In this article, we report the findings of a study conducted with 6 Grade 8 students in the United States. The students posed stories for open number sentences involving addition and subtraction of integers. We analysed the stories posed by the students to build models that describe the conceptual structures behind these posed stories -- the…

Although a good rational number understanding is of crucial importance for learners' general maths achievement, many learners have misconceptions about fractions. An often described misconception is that a fraction's numerical magnitude increases when its denominator, numerator, or both increase. The present intervention study investigated how…

In recent studies, test-score increases have been shown in rule-based intelligence test tasks, such as number series, after watching a corresponding video tutorial. An open question remains regarding the mechanisms involved. Specifically, taking notes to describe the relations between numbers might be linked to test scores, and is hypothesized to…

In this article, we explore Whitehead's claim that experience is fundamentally affective. We do so in the context of an Italian primary school classroom featuring the use of the multitouch application "TouchCounts." We study the way in which the children and the iPad take each other up and the meanings of number and arithmetic that…

Preschoolers' repeating patterning knowledge is predictive of their concurrent and later math and numeracy knowledge, but strong experimental evidence is needed to determine if these relations are causal. The purpose of the current Study was to examine the causal effects of repeating patterning and numeracy tutoring on repeating patterning,…

Humans perceptually extract quantity information from our environments, be it from simple stimuli in isolation, or from relational magnitudes formed by taking ratios of pairs of simple stimuli. Some have proposed that these two types of magnitude are processed by a common system, whereas others have proposed separate systems. To test these…

Despite the importance of mathematical understanding for academic and occupational success, students in the United States are not meeting necessary levels of mathematics achievement. Multi-tiered systems of support (MTSS) provide a framework for schools to allocate resources to best support students. Universal screening, a key element of MTSS,…

In many countries, teachers often have to set their own questions for tests and examinations: some of them even set their own questions for assignments for students. These teachers do not usually select questions from textbooks used by the students because the latter would have seen the questions. If the teachers take the questions from other…

In mathematically literate societies, numerical information is represented in 3 distinct codes: a verbal code (i.e., number words); a digital, symbolic code (e.g., Arabic numerals); and an analogical code (i.e., quantities; Dehaene, 1992). To communicate effectively using these numerical codes, our understanding of number must involve an…

In this article, we question what is an appropriate balance of ordinal and cardinal work in the early learning of number. We see an over-emphasis, in current research and practice, on the cardinal that leads, for example, to only using small numbers. We report on empirical work we have carried out in the UK and Canada that suggests the potential…

In this study, representations used by preservice mathematics teachers in the process of solving limit problems were determined, the inter-representation transformation competence levels were investigated and the relationship between them was examined. In this context, "Limit Representation Transformation Test" with a reliability of…

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students' understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real…

Representing repeating nonterminating decimals as rational numbers is a topic introduced in the seventh-grade Common Core State Standards for Mathematics. According to Content Standard 7.NS.2.D., students should be able to represent a rational number as a decimal and understand that the decimal will either end in zeros or eventually repeat (NGO…

Critical thinking skill was needed since problems in daily life required a solution. To solve the problems, the students collect the data as a consideration in making the right decision. Moreover, the students also need good critical thinking skills. To develop a good critical thinking skill, the researcher develops a textbook of Complex Analysis…

In this work, recurrent and linear sequences are studied, exploring the teaching of these numbers with the aid of a computational resource, known as Google Colab. Initially, a brief historical exploration inherent to these sequences is carried out, as well as the construction of the characteristic equation of each one. Thus, their respective roots…