Contextualizing Professional Development: Elementary Bilingual Teachers Explore Mathematics Problem Solving Sandra I. Musanti, Ph.D. Sylvia Celedón-Pattichis, Ph.D. University of New Mexico
2008 SACNAS NATIONAL CONFERENCE
National Science Foundation Award No. ESI-0424983
Center for the Mathematics Education of Latinos/as
Background Reform initiatives value teachers’ understanding of student mathematical thinking (NCTM, 2000). Research demonstrates impact of PD learning communities in which teachers inquire about their practice and analyze student work (Kazemi & Franke, 2004; NCTM, 2000).
Research on effective PD for teachers of bilingual and ELLs is still lacking(Téllez, 2004; Varghese, 2004). Need for research that explores PD approaches that support bilingual teachers’ mathematics instruction in students’ native language.
Redefining the Boundaries of Professional Development Classroom-based teacher-researchers collaboration to support mathematics teaching in Spanish (Cobb, 2000) Weekly researchers’ visits to the classroom to: Model, co-plan or/and observe CGI problem-solving lessons Meet for debriefing conversations after each session
PD monthly sessions with participating teachers and/or summer institutes
Cognitively Guided Instruction Framework for understanding how children’s mathematical thinking develops (Carpenter et al., 1999) Emphasis on explaining and justifying solutions Context-embedded word problems Example: “It was Javier’s birthday party. There was a big woodpecker ‘piñata.’ Children broke the ‘piñata’ and candy fell on the floor. Javier got 20 candies and Sergio got 35. How many more candies did Sergio get than Javier?”
Research Purpose This study explores: The impact of a collaborative teacher-researchers classroom-based PD Primary grades bilingual teachers’ understandings of teaching mathematics to Latino/a students How do bilingual teachers integrate CGI principles into their mathematics teaching?
Methods Ongoing longitudinal qualitative study Data analyzed: Field notes from classroom visits (N = 128) Teacher interviews from Fall 06, Spring 07, Fall 07 and Spring 08 (N=19) Content logs of videotaped classroom sessions from Fall 2007-Spring 08 (N= 27) Selected videotaped classroom sessions (N=6)
Participants Five bilingual teachers from an urban elementary school in New Mexico Promotes bilingualism and biliteracy Everyday Mathematics curriculum 86% Latino population (mostly Mexican immigrants)
The teachers:
Mrs. Carrera - Kinder - Novice - Mexico Mrs. Arenas - Kinder - Experienced - Guatemala Mrs. López - 1st grade - Experienced - Peru Mrs. Amado - 1st grade - Novice - Puerto Rico Mrs. Sánchez - 2nd grade - Novice - New Mexico
Understanding Student Thinking Contextualizing the word problems as a story familiar to students’ lives incorporating students as the main actors Using questioning strategies to scaffold students on explaining their thinking (Turner et al., in press)
Mrs. López’s Case Using questioning to scaffold students’ explanations (Turner et al., in press) Teacher: Belen has 8 pencils, and Alan has 3 pencils less than Belen. Alan and Belen are modeling the problem. Alan thinks for a while, then gets 5 pencils. Teacher: Belen has, how many? (to the class) Students: Eight Teacher: Alan has 3 pencils less than Belen. Who has more pencils? Students: Belen Teacher: How many more? Students: Three more Teacher: How many pencils does Alan have? Jose: He has 5. She had 8 and he has 3 less. Teacher: How many pencils does Alan have? (to the group) Students: Five Teacher: How do we know? Jaqueline: If she has 8 and we take away 3, then he has five.
Emphasis on students’ verbal and pictorial representations Teachers progressively focused on fostering students’ development of more sophisticated ways of talking about their mathematical thinking in their native language (Turner et al., in press).
Teachers encouraged students to represent their solutions to problems in varied ways (using drawings, algorithms, written words) (NCTM, 2001).
Analyzing Student’s Representations Mrs. López’s Case - First Grade Oscar had 3 toy cars, and Giovanny had 5 more toy cars than Oscar. How many toy cars did Giovanny have? The drawing contains the right answer, but the picture shows misinterpretation.
Scaffolding Students’ Verbalizations Mrs. Carrera’s Case Kindergarten bilingual Classroom Emphasis on retelling the story, sharing problemsolving strategies, and discussing efficient strategies Video
Importance of Accessing Peers’ ProblemSolving Strategies (1) (Turner et al., in press) “Exposing [students to mathematics problems] and talking about it and solving the problems together and listening to their classmates [is] more helpful than listening to the teacher . . .they think they can do it because they see another peer doing it. Because she’s not the teacher and if she can do it, I can do it. And that’s very important.” (Mrs. Amado, First Grade, Nov. 2007)
Importance of Accessing Peers’ Problem-Solving Strategies (2) Explaining their thinking impacts students’ internalization of problem solving strategies (Carpenter et al., 1999).
“If they are able to explain their thinking, then that solidifies the concept in their mind. They understand it well…If you can explain how you solved a certain problem, maybe you can transfer those problem-solving skills and make connections between problems.” (Mrs. Sánchez, Second Grade, Dec. 2007)
Opportunities to Learn Rigorous Mathematics for All Students Students’ opportunities to learn are shaped by teachers’ instructional decisions and the way they enact curriculum (Boaler, 2002).
“I wondered if my kinders...I always believed in their ability, but I thought they are so low, I knew I could take them through addition … but division and multiplication I wasn’t sure. But they were ready, they were ready. And that's what I really learned. Problem solving works and CGI works with very young students and it works really, really good. . . I am very happy . . .because it helped them to strengthen their abilities, according to what they can do. They really have come a long way.” (Mrs. Arenas, Kinder, May 2006)
Implications Bilingual teachers benefited from: Redefining the boundaries of PD creating classroom-based learning opportunities centered on exploring CGI problem solving in students’ native language Ongoing reflection and analysis of students’ mathematical thinking and different problem solving strategies Providing Latino students with opportunities to solve challenging mathematical problems and explain their reasoning in their native language
Contact Information Sandra Musanti
[email protected] Sylvia Celedón-Pattichis
[email protected] CEMELA Website
http://cemela.math.arizona.edu
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