05. furner p16 - concordia...

16 INTERVENTION IN SCHOOL AND CLINIC VOL. 41, NO. 1, SEPTEMBER 2005 (PP. 16–23)

to learn the material. All students can learn math throughacting out math problems; for instance, go on Internetfieldtrips with a typically able peer and manipulate tan-gible objects that help them to concretize abstract con-cepts. English Language Learners often need speciallydesigned instruction in English. By using the strategiesand approaches in this article, teachers can help supportthe teaching of language acquisition while teaching thecontent area. In reality, these strategies really are just bestpractice for the teaching of mathematics in general.

Teach vocabulary using realia anddemonstration. Teachers can use real ob-jects such as coupons, fruit, patterned blocks,

beans, Popsicle® sticks, marbles, buttons, or M&Ms®

as manipulatives in demonstrating math concepts. Thiscan reinforce the number of sentences visually, and diverse-needs learners can also practice English and

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TeachMathematics:

Strategies to Reach All Students

JOSEPH M. FURNER, NOORCHAYA YAHYA,

AND MARY LOU DUFFY

In this high-tech and globally competitive society, it isbecoming more and more important that all citizens beconfident in their ability to do mathematics. Knowledgeof mathematics is an important skill necessary to succeedin today’s world. All students deserve equal access to learn-ing math, and teachers must make the effort to ensurethis. The National Council of Teachers of Mathematics(NCTM, 2000), in their revised and updated standards,identified “equity” as their first principle for school math-ematics: “Excellence in mathematics education requires—high expectations and strong support for all students”(p. 11). NCTM has noted, “Equity requires accommodat-ing differences to help everyone learn mathematics” (p. 13).The NCTM has taken a prominent stand that as educa-tors we must take an equity-for-all-students approach toteaching mathematics. All students have the right to learnmath and feel confident in their ability to do math.Teachers must see to it that “mathematics can and will belearned by all students” (p. 13).

In this article we have listed 20 best practices orstrategies for teaching mathematics to reach all students.These teaching strategies may be effective with EnglishLanguage Learners (ELL), special education students, orwith those served in mainstream classes. With diverselearners, the use of the multimodal approach that incor-porates multiple intelligences caters to students’ short at-tention spans, as they are not expected to merely sit still

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VOL. 41, NO. 1, SEPTEMBER 2005 17

mathematics vocabularies. It is important to use concreteobjects for hands-on activities; they not only make thecomprehension of abstract math concepts easier but alsofun. Both ELL and special education students benefitfrom instruction structured from concrete to abstract.

Relate math problems and vocabularyto prior knowledge and background.Especially for teaching students from diverse

backgrounds, teachers can assess the current strategiesused by their students to learn math. For instance, Chi-nese students may be familiar with the use of an abacusto do their calculations. Teachers can perhaps ask thesestudents to show the others in class how an abacus isused. Honoring and recognizing students’ knowledgewill boost their self-esteem because students will feelthat they, too, have something to contribute to thelearning process despite their limited English abilities.Students with learning disabilities in the area of mathcan be powerful teachers to other students when theyexplain how they learned to accomplish specific skills orconcepts (Mastropieri et al., 2001, p. 23). In addition,teachers can prompt students to talk about their experi-ence in learning some of the math concepts in theircountry. By capitalizing on students’ prior knowledge,teachers who are empathetic to their students’ needsand backgrounds bridge the new knowledge to the old,making learning new math concepts more manageablefor these students. In some cases, by understanding howstudents solve problems, teachers can troubleshoot orfine tune the individual student’s process and make himor her more efficient learners.

Apply problems to daily life situations.Creative teachers can use a variety of ways tocoach students when applying problems to daily

life situations. For example, teachers can use restauranttake-out menus to teach students multiplication and di-vision. Not only do such activities link students withreal-life situations but they also create a fun learningenvironment. Such an environment will also promoteEnglish language acquisition for the non-native Englishstudents and model problem-solving techniques aloudfor special education students. Krashen’s (1985) meta-phoric use of “affective filter” in his affective filter hy-pothesis reinforces the idea that teachers can lower theaffective filter by fostering a spirit of mutual respect, highexpectations, and cooperative learning. By using real-world practice activities, the goal of generalizing skillslearned in class to their lives becomes more attainable.

