Are the words as important as the concepts? Using pedagogical language knowledge to expand analysis of mathematics teach
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Are the words as important as the concepts? Using pedagogical language knowledge to expand analysis of mathematics teaching with linguistically diverse students William Zahner 1
& Cristian
R. Aquino-Sterling 2
Received: 1 November 2019 / Revised: 30 August 2020 / Accepted: 8 September 2020 # Mathematics Education Research Group of Australasia, Inc. 2020
Abstract We examine how two ninth grade mathematics teachers in a linguistically diverse school used general-everyday and discipline-specific language, along with language access strategies, during a lesson on linear rates of change. We use the socioculturally based framework of “pedagogical language knowledge” (PLK) to understand and unpack the teachers’ use of general-everyday and discipline-specific language. We argue that the teachers’ language use corresponded to concrete instances of PLK in action in the multilingual mathematics classrooms examined. We then discuss the potential of PLK as a lens for examining the pedagogical and linguistic choices of secondary mathematics teachers in linguistically diverse mathematics classrooms in light of foundational works in language and mathematics education in linguistically diverse contexts. Keywords Pedagogical language knowledge . Multilingual mathematics classrooms .
Secondary . Mathematical discourse
Ms. Velázquez and Ms. West were two ninth grade mathematics teachers at Campo High School,1 a school in which most students were immigrants or the children of immigrants. Although English was the official language of instruction, over 90% of all students spoke a language other than English at home, and about 30% were classified as English learners. Early in the school year, both 1
All person and school names are pseudonyms to protect the identity of research participants.
* William Zahner [email protected]
1
Mathematics and Statistics Department, San Diego State University, San Diego, CA, USA
2
School of Teacher Education, San Diego State University, San Diego, CA, USA
W. Zahner, C. R. Aquino-Sterling
teachers taught a problem-based lesson that presented an opportunity to invoke the commutative property of addition in a meaningful context. When this opportunity arose in Ms. Velázquez’s class, she highlighted the equivalence of the expressions A + B and B + A. Then she asked her students to name the property that makes this true. One student, Susana, timidly volunteered “commutative.” Ms. Velázquez asked Susana to write the word commutative on the board. As Susana wrote, Ms. Velázquez emphasized the spelling and pronunciation of commutative. When the same opportunity arose in Ms. West’s class, Ms. West also introduced this term, asserting “the commutative property of addition says that A plus B is equal to B plus A.” However, when a student asked a clarifying question, Ms. West then downplayed the importance of naming properties, stating, “the words are not as important as understanding the concepts.”
Words, concepts, and pedagogy in multilingual mathematics classrooms Mathematics teachers in linguisticall
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