Multiple Factor Analysis

The knowledge explosion in combination with an overcrowded curriculum at all educational levels is causing many educators to place greater emphasis on attitude conceptualization. This paper confronts two interrelated problems, that problem dealing with the psychological concept of attitudes and the problem of attitude measurement. Conceptually, attitudes are explored from an affective, cognitive, behavioral, and biologic dimension. The result is a comprehensive attitude concept. The problem of attitude measurement is not that attitudes exist, nor that they are specific or general, but lies in the way that they are organized. With the current emphasis on computerized research and data analysis, it is astonishing that multiple factor analysis has been so infrequently used for attitude validation and instrumentation. As a measurement and analytic technique, multiple factor analysis provides the intrinsic power to isolate and identify attitudinal factors. Multiple factor analysis is a measurement technique designed to assess construct validity. As such, it unites psychometrics with psychological theory. Factor analysis as a computational technique and as a scale construction technique is explored. The principal component method of factor analysis is reviewed. Multiple factor analysis assists in the process of attitude scale construction in the following ways: 1.) determines the content (factorial) validity of a series of attitude statements by ascertaining whether they measure a single unitary characteristic or a complex of characteristics as reflected in an item intercorrelation matrix; 2.) contributes to the determination of construct validity by ascertaining the smallest number of factors that can be postulated to account for item intercorrelations 3.) provides the statistical research strategy upon which predictive and assessment instruments can be empirically determined from an unrotated factor matrix; and, 4.) serves in general as an objective basic research tool through which psychological traits underlying human attitudes can be derived.     

Disentangling the Nexus: Attitudes to Mathematics and Technology in a Computer Learning Environment

Gaining insights into students' attitudes and beliefs is a crucial step in understanding how the learning environment for mathematics is affected by the introduction of computers and other technology. We review research into the impact of technology on the teaching and learning of mathematics, although systematic evaluations are sparse. We discuss the relationship between affective variables and performance and having constructed appropriate measures of attitude, we present results from an extensive initial study. The study disentangles affects relating to mathematics and to computing and in doing so identifies attributes which are important where mathematics and computing interact. We report on the application of six Galbraith–Haines scales to 156 students, we discuss the implications of confidence, motivation, engagement and interaction with the technology in the learning environment and we demonstrate that the computing and mathematics attitude scales capture distinctive properties of student behaviour in this respect.     

Linking early science and mathematics attitudes to long-term science,technology, engineering,and mathematics career attainment: latent class analysis with proximal and distal outcomes

There is a need to identify students' early attitudes toward mathematics and science to better support their long-term persistence in science, technology, engineering, and mathematics (STEM) careers. Seventh graders from a nationally representative sample (N = 2,861) were classified based on their responses to questions about their attitudes toward mathematics and science using latent class analysis. Four distinct groups of students that differed in terms of their attitudes were identified. There were relationships between attitudinal group membership, demographic characteristics, mathematics and science achievement, and STEM career attainment. Females and underrepresented minorities were more likely to be in the positive attitude group. However, despite these early positive attitudes, females and underrepresented minorities were less likely to be employed in a STEM career some 20 years later. Information about student interests organized in this manner can be used to better target specific interventions to support and encourage persistence in STEM careers.     

What do I think about inclusive education? It depends on who is asking. Experimental evidence for a social desirability bias in attitudes towards inclusion

Recently, research has focused on attitudes towards inclusive education, and the majority of studies use questionnaires to measure this vital variable. In two consecutive experiments, we showed that attitudes towards inclusive education are not stable but instead are significantly influenced by social context. We manipulated information on the organisation conducting a survey regarding attitudes of participants towards inclusive education. The results show that the attitude of the organisation conducting the survey – as perceived by the participant – outperforms well-documented variables (e.g. sex, age, and contact to a person with disability) in predicting the attitudes of the participant towards inclusion. This one variable explains as much variance as all other predictors combined. We argue that social desirability is a neglected issue in research on attitudes towards inclusive education. Our findings challenge the validity of numerous studies on this topic because they show a positive bias in the attitudes of participants when they were surveyed by a university. Thus, we outline the first steps to reduce social desirability-induced validity problems in research on attitudes towards inclusion.     

