Motivational beliefs and cognitive processes in mathematics achievement, analyzed in the context of cultural differences: a Korean elementary school example

The relations among students’ motivational beliefs, cognitive processes, and academic achievement were investigated. A 51-item questionnaire together with a mathematics achievement test was administered to 459 fifth graders in Korean elementary school mathematics classrooms. Results indicated that, in general, students’ cognitive processes related closely to competence beliefs, task values, and achievement goals, and more importantly their success or failure in mathematics achievement was closely linked to competence beliefs, performance-avoidance goals, and persistence strategies. Positive evidence of performance-approach goals was observed in math learning relative to task goals. As expected, performance-avoidance goals turned out to be detrimental to students’ math learning. These findings are generally congruent with the motivational theories and support the position that students should be encouraged to adopt task goals and actively involve themselves in math class activities. However, it also behooves us to recognize the potential benefits of performance-approach goals in different cultural contexts, such as the Korean elementary school math classrooms.     

Longitudinal investigation of the curricular effect: An analysis of student learning outcomes from the LieCal Project in the United States

In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditional mathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including students of color; (4) the use of CMP contributed to significantly higher problem-solving growth for all ethnic groups; and (5) a high level of conceptual emphasis in a classroom improved the students’ ability to represent problem situations. (However, the level of conceptual emphasis bears no relation to students’ problem solving or symbol manipulation skills.)     

Teaching for understanding and/or self-regulated learning? A video-based analysis of reform-oriented mathematics instruction in Switzerland

In mathematics instruction, can a teacher implement surface features of instruction that foster self-regulated learning as well as achieve quality at the deeper level of instruction, that is, focus on higher-order thinking, problem-solving, and mathematical modeling? An educational reform effort in Switzerland, which is based on constructivist and sociocultural theories of mathematics learning, targets both these dimensions: self-regulated learning and conceptual understanding. We examined the realization of the two dimensions in classroom instruction in a video-based study of 79 eighth-grade math classes using three kinds of data: videotapes of mathematics lessons, student and teacher questionnaires, and achievement tests. As to the surface level of instruction, teachers reported how frequently they provided opportunities for self-regulated learning. With regard to the deeper level of instruction, teachers reported how frequently they provided opportunities for independent problem solving. In addition, we examined the extent to which teachers’ pedagogical beliefs reflected a constructivist orientation. The results showed that teachers implemented the two dimensions relatively independently of one another. Teachers’ constructivist-oriented beliefs influenced only opportunities provided for independent problem solving and did not affect opportunities for self-regulated learning. Opportunities for self-regulated learning had a positive effect on students’ learning experience. Professional development should encourage teachers to take greater account of both surface-level and deeper-level (quality) features of instruction.     

Motivation and students’ use of learning strategies: Evidence of unidirectional effects in mathematics classrooms

Considerable evidence indicates that student motivation and use of learning strategies are related. There is insufficient understanding, however, about their reciprocal effects—whether motivation affects strategy use, the converse, or whether the effects are bidirectional—and which components of motivation and strategies are involved. A two-wave longitudinal design was used to examine this issue among 9th grade students (N = 306) enrolled in high school mathematics classes during an academic term. A cross-lagged structural model found that students’ self-efficacy in mathematics and value predicted their reported use of learning strategies. There was no evidence, however, that learning strategy use predicted motivation and, thus, support for unidirectional effect of motivation during that time interval. Implications for models of self-regulated learning and instruction are discussed.     

Understanding STEM-focused high school students’ perceptions of task importance: The role of “standing out” and “fitting in” in mathematics class

One theoretical extension of Optimal Distinctiveness Theory (ODT;  and ) is that individuals will work toward the satisfaction of their own social identity needs for differentiation (standing out) and assimilation (fitting in). Because these needs serve as driving forces behind the attitudes people adopt, and the behaviors they enact, the motivational properties of these needs are likely to be manifest in achievement contexts. Bridging ODT and Expectancy-Value Theory, this article examines the prediction that academic tasks are seen by students as more important when they contribute to students’ ability to stand out (task differentiation) from and fit in (task assimilation) with their classmates. This prediction was supported among an ethnically diverse sample of STEM-focused high school students who rated the importance of 18 mathematics-related academic tasks. Additional analyses demonstrated that the association between task assimilation and task importance was stronger for students who perceived their academic learning environment to be performance-focused (performance goal structure). There also was a significant interaction between task differentiation and task assimilation, such that the association between task assimilation and task importance attenuated at higher levels of task differentiation. The present study is one of the few investigations to assess how students’ valuing within a single academic domain might fluctuate from one academic task to the next (e.g., taking notes versus working out problems on the board). The Discussion addresses the theoretical and practical significance of acknowledging differentiation and assimilation as vehicles for motivating students in the classroom.     

