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…

The rapid growth of the offer of available educational resources raises the issue of their appropriation by teachers. Although the term appropriation is widely used in mathematics education research, there is no clear conceptualization allowing researchers to understand the processes involved. In this paper, we attempt to fill this gap by…

The author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing…

This article is written to share teaching ideas about using commonly available computer applications--a spreadsheet, "The Geometer's Sketchpad", and "Wolfram Alpha"--to explore three classic and historically significant problems from the probability theory. These ideas stem from the authors' work with prospective economists,…

Previous studies in both typically and atypically developing children have shown that approximate number system (ANS) abilities predict formal mathematical knowledge later on in life. The current study investigated whether playing specially designed training games that targets the ANS system using nonsymbolic stimuli only would improve preschool…

Background: Rational numbers are of critical importance both in mathematics and in other fields of science. However, they form a stumbling block for learners. One widely known source of the difficulty learners have with rational numbers is the natural number bias, that is the tendency to (inappropriately) apply natural number properties in…

This investigation examined the thinking of 128 pre-service teachers about the magnitude of large numbers and the relationships between large numbers. These pre-service teachers responded to a written task asking them to place one billion on a number line that included zero and one trillion and to provide an explanation for their placement. One…

Proportional reasoning is important to the field of mathematics education because it lies at the crossroads of additive reasoning in the elementary school and multiplicative reasoning needed for more advanced mathematics. This research reports on the representations used by pre-service teachers (PSTs) as they responded to tasks involving…

Many students' knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's integrated magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process…

Children in developing countries often lack sufficient support for early learning skills prior to beginning school. This research evaluates an educational media intervention using an animated cartoon program, "Akili and Me." The program was originally created in Tanzania to teach early learning skills. This program was adapted in content…

Quantity recognition in whole number representations is a fundamental skill children need to acquire in their mathematical development. Despite the observed correlation to mathematics achievement, however, the ability to recognize quantities in structured whole number representations has not been studied extensively. In this article, we…

Since the introduction of the Common Core State Standards for Mathematics (CCSSM) in 2010, stakeholders in adopting states have engaged in a variety of activities to understand CCSSM standards and transition from previous state standards. These efforts include research, professional development, assessment and modification of curriculum resources,…

Despite an emphasis on manipulative algebraic techniques in secondary school algebra, many tertiary mathematics students have mastered these skills without conceptual understanding. A significant number of students with high tertiary entrance ranks enrolled in first semester university mathematics were found to have misconceptions relating to…

Research has shown that integer comparison is quick and efficient. This efficiency may be a function of the structure of the integer comparison system. The present study tests whether integers are compared with an unlimited capacity system or a limited capacity system. We tested these models using a visual search task with time delimitation. The…

This paper seeks to describe the importance of using the context of a candy shop and how focusing on discourse can deepen place value understanding in the base ten number system. Using the language of pieces (ones), rolls (tens), and boxes (hundreds) helps situate place value in a familiar context for K-2 students. Best practice in mathematics…