This paper reports on an experiment involving 108 sixth-grade French students in which the history of Chinese numeration was used in mathematics education. The aim of this study is to evaluate the relevance of using ancient number systems in mathematics education, which is common in French textbooks. In the experiment a pre-test with usual…

In this paper, dialogue among a group of adult women with basic adult education is examined. Women read books of mathematics in the context of a "dialogic mathematics gathering" (DMG). There is limited evidence in research on how adults develop their 'numerical understanding'. The objective of this study is to analyze how adults engage…

Magnitude understanding is critical for students to develop a deep understanding of fractions and more advanced mathematics curriculum. The research reports in this special issue underscore magnitude understanding for fractions and emphasize number lines as both an assessment and an instructional tool. In this commentary, we discuss how number…

The study was undertaken to establish the relationship between the roots of the perfect numbers and the "n" consecutive odd numbers. Odd numbers were arranged in such a way that their sums were either equal to the perfect square number or equal to a cube. The findings on the patterns and relationships of the numbers showed that there was…

Community college developmental math students (N = 657) from three math levels were asked to place five whole numbers on a line that had only endpoints 0 and 20 marked. How the students placed the numbers revealed the same three stages of behavior that Steffe and Cobb (1988) documented in determining young children's number sense. 23% of the…

Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times…

Proportional reasoning is important to students' future success in mathematics and science endeavors. More specifically, students' fluent and flexible use of scalar and functional relationships to solve problems is critical to their ability to reason proportionally. The purpose of this study is to investigate the influence of systematically…

Earlier institution-sponsored research revealed that about 20% of students in community college basic math and pre-algebra programs lacked a sense of part-whole relationships with whole numbers. Using the same tool with a group of 86 workforce students, about 75% placed five whole numbers on an empty number line in a way that indicated lack of…

The paper presents and analyses a sequence of events that preceded an insight solution to a challenging problem in the context of numerical sequences. A three­week long solution process by a pair of ninth­-grade students is analysed by means of the theory of shifts of attention. The goal for this article is to reveal the potential of this theory…

A web-based two-tier test (WTTT-NS) which combined the advantages of traditional written tests and interviews in assessing number sense was developed and applied to assess students' answers and reasons for the questions. In addition, students' major misconceptions can be detected. A total of 1,248 sixth graders in Taiwan were selected to…

Two-Way Immersion (TWI) programs have demonstrated positive outcomes in students' academic achievement in English, yet less is known about content teaching and learning in the non-English language in these programs. This study uses math instruction as a lens to identify pedagogical strategies and challenges in the teaching of math in Korean to…

In this paper, the use of guided hyperlearning, unguided hyperlearning, and conventional learning methods in mathematics are compared. The design of the research involved a quasi-experiment with a modified single-factor multiple treatment design comparing the three learning methods, guided hyperlearning, unguided hyperlearning, and conventional…

In two experiments, participants judged the average numerosity between two sequentially presented dot patterns to perform an approximate arithmetic task. In Experiment 1, the response was given on a 0-20 numerical scale (categorical scaling), and in Experiment 2, the response was given by the production of a dot pattern of the desired numerosity…

This study explores, from both constructivist and cognitive perspectives, teacher guidance in student-centered classrooms when addressing a common learning difficulty with equivalent fractions--lines or pieces--based on number line models. Findings from three contrasting cases reveal differences in teachers' facilitating and direct guidance…

In this article, I present research on some traditional numeracy practices of the Gusilay people group in Senegal and make recommendations for developing a numeracy programme for women. Based on a strong foundation of traditional knowledge and practices, the programme will aim to meet felt needs of women who are faced with new numeracy related…