Learning Environ Res (2013) 16:297–313 DOI 10.1007/s10984-013-9134-x ORIGINAL PAPER
Relationships between learning environment and mathematics anxiety Bret A. Taylor • Barry J. Fraser
Received: 3 May 2011 / Accepted: 23 August 2011 / Published online: 17 April 2013 Ó Springer Science+Business Media Dordrecht 2013
Abstract We investigated relationships between the learning environment and students’ mathematics anxiety, as well as differences between the sexes in perceptions of learning environment and anxiety. A sample of 745 high-school students in 34 different mathematics classrooms in four high schools in Southern California was used to cross-validate the What Is Happening In this Class? (WIHIC) learning environment instrument, together with an updated Revised Mathematics Anxiety Rating scale. Mathematics anxiety was found to have two factorially-distinct dimensions (namely, learning mathematics anxiety and mathematics evaluation anxiety) which yielded different patterns of results for sex differences and anxiety–environment associations. Relative to males, females perceived a more positive classroom environment and more anxiety about mathematics evaluation, but less anxiety about mathematics learning. Some statistically significant associations were found between anxiety and learning environment scales for learning mathematics anxiety but not for mathematics evaluation anxiety. Keywords Learning environments Mathematics anxiety Questionnaires Sex differences What Is Happening In this Class? (WIHIC)
Introduction When she was in her Algebra 2 class a few years ago, Jennifer was a responsible and dedicated 10th grade student who never created any problems, always did her homework, asked questions, and generally tried her best in class. One day, while the instructor was teaching about the mathematical concept of asymptotes, she asked a question: ‘‘If those two lines never touch each other, are they parallel?’’ It was carefully explained that, B. A. Taylor B. J. Fraser Concordia University, Irvine, CA, USA B. J. Fraser (&) Science and Mathematics Education Centre, Curtin University, GPO Box U1987, Perth, WA 6845, Australia e-mail:
[email protected]
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although they never touched each other, the two objects were still not considered parallel. Obviously, a previous instructor had explained the concept of parallel to her with that notion. That was the last straw for Jennifer. She stood up and yelled: ‘‘I’ve had it with all of you mathematics teachers! You’re all just a bunch of liars!’’ She proceeded to explain that mathematics teachers continually contradict each other because they don’t tell the ‘full story’. What caused this reaction? What had been building up inside her that finally had to be released? If she was willing to say these things, how many other students were feeling them? Questions like these have stuck with mathematics teachers, who wonder about the methods used in the classroom and whether they make a difference. The term ‘mathematics anxiety’ might be dismissed by some, but events like this tell us that we have run into something important and very real. The research reported in this article grew out of working with students like Jennifer. Are there components of the classroom environment that either fuel or reduce mathematics anxiety among high school students? Are there differences between the ways in which males and females feel anxiety regarding mathematics and perceive their learning environment? These questions served as the foundation of the research described here.
Recent research While much recent research has focused on the cognitive components of the mathematics classrooms, relatively less effort has been made to investigate possible associations between the learning environments in mathematics classrooms and affective areas of learning such as anxiety. Consideration of anxiety towards mathematics is considered by some as crucial for the improvement of mathematics education (McLeod 1992). If affective elements of students’ mathematical life are improved, then students’ openness and ability in endeavours involving mathematics are more likely to reach their full potential. This lack of intersection between mathematics education research and learning environments research has been identified by English (2002) in the Handbook of International Research in Mathematics Education. English states that stronger relationships between these two areas of research are important for enabling and encouraging students to reach their full potential in mathematics, as well as permitting insights from research into learning environments in other disciplines to be incorporated into the mathematics classroom. Fraser (1998) defines the learning environment as ‘‘the social, psychological, and pedagogical contexts in which learning occurs and which affect student achievement and attitudes’’ (p. 3). The field of learning environments has its roots in the work of Herbert Walberg and Rudolf Moos and their individual attempts at studying participants’ perceptions of various learning situations (Moos 1974, 1979; Walberg and Anderson 1968). Based on his research into a variety of human environments, Moos (1974) developed a scheme for classifying human environments into relationship, personal development and system maintenance and change dimensions. These dimensions enable various components of an environment to be classified and sorted. Moos later developed the Classroom Environment scale (CES; Moos 1979; Moos and Trickett 1974) which further allowed researchers to study learning environments specifically related to schools. Walberg’s research involving Harvard Project Physics led to the development of the Learning Environment Inventory (LEI) for assessing the perceptions of students involved in the
