Linking university mathematics classroom environments to student achievement: The mediation of mathematics beliefs

This study examined the relationships between university mathematics classroom environments, mathematics beliefs, and achievement in the context of mainland China. As a type of affect in mathematics learning, mathematics beliefs including mathematics conceptions and efficacy were examined as mediators. Based on analysis of a sample of 1443 undergraduate students from a university in northern China, the study not only found that the mathematics classroom environment was associated with both affective and cognitive mathematics outcomes, but also confirmed the mediating role of mathematics beliefs. Specifically, a desirable classroom environment was related to students’ cohesive conceptions, enhanced self-efficacy, and higher mathematics achievement. In contrast, students’ perceived difficulty of learning mathematics was connected to their fragmented conceptions, reduced self-efficacy and lower mathematics achievement. Implications of the study are discussed.     

Relationships between learning environment and mathematics anxiety

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.     

Modeling achievement in mathematics: the role of learner and learning environment characteristics

This study examined a structural model of mathematics achievement among Druze 8th graders in Israel. The model integrates 2 psychosocial theories: goal theory and social learning theory. Variables in the model included gender, father's and mother's education, classroom mastery and performance goal orientation, mathematics self-efficacy and self-regulated learning, mastery and performance goals, and mathematics achievement. Data on learner and learning environment variables and achievement in mathematics were collected from 273 boys and girls. Results indicate appropriate fit of the model for the entire sample. Invariance analysis across gender indicated that only 2 of the 11 path coefficients, mother's education on mathematics achievement and classroom mastery goal orientation on self-regulation, were not invariant across gender. The same pattern of relationships accounted for different amounts of variance in mathematics achievement for boys and girls.     

Motivational goal orientation, perceptions of biology and physics classroom learning environments, and gender

Researchers have reported persuasive evidence that students?? perceptions of their classroom learning environment account for significant variance in cognitive and affective outcomes (e.g. intrinsic motivation, self-concept, liking for particular subjects and students?? intention to drop out). The study reported in this paper investigated the relationship between students?? perceptions of classroom learning environment and motivational achievement goal orientations towards biology and physics, as well as the influence of gender. Participants (N?=?1538) were high school science students from the north-eastern region of Thailand. Our results suggest that motivational goals are linked to differences in students?? perceptions of learning environment and levels of biology and physics classroom anxiety. We found that females adopted significantly higher levels of mastery and performance approach goals towards biology, while males adopted significantly higher levels of mastery and performance approach goals towards physics. Males adopted significantly higher levels of performance avoidance goals towards both biology and physics. Positive associations emerged between gender and the adoption of specific performance goals, perceived degree of competition in biology and physics classrooms, and levels of biology and physics classroom anxiety. These results suggest that motivational goal orientations and perceptions of learning environment are gender-dependent and domain-specific for the two science content areas.     

Mathematics achievement and gender: A longitudinal study of selected cognitive and affective variables [grades 6–12]

This study examined the relationship of selected cognitive and affective variables to mathematics achievement for a random sample of 60 students as they progressed through 6th, 8th,10th and 12th grades. A consistent gender difference was found for stereotyping mathematics as a male domain. No consistent significant gender difference between means was found for spatial skills, verbal skill or mathematics achievement. Confidence, verbal skill and spatial visualization were each consistently positively correlated with mathematics achievement for both males and females. No gender difference was found for these correlations. However, spatial skills alone were found to be consistent significant predictors of mathematics achievement for females each year of the study, but not for males. Verbal skill was a consistent significant predictor of mathematics achievement for males, but not for females. The results of this study could lead to a reevaluation of the hypothesis that spatial skills help boys achieve in mathematics.     

