Do your students have the incorrect idea that addition "makes numbers bigger" and subtraction "makes numbers smaller"? Do they believe that subtraction is always "taking away"? What tasks can you offer--what questions can you ask--to determine what your students know or don't know--and move them forward in their…

Subtractions of the type M - S = ? can be solved by various strategies, including subtraction by addition. In this study, we investigated children's use of subtraction by addition by means of reaction time analyses. We presented 106 third to sixth graders with 32 large non-tie single-digit problems in both subtraction (12 - 9 = .) and addition…

The First Grade Pre-Screening is designed to be used at the start of the first grade school year so that teachers can obtain information about their incoming students. This information is intended to give teachers insight about what math and reading skills a student may or may not have at the beginning of the year. The information can aid teachers…

This paper reports an intervention phase of a design study aimed to assist second-grade Filipino children in solving addition word problems in English, a language they primarily encounter only in school. With Filipino as the medium of instruction, an out-of-school pedagogical intervention providing linguistic and representational scaffolds was…

The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…

Mathematics textbooks are a predominant resource in primary school in Greece, as well as in many other countries. The present study reports on both a content analysis of Greek mathematics textbooks with regard to the types of word problems represented in them and a quantitative analysis of children's achievement in these problems. For the purpose…

The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the…

During the winter of 2011, the author faced an instructional dilemma: Should she teach the concept of adding and subtracting fractions with unlike denominators using a "quick trick" for the sake of staying on schedule, or should she try something different in hopes that her students would gain understanding through their own methods? The latter…

This study examined interventions for addition and subtraction that were implemented through single-case design (SCD) research studies. We attempted to extend prior SCD meta-analyses by examining differences in effect sizes across several moderating variables and by including a novel index of effect, improvement rate difference (IRD). We also…

This study, an education program was developed to improve addition-subtraction skills of 6-year old children using educational toys and smart boards. The program was implemented with children, and its effects on their operational skills were analysed. The study group of the research is composed of 90 children who attended preschool classes in…

Math games can be powerful tools in helping students achieve automaticity in basic addition and related subtraction facts if both teachers and students use them purposefully. According to the National Council of Teachers of Mathematics (NCTM 2000), developing a solid mathematical foundation is essential for every child in prekindergarten through…

In a first experiment, adults were asked to solve one-digit additions, subtractions and multiplications. When the sign appeared 150 ms before the operands, addition and subtraction were solved faster than when the sign and the operands appeared simultaneously on screen. This priming effect was not observed for multiplication problems. A second…

This study explores the impact that co-designing a virtual manipulative, Fractions Lab, had on teachers' professional development. Tapping into an existing community of practice of mathematics specialist teachers, the study identifies how a cooperative enquiry approach utilising workshops and school-based visits challenged 23 competent primary…

This study investigated longitudinal pathways leading from early spatial skills in first-grade girls to their fifth-grade analytical math reasoning abilities (N = 138). First-grade assessments included spatial skills, verbal skills, addition/subtraction skills, and frequency of choice of a decomposition or retrieval strategy on the…

This study investigates the relationship between skills that underpin mathematical word problems and those that underpin numerical operations, such as addition, subtraction, division and multiplication. Sixty children aged 6-7 years were tested on measures of mathematical ability, reading accuracy, reading comprehension, verbal intelligence and…