Students enrolled in post-secondary developmental mathematics courses hold mathematical misunderstandings that begin before their college careers. Specifically, these students struggle with conceptual understanding of fractions, ratios, and proportions. The Common Core State Standards in Mathematics outline standards for K-12 mathematics…

The purpose of this study is to explore preservice teachers' (PTs') ability to implement multiple strategies using standard algorithms and alternative strategies and to investigate their conceptual knowledge of decimal operations. There were 37 PTs who participated in this study, all of whom attended a mathematics course in the K-8 Teacher…

Time is an essential construct for understanding our everyday lives and the wider world; however, it is commonly seen as a difficult topic by teachers and children throughout primary school. There is limited research into children's learning about time, and in particular, concerning young children's understandings of clocks. This study examines…

This study investigates early-years prospective teachers' definitions, examples, and non-examples of cylinder and prism. The data were collected from 72 early-years prospective teachers via written tasks and classroom discussions. In written tasks, they were requested to define and then to give different examples and non-examples of cylinder and…

The purpose of this study was to explore the variations in students' achievement on computational fluency assessments and variations in strategies for solving computation problems. Computational fluency was defined as a student's ability to compute flexibly, accurately, efficiently, and appropriately. Seven- and eight-year-old students completed…

The study investigates the mathematical and the pedagogical content knowledge among in-service and pre-service first- and second-grade mathematics teachers. The sample of 300 subjects consisted of 150 first- and second-grade in-service teachers and 150 pre-service teachers studying in a college of education, 75 of whom were first-year students and…

In this paper, we present a design experiment in a "Teaching Mathematics" course for prospective elementary teachers where we sought to develop a "measurement approach" to fractions. We focus on the conceptualization of the mathematical content of the approach. We attribute our progress in the conceptualization to our efforts…

The issue of this article is to identify and discuss what conditions may be necessary to build into tasks to make it likely for students to be involved in an algebraic Learning Activity inspired by Davydov. Data from a pilot study was used in which a group of students (N = 28) in grade 1 (7-year-olds) were invited to participate in discussions and…

Kindergarten children's (5-6 years old) ability to communicate geometric shapes, to their classmates, in different modes--verbally, gesturally, schematically--through a game, was investigated. The game motivated the children to describe the shapes in the different modes, by emerging children's thinking process, communication capacity as well as…

This review examines reasons for Malaysian pupils' underperformance in solving mathematics problems that demand numerical estimation and mental computation. Their underdeveloped number sense appears to be the major reason. According to the Ministry of Education, the national mathematics curriculum is unlikely to account for this underachievement.…

We analyze the results of a study conducted for the purpose of assessing the viability of an alternative starting point for teaching fractions. The alternative is based on Freudenthal's insights about fraction as comparison. It involves portraying the entities that unit fractions quantify as always being apart from the reference unit, instead of…

Our research programme, a part of which is presented in this paper, looked at four year old children's ability to use manipulatives in the construction of cube models. We looked at how pre-school children managed the creation of cube nets as a mathematical problem and whether graphical representations of solutions could become a useful tool in a…

Turkish primary mathematics curriculum emphasizes the role of problem solving for teaching mathematics and pays particular attention to problem solving strategies. Patterns as a subject and the use of patterns as a non-routine problem solving strategy are also emphasized in the curriculum. The primary purpose of this study was to determine how…

The purpose of this study was to deconstruct the relationship between visual static models and students' written solutions to fraction problems using a large sample of students' solutions. Participants in the study included 162 third-grade and 209 fourth-grade students from 17 different classrooms. Students' written responses to open-ended tasks…

Chinese pre-school children perform well in learning mathematics compared with English-speaking children. This study investigates the scenes behind Chinese preschool children's mathematics performance using teacher questionnaires and interviews. Results indicated that the Chinese number system appeared to afford advantages to Chinese children in…