"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards on Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

This study aims to determine the influence of teaching Fibonacci numbers and golden ratio through history of mathematics on student achievement and the opinions of students regarding this issue. This study was carried out by case study method with 30 students who attended the 8th grade of an elementary school in Erzincan in spring term of…

The goal of this study was to understand errors that student make when simplifying exponential expressions. College students enrolled in four college mathematics courses were asked to simplify and compare such expressions. Quantitative analysis identified three persistent errors: interpreting negative bases, negative exponents, and parentheses.…

How do teachers teach students to count rhythms? Teachers can choose from various techniques. Younger students may learn themed words (such as "pea," "carrot," or "avocado"), specific rhythm syllables (such as "ta" and "ti-ti"), or some other counting method to learn notation and internalize rhythms. As students grow musically, and especially when…

This research contrasted deaf and hearing students' interpretive knowledge of English sentences containing numeral quantifier phrases and indefinite noun phrases. A multiple-interpretation picture task methodology was used to assess 305 participants' judgments of the compatibility of sentence meanings with depicted discourse contexts.…

Many children have significant mathematical learning disabilities (MLD, or dyscalculia) despite adequate schooling. The current study hypothesizes that MLD partly results from a deficiency in the Approximate Number System (ANS) that supports nonverbal numerical representations across species and throughout development. In this study of 71 ninth…

Proficiency with fractions serves as a foundation for later mathematics and is critical for learning algebra, which plays a role in college success and lifetime earnings. Yet children often struggle to learn fractions. Educators have argued that a conceptual understanding of fractions involves learning that a fraction represents a magnitude…

It is assumed that basic numerical competencies are important building blocks for more complex arithmetic skills. The current study aimed at evaluating this interrelation in a longitudinal approach. It was investigated whether first graders' performance in basic numerical tasks in general as well as specific processes involved (e.g., place-value…

The current study investigated how young learners' experiences with arithmetic equations can lead to learning of an arithmetic principle. The focus was elementary school children's acquisition of the Relation to Operands principle for subtraction (i.e., for natural numbers, the difference must be less than the minuend). In Experiment 1, children…

We used both student interviews and diagnostic testing to reveal students' misconceptions about number representations in computing systems. This article reveals that students who have passed an undergraduate level computer organization course still possess surprising misconceptions about positional notations, two's complement representation, and…

Lamon ("Teaching fractions and ratios for understanding. Essential content knowledge and instructional strategies for teachers," 2nd edn. Lawrence Erlbaum Associates, Mahwah, 2005) claimed that the development of proportional reasoning relies on various kinds of understanding and thinking processes. The critical components suggested were…

We present a research report on addition and subtraction conducted with Down syndrome students between the ages of 12 and 31. We interviewed a group of students with Down syndrome who executed algorithms and solved problems using specific materials and paper and pencil. The results show that students with Down syndrome progress through the same…

School gardening has become increasingly popular as a context for learning in which children construct new knowledge, learn cultural and societal values related to ecological awareness, and develop and practice authentic or real-world skills (Blair, 2009; Bowker & Tearle, 2007). The present research was a longitudinal case study of children's…

We examined the impact of television viewing at ages 3 and 4 on vocabulary and at age 5 on executive functioning in the context of home learning environment and parental scaffolding. Children (N = 263) were seen in the lab when they were 3 years old and then again at ages 4 and 5. Parents completed measures assessing child television viewing and…

Gap thinking has been categorised as one of several whole number strategies that interfere with early fraction understanding. This study showed that this claim is not supported by interview data of Grade 6 students' gap thinking explanations during a fraction pair comparison task. A correlation with equivalence performance was uncovered, leading…