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.

Effects of using manipulative materials to teach remedial algebra to community college students on achievement and attitudes towards mathematics

This dissertation derived hypotheses from the theories of Piaget, Bruner and Dienes regarding the effects of using Algebra Tiles and other manipulative materials to teach remedial algebra to community college students. The dependent variables measured were achievement and attitude towards mathematics. The Piagetian cognitive level of the students in the study was measured and used as a concomitant factor in the study.^ The population for the study was comprised of remedial algebra students at a large urban community college. The sample for the study consisted of 253 students enrolled in 10 sections of remedial algebra at three of the six campuses of the college. Pretests included administration of an achievement pre-measure, Aiken's Mathematics Attitude Inventory (MAI), and the Group Assessment of Logical Thinking (GALT). Posttest measures included a course final exam and a second administration of the MAI.^ The results of the GALT test revealed that 161 students (63.6%) were concrete operational, 65 (25.7%) were transitional, and 27 (10.7%) were formal operational. For the purpose of analyzing the data, the transitional and formal operational students were grouped together.^ Univariate factorial analyses of covariance ($\alpha$ =.05) were performed on the posttest of achievement (covariate = achievement pretest) and the MAI posttest (covariate = MAI pretest). The factors used in the analysis were method of teaching (manipulative vs. traditional) and cognitive level (concrete operational vs. transitional/formal operational).^ The analyses for achievement revealed a significant difference in favor of the manipulatives groups in the computations by campus. Significant differences were not noted in the analysis by individual instructors.^ The results for attitude towards mathematics showed a significant difference in favor of the manipulatives groups for the college-wide analysis and for one campus. The analysis by individual instructor was not significant. In addition, the college-wide analysis was significant in favor of the transitional/formal operational stage of cognitive development. However, support for this conclusion was not obtained in the analyses by campus or individual instructor. ^

Diagnosis of Student’s Attitudes towards Mathematics in the First Year of Three Graduate Programs in Business Administration

The objective of this research was to determine the student’s attitudes towards Mathematics at the beginning of their graduate studies in Business Administration. The study used an exploratory, non-experimental, cross-sectional design. The instrument used was a questionnaire based on willingness, confidence, utility, motivation and anxiety with Likert questions. The study concluded that students have a negative attitude towards Mathematics; it is considered as a useful but difficult discipline and, for that reason, students show anxiety and lack of confidence when applying mathematical procedures.

Mathematical Communication, Conceptual Understanding, and Students' Attitudes Toward Mathematics

This action research study of my 8th grade classroom investigated the use of mathematical communication, through oral homework presentations and written journals entries, and its impact on conceptual understanding of mathematics. This change in expectation and its impact on students’ attitudes towards mathematics was also investigated. Challenging my students to communicate mathematics both orally and in writing deepened the students’ understanding of the mathematics. Levels of understanding deepened when a variety of instructional methods were presented and discussed where students could comprehend the ideas that best suited their learning styles. Increased understanding occurred through probing questions causing students to reflect on their learning and reevaluate their reasoning. This transpired when students were expected to write more than one draft to math journals. By making students aware of their understanding through communicating orally and in writing, students realized that true understanding did not come from mere homework completion, but from evaluating and assessing their own and other’s ideas and reasoning. I discovered that when students were challenged to communicate their reasoning both orally and in writing, students enjoyed math more and thought math was more fun. As a result of this research, I will continue to require students to communicate their thinking and reasoning both orally and in writing.

The effect of calculators on the numerical problem-solving skills and attitudes of primary students towards mathematics /

The purpose of this study was to determine the effect that calculators have on the attitudes and numerical problem-solving skills of primary students. The sample used for this research was one of convenience. The sample consisted of two grade 3 classes within the York Region District School Board. The students in the experimental group used calculators for this problem-solving unit. The students in the control group completed the same numerical problem-solving unit without the use of calculators. The pretest-posttest control group design was used for this study. All students involved in this study completed a computational pretest and an attitude pretest. At the end of the study, the students completed a computational posttest. Five students from the experimental group and five students from the control group received their posttests in the form of a taped interview. At the end of the unit, all students completed the attitude scale that they had received before the numerical problem-solving unit once again. Data for qualitative analysis included anecdotal observations, journal entries, and transcribed interviews. The constant comparative method was used to analyze the qualitative data. A t test was also performed on the data to determine whether there were changes in test and attitude scores between the control and experimental group. Overall, the findings of this study support the hypothesis that calculators improve the attitudes of primary students toward mathematics. Also, there is some evidence to suggest that calculators improve the computational skills of grade 3 students.