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program. When brought together with Moos’ work, and Lewin’s earlier work (1936) involving field theory (the environment and its interaction with an individual’s characteristics being determinants of human behavior), the complex study of learning environments began to take shape. Another underlying theme in the study of learning environments came from Murray’s (1938) work on the difference between outside observations and the perceptions of those directly involved within the specific environment being studied. Detached observation by an ‘impartial’ researcher had been the norm for many years in educational research. However, assessing the perceptions of both the students and teachers in a specific learning environment allows the researcher to get a more personal perspective and to find nuances that might be missed by those not directly involved. While the perceptions of those involved within a specific environment can be somewhat biased, external observers also bring their own expectations and personal histories into situations and therefore cannot be totally impartial either. Another distinction in the study of learning environments is the difference between the student’s view of his/her individual situation and of the class as a whole. Murray (1938) referred to the perceptions of the environment by participants as beta press (as opposed to the view of the outside observer which is known as alpha press). Stern, Stein and Bloom (1956) broadened this to distinguish between the views of a specific individual about his/ her environment (private beta press) and about the environment for the group as a whole (consensual beta press). This distinction leads to analysis of data from a variety of viewpoints and levels of statistical analysis, including the class mean or the individual student score. From this foundation, the field of classroom learning environments has grown and spread in its scope and depth, as demonstrated in the large number of research reports, literature reviews and books regarding this field, as well as the international attention that this area has received (Fisher and Khine 2006; Fraser 2007, 2012). The development of Learning Environments Research: An International Journal (Fraser 1998), as well as edited books from Goh and Khine (2002) and Fisher and Khine (2006), have helped to inform the worldwide educational community of the importance of this area of research and led to many questionnaires being developed for research in this field. This program of research has involved the development and validation of some widely-used questionnaires, such as the Questionnaire on Teacher Interaction (QTI, Wubbels and Levy 1993), Science Laboratory Environment Inventory (SLEI, Fraser et al. 1995) and Constructivist Learning Environment Survey (CLES, Taylor et al. 1997). One of the latest tools for investigating classroom learning environments is the What Is Happening In this Class? (WIHIC) survey designed by Fraser et al. (1996). This instrument quickly became popular worldwide for measuring students’ perceived psychosocial learning environments. The WIHIC has been shown to be valid and has been replicated in various countries and languages with large samples of 1,081 Australian and 1,879 Taiwanese students (Aldridge et al. 1999), 567 Australian and 594 Indonesian students (Fraser et al. 2010), 1,434 students in New York (Wolf and Fraser 2008), 924 students in Florida (Helding and Fraser 2013), 2,310 students in Singapore (Chionh and Fraser 2009), 763 students in the United Arab Emirates (MacLeod and Fraser 2010), 543 students in Korea (Kim et al. 2000) and 1,077 students in South Africa (Aldridge et al. 2009). A crucial component of the learning environment is the emotional and affective feelings that students bring into the classroom regarding a specific subject area. While feelings of joy and enjoyment are certainly helpful and welcomed in the classroom, feelings of fear
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and dread seem to be a part of some classrooms where some subjects, especially mathematics, are taught. Research into mathematics anxiety has its foundation in the general study of the psychology of anxiety, especially the work of Spielberger (1972), who describes anxiety as a ‘‘condition characterized by feelings of tension and apprehension’’ (p. 24). This tension is divided into two types of anxiety: state and trait. State anxiety is an emotional condition that varies in intensity and fluctuates over time, while trait anxiety is a feeling that is at the core of an individual who perceives a variety of situations as dangerous or threatening (Gaudry and Spielberger 1971). Mathematics anxiety is a form of state anxiety. Rachman (1998) provides four theories of anxiety to help to define it further. Two of the four theories, psychoanalytic and biological, could account for some of the anxiety perceived in a classroom, but probably neither would be the leading cause of mathematics anxiety. The other two theories, cognitive and learning, seem to be more in line with the common thoughts regarding mathematics anxiety. The fears associated with the learning process that generate avoidance behaviors (learning theory) or the reactions that come from the lack of knowledge regarding an event (cognitive theory) are directly connected to the anxiety associated with mathematics or mathematics classes. Anxiety can be considered as a negative mood that has been linked to poor academic outcomes (Ma 1999). In science education, science anxiety has been detected at the middle-school level (Chiarelott and Czerniak 1985) and in college science laboratory classes (Bowen 1999). Various studies have reported associations between student anxiety and student outcomes (Dane 2005; El-Anzi 2005), classroom environment (Fraser and Fisher 1982; Fraser et al. 1983) or teacher clarity (Rodger et al. 2007). Others have identified factors that impair the development of cognitive abilities from an affective perspective. Ellis et al. (1993) state that worry and emotionality have negative impacts on cognitive ability, with worry being defined as ‘‘intruding thoughts that reflect self-concern, doubt, or other negative affect’’ and emotionality as the ‘‘heightened arousal state of an individual’’ (p. 86). Wigfield and Meece (1988) assessed worry and emotionality among Grade 6–12 students and, later, joined with Eccles in a study which drew on selfefficacy theories to identify predictors of mathematics anxiety (Meece et al. 1990). They found that students’ current performance expectancies have the strongest direct effect on anxiety, but also that perceptions of the importance of mathematics also play a role in student anxiety levels. A recent feeling among some researchers is that the term ‘mathematics anxiety’ has become a catch-all for any negative feeling regarding mathematics and, therefore, it has lost some of its usefulness. While definitions seem to span the spectrum of possibilities (McLeod 1992), Buckley and Ribordy’s (1982) definition clarifies what most people think of when they hear the term mathematics anxiety: ‘‘Mathematics anxiety is an inconceivable dread of mathematics that can interfere with manipulating numbers and solving mathematical problems within a variety of everyday life and academic situations’’ (p. 1). Our study focused on the two dimensions of mathematics anxiety, namely, Learning Mathematics Anxiety and Mathematics Evaluation Anxiety, that are assessed by Plake and Parker’s (1982) Revised Mathematics Anxiety Rating scale (RMARS). Because of this conceptual distinction, it was important methodologically in our study to generate a separate score for each of the two distinct areas of anxiety when relating anxiety to the learning environment dimensions and when exploring sex differences in anxiety. Plake and Parker’s short 24-item RMARS has been used sparingly since its inception, but has yielded results that are just as reliable as with the original 96-item version of MARS (Capraro et al. 2001; Hannafin 1985; Kazelskis 1988; Plake and Parker 1982).
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Lester and Hand (1989) used RMARS to identify anxiety among students in a college-level statistics course, whereas Blum and Staats (1999) used it to investigate mathematics anxiety within a computer classroom setting. These studies, coupled with factor analysis results provided by researchers, suggested that the RMARS was likely to be a valid, reliable and appropriate for use in our study (Kazelskis 1988; Plake and Parker 1982). Many researchers agree that a key element in mathematics anxiety is the teacher in the classroom (Bekdemir 2010; Martinez and Martinez 1996; Tobias 1978; Zaslavsky 1994). Most research has focused on the negative ways in which instructors contribute to their students’ mathematics anxiety (Bekdemir 2010; Furner and Duffy 2002; Jackson and Leffingwell 1999; Oberlin 1982). Ho et al. (2000) claim that, while some tension is important for learning situations, instructors should avoid environments that involve negative situations such as nervousness and dread. The roles of teachers, especially their positive support and equitable treatment of students, are components that were investigated in this research. Likewise, research has shown that mathematics anxiety is experienced differently by the different sexes within a classroom (Campbell and Evans 1997). While Campbell and Evans’ research involved single-sex classrooms and the effect of this learning environment on mathematics anxiety, our research focused on coeducational classrooms involving both males and females within the same mathematics classroom and the roles that the instructor and environment play in influencing student perceptions. Also, research has shown that males and females respond to differing factors in relation to mathematics anxiety (Haynes et al. 2004). Males’ mathematics anxiety was strongly related to general test anxiety, whereas females’ mathematics anxiety levels were related to their perceived mathematics ability and an increase in their standardised achievement test scores.
Sample and methodology Data for our study were collected from 745 high-school students (Grades 9–12) in 34 classes from four schools in the Southern California area. These coeducational high schools, both public and parochial, have the diverse racial and ethnic breakdown shown in Table 1. With the high percentage of students in the sample schools coming from White/ Caucasian or Latino/Hispanic cultures, the sample is typical of many other surrounding high schools in the area. Selected mathematics classrooms across all grade levels from each school were used in the research (30 % in Grade 9, 30 % in Grade 10, 23 % in Grade 11 and 17 % in Grade 12). The sample also was representative of the population in terms of sex (52.3 % males).
Table 1 Demographics of high school students in the study School
Location
Enrolment
Racial/ethnic percentages Hispanic or Latino (%)
AfricanAmerican (%)
AsianAmerican (%)
White (%)
Other (%)
1
Tustin, CA
2,473
32.4
1.9
8.1
55.6
2.0
2
Anaheim, CA
2,087
51.2
2.8
12.4
29.9
3.7
3
Orange, CA
997
5.9
0.8
3.5
87.0
2.8
4
Tustin, CA
2,109
44.4
6.3
13.7
30.5
5.1
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While many more students completed some of the questionnaires used, the sample of 745 students used for the analyses reported in this article consisted only of individuals who provided complete data for all instruments. In order to investigate associations between the perceived learning environment and students’ mathematics anxiety, it was important that items in all instruments were completed by all included in the study. Two instruments were used to assess, respectively, students’ perceptions of the learning environment and their level of mathematics anxiety (associated with the learning of mathematics and the evaluation of their mathematics learning). Surveys were distributed and their completion was supervised by classroom teachers within a five-week period. Because the questionnaires have a strong history of successful use, especially in the United States, it was felt that it was appropriate for classroom teachers to collect the data without compromise or bias. The What Is Happening In this Class? (WIHIC) questionnaire was developed by Fraser et al. (1996) to measure students’ perceptions of seven psychosocial aspects of the classroom learning environment: Student Cohesiveness, Teacher Support, Involvement, Investigation, Task Orientation, Cooperation and Equity. This instrument was used in our study without any modifications. It has a five-point frequency response scale with alternatives ranging from Almost Never to Almost Always. There are eight items for each scale in the WIHIC. Confirmatory factor analysis of the WIHIC has been conducted to verify the validity and integrity of the instrument (Dorman 2003, 2008). Using a cross-national sample from the United Kingdom, Canada and Australia (N = 3,980), Dorman reported that the WIHIC is a valid measure of classroom environment and has a wide range of applications, especially in Western countries, a finding that has often been replicated by other researchers (Aldridge et al. 2009; Wolf and Fraser 2008). An updated version of Plake and Parker’s (1982) Revised Mathematics Anxiety Ratings scale (RMARS) was used to measure student levels of anxiety in two areas: Learning Mathematics Anxiety and Mathematics Evaluation Anxiety. MARS was originally created by Richardson and Suinn (1972) and consisted of 96 questions in these two areas. Later, it was reduced by Plake and Parker to 24 questions of which 16 are related to the Learning Mathematics Anxiety scale. Despite nearly 20 years of use, we felt that the previous items in the RMARS needed to be adapted to more current methods of mathematics instruction and terminology. This resulted in roughly half of the questions being modified in some way. The RMARS uses a five-point response scale ranging from Not At All Anxious to Very Much Anxious. Sex differences were examined via a two-way multivariate analysis of variance (MANOVA) with all of the learning environment and anxiety scales as dependent variables. The grade level of each student was also considered as an independent variable, as well as gender, to see if there was an interaction between gender and grade level. Wilks’ lambda (similar to a multivariate F score) was used to determine the statistical significance of differences in the set of scales as a whole prior to interpreting the univariate ANOVA for each individual scale. The effect size was also computed to give an indication of the magnitude of sex differences on each scale (Cohen 1988). This effect size, which was calculated by dividing the difference between means by the pooled standard deviation, expresses sex differences in standard deviation units.
