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Papers by Darrell Earnest

Handbook of Research on Transforming Mathematics Teacher Education in the Digital Age, 2000

Proceedings of the 9th International Conference of the …, 2010

This poster presents a case study of one Grade 6 student to illustrate and consider the role of i... more This poster presents a case study of one Grade 6 student to illustrate and consider the role of introducing key mathematical terminology as a semiotic means to objectify mathematical ideas at hand (Radford, 2003). The poster describes how in two classrooms ...

Cognition and Instruction, 2015

This article reports on students' problem-solving approaches across three representations-number ... more This article reports on students' problem-solving approaches across three representations-number lines, coordinate planes, and function graphs-the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a hierarchical representational narrative (HRN), a discursive narrative around a set of representations that model conventional mathematics in structurally consistent ways. A paper-andpencil assessment was administered to students in grades 5 and 8 along with videotaped interviews with a subset of students. Results revealed students' application of particular meta-rules, which reflect their attempts to find and make use of recurring patterns in mathematics discourse. One such meta-rule, consistent with the HRN, was characterized by students' coordination of geometric and numeric properties of an axis, whereas alternate meta-rules reflected coordinations inconsistent with conventional mathematics. Detailed analyses of problem-solving strategies are reported, and implications for theory, curriculum, and instruction are discussed.

International Group For the Psychology of Mathematics Education, Jan 6, 2003

We present classroom research 1 on a variant of the guess-my-rule game, in which nineyear old stu... more We present classroom research 1 on a variant of the guess-my-rule game, in which nineyear old students make up linear functions and challenge classmates to determine their secret rule. We focus on issues students and their teacher confronted in inferring underlying rules and in deciding whether the conjectured rule matched the rule of the creators. We relate the findings to the tension between semantically and syntactically driven algebraic reasoning.

Hands on, 1999

Abstract: Video and electronic media have the potential to bridge the gap between classroom resea... more Abstract: Video and electronic media have the potential to bridge the gap between classroom research and practice by providing rich and detailed data for grounded discussions about teaching and learning. Describes attempts to use digital video ...

This study analyzes the emergence and travel of ideas about fractions on the number line in three... more This study analyzes the emergence and travel of ideas about fractions on the number line in three upper elementary school mathematics classrooms. The findings indicate that students' public displays of ideas shifted during the course of the lesson, classrooms varied in their treatment of the number line, and shared discourse within classrooms was rooted in different understandings.

Teaching Children Mathematics, May 1, 2008

... By Darrell Earnest and Aadina A. Balti Incorporating algebra into the elementary grades has b... more ... By Darrell Earnest and Aadina A. Balti Incorporating algebra into the elementary grades has become a focus for teachers, principals, and administrators around the country. ... How many people will there be? Ashley, do you have a guess? Ashley: Twenty-two. ...

Teaching Children Mathematics, 2013

ABSTRACT Students had been learning about integers and fractions on the number line. For a lesson... more ABSTRACT Students had been learning about integers and fractions on the number line. For a lesson on mixed numbers, they solved an assessment problem at the beginning of the lesson. After the lesson, the authors interviewed two students individually and asked each girl to solve the same problem again.

Teaching Children Mathematics, 2008

Abstract: Incorporating algebra into the elementary grades has become a focus for teachers, princ... more Abstract: Incorporating algebra into the elementary grades has become a focus for teachers, principals, and administrators across the country. The Dinner Tables problem described in this article is a lesson commonly used in elementary grades for its algebraic potential. ...

… of the 27th International Conference for …, 2003

We present classroom research on a variant of the guess-my-rule game, in which nine-yearl-old stu... more We present classroom research on a variant of the guess-my-rule game, in which nine-yearl-old students make up linear functions and challenge classmates to determine their secret rule. We focus on issues students and their teacher confronted in inferring ...

Cognition and Instruction, 2010

This report provides evidence of the influence of a tutorial “communication game” on fifth grader... more This report provides evidence of the influence of a tutorial “communication game” on fifth graders’ generative understanding of the integer number line. Students matched for classroom and pretest score were randomly assigned to a tutorial (n = 19) and control group (n = 19). The tutorial group students played a 13-problem game in which student and tutor each were required to mark the same position on a number line but could not see one another's activities. To resolve discrepant solutions, tutor and student constructed agreements about number line principles and conventions to guide subsequent placements. Pre-/posttest contrasts showed that (a) tutorial students gained more than controls and (b) agreement use predicted gain. Analyses of micro-constructions during play revealed properties of student learning trajectories.

Powerful methods for analyzing the travel of ideas are essential for understanding the process of... more Powerful methods for analyzing the travel of ideas are essential for understanding the process of learning classroom communities. In this chapter, we argue that a genetic perspective provides a useful methodological frame. We describe specific empirical techniques for the study of the travel of ideas, and illustrate our approach with findings from recent investigations of lessons on integers and fractions for fifth grade.

Increasing numbers of mathematics educators, policy makers, and researchers believe that algebra ... more Increasing numbers of mathematics educators, policy makers, and researchers believe that algebra should become part of the elementary education curriculum. Such endorsements require careful research. This paper presents the general results of a longitudinal ...

We look at the emergence of 9-year old students' concept of additive difference. The concept enta... more We look at the emergence of 9-year old students' concept of additive difference. The concept entails a tension between process and object. But even more strikingly, reifying the concept requires that children adopt analogies across diverse representational contexts. We will look at examples of students' reasoning about children's heights in contexts associated with number lines, counting, line segment diagrams, and arithmeticalgebraic notation. The examples show that subtraction comprises a small yet essential part of the concept of difference. We consider implications for research and curriculum development in early algebra and early arithmetic education.