In this workshop, participants engaged with and reflected on authentic artifacts from data modeling projects related to the solar system and to deforestation that were completed by elementary students in grade 5 (average age 11). These authentic examples were used to ground a discussion of using a data modeling approach to help elementary students make sense of and meaningful integrated use of mathematics and science concepts and tools. School-based ways of helping teachers understand this approach in order to be able to use it in their classrooms were also discussed.

This research aimed to discuss the indigenous students’ learning effects of mathematics which was based on the self-designed localization and materialization of mathematics activities and had proceeded for one year. The quasi-experimental method was used in this research. There were 58 indigenous first grade students which were divided into three experimental groups (A, B, C) and one control group (D). Experimental instruments embodied written tests and manipulative tests which were designed by researchers according to the indicators proclaimed by Ministry of Education. The main findings were as followed: (1) The influence of localization and materialization of mathematics activities on the indigenous first grade students’ learning effects was limited. (2) According to the result of Paired T-test of the written and manipulative tests, most of scores of manipulative tests were higher written tests.

This study engaged fourth and fifth graders in solving a set of proportional tasks with focused discussion and concept development by the teacher. In order to understand the students’ ability to generalize the concept, they were asked to write problems that reflected the underlying concepts in the tasks and lessons. A qualitative analysis of the student generated problems show that the majority of the students were able to generalize the concepts. The analysis allowed for a discussion of problems solving approaches and a rich description of how students applied multiplicative reasoning in composing mathematics problems. These results are couched in a discussion of how the students solved the proportional reasoning tasks.

The need for developing mathematics curricula was clarified. Models of mathematics curriculum development in Egypt were identified as: \"Temporary Committees\" (TC), center of developing curriculum and educational materials (CDCEM), \"National conferences\" (NC) and \"Educational standards\" (ES). The advantages and disadvantages of each one of these models were evaluated. Then a new model was suggested covering the whole advantages of these models and avoiding their disadvantages.

Technologies associated with modern computing are being commonly used in education. Over the past few years, the usage has increased considerably. This increase is also attributed to the availability of more improved technology products and services at much lower costs. As a result, many successful educational multimedia products have been developed which have made significant contributions to learning and teaching mathematics at various levels. However, it is not always clear what exactly the position of technology in education is. In other words, to what extent does the technology-aided means of learning enhance learning and add value to the conventional materials? How are they supposed to supersede or excel the learning effectiveness of traditional methods of teaching? This paper explores the possibilities of utilizing the latest technologies such as Virtual Reality (VR) environments and Tablet PCs in conjunction with the traditional approaches and concepts in creating a balanced and more effective learning and teaching conditions. It also demonstrates how the creation of a situation where ‘one cannot see the wood for the trees’ can be avoided by striking the right balance.

Across the United States, there is a growing number of students for whom English is not their first language. These students experience many challenges adjusting to new educational environments. These students are often denied access to the full curriculum in mathematics (Reyes & Fletcher, 2003) and the resulting opportunities for higher level educational experiences in mathematics and the resulting higher economic employment options. Educators need support in understanding and responding to the linguistic and cultural challenges that these students face in learning mathematics. A course entitled Language, Culture, Mathematics and the LEP Learner is part of the doctoral courses available to Curriculum and Instruction students at UNC Charlotte. The course focuses on theoretical and applied models of teaching and learning mathematics for English as Second Language Learners. Research and current practice are reviewed with an emphasis on the design, implementation, and assessment of instruction for this population of learners. A qualitative analysis of students’ final research projects using narrative analysis methodologies showed that students (1) position issues within a larger sociocultural framework (2) advocate for the negotiation of pedagogical principles that blend language learning strategies with effective mathematics pedagogy and (3) identify assessment policies and processes that are supportive and limiting for these learners.

Online and other forms of distance learning are a permanent fixture in the educational landscape. Mathematics taught in distance formats pose an even greater challenge to students and teachers alike. As mathematics is a skill subject, demonstration of concepts and processes is crucial, if not critical, to learning, particularly to visual and kinesthetic learners. Video podcasts and screencasts are the answer to distance students’ need for demonstration and explanation of mathematical topics. In the current economic climate, however, expensive audio/video capture software and hardware, as well as a lack of technical media support, make it virtually impossible to create such course materials. Also, there is the question of ownership of intellectual property if created with institutional funds and/or resources. Free capture software and internet video hosting sites make it possible for an individual to create his or her own podcasts and screencasts for student use, retaining ownership of the created materials.Materials developed for online students can be made available to students in seated class. This benefits students who are unable to attend class, but can be made available to the entire class.

Single sex classes have recently been emphasized as an effective way to promote mathematics learning. Despite their popularity, the research on the effectiveness of such programs is mixed underscoring the need for additional research and discussion. This research is set in one of the twenty-five largest public school systems in the United States, where schools have recently been allowed to begin instructional initiatives with same sex classes in mathematics. Preliminary data on the effectiveness of one program will be highlighted. Achievement data, compared to traditional classes, will be considered to demonstrate the academic effectiveness of the project. Qualitative data analysis will provide a rich description of the affective issues relative to this innovation. The current project will be framed in critical analysis of the research literature and will discuss the potential benefits and disadvantages both from this current project and from the related literature.

Young children’s ‘alternative’ notions of science are well documented but their unorthodox ideas about arithmetic are less well known. For example, studies have shown that young children initially treat numbers as position markers rather than size symbols. Also, children often hold a transformational view of operations; that is, they are reluctant to accept the commutativity of addition and multiplication. This ‘alternative’ view of operations is often overlooked by teachers, keen to demonstrate the so called ‘laws’ of arithmetic. However, this paper argues that we should not be in any haste to replace these primitive intuitions; instead, we should show that transformational operations actually reflect how objects behave when acted on in the physical world. The paper draws on earlier research of the writer in which young children used signs for transformational arithmetic in game scenarios. In particular, it examines the feasibility of ‘sums’ in which the operator is distinguished from the operand. In short, this paper presents the theory behind an entirely new way of teaching arithmetic, based on children’s ‘alternative’ intuitions about numbers and operations.

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