Validity and reliability of WIHIC and RMARS The study’s first aim was to provide validity and reliability data for the instruments assessing learning environment and mathematics anxiety when used with high-school
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students in Southern California. One method that is commonly used to check the internal structure of an instrument is factor analysis, which identifies areas of an instrument that have common themes and are answered in a similar fashion by those participating in the study. Data collected from administering each questionnaire were analysed using a separate principal components factor analysis involving varimax rotation and Kaiser normalization for the WIHIC and RMARS. Factor loadings, scree plots, eigenvalues and percentages of variance were used to indicate factorial validity. Validity and reliability of WIHIC Table 2 shows the results of the factor analysis for the 56 items in seven scales for the WIHIC when used with our sample of 745 students in 34 classes. Only factor loadings greater than 0.40 are recorded in the table as recommended by Stevens (1992) and Fields (2006). As well, the bottom of Table 2 shows the eigenvalue and percentage of variance for each scale of the instrument. Factor analysis of the 56 WIHIC items demonstrated a strong factor structure, which is consistent with previous research (Aldridge et al. 2009; Dorman 2008; Wolf and Fraser 2008). The a priori seven-scale structure was replicated almost perfectly in that nearly all items have a factor loading of at least 0.40 on their own scale and less than 0.40 on all the other scales. The only exceptions were that, for the Student Cohesiveness scale, two items (Items 6 and 8) did not have a factor loading of greater than 0.40 on their own scale (see Table 2). The seven WIHIC scales together accounted for nearly 60 % of the variance and the eigenvalues were greater than 1 for each of the seven factors. All 56 items had factor loadings of less than 0.40 with all other scales except their own scale, while 54 of the 56 items had factor loadings greater than or equal to 0.40 with their own scale (Table 2). These results are a strong signal that the WIHIC’s factor structure is clear and repeatable, thus giving us confidence when using WIHIC data in investigating our other research questions. Reliability analysis was carried out using Cronbach’s alpha coefficient. The bottom of Table 2 shows that the alpha coefficients for the different scales of the WIHIC were high for two units of analysis (the student and class mean). When using the individual as the unit of analysis, reliability values for different WIHIC scales ranged from 0.82 to 0.91. Using the class mean as the unit of analysis, reliability coefficients ranged from 0.75 to 0.96. These results reflect a reliable instrument with a strong level of internal consistency. Overall these results suggest that the WIHIC is valid for use in high-school mathematics classes in Southern California. Our results compare favourably with other research that has involved factor and reliability analyses of the WIHIC in various countries and situations (Afari et al. 2013; Chionh and Fraser 2009; Dorman 2008; Zandvliet and Fraser 2005). Validity and reliability of RMARS The RMARS has proved to be a highly reliable and valid instrument for measuring mathematics anxiety for the past 30 years. Although the original RMARS consisted of 96 items, the updated version used in our research consists of 24 items assessing the two a priori scales called Learning Mathematics Anxiety (LMA) and Mathematics Evaluation Anxiety (MEA). Items from Plake and Parker’s (1982) original instrument were updated for our study to reflect contemporary mathematics education technology, terminology and methodology. The wording of all RMARS items is provided in Table 3. A five-point
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Table 2 Factor loadings, eignevalues, percentages of variance and alpha reliabilities for the What Is Happening In this Class? (WIHIC) questionnaire Item
Factor loadings Student cohesiveness
1
0.74
2
0.70
3
0.61
4
0.78
5
0.59
6
–
7
0.61
8
–
Teacher support
9
0.67
10
0.72
11
0.69
12
0.61
13
0.76
14
0.79
15
0.71
16
0.59
Involvement
17
0.74
18
0.79
19
0.65
20
0.73
21
0.60
22
0.67
23
0.43
24
0.56
Investigation
25
0.75
26
0.67
27
0.78
28
0.64
29
0.82
30
0.79
31
0.81
32
0.78
Task orientation
33
0.66
34
0.72
35
0.72
36
0.63
37
0.71
38
0.64
39
0.68
40
0.70
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Cooperation
Equity
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Table 2 continued Item
Factor loadings Student cohesiveness
Teacher support
