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Instructional Demands of Teaching Mathematics with English-Language Learners. Jenny T Sealy University of Michigan. Rationale. There is growing linguistic diversity in the world at large. - PowerPoint PPT Presentation
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Instructional Demands of Teaching Mathematics with English-Language Learners
Jenny T Sealy
University of Michigan
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Rationale There is growing linguistic diversity in
the world at large. There are increasing numbers of
students who are English-language learners (ELLs) in mathematics classrooms.
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Rationale Our current teaching force is under-
prepared to support the learning of English-language learners.
There is not enough research addressing specifically the teaching of mathematics with English-language learners.
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Overview The Language of Mathematics Review of Research
Methods Highlighted Studies
Instructional Demands & Research Recommendations
Implications for Teacher Education Discussion
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English-Language Learners
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English-language Learners Bring an additional
linguistic resource to the classroom
Are in the process of learning the English language used in the mathematics classroom
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The Language of Mathematics Vocabulary
Words borrowed from everyday English and redefined (e.g. line)
Created out of everyday English Locutions (e.g. least common multiple) Combinations (e.g. output)
Created by combining Greek and Latin words (e.g. triangle, parabola)
(Halliday, 1978; Han & Ginsburg, 2001; Usiskin, 1996)
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The Language of Mathematics
In the mathematics register words are arranged and used differently than everyday English
“A register is a set of meaning that is appropriate to a particular function of language, together with the words and structures which express those meanings.” (Halliday, 1978, p. 195)
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Mathematics Register Numbers are treated differently both
grammatically and conceptually. (Nesher & Katriel, 1986)
In everyday English they act as predicates (e.g. Three dogs)
In mathematics they are objects (e.g. Three is a prime number)
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The Language of Mathematics Sentences are generally more dense
and complex than everyday English and contain fewer contextual cues
Words are used to represent symbolic expressions that embody a set of processes (e.g. x3+(x+1)3 = 35 is translated into ‘the sum of the cubes of two consecutive numbers is 35’)
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The Language of Mathematics Is multi-semiotic (Lemke, 2003) and “exploits
the meaning potential of linguistic, symbolic, and visual systems of representation” (O’Halloran, 2003, p.189)
Symbolic and visual representation are intertwined (Cuoco, 2001)
Multiple representations form one integrating meaning-making system
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The Language of Mathematics
Linguistic Representation
Symbolic Representation
Visual Representation
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Consider 2/3
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0 1 2
A truck uses 2 litres of gas every 3 kms.
0.666666...
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The Language of Mathematics Symbols
Special rules for interpretation of meaning based on order, orientation, and position (Laborde, 1990)
x9, 915, 9x, f(9), 10019, (9, 13)…etc Visual representations
Graphs, diagrams..etc are powerful means to display trends and patterns
Gestures are a powerful means to add contextual cues to meaning (Roth, 2001)
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Review of Research How has the teaching and learning of
mathematics in classes containing English-language learners been conceptualized?
What key issues do teachers need to negotiate in this instructional space?
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Review of Research Methods:
Cross-disciplinary, integrative research review
Studies published 1984-2008 Findings:
104 pieces of relevant research - 63 articles, 37 books, 3 statistical reports & 1 dissertation
Studies fell under 3 main perspectives or conceptual stances
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Representation Perspective Studies using this perspective focused upon
the components of mathematical language Highlighted studies:
Role of language comprehension in problem solving
Comparison of mathematical vocabulary across languages
Flexible use of multiple representations
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Language Comprehension Language acts as a mediator in mathematics
problem solving (Ellerton & Clarkston, 1996; Mestre, 1988)
Language in tasks affect their level of cognitive demand (Campbell, Adams & Davis, 2007)
Recommendation - Make language more comprehensible by: Explicitly teaching math vocabulary Providing contextual cues (e.g. relia) Simplify language in problem statements
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Comparing Languages Mathematical language is a cognitive tool
The cognitive representation of numbers differ by language (Miura, Okamoto, Kim, Steere, 1993)
It is easier to learn to count in Chinese than in English (Miller & Stigler, 1987; Miura, 1987)
Commonly used mathematical terms have greater clarity in Chinese than English (Han & Ginsburg, 2001)
E.g. ‘Four-side shape’ versus Quadrilateral
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Multiple Representations The flexible use of multiple representations,
representational competency, is important for student learning
ELLs taught with multiple representations were better able to represent the math in word problems (Brenner et al, 1997)
Representational competence is positively linked to student achievement (Brenner, Herman, Ho, & Zimmer, 1999)
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Communication Perspective Studies using this perspective focused
upon the use of mathematical language Highlighted studies:
Model of mathematical language development
Word walking Selection of mathematical tasks
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Model of Mathematical Language Development
(Gawned, 1990).
