The purpose of this study was to examine the ways advanced mathematics students define "number" and the degree to which their definitions extend to different number domains. Of particular interest for this study are learners' fundamental conceptions of number and the implications for learners' interpretations of complex numbers (a + bi).…

Research on mathematical equivalence, and to some extent, on number structure in early grade mathematics, has shown that most students at primary and secondary levels understand these concepts instrumentally rather than relationally. The study reported in this paper uses a design research approach to explore both mathematical equivalence and…

The present study aimed to examine the opinions of in-and preservice middle school mathematics teachers about teaching four operations with integers through "number line" and/or "counters". Participants were 42 middle school mathematics teachers and 51 pre-service mathematics teachers. The data were collected through open-ended…

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students' understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real…

Research Findings: The aim of this study was to investigate U.S. preschool teachers' math teaching knowledge in a specific content domain: counting and numbers. One hundred in-service and pre-service teachers participated in the study; they completed a questionnaire that is composed of learning scenarios and scenario-based math teaching questions.…

The literature has shown that preservice elementary school teachers (PSTs) struggle to adequately attend to a number's multiplicative structure to determine divisibility. This study describes an intervention aimed at strengthening preservice and in-service teachers' procedural knowledge with respect to using a number's prime factorization to…

Rational number understanding is a critical building block for success in more advanced mathematics; however, how rational number magnitudes are conceptualized is not fully understood. In the current study, we used a dual-task working memory (WM) interference paradigm to investigate the dominant type of strategy (i.e., requiring verbal WM…

Adult proficiency in numeracy in the United States lags that of other developed nations, and the nonselective institutions that dominate the higher education sector struggle to address the learning needs of the sizeable proportion of students who enroll in their institutions and are deemed academically underprepared in mathematics. Research on…

This article examines prospective elementary teachers' conceptions of unitizing with whole numbers and fraction concepts and operations throughout a semester-long mathematics content course. Student work samples and classroom conversations are used to illustrate the types of unitizing understandings that prospective teachers bring to teacher…