Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.

Gender and grade differences in upper elementary school children’s descriptive and evaluative self-statements and self-esteem

Gender and developmental differences in self-description, self-evaluation and self-esteem were investigated using 957 elementary school children in grades 3 to 7. Gender differences were found for six of the seven descriptive statements and for five of the seven evaluative statements. The major gender stereotypical findings from previous studies were replicated. Boys reported higher scores than girls on descriptive and evaluative statements about their physical abilities and mathematics, while girls reported higher scores on descriptive and evaluative statements about reading. Declines over time were noted for all self-evaluations except having good relations with peers and for global self-esteem, providing some support for the notion that the decline in self-concepts and self-esteem may be attributed to the children's perceptions of themselves becoming more accurate and less egocentric in line with their cognitive capacity to integrate external feedback realistically.

Self-concept and self-esteem in elementary school children

Confusion exists with regard to the empirical and substantive link between self-concept and self-esteem in elementary school children and their relationship to self-description, self-evaluation, and global beliefs and feelings about oneself as a person. This study reports the results of investigating the relationships between these self-constructs using 957 elementary school children in Grades 3 to 7. The evidence suggests that self-concept is comprised of both descriptive and evaluative beliefs that children hold about certain characteristics, whereas self-esteem can be viewed as the global feelings and beliefs that children have about themselves as people.

Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Integrating engineering model eliciting activities in elementary school curricula

This paper argues for a future-oriented, inclusion of Engineering Model Eliciting Activities (EngMEAs) in elementary mathematics curricula. In EngMEAs students work with meaningful engineering problems that capitalise on and extend their existing mathematics and science learning, to develop, revise and document powerful models, while working in groups. The models developed by six groups of 12-year students in solving the Natural Gas activity are presented. Results showed that student models adequately solved the problem, although student models did not take into account all the data provided. Student solutions varied to the extent students employed the engineering context in their models and to their understanding of the mathematical concepts involved in the problem. Finally, recommendations for implementing EngMEAs and for further research are discussed.

Integrating Engineering Experiences within the Elementary Mathematics Curriculum

Engineering education for elementary school students is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to use the data to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results provide evidence that engineering model-eliciting activities can be successfully integrated in the elementary mathematics curriculum. These activities provide rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Measuring cognitive and dispositional characteristics of creativity in elementary students

This article describes the theoretical underpinning and development of a measurement instrument that provides teachers with a tool to observe the personal creativity characteristics of individual students. The instrument was developed by compiling a list of characteristics derived from the literature to be indicative of the personal characteristics of creative people. The list was then reduced by grouping like characteristics to 9 cognitive and dispositional traits that were considered appropriate for elementary students. The 9-item instrument was then administered in 24 classrooms to 520 Year 6 and Year 7 students. Factor analysis using maximum likelihood extraction with an oblimin rotation revealed a single factor with an eigenvalue greater than 1 and accounting for 63% of the variance. All 9 items on this factor loaded at .72 or greater. The results indicated that the Creativity Checklist has very high internal consistency and is a reliable measurement instrument (a = .93).

Integrating engineering education within the elementary and middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discussion paper argues for the integration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

Identity and text : developing self-conscious readers

Globalisation and societal change suggest the language and literacy skills needed to make meaning in our lives are increasing and changing radically. Multiliteracies are influencing the future of literacy teaching. One aspect of the pedagogy of multiliteracies is recruiting learners’ previous and current experiences as an integral part of the learning experience. This paper examines the implications of results from a project that examined student responses to a postmodern picture book, in particular, ways teachers might develop students’ self-knowledge about reading. It draws on Freebody and Luke’s Four Resources Model of Reading and recently developed models for teaching multiliteracies.

Investigating functional thinking in the elementary classroom : foundations of early algebraic reasoning

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers. These lessons were designed to enable students to build mental representations in order to explore the use of function tables by focusing on the relationship between input and output numbers with the intention of extracting the algebraic nature of the arithmetic involved. All lessons were videotaped. The results indicate that elementary students are not only capable of developing functional thinking but also of communicating their thinking both verbally and symbolically.