大学英语翻转课堂中学习者接受度的路径研究

本研究从理性行为和外语焦虑角度探索大学英语学习者对翻转学习的接受度的影响因素｡ 研究共提取输出态度､输入反感度､自主学习态度､课堂态度､效果预期及整体接受度六个因子｡路径分析显示效果预期､输入排斥度､课堂态度直接决定接受度;其他因子有间接影响｡回归分析发现整体接受度仍然是预测成绩的主要因素;而自主学习态度对口语成绩有较明显的预示力｡研究提示教师应该从内外机制加强整体接受度和自主性｡     

态度的结构及其教学启示

态度结构是指认知成分、情感成分和行为成分相互作用而构成的稳定结构。通过深入分析态度结构,归纳出态度的四大特性——稳定性、持久性、综合性和去情境性,总结出‘‘认知、情感、行为三成分齐头并进”、“关注学生原有的相关态度”、“重视儿童阶段的态度教学’、“注重实践和反馈”等原则,并在此基础上提炼出态度教学的具体策略。     

Research for a Movement

Reflecting from the Philippine experience, this article explores an emerging picture that characterizes contemporary Bible reading attitudes of college students. Six new attitude factor definitions are developed following the development of the Bible Reading (BR) attitude scale for college students constructed by this author in a separate study. Through empirical procedures, the pre-tested scale produced six new attitude factor definitions that displaced the nine original pre-test attitude sub-factors. Their Bible reading attitudes are described in terms of motivation, reading preference, and acquaintance. This research provides practitioners with useful attitudinal dimensions for youth formation particularly in biblical formation and religious education.     

The development and validation of the Attitudinal Learning Inventory (ALI): a measure of attitudinal learning and instruction

In this paper, we present the development and validation of a new measure of attitudinal learning—the Attitudinal Learning Inventory (ALI). While specific scales are available for measuring attitudes, they largely focus on established attitudes, not the impact of instruction on those attitudes. We developed the inventory with two explicit objectives: (1) to measure a broad range of attitude constructs representing a holistic view of attitudinal learning and instruction; and (2) to facilitate the measurement of attitudinal learning that can be useful for educational researchers beyond traditional metrics. The ALI was developed and validated across two samples of a total of 1009 participants with diverse demographics. The ALI comprises 15 scale items and exhibited good psychometric properties and conformed to the theoretical four-dimensional structure of attitudinal learning: cognitive, affective, behavioral, and social. The ALI was also shown to correlate with behavioral metrics of class engagement. Future uses of the new measure are discussed. Participants were taken from entirely online populations, and while demographically diverse, implementation of the scale with face-to-face instruction, in varied settings, and across different groups of learners is needed to provide additional evidence of its intended generalizability and consider possible biases.     

‘Come in with an open mind’: changing attitudes towards mathematics in primary teacher education

Background: The relationship between attitudes and behaviour has led to a focus on the role played by attitudes in the teaching and learning of mathematics.

Purpose: This paper reports on an investigation into student teachers’ self-reported attitudes towards mathematics in the context of a mathematics education programme. The programme had been developed by the authors in response to a new, reformed four-year undergraduate initial teacher education (ITE) for primary teachers in Ireland. The authors aimed to use the feedback to evaluate and develop the course further.

Sample: We report on the attitudes of 345 pre-service primary teachers enrolled in a four-year undergraduate ITE programme. 281 of these participants had matched survey data before and after participating in the mathematics education programme.

Method and Design: Four evaluation criteria were used as a conceptual framework for the evaluation of the mathematics education programme. A multi-method approach was taken in investigating the students’ attitudes to mathematics by using a scale as a quantitative measure of attitude alongside open-ended survey items that provided qualitative insights into changes in attitudes.

Results and conclusions: Results from the survey data suggested overall that the participants’ attitudes towards mathematics were more positive after they had experienced the mathematics education programme. Overall, the written responses suggested that according to self-reportage, participants perceived that participation in the mathematics education programme had affected their attitudes towards mathematics positively. Comments indicated that the ‘small group’ tutorial structure was particularly well received and was associated with opportunities to actively engage, explore, interact and reflect. Suggestions offered by the participants will be used to inform planning and development of the mathematics programme.     

