Tandem Learning Progressions Provide a Salient Intersection of Student Mathematics and Language Abilities

• In Event: Using Multiple Learning Progressions to Support Assessment

Abstract

Objectives

We describe development of an empirically-derived language learning progression and preliminary findings from its extension to analysis of student proportional reasoning explanations. Our goal is to gain an appreciation for and a deeper understanding of the dual functioning of mathematical knowledge and English language proficiency as they are manifest in student explanations.


Perspectives

Explanation is a cross-cutting language practice of College and Career Ready Standards (CCRS) and is highlighted in the ELPD Framework (CCSSO, 2012) that guides creation of English language development standards and assessments. In summative and formative assessment alike, under CCRS, students are required to display their mathematical learning through their explanation abilities (Bailey, Blackstock-Bernstein & Heritage, 2015). Progressions of explanatory language can provide a basis for teachers’ understanding of students’ language development (Bailey & Heritage, 2014).


Methods and Data Sources

Language progressions in both social and mathematics contexts were derived from a new longitudinal corpus of K-6 oral and written explanations elicited from 234 students across several time points. The increasing sophistication of eight language features can be arrayed on progressions intended to assist teachers in gauging the characteristics of language at word, sentence and discourse levels that students from diverse language backgrounds and experiences produce. We found the best fit for the eight language features in the students’ propositional reasoning explanations on the language progressions (i.e., either Not Evident, Emergent, Developing or Controlled). We then cross-tabulated placement on both the math and language progressions (Figure 1).


Results

Preliminary analysis of the explanations suggests that language seems necessary for math performance (i.e., 30% of explanations were High LANGUAGE-High MATH; few Low LANGUAGE-High MATH), but it is not sufficient; we placed 25% Low MATH-High LANGUAGE; 33% low on both progressions. This dual focus may help teachers more clearly target next steps instruction that different configurations of student performance need: One set of students will need assistance extending already learned explanation abilities to math (Low MATH-High LANGUAGE); another set will need both math and language assistance (Low-Low performance on the progressions); others will need help in explanation, but already have math skills (High MATH-Low LANGUAGE) which may be a profile fitting some English learner students (See Figure 1).

Figure 1. Possible configurations of “best fit” for student performance on the extremes of companion progressions.


Scholarly Significance

Emerging insights suggest ways that teachers can use progressions together to inform differentiated instruction and learning targeted to the needs of students. We find that sounding competent without domain knowledge is not common; it is very difficult to be cogent (e.g., cohesive and coherent explanations) without a grasp of proportional reasoning. Students need exposure to not only specialized mathematics vocabulary, but to extended discourse in mathematics, and this is essential for English learners who lack such exposure (Moschkovich, 2012). Applying tandem progressions has implications for the pre-service and in-service training teachers receive, especially the need for closer collaboration between mathematics and ESL/ELA teachers. Analyses of learning progressions applied in tandem give a more detailed and nuanced picture of what progression approaches to instruction and formative assessment might jointly deliver.

Authors

• Alison L. Bailey, University of California - Los Angeles

• Margaret Heritage, WestEd