Contextual differences in student motivation and self-regulated learning in mathematics,English, and social studies classrooms

Recent research on self-regulated learning has stressed the importance of both motivational and cognitive components of classroom learning. Much of this research has examined these components without consideration of potential contextual differences. Using a within-subject correlational design, the present study assessed mean level differences in students' task value, self-efficacy, test anxiety, cognitive strategy use, regulatory strategy use, and classroom academic performance by gender and across the subject areas of mathematics, social studies, and English. In addition, the relations among the motivational, strategy use, and performance measures were assessed using multivariate regressions. The participants were 545 seventh and eighth grade students (51% females) who responded to a self-report questionnaire. Results revealed mean level differences by subject area and gender in the motivation and cognitive strategy use variables, but not in regulatory strategy use or academic performance. In contrast, results indicated that the relations among these constructs was very similar across the three subject areas examined. Findings are discussed in terms of their importance for understanding the contextual nature of students' self-regulated learning.     

How gender stereotypes of students and significant others are related to motivational and affective outcomes in mathematics at the end of secondary school

We examined associations between the explicit mathematics-related gender stereotypes of students, parents, teachers, and classmates and students’ motivational-affective outcomes in mathematics (self-concept, interest, anxiety) at the end of Grade 9. Based on representative data from the German Trends in Student Achievement 2018 study (N = 30,019), results of latent multilevel mixture models show that boys’ and girls’ explicit beliefs in the stereotype favoring their own gender in-group (i.e., boys’/girls’ belief that boys/girls do better at mathematics) were related to higher levels of self-concept and interest and to lower anxiety. Parents’ gender stereotypes showed an incremental association with all three outcomes for girls but only with mathematics self-concept for boys. Gender stereotypes of teachers were not related to students’ outcomes. However, classmates’ stereotypes favoring girls or boys in mathematics were negatively associated with outcomes of the positively stereotyped group. Thus, a male student in a classroom with classmates who share the traditional stereotype that boys do better at mathematics than girls would hold a lower self-concept and interest and higher anxiety level after controlling for the beneficial individual association of himself having the same belief and his motivational and affective outcomes. Similarly, a girl’s motivational-affective outcomes would be more favorable in the same environment characterized by the shared traditional stereotype of mathematics as a male domain after controlling for the negative individual association. Shared stereotypes in the classroom could thus trigger social comparison processes to which students are more susceptible than to stereotypes of their teachers.     

Relationships between learning patterns and attitudes towards two assessment formats

The study examined the relationships between learning patterns and attitudes towards two assessment formats: open‐ended (OE) and multiple‐choice (MC), among students in higher education. Sixteen Semantic Differential scales measuring emotional reactions, intellectual reactions and appraisal of each assessment format, along with measures of learning processes, academic self‐concept and test anxiety, were administered to 58 students. Results indicated two patterns of relationships between the learning‐related variables and the assessment attitudes: high scores on the self‐concept measure and on the three measures of learning processes were related to positive attitudes towards the OE format but negative ones towards the MC format; low scores on the test anxiety measures were related to positive attitudes towards the OE format. In addition, significant gender differences emerged with respect to the MC format, with males having more favourable attitudes than females. Results were discussed in light of an adaptive assessment approach.     

Gender effects for student perception of the classroom psychosocial environment

A future shortage of science teachers has been predicted, and since women are presently underrepresented in the sciences, they are a good potential source for future science teachers. Unfortunately women appear to become less interested in science as they continue in school. Because the classroom psychosocial environment has been shown to be related to learning outcomes, it may contribute to women's lack of interest in sciences. This study compared the classroom environments perceived by fourth grade, seventh grade and high school boys and girls in classes taught by males and females to determine if any perceptual differences existed. The three, two factor MANOVAS (teacher gender by student gender) showed no differences for fourth grade students, one for seventh grade students and three for high school students. The seventh grade boys and girls perceived classes taught by females as having more friction than classes taught by males and high school boys and girls perceived classes taught by females as being more difficult than classes taught by males. Further, for the high school students it appears that classes are perceived more favorably when the opposite genders are combined. These perceptual differences combined with role modeling may contribute to the lack of women in science. More research is necessary to determine causal relationships.     

