Rebecca Ambrose

Screencasts: Formative Assessment for Mathematical Thinking

Increased attention to reasoning and justification in mathematics classrooms requires the use of more authentic assessment methods. Particularly important are tools that allow teachers and students opportunities to engage in formative assessment practices such as gathering data, interpreting understanding, and revising thinking or instruction. Screencast applications on mobile devices enable teachers to collect multiple modes of communications, which students use to generate mathematical explanations. As students’ explanations are recorded in the moment and contain verbalizations, written notations, and virtual gestures, teachers are able to gain insights into students’ understanding in greater depth than any one mode individually. Additionally, misconceptions and mistakes, which are often lost in written work, are documented and can be identified to specifically target interventions. In this report, a student-generated screencast example will highlight how this technology can be used as a formative assessment tool. Also discussed are potential limitations when using the technology in classrooms and possible solutions.

Children's Evolving Understanding of Polyhedra in the Classroom

To better understand the development of childrens thinking in three-dimensional geometry, we conducted a teaching experiment with 8- and 9-year olds in which children built and described polyhedra during several lessons. Analysis of pre-/post-assessments showed that children advanced in their geometric reasoning and began to identify, enumerate, and notice relationships between component parts of polyhedra. Our consideration of a class activity showed how examining a range of examples and non-examples enculturated students into the practice of attending to component parts. Promoting precise, formal definitions for components proved to be a significant challenge for the teacher in establishing norms for class discussions.

First-Grade Latino English-Language Learners’ Performance on Story Problems in English Versus Spanish

To explore whether teaching English-language learners (ELLs) with an emphasis on English story problems is appropriate, we compared the performance of a group of Latino first graders when working in Spanish and in English on two equivalent sets of story problems. The students’ performance was slightly higher in English than in Spanish but lower than monolingual students from other studies. ELLs’ success in English indicated that the children’s knowledge of conversational English was sufficient to comprehend story problems, leading us to conclude that teaching through story problems is a viable approach with ELLs.RésuméAfin de déterminer s’il convient d’enseigner les mathématiques aux apprenants en anglais langue étrangère en mettant l’accent sur les problèmes narratifs, nous avons comparé les performances d’un groupe d’étudiants latino-américains de première année lorsqu’ils travaillaient en espagnol et en anglais sur deux ensembles équivalents de problèmes narratifs. Les performances des étudiants sont légèrement supérieures en espagnol, mais inférieures à celles des élèves unilingues provenant d’autres programmes. Le succès des étudiants d’anglais langue étrangère indique que les habiletés de conversation anglaise des enfants étaient suffisantes pour qu’ils soient en mesure de comprendre les problèmes narratifs, ce qui nous porte à conclure que l’enseignement par le biais des problèmes narratifs constitue une approche valable avec les étudiants d’anglais langue étrangère.

First Encounter with Variables by First and Third Grade Spanish Students

This chapter presents findings from a teaching experiment on the initial understandings that primary Spanish students demonstrated when they were first introduced to the use of letters to stand for an indeterminate varying quantity in a functional relationship. We provide a detailed account of our task design and class activity to show how understanding of variable notation for functional relationships was cultivated. We discuss the degree to which results from previous studies generalize to the Spanish context. Our results, similar to those of previous studies, support the introduction of variables in elementary grades.

Mathematical Classroom Discussion as an Equitable Practice: Effects on Elementary English Learners’ Performance

ABSTRACT This mixed-method study examines the relationship between classroom discussion and student performance in twenty 3rd and 4th grade classrooms in northern California with 50% English language learners (ELLs). Discussions were scored on features including use of multiple approaches for solving problems, students’ opportunities to speak, equitable participation, explanations, and connections between ideas. A linguistically-modified math assessment measured student performance. Quantitative analysis using hierarchical linear modeling (HLM) showed that the discussion features variety of approaches and equitable participation significantly contributed to the explanation of between-class variation in assessment scores, above and beyond that explained by prior mathematics performance and English proficiency. Importantly, mathematical discussion was equally beneficial for students classified as ELLs and those not classified as ELLs. Two classroom vignettes illustrate the different features of discussion and offer insight into ways ELLs contributed to the discussion in different contexts.