Teaching Children Mathematics / December 2004/January 2005 249

RESEARCH, REFLECTION, PRACTICEDiane Torres-Velasquez with Gi lberto Lobo

Culturally responsive teaching is a dynamicform of teaching that builds on and supportsstudents’ home culture. The strategies that we

recommend in this article for English LanguageLearners (ELL) are based on research or classroomexperience. We provide real-life examples of howthe second author, Gilberto Lobo, implements theseideas in the context of data analysis.

Lobo was a veterinarian and a university profes-sor in Mexico. Now, as a dual language teacher offifth graders, he surrounds his students with allkinds of animals and plant life. Students witnessthe life cycle and the food chain. Theylearn mathematics and science inSpanish using hands-on experi-ences. More important, Lobo useslanguage and culture to capture thestudents’ attention in novel ways.He guides student learning in waysthat make the skills and knowledgetheir own. He is part of a three-way teaching team that includesMrs. Duran, who teaches readingand language arts in English,and Mr. Garcia, who teachessocial studies in English. Theteam collaboratively plansand evaluates student learn-ing each day. Lobo uses thefollowing strategies forincreasing the success of hisELL students:

• Relating mathematics to real-life experiences• Using mathematics as a tool for developing the

learning community• Using questions to help students develop the

language and concepts of mathematics • Explicitly teaching the vocabulary of mathemat-

ics using questions to help students develop thelanguage and concepts of mathematics

Relating Mathematics toReal-Life Experiences withthe Consensogram

Nieto (1999) reminds us that learning emerges fromand builds on prior experience. It begins with theassumption that everyone brings important experi-ences, attitudes, and behaviors to the process ofeducation (p. 6). Lobo uses the students’ real livesfor connections to the mathematics curriculum. Forexample, the students begin the school year bylearning about the class community with graphs.

Rather than teach a unit on graphing byusing a set of data from a mathemat-

ics text, the team has students col-lect data about themselves and

their real lives. Althoughstudents are learning aboutdata and its graphic repre-sentation, the primary pur-pose of this activity is forstudents to learn aboutthemselves and about oneanother. The studentsbegin the development oftheir learning community

through data collection,using a teaching tool called

the Consensogram (Langford

Culturally ResponsiveMathematics Teachingand English Language

Learners

Diane Torres-Velasquez, vlasquez@unm.edu, is an associate professor of special education atthe University of New Mexico. She teaches classes in bilingual special education and methodsin special education for mathematics and science. She is interested in the development of sci-entific and mathematical literacy, especially with English language learners. Gilberto Lobo,Lobobriz788@cs.com, is a teacher with the Albuquerque Public Schools. He teaches the math-ematics/science Spanish component of a dual language program for fifth graders. He serveson the board of directors of Dual Language New Mexico.

Edited by Julie Cwikla, julie_cwikla@yahoo.com, University of Southern Mississippi GulfCoast, Long Beach, MS 39560, and Armando Martinez-Cruz, amartinez-cruz@fullerton.edu,California State University—Fullerton, Fullerton, CA 92834. Readers are encouraged to sendmanuscripts appropriate for this section to “Research, Reflection, Practice,” TCM, 1906 Asso-ciation Dr., Reston, VA 20191-1502; or send electronic submissions to tcm@nctm.org.

Copyright © 2005 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be copied or distributed electronically or in any other format without written permission from NCTM.

250 Teaching Children Mathematics / December 2004/January 2005

1999), a statistical survey tool that measures agroup’s perceptions, views, and opinions. The Con-sensogram can also be used to provide informationabout students, or whoever is being sampled in thedata collection.

Students begin their data collection by answeringsurvey questions about their background. They writetheir response to each question anonymously on asticky note (all notes are the same size and one noteis used for each question). Notes are collected in abasket, read aloud, and grouped by the class into cat-egories of response. The teacher then uses the notesto make a bar graph of the responses to each ques-tion by physically aligning similar responses to dis-play the data. The class discusses the results of thesurvey, as represented on the graphs. After con-structing a bar graph with the sticky notes, Lobo hasstudents develop a data table with sections to includethe question, and the number of responses by frac-tion and then by percentage (see fig. 1). Studentsenter data on the computer and make computer-gen-erated graphs (see figs. 2 and 3).