Women and girls in mathematics—Equity in mathematics education

Conclusions What then can be said that is known about sex-related differences in mathematics and factors related to such differences? Certainly, when both females and males study the same amount of mathematics, differences in learning mathematics are minimal and perhaps decreasing. Many fewer females elect to study mathematics and therein lies the problem. Variables which appear to contribute to this non-election are females' lesser confidence in their ability to learn mathematics and their belief that mathematics is not useful to them. In addition, differential teacher treatment of males and females is important. All variables appear to be directly related to the stereotyping of mathematics as a male domain.There is nothing inherent (Sherman [30]) which keeps females from learning mathematics at the same level as do males. Intervention programs can and must be designed and implemented within schools which will increase females' participation in mathematics. Such programs should include male students, female students and their teachers. Only when such intervention programs become effective can true equity in mathematics education be accomplished.     

Influence of curriculum reform: An analysis of student mathematics achievement in Mainland China

This study investigated curriculum influences on student mathematics achievement by following two groups of students from fifth to sixth grade that were taught either the reformed curriculum or the conventional curriculum. Analyses with three-level modeling were conducted to examine learning outcomes of the students who were assessed three times over a period of 18 months. Achievement was measured with regard to computation, routine problem solving, and complex problem solving. Affective aspects included self-reported interest in learning mathematics, classroom participation, views of the nature of mathematics, and views of learning mathematics. The results showed overall improved performance among all the students over the time on computation, routine problem solving, and complex problem solving but not on the affective measures. There were differentiated patterns of performance between the groups. On the initial assessment, the reform group performed better than the non-reform group on calculation, complex problem solving, and indicated higher interest in learning mathematics. The two groups did not differ on the other achievement and affective measures at the first time of assessment. There was no significant difference in growth rate between the groups on the cognitive and affective measures except that the non-reform group progressed at a faster pace on calculation. Therefore, the non-reform group outperformed the reform group on computation at the third (last) assessment. These results are discussed with respect to the possible influence of the curriculum on student learning.     

Learning Environment and its Association with Student Satisfaction Among Mathematics Students in Brunei Darussalam

This article reports a study of lower secondary mathematics classroom learning environment in Brunei Darussalam and its association with students' satisfaction with learning mathematics among a sample of 1565 students from 81 classes in 15 government secondary schools. Students' perceptions of the classroom learning environments were assessed with a version of the My Class Inventory (MCI) that had been modified for the Brunei context. The study revealed a satisfactory factor structure for a refined three-scale version of the MCI assessing cohesiveness, difficulty and competition. This finding is noteworthy because the factorial validity of the MCI has not previously been established in past research in other countries. Also each scale displayed satisfactory internal consistency reliability and discriminant validity and was able to differentiate between the perceptions of students in different classes. A one-way MANOVA revealed that students generally perceived a positive learning environment in mathematics classes. Also the study supported earlier research suggesting that boys and girls hold different perceptions of the same classroom learning environments. Relationships between student satisfaction and classroom environment were investigated using simple and multiple correlation analyses, using both the individual student and class mean as units of analysis. Associations between satisfaction and the learning environment were statistically significant both at student and class levels for most MCI scales. This revised version was published online in August 2006 with corrections to the Cover Date.     

An Analysis of Some New Statistical Methods for Selecting Test Items

In this study, the relationship between student affective performance and classroom physical environment, social climate, and management style were investigated in a sample of classes in Hong Kong primary schools. The results of Pearson and canonical correlation analyses indicated that among the measures of classroom environment, perceived quality of physical environment and class master's expert power, personal power, and coercive power were the strongest predictors of affective performance. This finding supports the importance of class master's management style in the classroom environment. Students' attitudes toward school and teachers appeared to be most sensitive to variation in the classroom environment, and self-concept was the least sensitive among the seven student affective measures. Students' self-efficacy of learning and intention to drop out were moderately sensitive to classroom environment. Profiles of effective and ineffective classroom environments were also mapped. In effective classrooms, class masters care for students, pay attention to teaching, do not use force or punishment but do create a good classroom climate with their professional knowledge, personal morality, and personality. Physical environment and psychological environment are both important; a good classroom environment is highly correlated with student affective performance.     