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Use manipulatives to make problemsconcrete. Best practices in special educationcall for you to teach concepts with concrete

examples, and once the vocabulary and process is under-stood, then move to more abstract problems (Mercer &Mercer, 1998). The same practice is equally effectivewhen considering the needs of Limited English Profi-ciency (LEP) or learners from diverse backgrounds.Teachers can obtain commercial manipulatives, or theirstudents can make their own manipulatives (e.g., papermoney, buttons, blocks, rods, tangrams, pattern blocks,algebra tiles). The use of manipulatives provides teach-ers with a great potential to use their creativity to dofurther work on the math concepts instead of merely re-lying on worksheets. Consequently, students are learn-ing math in an enjoyable way, making connectionsbetween the concrete and the abstract.

Encourage drawings to translate andvisualize word problems. The Natural Ap-proach (Krashen, 1985; Terrell, 1981) is used

extensively with ELL students. One of the four princi-ples of this approach is that the teacher understands thatthe student will need to have a silent period beforebeing expected to speak English. One of the subsequentstrategies of the Natural Approach is to allow students,especially those at the beginning level of their Englishlanguage developmental stage, to use drawings and sym-bols in solving some of the math problems. The sametechniques are employed with students with learningdisabilities to allow them to process auditory informa-tion before making a verbal response. In fact, as a com-prehension strategy, teachers can use students’ drawingsand verbal rehearsals as testimony of their understand-ing of math concepts. This approach can alleviate frus-trations for both teachers and students.

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18 INTERVENTION IN SCHOOL AND CLINIC

Have ELL/special education studentspair with typical students for computer/cooperative activities.

According to Krashen, language is acquired in an“amazingly simple way—when we understand messages”(1985, p. vii). He termed this understandable languageas “comprehensible input.” Peer interaction betweennative and non-native speakers of English is one meansof promoting “comprehensible input” or understandablelanguage. In peer interaction, students are observed tohave used four communication strategies that contributeto the occurrence of comprehensible input: 1. embedding language within a meaningful context, 2. modifying language presented to non-native peers, 3. judiciously using paraphrase and repetition, and 4. consistently negotiating meaning (Diaz-Rico &

Weed, 1995).

When teachers make diverse pairings, students ac-complish content- or language-task goals as well as mathgoals through the use of computers. Collaborative workbetween the pair will promote student acquisition of theEnglish language and facilitate inclusion through thelearning of content areas such as math, science, socialstudies (Howell, 1996, p. 60). Students may be encour-aged to take group Internet field trips or work on apiece of software in a cooperative fashion.

Encourage children to think aloudwhen solving word problems, and havestudents give oral explanations of their

thinking, leading to solutions. The think aloudtechnique was a research tool originally used by psy-

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6chologists. This research instrument is now popularwith researches in the language and reading fields.When a person thinks aloud they are verbalizing theconcepts, processes, or metacognitive checks that en-able them to solve problems. According to Chamot & O’Malley (1989), metagcognitive knowledge includesawareness of task demands, of one’s own approach tolearning and experiences with similar tasks, and of ap-propriate strategies for the task. Encouraging childrento think aloud when solving problems helps teacherspinpoint students’ difficulties in solving math problems.In addition, it can also help teachers instill in their stu-dents the metacognitive knowledge and strategies whenlearning math concepts. Most times, in verbalizing step-by-step how a math problem is solved, students can self-correct their mistakes. Similarly, this process allows peercorrections to occur.

Have students write original wordproblems to exchange with classmates.When students write their own original word

problems, the teacher can use them as part of reviewgames among cooperative groups. For example, teacherscan divide students into groups of three or four andhave them collaboratively write word problems. Afterthe group has generated several math problems, thegroup members take turns writing and adding to theword problems. The group that comes up with the mostdifficult problem but displays clear and well-written wordproblems wins. This activity can reinforce students’ writing and reading skills.

Explain directions clearly, and repeatkey terms. Diaz-Rico and Weed (1995) asserted that “the difficulties that language

minority students have with the language of mathemat-ics lie in four major areas: vocabulary skills, syntax, se-mantics, and discourse features” (p. 137). These samelanguage difficulties are evident in many students withlearning disability profiles. Teachers who are sensitive to student language difficulties will explain directionsclearly and repeat key terms. There are several waysthat teachers can do this. Common classroom directionssuch as “hand work in” or “work quietly” should bewritten in bold letters and/or illustrated by drawings,cue cards, and diagrams posted on the classroom wall.Teachers should repeat routine-related directions everyday or have students take turns in repeating directionsso that all students will understand what is expected ofthem. As far as the learning of math formulae and sym-bols, teachers can assign group projects that elicit stu-dents’ help in illustrating math concepts.