One question on the Consensogram asks the stu-dents to think about why they are at school. Studentshave the following three options for a response:

1. Education is important.2. Education is important for my family, but not

for me.3. We don’t care, but there is no other place to go.

The majority of students tell the truth. The teachersnever get mad about the students’ opinions and cer-tainly never use the information against them inany way. Lobo explains:

If they do not feel that school is important, I tellthem that I don’t take it personally. I respecttheir opinion and invite them for a conversationwith me at any time about reasons that educa-tion could be important in their lives. I don’t tryto find out who says what. The reason for ask-ing these questions is to find out about thegroup, not to punish anyone for how they think.

In the survey questions, the teachers want to demon-strate the nature of data collection and its representa-tion. By tapping into questions that tell the studentsabout who they are, the class is turning thoughts,beliefs, and values into concrete mathematical dataof great significance. That is when teachers can turninformation into representations such as graphs, frac-tions, or decimals that have mathematical meaning.

Lobo explains, “You are using numbers for meaningwithout the pressure, because many of the kids arescared of ‘mathematics.’ ” Lobo and his team under-stand that learning is socially mediated and developswithin a culture and community. By collecting dataabout themselves, students are quickly able to iden-tify themselves on the graph and begin to think aboutwhat this data means in terms of describing the classas a group.

Mathematics as a Tool forDeveloping a Communityof LearnersLobo describes the classroom community as some-thing teachers are creating with students. The class-room is part of the community. In this community,the teachers connect mathematics to things stu-dents know, then use those skills to teach themmore about themselves and their culture. Theteacher’s role in creating a community of learnersis essential. Teachers’ expectations, beliefs, andvalues are constantly being conveyed through theiractions and through their language, even wheninterpreting graphs. Respect, or disrespect, forcommunity members and their values is conveyedthrough the lessons teachers create.

Culturally responsive teachers recognize theinfluence of culture and community in teaching(Gay 2000). They are aware that teaching is a polit-ical act (Nieto 1999). What teachers deem asimportant or unimportant, won-drous or boring, worthy of pride orshameful, is communicated to theirstudents one way or another,through their language andthrough their curriculum. Teacherscommunicate these ideas boththrough the things they say or do andthrough the things they do not say ordo. In other words, teaching—eventhe teaching of mathematics—is apolitical activity. The way in whichmathematics is taught, the purpose forwhich it is used, the models that teacherschoose to accept, and the information thatteachers value tell students what is impor-tant in their classroom and in their school.

Nieto (1999) stresses that the role ofthe teacher as cultural accommodator andmediator is fundamental to the promo-tion of student learning. Teaching isabout relationships (Nieto 1999). When

students can identify with the school and with theteachers, they are more likely to feel that they havea place in the classroom as learners. The teacherson Lobo’s team relate to their students by tellingthem about who they are. Lobo talks about his ownmove from Mexico, where he was a highlyrespected veterinarian and where he taught at theuniversity. He talks to the students candidly aboutthe types of jobs he held when he first arrived, andabout the hard work it took to become their teacher.By discussing how his household would respond tothe same questions as those used in this article, heis using the data represented on the graphs as astarting point for important conversations. Howdoes this relate to teaching mathematics?

In Lobo’s class, learning mathematicsis clearly a community activity.

Students are taught to dependon one another, to support

one another, and tovalue diversity.

They are taughtto use the com-munity and theworld aroundthem. They are

explicitly toldthat speaking

two languages andvaluing mathematics

are assets, and that learn-

ing mathematics is a way to a better future. Lobouses the graph as a starting point for discussions onthe importance of students’ bilingualism. Heknows that the students will learn English, but hestresses to them that continuing to learn their homelanguage is important. Is this mathematical? Yes.Without the graphic data as statistical evidence, thestudents and team teachers would not realize theextent of the use of non-English languages in theircommunity and around the world.

