Experts think in patterns and structures using the specific "language" of their domains. For mathematicians, these patterns and structures are represented by numbers, symbols and their relationships (Stokes, 2014a). To determine whether elementary students in the United States could learn to think in mathematical patterns to solve…

This research reports on a class of grade one students engaging with number concepts using the iPad application TouchCounts. It is theorized that students develop understandings of number based on a materially engagement with both social and material resources. Rhythm is the fundamental unit of analysis used to attend to student engagement with…

Being able to find the correct answer to a math problem does not always indicate solid mathematics mastery. A student who knows how to apply the basic algorithms can correctly solve problems without understanding the relationships between numbers or why the algorithms work. The Common Core standards require that students actually understand…

Learning of the mathematical number line has been hypothesized to be dependent on an inherent sense of approximate quantity. Children's number line placements are predicted to conform to the underlying properties of this system; specifically, placements are exaggerated for small numerals and compressed for larger ones. Alternative hypotheses…

In this paper we report on five Grade 6 students' responses to a proportional reasoning task. We conducted pair interviews within a longitudinal study focused on extending a hypothetical learning trajectory for length measurement. Results suggest that there exists a link between children's level of conceptual and procedural knowledge for length…

In this article Jessica Hunt explores the use of clinical interviews to gain a deep understanding of students' knowledge. Examples of clinical interviews are provided and advice for planning, giving and interpreting the results of interviews is also included.

Children's estimation skills on a bounded and unbounded number line task were assessed in the light of their familiarity with numbers. Kindergartners, first graders, and second graders (N = 120) estimated the position of numbers on a 1--100 number line, marked with either two reference points (i.e., 1 and 10: unbounded condition) or three…

Recent research has found that linguistic cues may affect children's number word acquisition. Two studies were undertaken to evaluate the use of singular/plural markings and small number words in Chinese and English and its effect on children's number concepts. The first study utilized the CHILDES data and investigated how singular/plural markings…

Sentences containing plural numerical expressions (e.g., "two boys") can give rise to two interpretations (collective and distributive), arising from the fact that their representation admits of a part-whole structure. We present the results of a series of experiments designed to explore children's understanding of this distinction…

As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.

This seven-year longitudinal study examined how children's spontaneous focusing on numerosity (SFON), subitizing based enumeration, and counting skills assessed at five or six years predict their school mathematics achievement at 12 years. The participants were 36 Finnish children without diagnosed neurological disorders. The results, based on…

When to introduce negative integers to children is an important issue in school mathematics; delaying their introduction can lead to lasting misconceptions such as one cannot subtract a larger whole number from a smaller. Yet understanding negatives involves a complex extension of whole-number knowledge. It is not known whether this extension is…

Research indicates that parental involvement in children's education is positively related to academic achievement in mathematics; however, there are few studies on the role of parental involvement in the context of developing countries. The purpose of this paper is to document the iterative development using design-based research (DBR) of a…

This article describes a study that investigates preschool teachers' knowledge of their young students' number conceptions and the teachers' related self-efficacy beliefs. It also presents and illustrates elements of a professional development program designed explicitly to promote this knowledge among preschool teachers. Results…

It is incredibly important for students who are at-risk for mathematics failure or who have a disability which hinders mathematical performance to improve in their mathematical achievement. One way to improve mathematical achievement is through building fluency in mathematics. Fluency in mathematics is the ability to solve problems automatically…