The purpose of this study was to identify and describe students' use of number sense as they solved story problem tasks. Three 8- and 9-year-old students participated in clinical interviews. Through a process of holistic and qualitative coding, researchers used the number sense view as a theoretical framework for exploring how students' number…

Research findings have established that students often struggle with mathematical symbols including common misconceptions for literal symbolic representations of variables but provide little evidence of when or how these misconceptions arise. This article reports findings from a study of grade 4-6 students' conception(s) for various…

The main goal of this paper is to show how Vasily Davydov's powerful ideas about the nature of mathematical thinking and learning can transform the teaching and learning of additive word problem solving. The name Vasily Davydov is well known in the field of mathematics education in Russia. However, the transformative value of Davydov's theoretical…

As a key concept in early mathematics curriculum, number sense is crucial for children's learning of other mathematics concepts. An earlier curriculum with a strong focus on number sense development presumably helps children perform better in mathematics later on. Chinese students outperformed their United States (U.S.) peers on number sense at…

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…

The aim of this paper is to investigate the ways in which the number line can function in solving mathematical tasks by first graders (6 year olds). The main research question was whether the number line functioned as an auxiliary means or as an obstacle for these students. Through analysis of the 32 students' answers it appears that the number…

This paper reports selected findings from a study of number sense proficiency of students aged 13 to 16 years in a state in Malaysia. A total of 1756 students, from thirteen schools in a state in Malaysia participated in this study. A majority (74.9%) of these students obtained an A grade for their respective year-end school examinations. The…

The main aim of this paper is to report on an investigation into primary pre-service and inservice teachers' content knowledge of decimals. The participants were asked to complete four decimal tasks including the ordering of decimals, operating with decimals and converting a fraction to a decimal. The results from both sets of participants are…

Math Teachers' Circles have been spreading since their emergence in 2006. These professional development programs, aimed primarily at middle-level mathematics teachers (grades 5-9), focus on developing teachers' mathematical problem solving skills, in line with the Common Core State Standards-Standards of Mathematical Practice. Yet, to date,…

Researchers (Ball, 2003; Ma, 1999; Schulman, 1986) have long investigated how a teacher's subject matter and pedagogical content knowledge impact on students' learning of mathematics. In an attempt to account for the relationship between teacher knowledge and student learning, this study examined four Romanian first grade teachers' knowledge about…