This practical book draws on Ronit Bird's teaching experience to create detailed strategies and teaching plans for students aged 9-16 who have difficulties with number. Activities and games are used to teach numeracy skills in these key areas: number components, bridging, multiplication, division and reasoning strategies. New to this edition: (1)…

Children's ability to discriminate nonsymbolic number (e.g. the number of items in a set) is a commonly studied predictor of later math skills. Number discrimination improves throughout development, but what drives this improvement is unclear. Competing theories suggest it may be due to a sharpening numerical representation or an improved ability…

Fuzzy sets have experienced multiple expansions since their conception to enhance their capacity to convey complex information. Intuitionistic fuzzy sets, image fuzzy sets, q-rung orthopair fuzzy sets, and neutrosophic sets are a few of these extensions. Researchers and academics have acquired a lot of information about their theories and methods…

We have observed that over 90% of our students, both undergraduate and graduate, know little about the existence and multiplicity of real roots of real numbers; for example the fifth root of -2. Most of those who may know the answers are unable to give a logical explanation of the validity of their answers.

Given its pedagogical appeal, the number line is a commonly used representation in the teaching and learning of fractions. However, behind its apparent simplicity, this mathematical object may involve layers of complexity when looked at from the perspective of affordances as is the case in this study. In particular, this in situ exploration…

Number and operations form the backbone of the school mathematics curriculum. A high school graduate should comfortably and capably meet an expression like, "Let f(x) be a function of a real variable x," implying that the student has a robust sense of the real number continuum. This understanding is a central objective of the school…

As a descriptive survey research, this study aimed to investigate the number sense skills of gifted in terms of number sense components. Participant of this research consisted of 123 gifted secondary school students, who were selected according to the convenience sampling method in Turkey. The data of this research were collected in the 2021-2022…

A study of pre-service primary school teachers' content knowledge regarding real numbers related to infinity, i.e., division by zero and denseness of the real number line, was conducted at a Swedish university. Data were collected twice during the respondents' teacher education using questionnaires and interviews on both occasions. The data were…

We replicated a study of a kindergarten mathematics intervention, ROOTS, delivered in the context of a research-based core program. We randomly assigned 62 classrooms to treatment (ROOTS) or a business-as-usual control. All classrooms implemented the research-based core program (Early Learning in Mathematics). Participants included 163 treatment…

The purpose of this study was to conduct a replication study of a kindergarten mathematics intervention, ROOTS, delivered within the context of a research base core program. In the study, sixty two classrooms were randomly assigned to treatment (ROOTS) or a business as usual control. All classrooms implemented a research based core program (Early…

This article describes Ulrich Kortenkamp's Place Value Chart app and the accompanying teacher guide developed by the members of an international research team led by regular contributor Kevin Larkin.

Numerical competencies acquired in preschool are foundational and predictive for children's later mathematical development. It remains to be determined whether there are gender differences in these early numerical competencies which could explain the often-reported gender differences in later mathematics and STEM-related abilities. Using a…

The book synergizes research on number across two disciplines--mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children's activity, including mental and physical actions. Subsequent chapters are organized into sections that…

Psychological studies of early numerical development fill a void in mathematics education research. However, conflations between magnitude awareness and number, and over-attributions of researcher conceptions to children, have led to psychological models that are at odds with findings from mathematics educators on later numerical development. In…

An instructional approach is presented for teaching the mole concept to high school introductory-level chemistry classes. Extensions to the strategy are presented for more advanced classes. The strength of the approach is based upon discovery. Students discover the Avogadro number and the mole concept. The discovery is based upon calculations that…