Lobo believes that the teachers need to know asmuch as possible about the parents so that they donot frustrate them: “We know that each family isdifferent. Some of the parents haven’t had manyyears of schooling and others have college degrees.Most of the students come from homes whereSpanish is spoken. We encourage them to continueusing Spanish at home.” He sees getting to knowthe students and their parents as a teacher’s respon-sibility. The teachers firmly believe that all the par-ents want a better life for their children and encour-age the students to make the choice of workinghard and getting a good education. Lobo providesstrong examples of the significance of the knowl-edge and skills under study to the lives of his stu-dents. He uses what he knows about his students—for example, many of the families come fromSpanish-speaking countries and many of his stu-dents are first-generation American citizens—toconnect mathematics education to their lives. Thenhe uses the mathematics (the data that arise aboutstudents and their families) to learn more about hisstudents to further inform his teaching.

The Language ofMathematics and the

Language of GraphsSkilled teachers recognize the importance

of language as a tool for teaching mathemat-ics (Whitin and Whitin 2003). They are able toshape and guide conversations using languageto help students further their development ofmathematical concepts. Lobo recognizes thatlearning to use the language of mathematicsgoes beyond having the skills to retell astory or have a conversation with a friend.He engages students in a higher level of aca-demic discourse or mathematical conversa-tion. For example, instead of simply describ-

ing what they see on a graph, students usesimulations to take on roles of professionals whowould need to know the skills of data collection

Teaching Children Mathematics / December 2004/January 2005 251

and analysis. He has students demonstrate their“expertise” about the community using the data onthe graphs, and the teacher as the client.

Statistics and data analysis carry their ownvocabulary and mathematical language. Friel, Cur-cio, and Bright (2001) closely examined what isknown about developing skills in the comprehen-sion and use of graphs. They define graph compre-hension as “graph readers’ abilities to derivemeaning from graphs created by others or by them-selves” (p. 132). Teachers of mathematics recog-nize that the development of number senseinvolves a lot of experiences working with num-bers and numerical concepts, bridging concreteobjects to abstract representations. In the sameway, students need a lot of experiences workingwith, thinking about, and talking about real dataand their representation in order to develop theirgraph sense. Whitin and Whitin (2003) examinedhow teachers guide conversation and discussions inmathematics to help students make conjectures andjustify their thinking when reading and talkingabout graphs. Following up a student’s observationwith a question such as “How can you tell that thegreen column is bigger?” gives the student theopportunity to explain his or her thinking.

Friel, Curcio, and Bright (2001) developed aframework for asking questions in guiding graphcomprehension. The elementary level requires stu-dents to extract information from the data. Thisinvolves locating the data on the graph and translat-ing the graphic representation into real information.Lobo guides the students through questions and dis-cussions about the data and about what is repre-sented on the graph. He might ask, “What do yousee on this graph?” The intermediate level requiresgraph readers to find relationships in the data, inte-grating and interpreting the information in thegraph. Here, Lobo asks, “What would it mean if, forexample, 95 percent of the parents in this class camefrom a Latin American country? What languagewould probably be spoken at home?” The mostadvanced level requires graph readers to analyze therelationships that are implicit in the graph—in otherwords, to read beyond the data. The researchersstress that especially at this third level, students needprior knowledge about the topic. These findings sup-port what we know about culturally responsiveteaching and the need to connect learning mathe-matics to what the students already know.

