Investigating feelings towards mathematics among Chinese kindergarten children

Prior to entering schooling settings, many children exhibit intuitive knowledge of mathematics and many have mastered basic addition combinations. However, often as a result of formal instruction, some children begin to dislike or fear mathematics. In this study, children at a kindergarten in China took a smiley-face survey to determine how their feelings and beliefs about mathematics were affected throughout their kindergarten years.Results suggest that even children in this study have a better number sense and mathematics achievement, they appear to develop mathematics anxiety in Chinese cultural context.

Early years teachers’ attitudes towards mathematics

Worldwide, there is considerable attention to providing a supportive mathematics learning environment for young children because attitude formation and achievement in these early years of schooling have a lifelong impact. Key influences on young children during these early years are their teachers. Practising early years teachers‟ attitudes towards mathematics influence the teaching methods they employ, which in turn, affects young students‟ attitudes towards mathematics, and ultimately, their achievement. However, little is known about practising early years teachers‟ attitudes to mathematics or how these attitudes form, which is the focus of this study. The research questions were: 1. What attitudes do practising early years teachers hold towards mathematics? 2. How did the teachers‟ mathematics attitudes form? This study adopted an explanatory case study design (Yin, 2003) to investigate practising early years teachers‟ attitudes towards mathematics and the formation of these attitudes. The research took place in a Brisbane southside school situated in a middle socio-economic area. The site was chosen due to its accessibility to the researcher. The participant group consisted of 20 early years teachers. They each completed the Attitude Towards Mathematics Inventory (ATMI) (Schackow, 2005), which is a 40 item instrument that measures attitudes across the four dimensions of attitude, namely value, enjoyment, self-confidence and motivation. The teachers‟ total ATMI scores were classified according to five quintiles: strongly negative, negative, neutral, positive and strongly positive. The results of the survey revealed that these teachers‟ attitudes ranged across only three categories with one teacher classified as strongly positive, twelve teachers classified as positive and seven teachers classified as neutral. No teachers were identified as having negative or strongly negative attitudes. Subsequent to the surveys, six teachers with a breadth of attitudes were selected from the original cohort to participate in open-ended interviews to investigate the formation of their attitudes. The interview data were analysed according to the four dimensions of attitudes (value, enjoyment, self-confidence, motivation) and three stages of education (primary, secondary, tertiary). Highlighted in the findings is the critical impact of schooling experiences on the formation of student attitudes towards mathematics. Findings suggest that primary school experiences are a critical influence on the attitudes of adults who become early years teachers. These findings also indicate the vital role tertiary institutions play in altering the attitudes of preservice teachers who have had negative schooling experiences. Experiences that teachers indicated contributed to the formation of positive attitudes in their own education were games, group work, hands-on activities, positive feedback and perceived relevance. In contrast, negative experiences that teachers stated influenced their attitudes were insufficient help, rushed teaching, negative feedback and a lack of relevance of the content. These findings together with the literature on teachers‟ attitudes and mathematics education were synthesized in a model titled a Cycle of Early Years Teachers’ Attitudes Towards Mathematics. This model explains positive and negative influences on attitudes towards mathematics and how the attitudes of adults are passed on to children, who then as adults themselves, repeat the cycle by passing on attitudes to a new generation. The model can provide guidance for practising teachers and for preservice and inservice education about ways to foster positive influences to attitude formation in mathematics and inhibit negative influences. Two avenues for future research arise from the findings of this study both relating to attitudes and secondary school experiences. The first question relates to the resilience of attitudes, in particular, how an individual can maintain positive attitudes towards mathematics developed in primary school, despite secondary school experiences that typically have a negative influence on attitude. The second question relates to the relationship between attitudes and achievement, specifically, why secondary students achieve good grades in mathematics despite a lack of enjoyment, which is one of the dimensions of attitude.

Building teachers' pedagogy practices in reasoning, to improve students' dispositions towards mathematics

Drawing on participatory action research, this study identifies the pedagogies necessary to advance reasoning, which is one of the proficiencies from the Australian Curriculum Mathematics, and explores how reasoning leads to greater productive disposition. With the current emphasis on STEM in schools, this research is timely. This thesis makes an original and substantive contribution to the understanding of why and how teachers can most effectively advance student proficiency in reasoning through targeted instructional strategies and style of instruction. The study explores the ways in which teacher practices, when focused on reasoning, enhance the disposition of students towards greater mathematical proficiency.