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Encourage students to follow the four-step problem-solving process. Students should be encouraged to use Polya’s

(2004) four-step problem-solving process and to writetheir thought processes as they go about solving prob-lems. This technique is a crucial part of the NCTM’s(1989, 2000) Standards. Polya’s method directs studentsto solve math problems by doing the following:

• Read and understand the problem. They may writethe problem in simpler terms.

• Develop a student-generated strategy for solving the problem, and discuss how they arrived at thisstrategy.

• Carry out their strategy/plan, and show all work justifying their answer.

• Look back and check to see that their solution appears to be reasonable.

Also, teach problem-solving strategies to students:working backward, drawing a picture, making a simplerproblem, looking for a pattern, learning by trial anderror, acting out, using a table. These strategies can en-rich and empower students mathematically as they prob-lem solve. Like all strategies, this one requires teacherdirection and modeling at first, then verbal rehearsal andpractice on simpler problems before moving to moredifficult ones or generalization (Mercer & Mercer, 1998).

Realize that not all math notations are necessarily universal. Although math is considered by many as an international

language, students from South America and many Eu-ropean countries write a period in large numbers wherecomma is written, and where their decimal mark is acomma, our decimal mark is a period. That is, our num-ber 4.547 is interpreted by these students as 4,547 orvice versa. Consequently, students with visual perceptualdifficulties may not accurately distinguish between thetwo notations regardless of their background or ethnic-ity. Another example of differing notational systems isthe methods used to divide numerals. Students fromSouth American and the Caribbean may display theirwork for division problems quite differently from theU.S. manner.

Example: 25,000 divided by 5U.S.: 5) 25000Haiti: 25,000 (5

Most of the world uses the metric system; thereforemath concepts based on feet, inches, miles, pounds, ounces,

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10cups, pints, quarts, and soforth have to be relearnedand practiced. Math conceptsthat are based on money andtime are not universal. Amer-ican coins may confuse new-comers with a relatively largenickel outweighing a coin oftwice the value and by nothaving the value written onthe coins in numbers.

Group students heterogeneously during cooperative learning. Cooperativelearning has positive results in the education

of students from diverse backgrounds (Kagan,1989). According to Cazden (1988), classrooms that emphasizeindividual performance, teacher-centered learning, andlittle or no student control of participation may be “cul-turally incongruent” with the backgrounds of many students. Not only does cooperative learning restore asense of comfort in a school setting where there are students with differing needs, it also offers students collective psychological support as they learn new con-tent. ELL students gain models for language develop-ment; students with disabilities gain models of positivebehavior. This support provides all parties, both teach-ers and students, with a workable socio-cultural com-promise between the home culture and culture of theschool. By grouping heterogeneously, students with di-verse needs can offer and enrich the mainstream stu-dents’ learning process with experience and knowledgeof their skills.

Make interdisciplinary connections towhat students are learning in math.Using themes in math lessons that can draw

interdisciplinary connections will reinforce learningskills from different disciplines. For instance, whenshowing students the difference between the metric sys-tem that they are familiar with and the standard systemin the United States, teachers can also teach map skillsfrom social studies class. One way to do this is to createa scenario where students play tourists who have just ar-rived in the United States. Given a map of the UnitedStates, they measure the distance between the airportand their destination using the scales provided, calculatethe distance in miles, and convert it to metric. Themore opportunities that a student has to connect newknowledge with existing knowledge increases the gen-eralization potential.

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Make cultural connections for studentswhen teaching mathematics. Teacherscan capitalize on the diverse cultural backgrounds

of their students when teaching mathematics. For in-stance, a world study math center can be set up in theclassroom in which students from multicultural back-grounds display the origins of math concepts from theircultures (e.g., algebra [Arabic], geometry [Greek], tan-grams [Chinese]). Math and art teachers can find com-mon themes in which they can team teach individualsubject matter concepts in their classes.