In discussing the results of the Consensogram,Lobo uses the types of open-ended questionsdescribed above to guide student observations

252 Teaching Children Mathematics / December 2004/January 2005

Figure 1Raw data from Consensogram by number and percentage

CONSENSOGRAM: Where Students’ Parents Were Born

CONSENSOGRAM: Where Students Were Born

State/Country Number Percentage

1. CIUDAD DE MEXICO (D.F) 2 4.88%

2. CHIHUAHUA, MEX. 30 73.17%

3. GUERRERO, MEX. 2 4.88%

4. JALISCO, MEX. 1 2.44%

5. NUEVO MEXICO, U.S.A. 5 12.20%

Born in Mexico 85%Born in U.S.A. 15%

CONSENSOGRAM: Prominent Language in the Home

State/Country Number Percentage

1. CHIHUAHUA, MEX. 8 38.10%

2. GUERRERO, MEX. 1 4.76%

3. NUEVO MEXICO, U.S.A. 6 28.57%

4. TEXAS, U.S.A. 3 14.29%

5. CALIFORNIA, U.S.A. 2 9.52%

6. UTAH, U.S.A. 1 4.76%

TOTAL = 21 100.00%

Question Number Percentage

1. Spanish is the most prominent languagespoken in the home.

17 80.95%

2. My parents speak in Spanish and we answerin English.

2 9.52%

3. English is the most prominent languagespoken in the home.

2 9.52%

TOTAL = 21 100.00%

Born in Mexico 43%Born in U.S.A. 57%

about data, about themselves, and about their com-munity. At the most advanced level, Lobo uses theConsensogram to prompt the students to thinkahead about their future in comparison to the pre-sent, as represented in the graphs. He inspires theclass to “read beyond the data.” He asks students tocompare the first two graphs (see figs. 2 and 3)about the birthplaces of students and their parents.After interpreting and analyzing the data on thesegraphs, he takes students a level further by askingthem to predict data from the third graph (seefig. 4). Lobo relates to his students in ways thatcould affect their future selves and their self-esteem. In the following example, Lobo uses thequestion of where students are from, uses thegraphs, and turns the question into one of patternsof migration. After the students have mathemati-cally analyzed the data collected on parents’ andstudents’ birthplace, Lobo asks the following:

Look at graphs 1 and 2. Do you see how it [thedata] is changing? (This question refers to thebirthplaces graphed for parents [see fig. 2] ascompared with the birthplaces graphed for stu-dents [see fig. 3].) How could this graph help uspredict patterns of migration?

Compare this with how animals migrate. Whydo they migrate? (Students provide answers suchas the effects of extreme weather conditions, thelack of food, and so on. With the animals in theclassroom, they have already had this discussion.)OK, so why do humans migrate?

Now look at this third graph [see fig. 4].These are the students in this class. What do youthink will happen to the children of these kids?They probably will be born in the United States.How will life be different for them? Do youthink that they will grow up speaking Spanish athome? If you don’t speak to your children inSpanish, will they be able to speak it?

Do you see how it [the data] is changing?(This involves a future projection for which datacannot yet be collected.)

Teaching VocabularyExplicitlyTeachers should teach both mathematics and Eng-lish vocabulary explicitly and in ways that the stu-dents will not forget. Lobo uses multi-modalactivities, analogies, and even props to introduce,practice, and enhance storage and retrieval of corevocabulary. When teaching vocabulary, Lobogives students a lot of opportunities to hear himuse the vocabulary in context. One way he doesthis involves finding graphs using student inter-ests, such as sports, local elections, and so on.Using real graphs from newspapers, magazines,and the Internet, he teaches the vocabularydirectly. He gives the students the key words ofthe topic and makes sure that they have a precisewritten definition from which to study. He dis-cusses the data from real graphs with students andinvolves the students in conversations about the

Teaching Children Mathematics / December 2004/January 2005 253

Figure 2Bar graph of where students’ parents were born by percentage

Ciudad deMexico,(D.F.)

State/Country

Consensogram: Students’ Parents’ Birthplace

100.00%

50.00%

0.00%Per

cent

age

Chihuahua,Mexico

Guerrero,Mexico

Jalisco,Mexico

Nuevo Mexico,U.S.A.

topics of the graph (such as data on sports heroesand television show preferences). He allows manyopportunities for the students to practice using thelanguage. For instance, he has the students com-pete in friendly academic games. He also givesthe students a study guide. Students work togetherto fill in blanks in the study guide, then take thecompleted guide home to practice with their par-ents. In one game, students form teams, and eachteam member learns to support and depend on the

other. These games drill vocabulary in fun waysas students compete to show what they knowabout new terms, their meanings, and how to usevocabulary in context.