Identifying affective domains that correlate and predict mathematics performance in high-performing students in Singapore

Past studies have shown that distinct yet highly correlated sub-constructs of three broad mathematics affective variables: (a) motivation, (b) attitudes and (c) anxiety, have varying degree of correlation with mathematics achievement. The sub-constructs of these three affective constructs are as follows: (a) (i) amotivation, (ii) external regulation, (iii) introjection, (iv) identification, (v) intrinsic motivation; (b) (i) enjoyment of mathematics, (ii) self-confidence in mathematics, (iii) perceived value of mathematics; (c) (i) anxiety with mathematics and (ii) ease with mathematics. This study identifies, both within and across these three affective variables, the key sub-constructs that educators should focus upon when selecting learning process variables for mathematics achievement. Results were analysed using a series of stepwise regression analyses using data from 1018 Grade 12 students enrolled in a top pre-tertiary institution in Singapore, both for concurrent and predictive relationships, and also for both genders. Results of this study showed that after taking into account self-confidence in mathematics and ease with mathematics, all other sub-constructs of mathematics motivation, attitudes and anxiety were not significantly correlated with mathematics achievement. This is true for both concurrent and predictive relationships, and for both genders. Implications of the results of this study are twofold. First, results of this study provide educators with priority affective variables to focus upon in their efforts to enhance performance in mathematics via the affective domain. Second, in situations where administration time is limited, it may be possible to consider only self-confidence and ease with mathematics when investigating relationships between affect and mathematics achievement.     

Utilizing online learning data to design face-to-face activities in a flipped classroom: a case study of heterogeneous group formation

This study investigates the possibility of utilizing online learning data to design face-to-face activities in a flipped classroom. We focus on heterogeneous group formation for effective collaborative learning. Fifty-three undergraduate students (18 males, 35 females) participated in this study, and 8 students (3 males, 5 females) among them joined post-study interviews. For this study, a total of 6 student characteristics were used: three demographic characteristics obtained from a simple survey and three academic characteristics captured from online learning data. We define three demographic group heterogeneity variables and three academic group heterogeneity variables, where each variable is calculated using the corresponding student characteristic. In this way, each heterogeneity variables represents a degree of diversity within the group. Then, a two-stage hierarchical regression analysis was conducted to identify the significant group heterogeneity variables that influence face-to-face group achievement. The results show that the academic group heterogeneity variables, which were derived from the online learning data, accounted for a significant proportion of the variance in the group achievement when the demographic group heterogeneity variables were controlled. The interviews also reveal that the academic group heterogeneity indeed affected group interaction and learning outcome. These findings highlight that online learning data can be utilized to obtain relevant information for effective face-to-face activity design in a flipped classroom. Based on the results, we discuss the advantages of this data utilization approach and other implications for face-to-face activity design.

     

Couples' affective orientations and their verbal abusiveness

Four measures of affective orientation: awareness of affect as information, posses‐sion of positive feelings, and expression of positive and negative emotions were employed to examine the relationships between functional males’ and females’ affective orientations and the level of verbal abuse reported in their relationships. Females reported having higher levels of affective awareness on all four measures of affective orientation. Contrary to expectations, males’ and females’ awareness of affect as information to guide interactions and positive feelings were not associated with reported verbal abuse. Males’ and females’ expressions of negative emotions, however, were significantly negatively associated with verbal abuse in the relationships. Males’ positive emotional expressiveness was significantly negatively associated with self‐reported verbal abuse in the relationship. Functional males and females reported experiencing similar levels of verbal abuse within their relationships.     