Involvement
Investigation
Task orientation
Cooperation
41
0.52
42
0.68
43
0.67
44
0.70
45
0.76
46
0.77
47
0.64
48
0.66
Equity
49
0.68
50
0.68
51
0.68
52
0.76
53
0.75
54
0.78
55
0.67
56
0.74
Eigenvalue
1.65
1.87
1.76
15.13
3.10
4.00
5.59
% of variance
2.94
3.34
3.15
27.01
5.54
7.15
9.99
Alpha reliability Student
0.82
0.90
0.88
0.91
0.88
0.90
0.91
Class mean
0.75
0.94
0.89
0.91
0.94
0.91
0.96
Only factor loadings greater than 0.40 are shown Sample of 745 students in 34 classes
response scale (ranging from Not At All Anxious to Very Anxious) was used for the 16 LMA items and the 8 MEA items. Factor analysis of our RMARS data (Table 3) revealed exactly the same two-dimensional structure as in Plake and Parker’s original version. Table 3 shows that over 50 % of the variance in the instrument was attributable to the two factors (42.17 % for LMA and 12.15 % for MEA), and that each of the 24 items had a factor loading of less than 0.40 with the other scale but greater than 0.40 with its own scale. Therefore, the RMARS appears to have a factor structure that was well defined with this sample. This was also confirmed by the eigenvalues for each of the factors (10.12 for LMA and 2.92 for MEA). The RMARS also demonstrated high internal consistency reliability as measured by the Cronbach alpha coefficient for two units of analysis (see the bottom of Table 3). The Learning Mathematics Anxiety scale had an alpha reliability coefficient of 0.92 using the individual as the unit of analysis and 0.96 with the class mean as the unit of analysis. The Mathematics Evaluation Anxiety scale had high alpha reliability coefficients also (0.91 for the individual level and 0.94 for the class mean level). These high values provide
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Table 3 Factor loadings, eigenvalues, percentages of variance, and alpha reliabilities for a modified version of the Revised Mathematics Anxiety Ratings scale (RMARS) measuring Learning Mathematics Anxiety and Mathematics Evaluation Anxiety Item
Question wording
Factor loadings Learning Mathematics Anxiety
Mathematics Evaluation Anxiety
1
Watching a teacher work an algebra equation on the blackboard
0.68
2
Being given a mathematics textbook on the first day of class
0.53
5
Solving a square root problem
0.60
6
Reading and interpreting graphs and charts
0.55
7
Getting your schedule and seeing a mathematics class on it
0.74
8
Listening to another student explain a mathematics formula to you
0.69
9
Walking into a mathematics class
0.77
10
Looking through the pages of a mathematics textbook
0.69
11
Starting a new chapter in a mathematics class
0.70
12
Walking onto campus and thinking about a mathematics course
0.65
13
Picking up a mathematics textbook to begin working on a homework assignment
0.66
15
Reading a word associated with mathematics, such as ‘‘geometry’’ or ‘‘average’’
0.63
21
Waiting to receive a mathematics test on which you expected to do well
0.42
22
Listening to a lecture in a mathematics class
0.65
23
Having to use a calculator or table to solve a problem
0.75
24
Being told how to solve an algebra equation or write a geometry proof
0.51
3
Being given a homework assignment of difficult problems
4
Thinking about an upcoming mathematics test
0.77
14
Taking an examination (quiz) in a mathematics course
0.81
16
Working on an abstract mathematical word problem
0.69
17
Reading a formula in a mathematics class
0.53
18
Taking an examination (final) in a mathematics class
0.87
19
Getting ready to study for a mathematics test
0.71
20
Being given an unannounced quiz in a mathematics class
0.86
0.75
Eigenvalue
10.12
2.92
% of variance
42.17
12.15
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Table 3 continued Item
Question wording
Factor loadings Learning Mathematics Anxiety
Mathematics Evaluation Anxiety
Alpha reliability Student
0.92
0.91
Class mean
0.96
0.94
Only factor loadings greater than 0.40 are listed Sample of 745 students in 34 classes
confidence in using the instrument to measure these two types of mathematics anxiety in Southern Californian high schools. The results of the factor and reliability analyses are consistent with previous research using the RMARS or the parent version of the MARS (Blum and Staats 1999; Capraro et al. 2001; Hannafin 1985; Plake and Parker 1982; Richardson and Suinn 1972), even with the modifications and updating undertaken for our study. In particular, these validation results highlight the importance of maintaining two distinct dimensions of anxiety (learning and evaluation) when investigating our other research questions (involving sex differences in anxiety and anxiety–environment associations).