A comparison of performance and attitudes in mathematics amongst the ‘gifted’. Are boys better at mathematics or do they just think they are?

This paper explores gender differential performance in ‘gifted and talented’ 9‐ and 13‐year‐olds in a mathematics assessment in England. Boys’ and girls’ attitudes to mathematics and their views about which gender is better at mathematics are also considered. The study employs the use of a matched sample of boys and girls so that school, age and previous achievement in mathematics can be controlled whilst exploring performance on World Class Test items. The main result of this research was that there was no significant gender difference in performance for the 9‐ or the 13‐year‐olds. However, attitudinal differences were found, including a seemingly commonly held stereotypical view of mathematics as a boys’ subject. These results are important since the uptake of higher level mathematically‐based courses by girls is poor. Further findings reveal that where ‘gifted’ girls perform as well as ‘gifted’ boys, their confidence in the subject is lower than their performance might suggest. This work is also discussed in the light of related research findings and in relation to stereotype threat theory.     

Changing Attitudes to University Mathematics Through Problem Solving

University mathematics is often presented in a formal way that causes many students to cope by memorising what they perceive as a fixed body of knowledge rather than learning to think for themselves. This research studies the effects on students' attitudes of a course encouraging co-operative problem-solving and reflection on the thinking activities involved. The attitudinal questionnaire was shown to the students' teachers who were asked to specify the attitudes they expect from their students and the attitudes they prefer. This was used to give a ‘desired direction of change’ from expected to preferred. Before the course, half the students responded that university mathematics did not make sense. A majority declared negative attitudes such as anxiety, fear of new problems and lack of confidence. During the problem-solving course the changes were almost all in the desired direction. During the following six months of standard mathematics lecturing, almost all changes were in the opposite direction. This revised version was published online in July 2006 with corrections to the Cover Date.     

ATTITUDES OF OLDER ADULTS TOWARD A COMPUTER TRAINING PROGRAM

Many older adult have an interest in learning to use computers. The study reported in this article examined whether older adults' attitudes toward computers can be influenced by direct, customized computer training. Thirty older participants who registered for introductory computer courses offered at a SeniorNet computer lab completed the Attitudes Toward Computers Questionnaire (ATCQ) before and after class participation. Attitudes were assessed on seven dimensions. There was borderline statistical significance for the “comfort” attitude dimension, which assesses the respondent's feeling of comfort with the computer and its use. No significant differences were found for the remaining six attitude dimensions. The results underscore the importance of the intervention design in eliciting attitude change. Based upon the findings of this research, several actions have taken place to increase comfort and efficacy and to control attitudinal dimensions, thereby providing more meaningful experiences for the participants.     

Attitudes of high-school students taught using traditional and reform mathematics curricula in middle school: a retrospective analysis

This paper presents findings from a larger research project that provides insight into the attitudes of high-school students who were taught using different types of mathematics curricula when they were in middle school. A total of 44 12th-grade students from 10 high schools in the same urban school district were interviewed. Eighteen (41%) of them had been taught using a reform curriculum in middle school and 26 (59%) had been taught using a more traditional curriculum. Using Di Martino and Zan’s three-dimensional model for attitude, we found that the high-school seniors who had been taught using the reform curriculum in middle school harbored attitudes toward mathematics that differed significantly from the attitudes of those who had been taught using a traditional curriculum in middle school. Our analysis of the student interviews culled seven themes that provide fine-grained information about the students’ attitudes toward mathematics. Significantly greater percentages of reform students than traditional students had a relational Vision of mathematics as opposed to an instrumental Vision; however, there was no significant difference between the proportions of reform and traditional students who had a positive Emotional Disposition toward mathematics or a positive Perceived Competence in mathematics.     

‘Me and maths’: towards a definition of attitude grounded on students’ narratives

The attitude construct is widely used by teachers and researchers in mathematics education. Often, however, teachers’ diagnosis of ‘negative attitude’ is a causal attribution of students’ failure, perceived as global and uncontrollable, rather than an accurate interpretation of students’ behaviour, capable of steering future action. In order to make this diagnosis useful for dealing with students’ difficulties in mathematics, it is necessary to clarify the construct attitude from a theoretical viewpoint, while keeping in touch with the practice that motivates its use. With this aim, we investigated how students tell their own relationship with mathematics, proposing the essay “Me and maths” to more than 1,600 students (1st to 13th grade). A multidimensional characterisation of a student’s attitude towards mathematics emerges from this study. This characterisation and the study of the evolution of attitude have many important consequences for teachers’ practice and education. For example, the study shows how the relationship with mathematics is rarely told as stable, even by older students: this result suggests that it is never too late to change students’ attitude towards mathematics.     