1. The Language of Social Interaction: ‘Real World’ Language
2. The Language of the Classroom
3.1 Language of Reasoning
3.2 Activity Specific Language
3.3 Language of the Mathematics
Curriculum
3.4 Literacy of Mathematics
4. Construction of Meaning in Mathematics
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Word Walking Students make substitutions in word
problems that keep the meaning in everyday English but change the mathematical meaning
Such substitutions that affect the mathematical model of the problem are called word walking (Mitchell, 2001)
“through the last half of the trip” “in the last part of the trip”
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Task Selection Tasks set in familiar contexts and
designed to engage students in the action described in the problem can facilitate the expression of ELLs reasoning through word and gesture (Dominguez, 2005)
Tasks that require students to talk and produce output are crucial for language acquisition (Cummins & Swain, 1986)
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Participation Perspective Studies using this perspective focused
on participation in a mathematical language community
Highlighted studies: Teacher’s role in establishing norms that
support ELLs Role of code-switching in the classroom Teacher’s role as expert participant
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Norms that Support Participation
The structuring and use of small group discussion can support ELLs participation in mathematical discussions
It can also prepare students for participation in whole class discussions (Brenner, 1998)
“The teacher plays a central role in establishing norms for mathematical aspects of students’ activity” (Yackel & Cobb, 1996, p.475)
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The Role of Code-Switching A study in South Africa (Setati & Adler, 2001), with
11 official languages, found code-switching to be a useful classroom strategy
Students freely explored mathematical ideas in their preferred language and then formally express conjectures to the class in English
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Expert Participant In the mathematical language community of
the classroom the teacher acts as the expert participant who models what it means to communicate mathematically in the wider mathematics community
The teacher supports ELLs by: encouraging language production, providing feedback and modeling the target language (Adler, 1999; Aljaafreh & Lantolf, 1994; Cummins & Swain, 1986; Doughty & Long, 2003; Ellis, Loewen & Erlam, 2006; Moschkovich, 1999)
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Gesture & Assessment Gesture is a powerful means of
communication and has a significant role in teaching and learning See Roth’s (2001) review
There are several difficulties in accurately assessing ELLs See Abedi, Hofstetter & Lord’s (2004)
review
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Instructional Demands Shift in the work of the mathematics
teachers Teach both mathematics & language (Bay-
Williams & Herrera, 2007; Freeman, 2004)
Selection of appropriate tasks and activities
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Instructional Demands Making language comprehensible to
students Managing the overlap and interplay
between everyday English and mathematical English in the classroom
Guide ELLs learning while being aware that their verbalizations may not reliably display their mathematical thinking
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Common Recommendations Use multiple representations Maximize students’ opportunities to
communicate Select tasks that facilitate student
learning of mathematics and language Allow code-switching where feasible to
make use of students’ additional linguistic resources
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Implications for Teacher Education Attention to the development of teachers’
representational competence Course and professional development (PD)
offerings that provide training on language learning
A change in both teachers’ and our conception of the work of mathematics teachers to include attention to language learning
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Discussion What other instructional demands have
you identified from your own work with mathematics teachers who work with English-language learners? What recommendations can we suggest for
managing these demands? What implications do they have for teacher
education?
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Discussion “A vision of reform aimed at the academic
achievement of ELLs requires integrating knowledge of academic disciplines with knowledge of English language and literacy development.” (Lee, 2005, p.492)
What does this mean for us in mathematics education? Given the unique nature of mathematical language Given the Communication Standard (NCTM, 2000)
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Questions?
Please note the handouts of research references at the front.
