Young learners' language aptitude is understudied due to a lack of tests covering this period of life. Young learners, in contrast with adults, are still acquiring their L1. Consequently, a language-dependent aptitude test should be carefully designed for it to be valid. An additional challenge is found when the young learners who are to take the…

At the start of every school year, teachers typically wonder what their new students know coming into the grade level. Sometimes, though, they place too much emphasis on what children do not know or have forgotten over summer break. After all, those gaps can be glaring. Helping their students grow is like helping an acorn grow; they must watch for…

Eliciting, responding to, and advancing students' mathematical thinking all lie at the heart of great teaching. In this article, the authors describe a formative assessment approach that teachers can use to learn more about their students' mathematical thinking and inform their instructional decisions. This assessment approach draws on a widely…

This theoretical paper outlines the process of defining "mathematical giftedness" for a present study on how primary school teaching shapes the mindsets of children who are mathematically gifted. Mathematical giftedness is not a badge of honour or some special value attributed to a child who has achieved something exceptional.…

Students on the autism spectrum present with difficulties in a variety of areas, including social understanding, emotional regulation, academics, and behavior. Professionals working in the field of autism must identify and address these areas of need given each individual child's specific cognitive profiles. In this article the authors highlight…

Several decades ago, V. A. Krutetskii conducted a multiyear study to investigate the various types of thinking that academically advanced, or as he called them, gifted mathematicians used. Following an in-depth look at Krutetskii's nine ways of thinking, a model is proposed that will provide direction for teachers in selecting problems. The model…

Since 2001, the authors have been working with groups of teachers to investigate students' early algebraic thinking--learning representations, connections, and generalizations in the elementary school grades. They began paying attention to students' explicit remarks about regularities in the number system or what students imply by their…

Tiering and scaffolding are two differentiation strategies that teachers use to support access to a high-quality mathematics curriculum for all students. This article provides examples demonstrating a thinking process for planning tiered activities that focus on important mathematical understandings. Also described are possible scaffolds that can…

Many people feel mathematics education in the U.S. is in need of improvement. Fennema and Franke (1992) note that teachers' knowledge (or lack thereof) is often associated with poor instruction and thus, low student achievement on instruments which measure mathematical aptitude. For this reason, universities across the country have become…

President Bush says that the No Child Left Behind Act is working, pointing to student-achievement results from a single subsection of the National Assessment of Educational Progress (NAEP) and tentative Reading First data. But the evidence available to support his claim is questionable. The data Mr. Bush cited are from just the "long-term…

Social, physical, emotional, and cognitive developmental rates for gifted children do not correspond to each other and--except for physical development--do not necessarily correspond to age peer norms. Giftedness itself causes asynchrony; that is, it causes children to be out of sync with other components. In the classroom, the teacher is…

Gifted children in the preschool and primary grades may demonstrate advanced abilities in the verbal areas in several different ways. Many gifted children show precocious oral language ability by talking early and with greater complexity and manipulation of language than their age peers. Some gifted children also demonstrate precocious reading…

Developing mathematical talent at the elementary level is a complex issue--one that is influenced by many components. The three main factors are: (1) levels of Math giftedness; (2) teacher background; and (3) appropriate resource materials. Keeping these issues in mind and knowing that each district and, indeed, each student is unique, this…

Under Title V, Guidance, Counseling, and Testing of the "National Defense Education Act of 1958," the Congress of the United States has recognized the value of tests as a tool which may be used to help make an early determination of the aptitudes and abilities of the students in U.S. schools. This bulletin attempts to explain the use and…