This study is concerned with the analysis of mathematical textbook tasks at the second-level in Ireland, in the context of the introduction of the revised curriculum entitled 'Project Maths'. A total of 7635 tasks on the topics of Pattern, Sequences and Series, and Differential Calculus were analysed; these tasks were selected from editions of…

The aim of this study is to reveal and evaluate the attending and interpreting skills of student thinking of prospective teachers, as well as their instructional suggestions as responding skills. The current study was conducted with 29 prospective mathematics teachers (PMTs) within a qualitative design in the context of probability. First, three…

The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of…

This study aimed to explore learners' discourse patterns and outcomes while using a visible-annotation tool as a collaborative representation tool. The tool used in this study introduced two types of sharing activities before the problem-solving phase to support sequential knowledge construction. Forty participants were randomly assigned to one of…

This article begins with a theoretical discussion of the characteristics that a task should feature to be regarded as a mathematics problem suitable for pre-primary students. Those considerations are followed by a report of a classroom experience in which three problems involving quotative or partitive division were posed to pre-primary school…

This paper analyses the tasks allotted to students, featuring two thematic units in the 6th grade Geography textbook published in 2018 by the Didactic and Pedagogic Publishing House Ltd., Bucharest and used in the schools in Romania during the 2018-2019 school year. After a brief analysis of the textbook and its lesson structure, we studied the…

Flexibility in transforming algebraic expressions is recognized as fundamental for a rich procedural knowledge. Here, flexibility in-depth is proposed as the ability to apply one strategy to a wide range of unfamiliar expressions. In this study, design experiments with four groups of students were conducted to support students' flexibility…

Private speech utterances (PS) from 24 preschool children and 24 adults were obtained under (noninteracting) listener present and listener absent conditions using 2 tasks with an identical structure. Children produced significantly more PS in the listener present condition. Similar results were obtained with adults, albeit with a reduced incidence…

This study analyzes six seventh grade Israeli mathematics textbooks, examining (1) the extent to which students are required to justify and explain their mathematical work, and (2) whether students are asked to justify a mathematical claim that is stated by the textbook or a mathematical claim that they themselves generated when solving a problem.…

We analyzed the statistical content within mathematics textbooks used in courses for preparing elementary teachers. Six textbooks commonly used in the United States comprised our sample. Each task in statistical sections was analyzed using both the levels of the GAISE framework (Franklin et al. 2007) and phases of the statistical problem solving…

Background: Context-based learning approaches are used to enhance students' interest in, and knowledge about, science. According to different empirical studies, students' interest is improved by applying these more non-conventional approaches, while effects on learning outcomes are less coherent. Hence, further insights are needed into the…

We analyze probability content within middle grades (6, 7, and 8) mathematics textbooks from a historical perspective. Two series, one popular and the other alternative, from four recent eras of mathematics education (New Math, Back to Basics, Problem Solving, and Standards) were analyzed using the Mathematical Tasks Framework (Stein, Smith,…

Describes differences in formative evaluation techniques between instructional designers and subject matter experts. Content analysis based on think-aloud data focusing on differences in task interpretation, problem identification and revision statements, and review strategies is discussed; use of instructional systems design models by…

This paper discusses two related areas in which recent advancements in cognitive science and educational technology may affect instructional design theory. These are: (1) the analysis of information-to-be-learned; and (2) the linkage of learning theory to instructional prescriptions. The first area proposes extensions to current methods of…

Scientific advancements in cognitive science and instructional technology extend the behaviorally-oriented learning paradigm of instructional design and management in three major areas: (1) analysis of information-to-be-learned; (2) means of evaluating learners; and (3) linkage of learning theory to instructional prescriptions. The two basic types…