations occurring daily in their classrooms.
  • Generating and disseminating knowledge that supports our mission of advocacy for all students.
  • Informing the public and influencing educational policies that protect our students and enhance the educational experiences of all of our students.Informing families about the opportunities available to their children and working continuously and ardently to enable these children to become mathematically proficient.

 As mathematics educators, we will continue to stand with our students and their families, advocate for them and affirm their futures.

We welcome your thoughts, comments, and ideas on this subject.

Taking a Stand Part 2

TODOS in its “Taking a Stand for Humanity” statement after the presidential election presented our belief that we must work to create a more just, humanizing, and equitable mathematics education experience for all. Education happens within a context. One such context is the political climate in which children exist. Regardless of political views, we cannot stand by and watch while the civil rights guaranteed by the Constitution of the United States are swept aside by executive orders.  To reiterate,  “We must find strength and resolve to reach out to people hurting, scared, and uncertain of their futures. We must find ways to support educators to hold space for listening, emotions, and deeper understanding. We have much work to do.”

We at TODOS believe in the following:

  • Human Rights.  We support the rights of immigrants and others who are being attacked.
  • Mutual Respect. We support the rights for all and denounce rudeness, divisiveness, and spite that are becoming the norm.
  • Science. We believe in the laws of science that are being attacked by powerful people.
  • Social Justice. We challenge “the roles power, privilege, and oppression play” in our society. (From the TODOS and NCSM joint position statement on Social Justice in Mathematics.

As Robert Frost said in his poem, Mending Wall: “Something there is that doesn't love a wall, that wants it down."

We at TODOS pledge to continue our work to support all children and to tear down the walls that prevent them from reaching their full potential. We will continue to speak out when prejudice outweighs justice.


Standing for Equity and Social Justice

Standing for Equity and Social Justice

My family, as is true for most Americans, is a product of immigration.  My great grandparents left Ireland because of the prejudice and fear that permeated that country in the thousand years for which it was a possession of another.  The people of Ireland were treated as sub-human, criminal, and left to starve. And so they left.  They came to America.
This is my country.  My country, of which Emma Lazarus wrote:
“Give me your tired, your poor,
Your huddled masses yearning to breathe free,
The wretched refuse of your teeming shore.
Send these, the homeless, tempest-tossed to me,
I lift my lamp beside the golden door!”
The events in Charlottesville and elsewhere paint a different picture, a picture of a country riddled with hate, with white supremist attitudes that are both born of and belied by history, science and good will.
As mathematics educators we are beholden to the children under our care and our tutelage.  Their dreams of the future are the hope of the future of this country and of the world.  Their dreams have been the dreams of each generation and always we, the educators, have the responsibility to equip them with the tools to achieve these dreams. 
In the words of Brooks & Dunn in the song, Only in America,
“Only in America
Where we dream as big as we want to
We all get a chance
Everybody gets to dance
Only in America”
 The vision of America in the songs that have defined the United States for generations is again slipping away. The Emancipation Proclamation was signed into law over 150 years ago, Rosa Parks sat down on that bus over 60 years ago, and over 50 years ago, César Chavez went on his hunger march  and Martin Luther King was murdered. Yet still we do not match our picture of ourselves. In this county, not everybody gets to dance. What can we, as members of TODOS, do to actualize the vision of America as a place for ALL people?  Taking the beginning of the Preamble to the Constitution and drawing on the essence of the NCSM/TODOS position paper on Social Justice we have the following:
“We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity…” {Constitution} …Do agree to treat each other with respect, educate each and every one of our children for their future through acknowledging the wrongs that have been done, taking action to ensure that these wrongs will not recur and hold ourselves accountable for supporting and incentivizing mathematics teachers and leaders to live the words of this message.
Without our commitment to this work, the dream of America will fail.  Our children are our future.  As children watched the events in Charlottesville, what conclusions did they reach?  What is our response as educators to their confusion and uncertainty? As the President of the Benjamin Banneker Association, Brea Ratliff, has stated, “They need to know that we will always stand up for what's right.” TODOS commits to this.  Integrity matters, social justice is about the way in which human rights are manifested in the everyday lives of people at every level of society. It is not about financial gain or professional advancement or putting oneself before the good of others.
As schools start up for another year of hopeful progress, let each of us commit to turning the tide, to working within our classrooms, schools, districts, counties and states to advocate for each and every child, for each of them represents the future of America. The TODOS Advocacy Committee will be working on this and other issues in the coming year.  Please stay tuned and become involved in the rebuilding of the dream.
Diane Kinch