Teachers in early childhood and elementary classrooms (grades K-5) have been using ten-frames as an instructional tool to support students' mathematics skill development for many years. Use of the similar five-frame has been limited, however, despite its apparent potential as an instructional scaffold in the early elementary grades. Due to scant…

Behavioral indices (e.g., infant looking) are predominantly used in studies of infant cognition, but psychophysiological measures have been increasingly integrated into common infant paradigms. The current study reports a result in which behavioral measures and physiological measures were both incorporated in a task designed to study infant number…

In the present work, we conducted a series of experiments to explore the processing stages required to name numerals presented in different notations. To this end, we used the semantic blocking paradigm previously used in psycholinguist studies. We found a facilitative effect of the semantic blocked context relative to the mixed context for Arabic…

Mapping of number onto space is fundamental to mathematics and measurement. Previous research suggests that while typical adults with mathematical schooling map numbers veridically onto a linear scale, pre-school children and adults without formal mathematics training, as well as individuals with dyscalculia, show strong compressive,…

The use of computer algebra systems such as Maple and Mathematica is becoming increasingly important and widespread in mathematics learning, teaching and research. In this article, we present computerized proof techniques of Gosper, Wilf-Zeilberger and Zeilberger that can be used for enhancing the teaching and learning of topics in discrete…

One crucial issue in mathematics development is how children come to spontaneously apply arithmetical principles (e.g. commutativity). According to expertise research, well-integrated conceptual and procedural knowledge is required. Here, we report a method composed of two independent tasks that assessed in an unobtrusive manner the spontaneous…

While some students are enjoying days at the park or at the beach, forty middle school students are in a classroom solving challenging mathematics problems. The second Math Camp for middle school students was offered in 2013 at a western university for students from local school districts. For three days, these students met from 10 a.m. to 3 p.m.…

Encouraging students to reason with quantitative relationships can help them develop, understand, and explore mathematical models of real-world phenomena. Through two examples--modeling the motion of a speeding car and the growth of a Jactus plant--this article describes how teachers can use six practical tips to help students develop quantitative…

Task-cuing experiments are usually intended to explore control of task set. But when small stimulus sets are used, they plausibly afford learning of the response associated with a combination of cue and stimulus, without reference to tasks. In 3 experiments we presented the typical trials of a task-cuing experiment: a cue (colored shape) followed,…

In order to help children gain a more robust understanding of place value, teachers must understand the connections and relationships among the related concepts as well as possess knowledge of how children learn early number concepts. Unfortunately, teachers' familiarity with the base-ten number system and/or lack of an understanding of…

The study assessed the relations among acuity of the inherent approximate number system (ANS), performance on measures of symbolic quantitative knowledge, and mathematics achievement for a sample of 138 (64 boys) preschoolers. The Weber fraction (a measure of ANS acuity) and associated task accuracy were significantly correlated with mathematics…

Logarithms continue to play an important role in mathematics (most significantly in calculus), science, and engineering. It is therefore important for students to understand logarithms as real numbers as well as the characteristics of logarithmic functions. Exploration of challenges in understanding logarithms as real numbers and logarithmic…

Annual National Assessment (ANA) performance in Mathematics across the primary grades in South Africa indicates a decrease in mean performance across Grades 1-6. In this paper, we explore the apparently high performance in Grade 1 through a comparative investigation of learner responses on two assessments: the Grade 1 ANA taken in February 2011 by…

There have been a number of behavioral and neural studies on the processing of syntactic gender and number agreement information, marked by different morpho-syntactic features during sentence comprehension. By using the event-related potential (ERP) technique, the present study investigated whether the processing of semantic gender information and…

Typologists have long observed that there are certain distributional patterns that are not evenly distributed among the world's languages. This discussion note revisits a recent experimental investigation of one such intriguing case, so-called "universal 18", by Culbertson, Smolensky, and Legendre (2012). The authors find that adult learners are…