Darrell Earnest

Darrell Earnest
University of Massachusetts Amherst | UMass Amherst · Department of Teacher Education and Curriculum Studies

Ph.D.

About

27
Publications
17,734
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771
Citations

Publications

Publications (27)
Article
This article investigates the interplay of time words with how children position hands on an analog clock. Using a mathematics discourse framework (Sfard, 2008), we analyzed how students interpreted precise (e.g., 2:30) and relative (e.g., half past 11) times, finding that particular words are dynamically interwoven with activity. Interviews with s...
Article
Around the globe, young students are expected to learn about time, yet how is it that they themselves make sense of this topic? From a sociocultural perspective, sense-making about time emerges in relation to properties of available tools and representations, such as analog clocks or digital notation. Such interactions with the symbols and structur...
Chapter
Curriculum is a key resource that the vast majority of teachers utilize, yet authentic connections to children’s everyday experiences are not necessarily straightforward with curriculum materials. Because curriculum materials have a direct influence on teachers’ instruction, we must prepare teachers to analyze curriculum in ways that enable integra...
Article
A common context for instruction in early algebra involves time, an invisible and intangible quantity commonly represented as intervals of length. This paper presents a case study of syntactically guided reasoning with the structure of an analogue clock involving a second-grade student. As her descriptions shifted from clock-reading procedures to a...
Article
Full-text available
Curriculum materials are integral to the mathematics classroom, yet little is known about how teachers read curriculum in order to envision enactment. Through an assignment involving an approximation of actual teaching practice, we investigated prospective teachers’ documentational genesis (Pepin et al. in ZDM 45:929–943, 2013) from curriculum mate...
Article
Translating a mathematics lesson from curriculum materials into instruction is not straightforward, and launching, or beginning, a lesson such that students will become productively engaged in the target mathematics is nontrivial. The purpose of the study was to investigate preservice teachers’ curricular noticing as they draw upon curriculum mater...
Article
Building on the work of Professional Noticing of Children's Mathematical Thinking, we introduce the Curricular Noticing Framework to describe how teachers recognize opportunities within curriculum materials, understand their affordances and limita-tions, and use strategies to act on them. This framework builds on Remillard's (2005) notion of partic...
Article
Full-text available
Elementary students have difficulty with the topic of time. The present study investigated students’ actions to position hour and minute hands on an analog clock to indicate particular times of the day. Using one-on-one interviews with students in Grades 2 and 4 (n = 48), we analyzed whether students were more accurate for one hand indicator (hour...
Article
Share news about happenings in the field of elementary school mathematics education, views on matters pertaining to teaching and learning mathematics in the early childhood or elementary school years, and reactions to previously published opinion pieces or articles. Find detailed department submission guidelines at http://www.nctm.org/WriteForTCM.
Article
Fourth graders engage in mathematical reasoning and problem solving that leads to insights about the relationship between hour and minute units.
Chapter
This chapter presents a new theoretical construct, curricular noticing, used to understand how teachers interact with curriculum materials, and shares findings from four coordinated research studies. Curricular noticing draws from work on professional noticing of children’s mathematical thinking and is defined as how teachers make sense of the comp...
Article
This article reports on elementary students' understanding of time in the context of common classroom manipulatives and notational systems. Students in Grades 2 (n = 72) and 4 (n = 72) participated in problem-solving interviews involving different clocks. Quantitative results revealed that students' performances were significantly different as a fu...
Conference Paper
Full-text available
This paper explores the construct of curricular noticing, defined as the act of teachers making sense of the complexity of content and pedagogical opportunities in written or digital curricular materials (Dietiker, Amador, Earnest, Males, & Stohlmann, 2014), and reports the results of four exploratory studies aimed to examine the Curricular Noticin...
Article
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),...
Chapter
Full-text available
There is no longer any question about whether elementary school children can or should be engaged in algebraic reasoning—they can be and they should be. Research has provided compelling evidence that a functions approach to elementary algebra, in which instruc-tion builds on young children's understanding of arithmetic through functions, supports a...
Article
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.
Article
Full-text available
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...
Conference Paper
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 mathematical terminology provided a context for discussing graphs of linear functions, wherea...
Article
Full-text available
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. Instructional strategies for supporting algebra instruction use an example from a third-g...
Article
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Algebra instruction has traditionally been postponed until adolescence because of historical reasons (algebra emerged relatively recently), assumptions about psychological development ("developmental constraints" and "developmental readiness"), and data documenting the difficulties that adolescents have with algebra. Here we provide evidence that y...
Article
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We present classroom research on a variant of the guess-my-rule game, in which nine-year-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....
Article
Full-text available
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 context...
Article
Full-text available
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 classroom investigation of children's thinking and representations over two and a half years...

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