Ecological perspectives and wellness

Since the industrial revolution, the development of a lifestyle lived predominantly indoors has resulted in less contact with nature. Research over the last twenty years has gradually been identifying the human health benefits attributed to re-connecting with the natural environment. The significance of feeling connected to natural environments, families and friends are described as a foundational requirement for human health and wellbeing (Maller et al., 2008). Also, the early findings of Schultz‟s (2002) work indicated that by feeling connected to the natural world a person is more likely to be committed to positively interact with and protect the natural world. Research on young people has indicated that young people are even more disconnected from the natural world. Leading some writers to call this disconnection a crisis termed “Nature Deficit Disorder.” Participants (n = 131) from 1st year university Physical Education and Human Movement Studies were asked to complete two questionnaires the Connectedness to Nature scale (CNS) (Mayer & Frantz, 2004) and the New Ecological Paradigm Scale (NEP) (Dunlap, Van Liere, Mertig, & Jones, 2000). The NEP and CNS are two scales most commonly used to explore beliefs and feelings of connectedness to the natural world (Schultz, 2002). The NEP was developed over thirty years ago by Dunlap and Van Liere (1978) and originally termed the New Environmental Paradigm. The NEP is now the foremost International tool for measuring beliefs about the natural world (Dunlap, 2008). The CNS measures an individual‟s trait levels of emotional connection to the natural world. It is a relatively new tool for understanding ecological behaviour based on ecopsychology theory and employed to predict behaviour (Mayer and Frantz, 2004). Both questionnaires are based on a 1-5 scale (Strongly disagree to Strongly agree). By combing both scales the researchers aim to develop a snap shot of beliefs and emotional feelings towards the natural world and therefore an idea of intended behaviour. The two questionnaires were combined as one online survey with additional material asking for demographics and self assessments of type of leader included before the surveys. An email inviting outdoor leaders to participate was sent out to networks and interest groups. A basic descriptive statistical analysis was used to interpret data.

Social identification dimensions as mediators of the effect of prototypicality on intergroup behaviours

Cameron (2004) proposed a three-dimensional model and measure of social identification consisting of cognitive centrality, in-group affect, and in-group ties. This approach has received growing theoretical and empirical support; however, little research has examined how these dimensions of social identification may relate differentially to intergroup outcome behaviors. The current research sought to address this question by examining the possible mediating role the dimensions of social identification on the relationship between prototypicality of group members and the intergroup outcome behaviors of in-group favoritism, out-group derogation, and collective self-esteem. The current study examined university students’ (N = 235) feelings towards students from their own and another local university. Structural equation modeling was used to identify the most appropriate and parsimonious models of these pathways. The results showed support for the utility of measuring social identification using a multidimensional approach with unique meditational pathways emerging for the distinct intergroup behaviors.

Towards a classification of criterion referenced assessment models in mathematics courses : student and academic perspectives

We present the findings of a study into the implementation of explicitly criterion- referenced assessment in undergraduate courses in mathematics. We discuss students' concepts of criterion referencing and also the various interpretations that this concept has among mathematics educators. Our primary goal was to move towards a classification of criterion referencing models in quantitative courses. A secondary goal was to investigate whether explicitly presenting assessment criteria to students was useful to them and guided them in responding to assessment tasks. The data and feedback from students indicates that while students found the criteria easy to understand and useful in informing them as to how they would be graded, it did not alter the way the actually approached the assessment activity.

Getting skilled for education, training and employment : Indigenous Cultural Knowledges and mainstream knowledges of mathematics

This abstract is a preliminary discussion of the importance of blending of Indigenous cultural knowledges with mainstream knowledges of mathematics for supporting Indigenous young people. This import is emphasised in the documents Preparing the Ground for Partnership (Priest, 2005), The Indigenous Education Strategic Directions 2008–2011 (Department of Education, Training and the Arts, 2007) and the National Goals for Indigenous Education (Department of Education, Employment and Work Relations, 2008). These documents highlight the contextualising of literacy and numeracy to students’ community and culture (see Priest, 2005). Here, Community describes “a culture that is oriented primarily towards the needs of the group. Martin Nakata (2007) describes contextualising to culture as about that which already exists, that is, Torres Strait Islander community, cultural context and home languages (Nakata, 2007, p. 2). Continuing, Ezeife (2002) cites Hollins (1996) in stating that Indigenous people belong to “high-context culture groups” (p. 185). That is, “high-context cultures are characterized by a holistic (top-down) approach to information processing in which meaning is “extracted” from the environment and the situation. Low-context cultures use a linear, sequential building block (bottom-up) approach to information processing in which meaning is constructed” (p.185). In this regard, students who use holistic thought processing are more likely to be disadvantaged in mainstream mathematics classrooms. This is because Westernised mathematics is presented as broken into parts with limited connections made between concepts and with the students’ culture. It potentially conflicts with how they learn. If this is to change the curriculum needs to be made more culture-sensitive and community orientated so that students know and understand what they are learning and for what purposes.