The meaning of mathematics instruction in multilingual classrooms: analyzing the importance of responsibility for learning

In the multilingual mathematics classroom, the assignment for teachers to scaffold students by means of instruction and guidance in order to facilitate language progress and learning for all is often emphasized. In Sweden, where mathematics education is characterized by a low level of teacher responsibility for students’ performance, this responsibility is in part passed on to students. However, research investigating the complexity of relations between mathematics teaching and learning in multilingual classrooms, as well as effect studies of mathematics teaching, often take the existence of teachers’ responsibility for offering specific content activities for granted. This study investigates the relations between different aspects of responsibility in mathematics teaching and students’ performance in the multilingual mathematics classroom. The relationship between different group compositions and how the responsibility is expressed is also investigated. Multilevel structural equation models using TIMSS 2003 data identified a substantial positive influence on mathematics achievement of teachers taking responsibility for students’ learning processes by organizing and offering a learning environment where the teacher actively and openly supports the students in their mathematics learning, and where the students also are active and learn mathematics themselves. A correlation was also revealed between group composition, in terms of students’ social and linguistic background, and how mathematics teaching was performed. This relationship indicates pedagogical segregation in Swedish mathematics education by teachers taking less responsibility for students’ learning processes in classes with a high proportion of students born abroad or a high proportion of students with low socio-economic status.     

What can teachers do to raise pupil achievement?

Improving weak teaching may be one of the most effective means of raising pupil achievement. However, teachers’ classroom practices and the teaching ‘process’ may matter more to student learning than teachers’ observed résumé characteristics (such as certification and experience). There may also be important differences in teacher characteristics across government and private schools which may help explain the large documented public-private achievement differences often found in studies. This paper delves into the black-box representing ‘teaching’ to uncover the teacher characteristics and teaching practices that matter most to pupil achievement. This is done using unique school-based data, collected in 2002-2003 from government and private schools from one district in Punjab province in Pakistan. The data allow exploitation of an identification strategy that permits the matching of students’ test scores in language and mathematics to the characteristics of teachers that teach those subjects. Within pupil (across subject rather than across time) variation is used to examine whether the characteristics of different subject teachers are related to a students’ mark across subjects. The data are also unique in asking all subject teachers questions pertaining to their teaching practices and these, often unobserved, ‘process’ variables are included in achievement function estimates. Our pupil fixed-effects findings reveal that the standard résumé characteristics of teachers do not significantly matter to pupil achievement. Perversely, however, teachers are found to be rewarded with higher pay for possessing these characteristics, highlighting the highly inefficient nature of teacher pay schedules. Our findings also show that teaching ‘process’ variables matter significantly to student achievement. There are important differences across school-types.     

Learning environment, attitudes and conceptual development associated with innovative strategies in middle-school mathematics

This study of middle-school students in California focused on the effectiveness of using innovative teaching strategies for enhancing the classroom environment, students’ attitudes and conceptual development. A sample of 661 students from 22 classrooms in four inner city schools completed modified forms of the Constructivist Learning Environment Survey (CLES), What Is Happening In this Class? (WIHIC) questionnaire and Test of Mathematics Related Attitudes (TOMRA). Data analyses supported the factor structure, internal consistency reliability, discriminant validity and the ability to distinguish between different classes for these questionnaires when used with middle-school mathematics students in California. The effectiveness of the innovative instructional strategy was evaluated in terms of classroom environment and attitudes to mathematics for the whole sample, as well as for mathematics achievement for a subgroup of 101 students. A comparison of an experimental group which experienced the innovative strategy with a control group supported the efficacy of the innovative teaching methods in terms of learning environment, attitudes and mathematics concept development. Also associations were found between perceptions of classroom learning environment and students’ attitudes to mathematics and conceptual development.     