Students play a variation of “Spin the Bottle” bygroups. In this case, students would have heard,learned about, and studied words such as horizon-tal, vertical, perpendicular, statistics, data, table,axis, percentage, and fraction. (Table is a wordwith multiple meanings and can be confusing forELL students if it is not explained carefully.) Whenthe bottle points to one group after the first spin,that group asks the vocabulary question. The sec-ond spin is the group that provides the definitionand uses the word correctly. If the definition anduse are correct, that group has a chance to ask thefirst group a question in return. If both groupsanswer correctly on both rounds, they both win aprize. Otherwise, no one wins and both groupsdedicate themselves to learning the words better.

The excitement of the review before the compe-tition is contagious! During the actual rounds ofcompetition, students hold their breath. Theyunderstand that they are accountable for knowingthe vocabulary and are eager to show what theyknow. How does Lobo make this common gameexciting? He has high expectations for his students.As students succeed, he instills a sense of pride intheir accomplishments: “Ah! Maestro Rodriguez,you really know your field! Where did you study?”(In a Latin American country, being called a “mae-stro” is the highest compliment. The term isreserved for the most esteemed university profes-sor or highest authority on a subject.) Typically, the

254 Teaching Children Mathematics / December 2004/January 2005

Figure 3Bar graph of where students were born by percentage

Consensogram: Students’ Birthplace

Chihuahua,Mexico

Guerrero,Mexico

NuevoMexico,U.S.A.

Texas,U.S.A.

California,U.S.A.

Utah,U.S.A.

40.00%

30.00%

20.00%

10.00%

0.00%

Per

cent

age

Figure 4Bar graph of prominent language spoken in the home by percentage

Prominent Language Spoken in the Home

Spanish Parents = Spanish,Children = English

English

100.00%

80.00%

60.00%

40.00%

20.00%

0.00%

Per

cent

age

Prominent Language

student beams and exclaims proudly that she stud-ied at Truman, their current school.

ConclusionThis article has discussed and illustrated somestrategies for teaching culturally responsive mathe-matics to ELL students. Learning to use any lan-guage is a complex activity, even when it is yournative language. Many of the strategies that Lobouses in his mathematics classroom are not limitedto the teaching of mathematics, nor are they limitedto the teaching of language. They can be used inother subject areas and by native speakers of Eng-lish. These strategies help students perceive anddescribe their world, their community, and them-selves using mathematics and language, and theyhelp students connect to their world, their peers,and their teachers. The strategies presented heredid not exclusively teach mathematics, nor did theyexclusively teach language. For example, thedevelopment of the learning community is anactivity more related to culture and relationshipsthan to any particular mathematical concept or lan-

guage skill. Yet Lobo uses these strategies to sup-port the teaching of mathematics in ways that aremeaningful for his ELL students. Cultural rele-vance, language development, and development ofgraph sense can help connect mathematics to stu-dents’ lives and teach them to think critically abouttheir future.

ReferencesFriel, Susan N., Frances R. Curcio, and George W.

Bright. “Making Sense of Graphs: Critical FactorsInfluencing Comprehension and Instructional Impli-cations.” Journal of Research in Mathematics Educa-tion 32 (March 2001): 124–58.

Gay, Geneva. Culturally Responsive Teaching: Theory,Research, and Practice. New York: Teachers CollegePress, 2000.

Langford, David. Tool Time: Choosing and Implement-ing Quality Improvement Tools. Molt, Mont.: Lang-ford International, 1999.

Nieto, Sonia. The Light in Their Eyes: Creating Multi-cultural Learning Communities. New York: TeachersCollege Press, 1999.

Whitin, David J., and Phyllis Whitin. “Talk Counts: Dis-cussing Graphs with Young Children.” Teaching Chil-dren Mathematics 10 (November 2003): 142–49. ▲

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