Rewrite word problems in simple terms.Students with limited language skills, includingthose who are literate in their first language and

students with language-based learning disabilities, oftenhave not mastered the technical vocabulary related tobasic math operations. These problems center aroundconcepts and vocabulary such as words of a technicalnature such as denominator, quotient, and coefficientand words such as rational, column, and table. By havingstudents work collaboratively in heterogeneous groupsto write math problems, teachers perhaps will be able tosee how these technical terms might be used or evenavoided when students express these problems in theirown words. Teachers can also paraphrase and modifysome of the more challenging questions by highlightingkey terms (Mercer & Mercer, 1998). For instance, in theproblem “Five times a number is two more than tentimes the number,” students must recognize “a number”and “the number” refer to the same quantity. However,consider this problem: “The sum of two numbers is 77.If the first number is ten times the other, find the num-ber”; students need to know they are dealing with twonumbers (Dale & Cuevas, 1992). In the above example,teachers can use pictures and symbols to illustrate theproblem, and they can also emphasize the differencethat grammatical articles (such as “a” and “the”) canmake to the semantics of the problem.

Concretize math concepts with TotalPhysical Response (TPR; Asher, 1982).TPR is an approach to second language

acquisition that is based on the model of how childrenlearn their first language. It can be applied not only tonon-native English speakers but also to students withdisabilities. In the TPR approach, instructors describeprocedures while modeling actions. In math, teacherscan use TPR to illustrate problem-solving math ques-tions. For instance, in demonstrating the math conceptsof “equal,” “more than,” “less than” (=, >, <), teachers

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14organize two groups of students, with one group con-taining more students than the other. A more complexTPR activity would be to have the students role play askit to demonstrate the concept of expansion. Studentscan line up in a row to play molecules in a rod, whileone student plays the fire heating the rod. More stu-dents are added to the original row to signify expansionof the rod, and spectators can measure the length of arod and record the difference. Many other creative activities can be made up using TPR. Students will havea lot of fun learning math using this approach becauseteachers are involving students in math concepts insteadof solely talking about math concepts.

Create word bank charts and hangthem in the classroom for viewing.Teaching vocabulary in mathematics instruction

is a crucial first step to learning new skills. Creating aliterate environment where the classroom is filled withword list charts is important. Teachers can keep wordlists for each unit of study and add new words as theyappear throughout a unit. Teachers should be encour-aged to write mathematics vocabulary both in Englishand also in the language of their LEP students. In doingthis, teachers are encouraging students to maintain andpreserve their mother tongue along with seeing andusing these new words in English.

Take Internet field trips and use mathematics software. The Internet andcomputer software are now being used as an

instructional tool to explore, investigate, problem solve,interact, reflect, reason, communicate, and learn manyconcepts that are in U.S. school curricula. Students areable to take virtual tours of places like the Bronx Zoo,the White House, the Louvre Museum and also haveaccess to information from NASA, the United Nations,and so forth. The number of Web sites and educationalsoftware available designed for teachers and students

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with the intent to teach concepts is becoming endless.Web sites like funschool.com or www.funbrain.com areideal for both teachers and students to teach/learn a multi-tude of math and reading/language concepts K–12, andsoftware like Mathblaster, Tesselmania, and Geometer’sSketchpad can make the learning of mathematics reallydynamic. Many Web sites are designed for teachers, stu-dents, and parents and keep track of student achieve-ment and record keeping as well as provide learning inan exciting and interactive way. Today more and moreteachers can bring their students to sites to access infor-mation or interact and learn concepts on just about anytopic under the sun.

Teachers may want to group students in pairs at com-puters and bookmark the sites for the students in advance.You can also create a worksheet, treasure hunt, or activ-ity sheet with the Web sites listed, along with a guide ofquestions to answer and activities to do as they visit var-ious sites while taking their Internet Field Trip (Furner,Doan-Holbein, & Scullion-Jackson, 2000).

Many Web sites include the actual pictures of thecurrently used math manipulatives that are used inclassrooms across the country to help reinforce mathconcepts in a concrete way. Students can explore thegeometrical math concept of a tessellation and actuallycreate their own while learning geometry and spatialsense objectives. The possibilities are endless when youinfuse the Internet into instruction.

Ameis and Ebenezer (2000) have recently written abook called Mathematics on the Internet in which theyprovide resources and suggestions for teaching mathe-matics via the Internet. The book connects math con-cepts K–12 to many Web sites that can be used to helpteach these concepts.

Parents of homeschooled children can benefit fromInternet use as a means to learn via Internet Field Trips.The Internet has a definite role to play in the reform oftraditional teaching. By using educational software andthe Internet, students can now learn in ways that aremore exciting and challenging. The Internet also pro-vides students with tools to access information and be-come independent life-long learners in an age that willincreasingly depend on technology to survive in a com-plex multicultural world.

