Specific acts of problem solving with rates and ratios were interpreted using a journey metaphor derived from Skemp's (1979) construct of director systems. To successfully undertake a problem solving journey a learner must recognise their starting place (present state), have a sense of destination (goal state), and co-ordinate sub-routes along the…

The present study explores reasoning and argumentation in Greek mathematics and physics texts in specific topics related to the notion of periodicity. In our study, argumentation is taken as the sequence of the modes of reasoning (MsoR) that an author develops in a text when organizing and presenting new knowledge. Inductive content analysis was…

Getting students adopt the habits of mind specific to many disciplines can be seen as an anchor that will support them to solve the problems in their daily lives. Starting from this premise, a new subject, featuring the habits of mind and how to use and improve them in educational environments seems to worth thinking on. This article describes an…

Over the past few decades, there has been extensive debate as to whether humans represent number abstractly and, if so, whether perceptual features of a set such as cumulative surface area or contour length are extracted more readily than number from the external world. Here we show that 7-month-old infants are sensitive to smaller ratio changes…

Gestures such as finger counting, pointing, and touching have been found to facilitate mathematical development in preschool and school-aged children. However, little is known about the types of mathematically related gestures used by parent-toddler dyads to facilitate early mathematics learning during the first 3 years of life. A total of 24…

This article reports the results of a study that investigated pre-service mathematics teachers' modelling processes in terms of representational fluency in a modelling activity related to a cassette player. A qualitative approach was used in the data collection process. Students' individual and group written responses to the mathematical modelling…

Technology is now being utilized in schools in an effort to address the lack of engagement most students have experienced in mathematics when learning foundational skills at the elementary school level. While there are a number of studies that have described teacher perceptions of engagement through the use of technology during the school day,…

This research analyzed how fractions are taught in the fourth grade of elementary school in Flanders. Analysis centered on the presence of five features of instruction recommended by research on teaching and learning fractions (i.e., multiple solution pathways, linking representations, estimation and justification of the solution, collaboration,…

Educators, researchers, and policy makers increasingly recognize that participation in classroom mathematics discussions, especially engaging with others' ideas, can promote students' mathematics understanding. How teachers can promote students' high-level engagement with others' ideas, and the challenges teachers face when trying to do so, have…

This study examined how evidence of students' mathematical understanding was influenced by elementary schoolteachers' enactment of instructional practices emphasized during a mathematics professional development program. Videos and field notes were collected during lessons for two teachers from the program and two matched comparison teachers.…

In a recent study, Gevers and colleagues (2010, "Journal of Experimental Psychology: General," Vol. 139, pp. 180-190) showed that the SNARC (spatial numerical association of response codes) effect in adults results not only from spatial coding of magnitude (e.g., mental number line hypothesis) but also from verbal coding. Because children are…

School leaders are seeking ways to improve teacher quality as expectations on high-stakes test scores increase. An elementary school has had difficulty meeting state standards in mathematics and has struggled to show that students have learned the content. Researchers have found that the beliefs and experiences of educators influence classroom…

Literacy has been studied extensively in the context of children's play, but few studies exist of numeracy development through play. The purpose of this study was to investigate the frequency and type of numeracy exchanges that occurred spontaneously during parent-child play. Twenty-six 4-year-olds and their mothers played with a variety of toys,…