When do children begin to learn mathematics? Views of preschool practitioners in regional and rural Australia

Preschool directors, teachers, and assistants from regional and rural eastern Australia were interviewed in the autumn of 2008 to discover their knowledge and beliefs concerning whether young children had the capacity to solve mathematical problems, when young children begin to think mathematically, and their observations of children’s mathematics learning. Respondents overwhelmingly agreed that preschool children were capable of mathematical activity and thought. Fifty eight (88%) respondents believed that children had begun to exhibit mathematical thinking by age 3; 30 (46%) by their first birthday. Practitioners interviewed were able to provide examples of both incidental and planned mathematical activities across a breadth of content, including number and operations, measurement, geometry, and fundamental classifying and ordering activities. The practitioners also demonstrated a creditable awareness of children who seemed to have a good grasp of mathematics. Many practitioners realized that mathematical proclivity could be shown in the processes children use as they engaged in mathematical activity and solved mathematical problems.

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.

Multicultural education : the understandings of preschool teachers in Singapore

For multicultural education to be effective, it must be introduced in the early years and reinforced throughout the school years. It is important for teachers of young children to be equipped with the appropriate knowledge, skills and positive attitudes to promote multiculturalism in their classrooms. This paper reports on a survey involving preschool teachers in Singapore who were participating in an in-service training course. The teachers completed a questionnaire to indicate their understandings of multicultural education and their perceptions of its importance in early childhood education. The findings indicated that the teachers endorsed the need for multicultural education in preschools and the importance of children learning tolerance and understanding of other cultures in the Singaporean context. However, while preschool teachers held positive attitudes towards multicultural education, there was limited understanding of the challenges in implementing an anti-bias teaching and curriculum approach. The implications of these findings for preschool teacher education programs in Singapore and in other countries focus on supporting teachers in developing more critical and deeper understandings of multiculturalism.

What do education students value in primary mathematics curriculum?

In this paper the priorities that second year education students hold for primary mathematics content and student learning are presented. Data were collected from students who participated in a tutorial task that was used to engage students in discussion about primary mathematics curriculum. The data were collected annually for four years. Reflections about the mathematics subjects in the course are made within the context of current research and mathematics curriculum policy. Inferences are drawn about education students’ beliefs.

Mathematical thinking of preschool children in rural and regional Australia : research and practice

At what age do young children begin thinking mathematically? Can young children work on mathematical problems? How do early childhood educators ensure young children feel good about mathematics? Where do early childhood educators learn about suitable mathematics activities?

A good early childhood start in mathematics is critical for later mathematics success. Parents, carers and early childhood educators are teaching mathematics, either consciously or unconsciously, in any social interaction with a child.

Mathematical Thinking of Preschool Children in Rural and Regional Australia is an extension of a conference of Australian and New Zealand researchers that identified a number of important problems related to the mathematical learning of children prior to formal schooling. A project team of 11 researchers from top Australian universities sought to investigate how early childhood education can best have a positive influence on early mathematics learning.

The investigation complements and extends the work of Project Good Start by focusing attention on critical aspects of parents, carers and early childhood educators who care for young children. Early childhood educators from regional and rural New South Wales, Queensland and Victoria were interviewed, following a set of structured questions. The questions focused on: children’s mathematics learning; support for mathematics teaching; use of technology; attitudes to mathematics; and assessment and record keeping.

The researchers also reviewed research focusing on the mathematical capacities and potential foundations for further mathematical development in young children (0–5 years) published in the last decade and produced an annotated bibliography. This should provide a good basis for further research and reading.

Based upon the results of this investigation, the researchers make 11 recommendations for improving the practices of early childhood education centres in relation to young children’s mathematical thinking and development. The implications for policy and decision makers are outlined for teacher education, the provision of resources and further research.

Studying mathematics teacher education: analysing the process of task variation on learning

Self-study of variations to task design offers a way of analysing how learning takes place. Over several years, variations were made to improve an assessment task completed by final-year teacher candidates in a primary mathematics teacher education subject. This article describes how alterations to a task informed on-going developments in self-study of one assessment task employed in an online subject. Analysis of my journal, notes from conversations with colleagues, teacher candidates’ work on the task and responses to online forums, and survey data inspired variations focused on better exploration of key concepts involved in the task, raising of focal awareness, developing a stronger professional eye in the students and the author, adaptations for multiple curriculum levels, and explorations of dual teacher–student perspectives. The overall challenge has been to support teacher candidates to learn to design effective open-ended tasks with a critical professional eye. Descriptions of the changes made to the task and the development of my own professional eye as a consequence of the application of self-study are included. Data show that variations to the task increased teacher candidates’ understanding of mathematics problem posing and generated pedagogical insights for task design.

Teaching and aligning upper level mathematics classes to Michigan high school content expectations in an alternative education setting : approaches and issues

After teaching regular education secondary mathematics for seven years, I accepted a position in an alternative education high school. Over the next four years, the State of Michigan adopted new graduation requirements phasing in a mandate for all students to complete Geometry and Algebra 2 courses. Since many of my students were already struggling in Algebra 1, getting them through Geometry and Algebra 2 seemed like a daunting task. To better instruct my students, I wanted to know how other teachers in similar situations were addressing the new High School Content Expectations (HSCEs) in upper level mathematics. This study examines how thoroughly alternative education teachers in Michigan are addressing the HSCEs in their courses, what approaches they have found most effective, and what issues are preventing teachers and schools from successfully implementing the HSCEs. Twenty-six alternative high school educators completed an online survey that included a variety of questions regarding school characteristics, curriculum alignment, implementation approaches and issues. Follow-up phone interviews were conducted with four of these participants. The survey responses were used to categorize schools as successful, unsuccessful, and neutral schools in terms of meeting the HSCEs. Responses from schools in each category were compared to identify common approaches and issues among them and to identify significant differences between school groups. Data analysis showed that successful schools taught more of the HSCEs through a variety of instructional approaches, with an emphasis on varying the ways students learned the material. Individualized instruction was frequently mentioned by successful schools and was strikingly absent from unsuccessful school responses. The main obstacle to successful implementation of the HSCEs identified in the study was gaps in student knowledge. This caused pace of instruction to also be a significant issue. School representatives were fairly united against the belief that the Algebra 2 graduation requirement was appropriate for all alternative education students. Possible implications of these findings are discussed.

Online Education: What Works in Mathematics

Florida State University and University of Helsinki Information technology has the potential to deliver education to everybody by high quality online courses and associated services, and to enhance traditional face-to-face instruction by, e.g., web services offering virtually unlimited practice and step-bystep solutions to practice problems. Regardless of this, tools of information technology have not yet penetrated mathematics education in any meaningful way. This is mostly due to the inertia of academia: instructors are slow to change their working habits. This paper reports on an experiment where all the instructors (seven instructors and six teaching assistants) of a large calculus course were required to base their instruction on online content. The paper will analyze the effectiveness of various solutions used, and finishes with recommendations regarding best practices.

A Didactic Model of Computer Supported Education in Higher Mathematics

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016