Use children’s literature to teach mathematics and develop the language. Teachers can reach a child in a

non-threatening way by reading children’s literaturethat helps teach math concepts and connect the learner’smathematical understanding and at the same time not

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intimidate, threaten, or turn-off a child to mathematicslike some traditional approaches may have. Children’sand adolescents’ literature can be a beneficial way ofteaching mathematics.

Benefits of Using Literature in Mathematics• Teaches math concepts in the context of a story• Incorporates integrated studies with reading, writing,

speaking, listening, and so on• Develops mathematical thinking• Prevents math anxiety and creates a less math-anxious

classroom environment• Allows for a variety of responses• Makes historical, cultural, and practical application

connections• Allows for the use of manipulatives as it relates to the

story• Assesses a child’s understanding by reading/questioning• Offers a wide range of books that can be used to

teach most math concepts K–8• Leads to problem solving and active involvement

from the story’s context• Provides a shared experience for students and teacher

Teachers can address the NCTM’s “CommunicationStandard” by incorporating literature in the teaching ofmathematics (2000). Teachers can also have students dis-cuss math from the stories and write about such conceptsto demonstrate their understanding of math concepts aswell as their feelings toward math. In their book Books YouCan Count On: Linking Mathematics and Literature, Griffithsand Clyne (1991) wonderfully illustrated many examplesof how to connect children’s literature into a math lesson.Here we have included a sample of some of our own sug-gestions of activities tying literature and writing to math-ematics.

Using auditory, visual, and kinestheticteaching approaches for differentlearning styles enables teachers to

reach more students than the traditional direct-instruction or paper and pencil drill andpractice forms of instruction. Some teachers usemanipulatives, others allow verbal rehearsals, some mayuse the new series of math teaching videos by MathVantage or make math visual using math software or thecomputer screen. Another option would be to considerkinesthetic learners. These learners learn best by doing.They complete the task by mounting a whole-body ef-fort. Sometimes the overwhelming energy put forth bythis type of learner can lead to a loss of focus. Studentsget off track and miss their objective. One way to meet

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the needs of these students is to incorporate refocusingactivities as part of the transition process. Moskowitz(1978) suggested that classrooms that offer techniquesdesigned to relax students, increase the enjoyment oflearning, raise self-esteem, and blend self-awarenesswill increase students’ potential. For example, studentsmay need a moment to stop and focus before beginninga group activity. This would involve the whole class or asmall group taking a moment to close their eyes andthink about what they need to do next. The students donot need words to project what they need to do; theyhopefully think through the next step. Learners of vary-ing modalities can focus and plan their next step. Teach-ers must take into consideration the modalities of theirstudents and try to reach each child regardless of his orher learning style.

Summary

These suggestions are by no means exhaustive. With thisgrab bag of strategies, teachers can creatively design theirlesson activities to meet students’ individual needs. Wehave offered strategies and techniques that will match thelearning styles of all students—reaching all students usingteaching styles that adapt to students’ multiple intelli-gences. With the ESE learners, the use of the multimodalapproach that incorporates the multiple intelligencecaters to students’ short attention spans as they are notexpected to only sit still to learn the materials. With theEnglish Language Learners, we have included the SDAIE(Specially Designed Academic Instruction in English) ap-proach, which supports the teaching of language acqui-sition while teaching the content area such as math. In allof the 20 strategies, language objectives are incorporatedin teaching math concepts; therefore, ELL are given the

opportunity to simultaneously develop their English lan-guage skills as they are learning math. Math teachers todaymust work hard to eliminate and prevent any math anxi-ety their students may develop or carry with them (Furner& Duffy, 2002). Our children today are not only com-peting for jobs with others in the United States but withothers from around the globe who are confident in theirability to do mathematics in this competitively global so-ciety. Content area teachers can also play a crucial role inthe language learning process of their students, and pri-mary teachers no longer have to be the sole responsibleparty in teaching ELL the English language; rather, boththe content area teachers and the primary teachers canwork as a team to help the ELL in their academic work.Each day the diversity of students grows within the con-finement of our classrooms, so teachers have to tirelesslykeep abreast with their research of diverse teaching strate-gies to reach all students. Equity in mathematics instruc-tion requires teachers to provide accommodations soeveryone in the class can learn mathematics. The bestpractices mentioned here can assist teachers in reachingall students mathematically.