Attitudinal and motivational variables related to mathematics achievement in Jordan: findings from the Third International Mathematics and Science Study (TIMSS)

The purpose of the present study was to examine the effects of student-related variables on achievement in mathematics. The sample consisted of 3736 13-year-old Jordanian 8th-graders who participated in the Third International Mathematics and Science Study (TIMSS). The participants completed a student questionnaire and participated in the mathematics test. Of the matrix of affective variables reported to lead to the variation in mathematics achievement were educational aspiration, attitude, success attribution, confidence in ability and perception of importance of mathematics. A structural equation model was used to estimate and test the hypothesized relationships of the factors with achievement in mathematics. Results from this study indicate that four attitudinal and motivational variables had strong positive total and direct effects; and two variables had negative total and direct effects on mathematics achievement. Recommendations for future research were suggested.     

Clarifying an Elusive Construct: a Systematic Review of Writing Attitudes

Although research recognizes that student attitudes toward writing have the potential to influence a variety of writing outcomes, there is no consensus as to what writing attitude signifies. Further, disparities between conceptualizations of writing attitude make the extant literature difficult to reconcile. In the present study, we systematically review writing attitude research published between 1990 and 2017. Our search procedure and quality analysis led to the retention of 46 articles examining the writing attitudes of students and teachers. Relatively few studies (n = 10) provided an explicit definition of writing attitudes. Further, although the authors of many studies (n = 16) conceptualized writing attitude as including a measure of liking/disliking writing, there was considerable variability in both conceptualization and operationalization throughout the literature, with some studies including measures of self-efficacy, perceived value, and other related constructs. Student writing attitudes were measured in a majority of the included studies (n = 33), and teacher writing attitudes were measured in substantially fewer studies (n = 6). Based on the findings of this review, we offer suggestions for researchers making inferences from studies of writing attitudes. Themes of the reviewed literature and implications for future research are also discussed.     

Relationship between perceived levels of classroom individualization and science-related attitudes

Relationships between perceived levels of classroom individualization and science-related attitudes were explored for a sample of 712 junior high school science students. Five dimensions of perceived individualization (personalization, participation, independence, investigation, and differentiation) were measured with the Individualized Classroom Environment Questionnaire (ICEQ), while seven distinct attitudes were measured with the Test of Science-Related Attitudes (TOSRA). Hierarchical regression analyses revealed that the set of individualization variables accounted for a significant increment in end-of-year attitude scores, beyond that attributable to corresponding beginning-of-year attitude scores, for four of the seven attitudes considered. Significant associations between an individual individualization variable and an attitudinal dimension were positive in all cases. The study also provided support for the reliability and validity of the ICEQ and TOSRA and for their general usefulness in science education research.     

The effect of a brief teacher training on student achievement

On the basis of previously determined correlations between teacher behavior and student achievement, a training program for mathematics teachers was developed. Previous research had established that this training did change the behavior of teachers. This article reports the effects of the training program on teacher behavior, student achievement, and student attitudes towards mathematics. From this study it appeared that the timing of the training was important for its effect on student achievement. There was no effect on student attitude.     

Research mathematicians as teacher educators: focusing on mathematics for secondary mathematics teachers

We believe that professional mathematicians who teach undergraduate mathematics courses to prospective teachers play an important role in the education of secondary school mathematics teachers. Thus, we explored the views of research mathematicians on the mathematics that should be taught to prospective mathematics teachers, on how the courses they teach can serve teachers in their work with school students, and on the changes they would implement if their courses were designed specifically for prospective teachers. We constructed profiles of the four mathematicians based on their responses to a clinical interview. We employed the construct of mathematics teacher-educators’ triad in the reflective analysis of our findings and extended the construct based on the results of this study. In conclusion, we commented on potential ways to draw stronger connections between university mathematics and the mathematics taught in schools.