Gender Differences in Lunar‐related Scientific and Mathematical Understandings

This paper reports an examination on gender differences in lunar phases understanding of 123 students (70 females and 53 males). Middle‐level students interacted with the Moon through observations, sketching, journalling, two‐dimensional and three‐dimensional modelling, and classroom discussions. These lunar lessons were adapted from the Realistic Explorations in Astronomical Learning (REAL) curriculum. Students’ conceptual understandings were measured through analysis of pre‐test and post‐test results on a Lunar Phases Concept Inventory (LPCI) and a Geometric Spatial Assessment (GSA). The LPCI was used to assess conceptual learning of eight science and four mathematics domains. The GSA was used to assess learning of the same four mathematical domains; however, the GSA test items were not posed within a lunar context. Results showed both male and female groups to make significant gains in understanding on the overall LPCI test scores as well as significant gains on five of the eight science domains and on three of the four mathematics domains. The males scored significantly higher than the females on the science domain, phase—Sun/Earth/Moon positions, and on the mathematics domain geometric spatial visualisation. GSA results found both male and female groups achieving a significant increase in their test scores on the overall GSA. Females made significant gains on the GSA mathematics domains, periodic patterns and cardinal directions, while males made significant gains on only the periodic patterns domain. Findings suggest that both scientific and mathematical understandings can be significantly improved for both sexes through the use of spatially focused, inquiry‐oriented curriculum such as REAL.     

Classroom learning environment and motivation towards mathematics among secondary school students in Uganda

This article reports a study of secondary students’ perceptions of mathematics classroom learning environment and their associations with their motivation towards mathematics. A sample of 81 students (19 male and 62 female) in two schools were used. Student perceptions of the classroom environment were assessed using a modified What Is Happening In this Class? (WIHIC) questionnaire. Associations between student perceptions of the learning environment and motivation towards mathematics were examined using simple correlation and multiple regression analyses. The results of the t tests for independent samples indicated a statistically significant difference in student perceptions between different school types. Student perceptions on some of the modified WIHIC scales were statistically significantly associated with student motivation. The results suggest that teachers wishing to improve student motivation towards mathematics, in general, should emphasise the learning environment dimensions that are assessed by the WIHIC. The findings have implications for teachers of mathematics and head teachers, particularly those in secondary schools.     

Construct validity of self-concept in TIMSS’s student background questionnaire: a test of separation and conflation of cognitive and affective dimensions of self-concept among Saudi eighth graders

The aims of this study are to: (a) assess if cognitive self-concept (competence) and affective self-concept in mathematics and science are different constructs, (b) evaluate the construct validity of self-concept in the context of conflation and separation, and (c) test if the relationships among cognitive and affective variables are invariant across gender. The data for this study were obtained from the Trends in International Mathematics and Science Study 2007 database. Data about 2,687 out of 4,099 eighth grade Saudi students were subject to various analyses. The variables used in this study were mathematics and science self-concepts, and mathematics and science subject value as part of the Students Background Questionnaire. The relationships among constructs were examined with the use of SPSS16 and the structural equation modeling software, AMOS16. The results demonstrated that subject value and self-concept were different constructs. Also, the results demonstrated that cognitive and affective self-concepts were independent, but strongly related constructs, and the structure of the construct was clearer when self-concept was separated into cognitive and affective components than when it was conflated. The relationships among cognitive, affective, and subject value in mathematics and science were invariant across gender. However, their relationships with achievement were not invariant across gender.     

School belonging and math attitudes among high school students in advanced math

This study used the Trends in International Math Science (TIMSS) 2015 Advanced data from nine countries to examine the relationship between students’ sense of school belonging and their attitudes towards mathematics, and the extent to which student gender moderated these relationships. Results showed that students’ sense of school belonging emerged as a statistically significant, positive predictor of students’ liking and valuing of mathematics. For most countries, no significant moderating effect of student gender was observed. However, among Portuguese students, the relationship between students’ sense of school belonging and each attitude measure was stronger for males than for females.