Sex differences Sex differences were examined with a two-way multivariate analysis of variance (MANOVA) with all of the learning environment and anxiety scales as dependent variables. The grade level of each student was also considered as an independent variable, as well as sex, to see if there was an interaction between sex and grade level which could influence the results. Wilks’ lambda (similar to a multivariate F score) was used to determine the statistical significance of differences in the set of scales as a whole. Effect sizes were also computed to give an indication of the magnitude of differences (Cohen 1988). Because no interaction between grade level and sex was identified in the MANOVA, this interaction was not investigated further. Because Wilks’ lambda criterion indicated statistically significant sex differences for the whole set of dependent variables, the univariate ANOVA was interpreted for each individual scale (see Table 4). Because grade level was not a variable of interest in my study, any results for grade level differences have been ignored in the present article. The average item mean, average item standard deviation, effect size and ANOVA results for each learning environment and anxiety scale are shown in Table 4. These results can inform us about the way in which males and females differ in their views of various components of the learning environment and mathematics anxiety. The average item mean is the scale mean divided by the number of items in the scale. For example, the average item mean for males for Student Cohesiveness of 3.85 suggests that the practices described in this scale’s items occurred with a frequency close to the Often response. Because
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Table 4 Average item mean, average item standard deviation, and sex difference (effect size and MANOVA results) for each classroom environment and mathematics anxiety scale Scale
M
SD
Difference
Male
Female
Male
Female
d
F
Student cohesiveness
3.85
4.00
0.66
0.69
0.22
Teacher support
3.42
3.62
0.86
0.85
0.23
Involvement
2.86
2.79
0.86
0.83
0.01
-1.31
WIHIC 8.46* 9.27*
Investigation
2.55
2.40
0.87
0.84
0.17
-4.70
Task orientation
4.01
4.28
0.75
0.63
0.39
23.79**
Cooperation
3.47
3.72
0.87
0.87
0.28
16.03**
Equity
4.16
4.35
0.81
0.75
0.24
7.63*
Learning Mathematics Anxiety
1.94
1.80
0.78
0.67
0.19
-8.85**
Mathematics Evaluation Anxiety
2.55
2.74
0.97
1.04
0.19
5.72*
RMARS
Sample of 745 students in 34 classes Effect size d = (M1–M2)/SD pooled * p \ 0.05, ** p \ 0.01
different scales do not necessarily consist of the same number of items, the average item mean allows us to compare different scales’ averages meaningfully. For five of the seven WIHIC scales, differences were statistically significant between the sexes: Student Cohesiveness, Teacher Support, Task Orientation, Cooperation and Equity. The effect size for each of these significant sex differences was in Cohen’s (1988) moderate range (ranging from 0.22 to 0.39 standard deviations). The means for all five scales for which sex differences were statistically significant were all higher for the females than the males. As females of high-school age seem to be more social and interactive than males, as well as slightly more motivated as a group regarding academic achievement, these findings are fairly plausible as each of these scales has to do with motivation and interaction among students. This replicates previous research into sex differences using the WIHIC which revealed that generally females viewed the environment more favourably than males (Fraser et al. 1995). Sex differences for Teacher Support and Equity point to some unanticipated and interesting findings. Overall, it seems that, relative to males, females in this sample were more positive regarding the level of teacher support and equity in their high school mathematics classrooms than has been previously reported in other mathematics education research (Levine 1995; Tobias 1978; Zettle and Raines 2000). The MANOVA results for the RMARS (Table 4) revealed statistically significant sex differences for both Learning Mathematics Anxiety and Mathematics Evaluation Anxiety scale, but the associated effect sizes for anxiety scales were relatively small (about onefifth of a standard deviation). Nevertheless, the interpretation of these findings is interesting in that females were more anxious than males regarding testing of mathematical concepts, but males were more anxious regarding the learning of the mathematics in the classroom context. This fascinating pattern of results highlights the importance of maintaining the two distinct dimensions of anxiety (as using a single overall scale of anxiety probably would have obscured these sex differences).
