This Brief Report presents an example of assessment validation using an argument-based approach. The instrument we developed is a Brief Assessment of Students' Mature Number Sense, which measures a central goal in mathematics education. We chose to develop this assessment to provide an efficient way to measure the effect of instructional practices…

Students' ability to operate with increasingly more complex units has been shown to be a key factor in their conceptual development. These abilities have been characterized as "stages of units coordination." This article focuses on the domain of composing and decomposing composite units. Using data from a teaching experiment with a…

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…

The efficacy of a research-based number-sense intervention for low-achieving kindergartners was examined. Children (N = 126) were randomly assigned to 1 of 3 conditions: a number-sense intervention followed by a number-fact practice session, an identical number-sense intervention followed by a number-list practice session, or a business-as-usual…

This study evaluated the effects of a mathematics software program, the Building Blocks software suite, on young children's mathematics performance. Participants included 247 Kindergartners from 37 classrooms in 9 schools located in low-income communities. Children within classrooms were randomly assigned to receive 21 weeks of computer-assisted…

The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…

The goal of this study is to uncover the successes and challenges that preservice teachers are likely to experience as they unpack lesson-level mathematical learning goals (i.e., identify the subconcepts and subskills that feed into target learning goals). Unpacking learning goals is a form of specialized mathematical knowledge for teaching, an…

The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it is a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use…

Stimulus conditions were found to interact with conservation level and relation type. (MM)

A 30-minute lesson on exponents was taught to 249 fourth graders assigned randomly to groups of 1, 2, 5, or 23. Students in the smaller groups had better attainment of ten objectives than did those in the group of 23. Individual instruction was better than instruction in groups of five. (MS)

The ability of 135 first, second, and third grade classes to solve open sentences involving sums between 10 and 18 was investigated. Performance appeared to be related to grade level, operation, the position of the placeholder, and the existence of a solution within the set of whole numbers. (Author/DT)

Reported is a study of the interaction between figural and semantic abilities (as defined in Guilford's Structure of the Intellect") and success in a programmed unit in modular arithmetic. The subjects were prospective elementary teachers. Significant interactions were found between both figural and semantic factors and methods of instruction.…

Reported is a study which compared two instructional methods involving discovery learning and a verbal didactic instructional method. The verbal didactic method was significantly better for immediate learning; the verbal didactic method and a guided discovery method were better for retention. No differences were noted regarding transfer. (CT)

Investigated was the feasibility of inducing number conservation through training kindergarten children on reversibility tasks not related to the criterion measure. (JG)

Grade four students who studied 3, 5, 10 or 12 value systems of numeration were compared with similar students who studied only a decimal system. A test was designed to measure understanding of the decimal system, processing decimal numerals, and place-value systems in general. Data analysis using multivariate analysis of covariance is presented.…