Students' conflicting attitudes towards games as a vehicle for learning mathematics : a methodological dilemma

Mathematics games are widely employed in school classrooms for such reasons as a reward for early finishers or to enhance students' attitude towards mathematics. During a four week period, a total of 222 Grade 5 and 6 (9 to 12 years old) children from Melbourne, Australia, were taught multiplication and division of decimal numbers using calculator games or rich mathematical activities. Likert scale surveys of the children's attitudes towards games as a vehicle for learning mathematics revealed unexpectedly high proportions of negative attitudes at the conclusion of the research. In contrast, student interview data revealed positive associations between games and mathematical learning. This article reports on the methodological dilemma of resultant conflicting attitudinal data related to game- playing. Concerns arising from the divergence in the results are raised in this article. Implications based on the experience of this study may inform educational researchers about future methodological choices involving attitudinal research.

Effects of cooperative and individual integrated learning system on attitudes and achievement in mathematics

This study compares the effects of cooperative delivery (CD) and individual delivery (ID) of integrated learning system (ILS) instruction in mathematics on achievement, attitudes and behaviors in adult (16-21 yrs.) high school students (grades 9-13). The study was conducted in an urban adult high school in Miami-Dade County Public Schools using a pre-test/post-test design. Achievement was measured using the Test of Adult Basic Education (TABE) by CTB MC-Graw-Hill and Compass Learning. An attitudinal survey measured attitudes towards mathematics, the computer-related lessons, and attitudes toward group activities. Behavior was assessed using computer lab observations. ^ Two-way analyses of variance (ANOVA) were conducted on achievement (TABE and Compass) by group and time (pre and post). A one-way ANOVA was conducted on the overall attitude by group on the five components (i.e., content mathematics, delivery/computers, cooperative, partners, and self efficacy) and a one-way ANOVA was conducted on the on-task behavior by group. ^ The results of the study revealed that CD and ID students working on mathematics activities delivered by the ILS performed similarly on achievement tests of the TABE. The CD-ILS students had significantly better overall mathematics attitudes than the ID-ILS students and the ID-ILS group was on-task significantly more than the CD-ILS group. This study concludes that regularity and period of time over which the ILS is used may prove to be important variables although there were insufficient data to fully investigate the impact of models of use. Additionally, a minimum amount of time-on-system is necessary before gains can become apparent in innumeracy and increasing exposure to the system may have beneficial effects on learning. ^

Attitudes towards American brands and brand America

A study of 556 students at colleges and universities in Australia, Hong Kong and Singapore explored the relationship between attitude towards the United States and brand attitudes and preferences. Singaporean student attitudes towards both the US Government and US people were higher than were those of the Australian and Hong Kong students. Coke, Nike and McDonald's were among both the most-liked and disliked US brands among the international students, a finding suggesting that brands may possess both a 'lovemark' status, as described in the literature, and its opposite — 'loathemark' status — within the same demographic group. US brand preference scores did not offer support for the belief that international consumers 'vote with their pocketbooks' by refusing to purchase US brands if they have a negative attitude towards the United States. Among Hong Kong and Singaporean students, favourable attitudes towards the purchase of US brands was found to be positively related to favourability towards the US Government.

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.

