This study explores the effects of counting objects and reciting numbers in preschool on 1st-grade math performance. Data on 3,125 low-income preschoolers' (4-to 5-year-olds) counting abilities (orally reciting numerals in chronological order and counting blocks) were collected during a fall session (between September 15 and December 15) and were…

The 43rd meeting of Canadian Mathematics Education Study Group (CMESG) was held at St. Francis Xavier University in Antigonish, Nova Scotia (May 31-June 4, 2019). This meeting marked only the third time CMESG/GCEDM (Groupe Canadien d'Étude en Didactique des Mathématiques) had been held in Nova Scotia (1996, 2003), and the first time it had been…

One original, and continuing, source of interest in large numbers is observation of the natural world, such as trying to count the stars on a clear night or contemplation of the number of grains of sand on the seashore. Indeed, a search of the internet quickly reveals many discussions of the relative numbers of stars and grains of sand. Big…

Unlike old perceptions of algebra as a subject that needs to be taught in the upper grade levels of schooling, much of the recent research reports that young students are capable of reasoning algebraically. It is important to note that the recommendation to include algebraic experiences in the early grades is not made simply to introduce typical…

The aim of this paper is to investigate the role that auxiliary means (manipulatives such as cubes and representations such as number line) play for kindergartners in working out mathematical tasks. Our assumption was that manipulatives such as cubes would be used by kindergartners easily and successfully whereas the number line would be used by…

Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use…

Knowing number facts up to 10 become crucial if we want students to solve addition and subtraction problems using more abbreviated strategies. Otherwise, students will keep counting one-by-one until they get an answer. One of important number facts is number pairs that make ten because it is an important "benchmark" that students will…

Although the psychophysics of infants' nonsymbolic number representations have been well studied, less is known about other characteristics of the approximate number system (ANS) in young children. Here three experiments explored the extent to which the ANS yields abstract representations by testing infants' ability to transfer approximate number…

It is important to avoid ambiguity with numbers because unfortunate choices of numbers can inadvertently make it possible for students to form misconceptions or make it difficult for teachers to tell if students obtained the right answer for the right reason. Therefore, it is important to make sure when introducing basic summary statistics that…

The systematic use of alternative normalization constants for 3j symbols can lead to a more natural expression of quantities, such as vector products and spherical tensor operators. The redefined coupling constants directly equate tensor products to the inner and outer products without any additional square roots. The approach is extended to…

This article deals with a short history of mathematics and mathematical scientists during the ancient and medieval periods. Included are some major developments of the ancient, Indian, Arabic, Egyptian, Greek and medieval mathematics and their significant impact on the Renaissance mathematics. Special attention is given to many results, theorems,…

Previous research shows a correlation between individual differences in people's school math abilities and the accuracy with which they rapidly and nonverbally approximate how many items are in a scene. This finding is surprising because the Approximate Number System (ANS) underlying numerical estimation is shared with infants and with non-human…

Many students experience great difficulty understanding the meaning of fractions. For many students who have spent their early mathematics lessons focusing on counting (whole) numbers, recognising that there are many numbers between those whole numbers called fractional numbers, is quite revolutionary. The foundation of understanding fractions is…

The goal of the presented experiments was to investigate the dynamic interplay of task shielding and its relaxation during task switching. Task shielding refers to the finding that single task sets in terms of 2-choice categorization rules help shielding against distraction from irrelevant stimulus attributes. During task switching, this shielding…

We studied the cognitive abilities of a 13-year-old deaf child, deprived of most linguistic input from late infancy, in a battery of tests designed to reveal the nature of numerical and geometrical abilities in the absence of a full linguistic system. Tests revealed widespread proficiency in basic symbolic and non-symbolic numerical computations…