Attitudes and interests towards biotechnology: The mismatch between students and teachers

Increasing the scientific literacy of Australians has become an educational priority in recent times. The ‘Science State – Smart State’ initiative of the Queensland Government involves an action plan for improving science education that includes a Science for Life action. A desired outcome is for an increased understanding of the natural world so that responsible decisions concerning our future wellbeing can be made in an age of science and technology. Biotechnology is a technology that is having profound impact on our lives. This paper describes how 15-16 year old students and biology teachers revealed a mismatch in both attitudes and interests towards biotechnology between the students and teachers. The findings are of interest as the teachers are writing biotechnology into their work programs in response to new syllabus documents. The teacher’s areas of interest did not match those of the students, possibly resulting in a curriculum the teachers want to teach, but the students do not want to learn.

Towards a model for the analysis and description of mathematical knowledge and understanding

Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the strengths of each learning theory and so positively impact upon contemporary educational practice. This research activity is based upon Popper’s notion of three knowledge worlds which differentiates the knowledge shared in a community from the personal knowledge of the individual, and Bereiter’s characterisation of understanding as the individual’s relationship to tool-like knowledge. Using these notions, a re-conceptualisation of knowledge and understanding and a subsequent re-consideration of learning theories are proposed as a way to address the challenge set by literature. Referred to as the alternative theoretical framework, the proposed theory accounts for the scaffolded transformation of each individual’s unique understanding, whilst acknowledging the existence of a body of domain knowledge shared amongst participants in a scientific community of practice. The alternative theoretical framework is embodied within an operational model that is accompanied by a visual nomenclature with which to describe consensually developed shared knowledge and personal understanding. This research activity has sought to iteratively evaluate this proposed theory through the practical application of the operational model and visual nomenclature to the domain of early-number counting, addition and subtraction. This domain of mathematical knowledge has been comprehensively analysed and described. Through this process, the viability of the proposed theory as a tool with which to discuss and thus improve the knowledge and understanding with the domain of mathematics has been validated. Putting of the proposed theory into practice has lead to the theory’s refinement and the subsequent achievement of a solid theoretical base for the future development of educational tools to support teaching and learning practice, including computer-mediated learning environments. Such future activity, using the proposed theory, will advance contemporary mathematics educational practice by bringing together the strengths of cognitivist, constructivist and post-constructivist learning theories.

Towards improving public understanding of judgement practice in standards-referenced assessment : an Australian perspective

Internationally there has been a move towards standards-referenced assessment with countries such as Australia developing a National Curriculum and Achievement Standards, New Zealand adopting National Standards for literacy and numeracy that involve schools making and reporting judgements about the reading, writing and mathematics achievement of children up to Year 8 (the end of primary school) and in Canada, classroom assessment standards aimed at the improvement of assessment practice of K-12 education are being formulated. Standards-driven reform has major implications for teachers’ work. The consequences of adopting a standards-driven approach to educational change by systems are often under-estimated with the unintended effects not fully understood by either the policy writers, and the public, including parents. It is for these reasons that the contention developed in this article relates to the teacher’s role, which it is argued remains central to policy focused on the improvement of the quality of education and educational standards.

Towards a single crystal Raman spectrum of kaolinite at 77 K

The Raman spectra at 77 K of the hydroxyl stretching of kaolinite were obtained along the three axes perpendicular to the crystal faces. Raman bands were observed at 3616, 3658 and 3677 cm−1 together with a distinct band observed at 3691 cm−1 and a broad profile between 3695 and 3715 cm−1. The band at 3616 cm−1 is assigned to the inner hydroxyl. The bands at 3658 and 3677 cm−1 are attributed to the out-of-phase vibrations of the inner surface hydroxyls. The Raman spectra of the in-phase vibrations of the inner-surface hydroxyl-stretching region are described in terms of transverse and longitudinal optic splitting. The band at 3691 cm−1 is assigned to the transverse optic and the broad profile to the longitudinal optic mode. This splitting remained even at liquid nitrogen temperature. The transverse optic vibration may be curve resolved into two or three bands, which are attributed to different types of hydroxyl groups in the kaolinite.