A study of the attitudes towards unethical selling amongst Chinese salespeople

The latter part of the twentieth century saw the Chinese economy moving towards a socialist market economy rather than a planned system. Despite growing interest in Chinese business ethics, little work has examined ethical issues concerning the Chinese sales force. This study draws from existing work on Chinese and Western business and sales ethics to develop hypotheses regarding the perceptions of unethical selling behaviour of modern Chinese salespeople. A survey of Chinese sales executives is conducted and statistically analysed. Results are compared with those reported in previous US-based research with regard to differences in perceptions of unethical selling behaviour. The results indicate that contemporary Chinese salespeople were more favourably disposed than expected towards unethical selling behaviour, and also more favourably disposed than previously studied US salespeople. Younger Chinese salespeople evaluated unethical behaviours more favourably than older ones. The results are discussed, along with implications for theory, practice and future work.

Elderly people's use of and attitudes towards assistive devices

People in developed countries are living longer with the help of medical advances. Literature has shown that older people prefer to stay independent and live at home for as long as possible. Therefore, it is important to find out how to best accommodate and assist them in maintaining quality of life and independence as well as easing human resources. Researchers have claimed that assistive devices assist in older people’s independence, however, only a small number of studies regarding the efficiency of assistive devices have been undertaken of which several have stated that devices are not being used. The overall aim of this research was to identify whether the disuse and ineffectiveness of assistive devices are related to change in abilities or related to the design of the devices. The objective was to gather information from the elderly; to identify what assistive devices are being used or not used and to gain an understanding on their attitudes towards assistive devices. Research was conducted in two phases. The initial phase of the research was conducted with the distribution of questionnaires to people over the age of fifty that asked general questions and specific questions on type of devices being used. Phase One was followed on by Phase Two, where participants from Phase One who had come in contact with assistive devices were invited to participate in a semi-structured interview. Questions were put forth to the interviewee on their use of and attitudes towards assistive devices. Findings indicated that the reasons for the disuse in assistive devices were mostly design related; bulkiness, reliability, performance of the device, difficulty of use. The other main reason for disuse was socially related; elderly people preferred to undertake activities on their own and only use a device as a precaution or when absolutely necessary. They would prefer not having to rely on the devices. Living situation and difference in gender did not affect the preference for the use of assistive devices over personal assistance. The majority strongly supported the idea of remaining independent for as long as possible. In conclusion, this study proposes that through these findings, product designers will have a better understanding of the requirements of an elderly user. This will enable the designers to produce assistive devices that are more practical, personalised, reliable, easy to use and tie in with the older people’s environments. Additional research with different variables is recommended to further justify these findings.

Teachers' attitudes towards the gifted : the importance of professional development and school culture

Given that teachers have one of the most significant influences on the educational development of gifted students, reports of negative attitudes and beliefs in popular myths about giftedness are cause for concern. It is important to understand teachers’ attitudes and beliefs to implement effective training and educational practices to improve education for gifted students. This study explored the attitudes of Australian primary school teachers (N = 126) towards intellectually gifted children and their education at eight schools. These schools could be categorised into four different classifications in regards to their involvement in gifted education. Key findings include significant associations between teachers’ attitudes and their school classifications (p < .001), and their participation in gifted and talented education inservice training (p < .001). Findings from this study suggest that further teacher training and school-wide involvement in gifted education may assist in improving attitudes towards intellectually gifted children and their education.

Attitudes towards inclusion : gaps between belief and practice

General education teachers in the Republic of Korea were investigated regarding their participation in programs to include students with disabilities in general education settings. Previous studies have shown that even general education teachers with positive attitudes towards inclusion are reluctant in practice to have students with disabilities in their classrooms. This study examines 33 Korean general education teachers from three primary schools in Seoul regarding their attitudes towards, and willingness to accommodate, the needs of a student with a disability. The results show that 41.37% of general education teachers had positive attitudes towards inclusion programs, while 55.16% were unwilling to actually participate. Quantitative data obtained through a questionnaire was supplemented by qualitative data obtained through interviews. The interviews focused on the positive and negative effects of inclusion, as well as problems in implementing inclusive education programs. The findings will be discussed in the light of previous international research and will highlight links between the age and teaching experience of general education teachers and their negative attitudes towards inclusion.