Cognitive Demands and Second-Language Learners: A Framework for Analyzing Mathematics Instructional Contexts

Abstract

The issues involved in teaching English language learners mathematics while they are learning English pose many challenges for mathematics teachers and highlight the need to focus on language-processing issues related to teaching mathematical content. Two realistic-type problems from high-stakes tests are used to illustrate the complex interactions between culture, language, and mathematical learning. The analyses focus on aspects of the problems that potentially increase cognitive demands for second-language learners. An analytical framework is presented that is designed to enable mathematics teachers to identify critical elements in problems and the learning environment that contribute to increased cognitive demands for students of English as a second language. The framework is proposed as a cycle of teacher reflection that would extend a constructivist model of teaching to include broader linguistic, cultural, and cognitive processing issues of mathematics teaching, as well as enable teachers to develop more accurate mental models of student learning.Correspondence should be sent to Anne E. Campbell,

An examination of monolingual preservice teachers’ set-up of cognitively demanding mathematics tasks with emergent multilingual students

“…Hence, it is essential for teachers to provide EBs with scaffolding in this first phase so they can fully understand the problem statement and expectations before they begin the solving process. Research has suggested that EBs are capable of problem solving if they understand the problem statements (Campbell et al, 2007).…”

“…Thus, the differences among learners can be negotiated and understood through conversations and social interactions. Eventually, a common space (Campbell, 2007) will be constructed where they understand each other while their differences still exist.…”

“…Researchers have examined different aspects of teachers' instructional practice in order to learn how to support the mathematical learning of EBs (de Araujo et al, 2018) including providing linguistic support (Echevarria, Vogt, & Short, 2010), applying nonverbal activities (Ahn et al, 2015;Fernandes, 2012;Morales, Khisty, & Chval, 2003), utilizing visuals with mathematical information (I & Stanford, 2018) and integrating students' culture and previous experiences (Aguirre et al, 2013;Lipka, Sharp, Adams, & Sharp, 2007). Campbell et al (2007) proposed a model specific to the use of problem solving with EBs. This model describes how the interactions between the teacher and students construct the classroom experience, especially when a teacher has a different cultural/linguistic background from her/his students.…”

“…In Campbell et al (2007)'s model, the teacher and students build common understandings of mathematical concepts and language through the interactions based on their common "interpretation of the problem-solving situation" (Lesh & Doerr, 2003, p. 9).…”

“…We argue that while working with EBs, the set-up may hold particular relevance as it is the phase of task enactment through which the teacher is working with students to develop shared understandings of and expectations for their work on the task (Campbell, Adams, & Davis, 2007;Jackson et al, 2013). Thus, the research question guiding this study was, What common instructional strategies were implemented during task set-up by monolingual preservice teachers who maintained the cognitive demand of mathematical tasks with emergent bilingual/multilingual students?…”