ABOUT THE AUTHORS

Joseph M. Furner, PhD, is an associate professor of mathe-matics education at Florida Atlantic University in Jupiter,Florida. His research interests are related to math anxiety, theimplementation of the NCTM Standards, ESOL issues as theyrelate to math instruction, the use of technology in mathemat-ics instruction, math manipulatives, and children’s literature inthe teaching of mathematics. Prior to teaching at the universitylevel, Dr. Furner taught middle school mathematics in NewYork and at the American School in Mexico City, Mexico, andmost recently taught high school mathematics at Colegio NuevaGranada in Bogota, Colombia. Noorchaya Yahya, PhD, is anassociate professor of TESOL Education at Florida AtlanticUniversity in Port Saint Lucie, Florida. She trains South Floridapre- and in-service teachers in all areas of TESOL Education:Methodology, Curriculum, and Instruction; Language Assess-ment; and Applied Linguistics for K–12 teachers. Her main re-search interests are ESL writing, ESL in content area teaching,and teachers’ reflections of their teaching processes. She haspublished several articles in her research areas and co-authoredtwo books, Why TESOL?: Theories and Issues in Teaching Englishas a Second Language for K–12 Teachers and Fundamentals of Teach-ing English to Speakers of Other Languages in K-12 MainstreamClassrooms. Mary Lou Duffy, PhD, is an associate professor ofexceptional student education at Florida Atlantic University’sJupiter campus. Dr. Duffy teaches courses in classroom manage-ment, assessment, and strategy instruction. Her research inter-ests include issues related to transition from school to worksettings for individuals with disabilities and quality instructionalpractices for teachers of exceptional students. Address: JosephM. Furner, Florida Atlantic University, College of Education,5353 Parkside Dr., Jupiter, FL 33458; e-mail: [email protected]


REFERENCES

Ameis, J. A., & Ebenezer, J. V. (2000). Mathematics on the internet: A re-source for K-12 teachers. Upper Saddle River, NJ: Merrill.

Asher, J. (1982). Learning another language through actions: The completeteachers’ guidebook. Los Gatos, CA: Sky Oaks.

Cazden, C. (1988). Classroom discourse. Portsmouth, NH: Hienemann. Chamot, A., & O’Malley, J. (1989). The cognitive academic language

learning approach. In P. Rigg and V. Allen (Eds.), When they don’t allspeak English. Urbana, IL: National Council of Teachers of English.

Dale, T., & Cuevas, G. (1992). Integrating mathematics and languagelearning. In P. Richard-Amato & M. Snow (Eds.), The multiculturalclassroom. White Plains, NY: Longman.

Diaz-Rico, L. T., & Weed, K. Z. (1995). The crosscultural language develop-ment handbook: A complete K-12 reference guide. Boston: Allyn & Bacon.

Furner, J. M., Doan-Holbein, M. F., & Scullion-Jackson, K. (2000).Taking an internet field trip: Promoting cultural and historical di-versity through mayan mathematics. TechTrends, 44(6), 18–22.

Furner, J. M., & Duffy, M. L. (2002). Equity for all students in the newmillennium: Disabling math anxiety. Intervention in School and Clinic,38(2), 67–74.

Griffiths, R., & Clyne, M. (1991). Books you can count on: Linking math-ematics and literature. Portsmouth, NH: Heinemann.

Howell, R. D. (1996). Technological aids for inclusive classrooms.Theory Into Practice, 35, 58–65.

Kagan, S. (1989). Cooperative learning: Resources for teachers. San JuanCapistrano, CA: Resources for Teachers.

Krashen, S. (1985). The input hypothesis: Issues and implications. New York:Longman.

Mastropieri, M. A., Scruggs, T., Mohler, L., Bernak, L., Spencer, V.,Boon, R. T., et al. (2001). Can middle school students with seriousreading difficulties help each other and learn anything? LearningDisabilities Research and Practice, 16(1), 18–27.

Mercer, C. D., & Mercer, A. R. (1998). Teaching students with learningproblems (5th ed). Upper Saddle River, NJ: Merrill/Prentice Hall.

Moskowitz, G. (1978). Caring and sharing in the foreign language class.Cambridge, MA: Newbury House.

National Council of Teachers of Mathematics. (1989). Curriculum andevaluation standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (2000). Principles andstandards for school mathematics. Reston, VA: Author.

Polya, G. (2004). How to solve it: A new aspect of mathematical methods.New Jersey: Princeton University Press.

Terrell, T. (1981). The natural approach in bilingual education. In C. F.Leyba (Ed.), Schooling and language minority students: A theoreticalframework. Los Angeles: Evaluation, Dissemination and AssessmentCenter, California State University.

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