Activating positive affective experiences in the classroom: “Nice to have” or something more?

This study investigated students’ activating positive affective experiences in mathematics lessons, their antecedents, their cognitive and motivational consequences, as well as their effect on achievement. The participants were 682 Grade 8 and 9 students from 37 classes from Germany and Switzerland who participated in a video study of lessons on the Pythagorean theorem. Control and value beliefs as well as autonomy support proved to be relevant predictors of positive affective experiences. Moreover, positive affective experiences were associated with more cognitive activity during the lessons, which for its part predicted achievement in the posttest. In a follow-up test, there was also an indirect effect of positive affective experiences on achievement, mediated by cognitive activity and expectancy of success.     

Comparing opportunity to learn and student achievement gains in southern African primary schools: A new approach

A popular explanation for low student achievement in many developing countries’ primary schools is that students have relatively little opportunity to learn (OTL) the skills needed for academic success. However logical this explanation may be, surprisingly little empirical evidence has been presented to support it. In this paper we address this gap by estimating the effect of OTL on students’ academic performance using rich data we gathered on the teaching process in a large number of South African and Botswana Grade 6 classrooms. We use an innovative classroom fixed effects approach to estimate the impact of OTL on students’ mathematics achievement gains. We found statistically significant but very different results for our South Africa and Botswana samples. The discussion of those results in the context of differences in the two school systems gives us insights into the importance and limits of OTL as an explainer of student learning in low achievement schools.     

THE ROLE OF TEACHER CHARACTERISTICS AND PRACTICES ON UPPER SECONDARY SCHOOL STUDENTS�� MATHEMATICS SELF-EFFICACY IN NYANZA PROVINCE OF KENYA: A MULTILEVEL ANALYSIS

The study identified two dimensions of teacher self-efficacy and practices and five dimensions of students’ mathematics self-efficacy and sought to determine the extent to which teacher characteristics and practices can enhance secondary school students’ self-efficacy. Data were collected from 13,173 students in 193 teachers’ classrooms from 141 schools in the 10 districts of Lake Victoria Region of Kenya. Two-level hierarchical linear model revealed that teachers’ frequent use of mathematics homework, their level of interest and enjoyment of mathematics, as well as their ability and competence in teaching mathematics were found to play a key role in promoting students’ mathematics self-efficacy. Teachers’ ability and competence in teaching were also found to be effective in narrowing the gender gap in students’ self-confidence and competence in mathematics. The study recommends that teacher training colleges emphasize such teacher practices and values in order to enhance students’ mathematics self-efficacy, reduce their level of anxiety and fear of mathematics, and consequently, enhance their achievement in mathematics. Professional development opportunities should also be made available to in-service teachers to continually update their knowledge and skills and develop new strategies for teacher effectiveness.     

Positive biases in self-assessment of mathematics competence, achievement goals, and mathematics performance

The study examined how biases in self-evaluations of math competence relate to achievement goals and progress in math achievement. It was expected that performance goals would be related to overestimation and mastery goals to accurate self-assessments. A sample of French high-school students completed a questionnaire measuring their math achievement goals and their perceived competence in math. Students’ math grades for the three trimesters of the school year were collected from school records. Bias in self-evaluations was computed by comparing students’ rating on the ‘perceived competence in math’ scale with their actual math achievement as measured by their second trimester math grades. Students were classified into one of three groups (over-raters, accurate raters, or under-raters) depending on whether their self-perceptions of competence in math were higher than, similar to, or lower than their relative math achievement in their class. As expected, overrating of one's performance was related to performance goals. Furthermore, the over-raters were the only group who progressed in their math achievement from Trimester 2 to 3. No relation was found between mastery goals and accurate self-assessment.     

Achievement goals,efficacy beliefs and coping strategies in mathematics: The roles of perceived parent and teacher goal emphases

This study examines children’s perceptions of the achievement goals parents and teachers emphasize for them in mathematics, and the relation of these goals to children’s personal achievement goals, self-efficacy beliefs, and coping strategies. