Mathematical power of special-needs pupils : an ICT-based dynamic assessment format to reveal weak pupils' learning potential

This paper reports a study aimed at revealing special-educational-needs pupils' learning potential by means of an ICT-based assessment including a dynamic visual tool that might help pupils when solving mathematics problems. The study focused on subtraction problems up to 100, which require 'borrowing'. These problems, in which the value of the ones-digit of the subtrahend is larger than the ones-digit of the minuend, are known as a serious difficulty for weak pupils in mathematics. Seven of such problems from a standardised test were placed in the ICT environment. Data were collected from two test conditions: the standardised written test format and the ICT version of the test items including the tool that provided pupils with a set of virtual manipulatives. The 37 pupils involved in the study were 8–12 years old and from two special-education schools in the Netherlands. Comparison of the performance scores in the two formats showed that an ICT-based assessment format, including a dynamic visual tool, can reveal weak pupils' learning potential and strategy use. The study also pointed out that 'partial-tool use', ie, not carrying out the complete subtraction operation with the tool, can provide sufficient support to find the correct answer.

Critical perspectives on communities of mathematical inquiry

While the notion of Communities of Inquiry (CoI) has its origins in philosophy, there has been widespread interest in mathematics classrooms as Communities of Mathematical Inquiry (CoMI). This paper outlines the structure and content of Research Forum 2: Critical Perspectives on Communities of Mathematical Inquiry, gives a brief review of research in the area, and highlights some key issues.

Spatial thinking processes employed by primary school students engaged in mathematical problem solving

This thesis describes changes in the spatial thinking of Year 2 and Year 4 students who participated in a six-week long spatio-mathematical program. The main investigation, which contained quantitative and qualitative components, was designed to answer questions which were identified in a comprehensive review of pertinent literatures dealing with (a) young children's development of spatial concepts and skills, (b) how students solve problems and learn in different types of classrooms, and (c) the special roles of visual imagery, equipment, and classroom discourse in spatial problem solving. The quantitative investigation into the effects of a two-dimensional spatial program used a matched-group experimental design. Parallel forms of a specially developed spatio-mathematical group test were administered on three occasions—before, immediately after, and six to eight weeks after the spatial program. The test contained items requiring spatial thinking about two-dimensional space and other items requiring transfer to thinking about three-dimensional space. The results of the experimental group were compared with those of a ‘control’ group who were involved in number problem-solving activities. The investigation took into account gender and year at school. In addition, the effects of different classroom organisations on spatial thinking were investigated~one group worked mainly individually and the other group in small cooperative groups. The study found that improvements in scores on the delayed posttest of two-dimensional spatial thinking by students who were engaged in the spatial learning experiences were statistically significantly greater than those of the control group when pretest scores were used as covariates. Gender was the only variable to show an effect on the three-dimensional delayed posttest. The study also attempted to explain how improvements in, spatial thinking occurred. The qualitative component of the study involved students in different contexts. Students were video-taped as they worked, and much observational and interview data were obtained and analysed to develop categories which were described and inter-related in a model of children's responsiveness to spatial problem-solving experiences. The model and the details of children's thinking were related to literatures on visual imagery, selective attention, representation, and concept construction.

Mathematics as a second language : looking for a bridge between mathematical language and the language of thought

Our thoughts are in one language, and mathematical results are expressed in a language foreign to the way we think. Mathematics is a unique foreign language with all the components of a language; it has its own grammar, vocabulary, conventions, synonyms, sentence structure, and paragraph structure. Students need to learn these components to partake in a thorough discussion of how to read, write, speak and think mathematics. Beginning with the students natural language and expanding that language to include symbolism and logic is the key. Providing lessons in concrete, pictorial, written and verbal terms allows the instructor to create a translation bridge between the grammar of the mother language and the grammar of mathematics. This papers presents methods to create the translation bridge for students so that they become articulate members of the mathematics community. The students "mother" language, expanded to include the symbols of mathematics and logic, is the the key to both the learning of mathematics and its effective application to problem situations. The use of appropriate language is the key to making mathematics understandable.

Course websites, computer proficiency and need for achievement : implications for MBA student performance

Course websites have become a basic requirement for course promotion and delivery in many universities. This study explores the relationship between perceived usefulness of course websites and student performance in an accounting course within a Masters of Business Administration (MBA) programme. Data from 48 students were found to support several hypotheses. Specifically, the findings of the study indicate that there is a significant correlation between the perceived usefulness of course website features such as lecture notes, tutorial questions and solutions and the frequency of use or access by students of such course website features. Further, we found that the perceived usefulness of course websites was positively related to students’ computer proficiency, but not with the frequency with which students missed classes. The findings also indicate that students with high need for achievement achieved better performance scores, but there was no significant relationship between perceived usefulness of course website and performance. These findings have several implications for the design and development of course websites at post-graduate level, and for future research examining the link between information technology and accounting education.

Mathematical modelling of the crankshaft pin grinding process

Novel mathematical models to predict crankshaft pin grinding forces, out-of-roundness and thermal damage were developed as part of this thesis. The models were validated at a local automotive manufacturer's plant. The outcomes of this research have resulted in reduced scrap and warranty costs, improved manufacturing process quality and reduced lead times.

Developing mathematical understanding

The notion of scaffolding is used to introduce research on differentiated learning trajectories that make use of activities termed 'prompts'. The prompts are used to enable children to develop the necessary mathematical understanding and skills to keep up with the rest of the class.  They focus on aspects of teaching that teachers identified as important aspects of classroom interactivity that contribute to the understanding: the use of physical representation of concepts: actions aimed at building conceptual links; and the use of language based activity.

Developing mathematical concepts in Australian pre-school settings : the background

The SIMERR project Mathematical Thinking of Pre-school Children in Rural and Regional Australia: Research and Practice included a review of relevant research literature with the aim of making this accessible to researchers as well as early childhood teachers and educators. This paper introduces the methods used in the project and provides a brief summary of the literature pertaining to the development of mathematical concepts.

Assessment of mathematical development in early childhood : some views of preschool practitioners in regional and rural Australia

As part of the project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice directors, teachers, and assistants in prior-to-school settings from regional and rural eastern Australia were interviewed to ascertain their beliefs and practices concerning early childhood mathematics. This paper reports the responses to  uestions about their assessment of children’s mathematical activity and development. The practitioners provided examples of both incidental and planned assessment activities, the different forms these took, methods of recording, and how the results were used.

Tasks and pedagogies that facilitate mathematical problem solving

This is a report from one aspect of a project seeking to identify teacher actions that support mathematical problem solving. The project developed a planning and teaching model that describes the type of classroom tasks that can facilitate mathematical problem solving, the sequencing of the tasks, the nature of teaching heterogeneous groups, ways of dfferentiating tasks, and particular pedagogies. We report here one teacher's implementation of the
model using a unit of work that he planned and taught. The report provides important insights into the implementation of the theoretically founded model and the responses of students. We found that the model can be used for planning and teaching and for encouraging problem solving. The model has a positive effect on the learning of most students. Specific teachers actions were identified in order to address the needs of the students we are most
keen to support, those experiencing dfficulties.

How early childhood practitioners view young children's mathematical thinking

Interviews were held with 64 professionals in childcare centres. This paper reports on their responses to 3 questions seeking their perceptions of mathematical thinking in very young children. Generally, the interviewees were found to have a good sense of mathematical concepts relevant to babies and toddlers, and they cited evidence of young children’s mathematical development. It is concluded that this practical knowledge would provide a strong foundation for further professional development.