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309
Table 5 Simple correlation and multiple regression analyses for associations between anxiety and classroom environment scales Environment scale
Learning Mathematics Anxiety r
Mathematics Evaluation Anxiety
b
r
b
-0.04
Student cohesiveness
-0.13**
-0.14**
Teacher support
-0.04
-0.00
0.03
0.00
0.01
0.04
-0.00
-0.00
Involvement Investigation
0.06
Task orientation
-0.09*
Cooperation
-0.08*
Equity
-0.07
Multiple correlation, R
-0.13
0.01*
0.01
0.00
-0.02*
-0.03
-0.01
0.01
0.02
0.01
-0.01
0.02
0.00
0.17**
0.10
* p \ 0.05, ** p \ 0.01
Associations between anxiety and learning environment Table 5 shows the results of simple correlation and multiple regression analyses for associations between each of the two mathematics anxiety scales and the seven learning environment scales. The correlation coefficient (r) and the standardised regression coefficient (b) are shown for each learning environment scale. The multiple correlation coefficient (R) is also shown for each anxiety scale. Table 5 reflects a somewhat different pattern of anxiety–environment associations for the two different anxiety dimensions. Mathematics Evaluation Anxiety showed no significant relationship with any classroom environment scale for either the simple correlation or multiple regression analyses. It appears that specific emphases in the learning environment in these classes did not contribute to anxiety associated with the evaluation process. This is not totally unexpected because the evaluation process for testing of mathematics knowledge probably is not as dependent on the classroom situation and environment as is the personal motivation and goals of each student. Although the simple correlations between the Learning Mathematics Anxiety and classroom environment scales were not strong, there were statistically significant negative correlations with anxiety for the scales of Student Cohesiveness, Cooperation and Task Orientation. The multiple regression analysis using Learning Mathematics Anxiety as the dependent variable also yielded a statistically significant multiple correlation of 0.17, with Student Cohesiveness and Task Orientation being significant independent predictors of Learning Mathematics Anxiety. It appears that students are less anxious about the situation and environment surrounding mathematics lessons and the classroom when there is more peer interaction and acceptance (Student Cohesiveness) and more motivation and time on task (Task Orientation). Again, the results reported in Table 5 for anxiety–environment associations support the usefulness of maintaining the two district dimensions of mathematics anxiety.
Conclusion This study combined the fields of mathematics education and learning environments as recommended by English (2002). In particular, we investigated the important topic of mathematics anxiety from a learning environments perspective.
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Our sample consisted of 745 high school mathematics students in 34 classes in four typical schools in California. The seven-scale What Is Happening In this Class? (WIHIC) questionnaire was used to assess the classroom learning environment, whereas a modified version of the two-scale Revised Mathematics Anxiety Rating scale (RMARS) was used to assess mathematics anxiety. As well as validating these two questionnaires, our research focused on sex differences in perceived learning environment and mathematics anxiety, as well as associations between mathematics anxiety and the learning environment. A major contribution was that our study provided strong support for the validity of the seven-scale WIHIC and two-scale RMARS when used specifically with mathematics students in California. For example, each instrument exhibited strong factorial validity, with WIHIC scales accounting for nearly 60 % of the variance and RMARS scales accounting for over 50 % of the variance. With the student as the unit of analysis, the internal consistency reliability (Cronbach alpha coefficient) for different scales ranged from 0.82 to 0.91 for the WIHIC and from 0.91 to 0.92 for the RMARS. Sex differences were found in both learning environment perceptions and anxiety. Females had statistically significantly more favourable perceptions of the classroom environment on the five WIHIC scales of Student Cohesiveness, Teacher Support, Task Orientation, Cooperation and Equity. Effect sizes for these five scales were modest in size and ranged from 0.22 to 0.39 standard deviations. This pattern, in which females perceive the learning environment more favourably than do males, replicates past research (Fraser et al. 1995). Although sex differences in anxiety were relatively small in magnitude (around onefifth of a standard deviation), they were statistically significant but in opposite directions for the two distinct dimensions of anxiety. Whereas females were more anxious than males regarding testing of mathematical concepts, males were more anxious than females regarding the learning of mathematics. While associations between anxiety and classroom environment were not strong, it is noteworthy that a different pattern of anxiety–environment associations emerged for each of the two distinct aspects of anxiety. Mathematics evaluation anxiety showed no statistically significant relationship with classroom environment, but learning mathematics anxiety was significantly related to several learning environment scales, especially Student Cohesiveness and Task Orientation. As anticipated, the relationship between anxiety and learning environment was negative, suggesting the possibility of reducing students’ mathematics anxiety through creating a positive classroom environment. Overall, the most salient finding is that mathematics anxiety appears to have two factorially-distinct dimensions (Learning Mathematics Anxiety and Mathematics Evaluation Anxiety), which yield different patterns of results for sex differences and for anxiety– environment associations. Tobin and Fraser (1998) have identified several advantages in combining quantitative and qualitative methods in learning environments research and have advocated the use of mixed-methods designs. Aldridge et al. (1999) have illustrated the use of a mixed-methods approach in a study in Taiwan and Australia that combined the use of a learning environments questionnaire with interviews and narratives. In future research into learning environments and mathematics anxiety, we strongly recommend the use of mixed methods. References Afari, D., Aldridge, J. M., Fraser B. J., & Khine, M. S. (2013). Students’ perceptions of the learning environment and attitudes in game-based mathematics classrooms. Learning Environments Research, 16, 131–150.
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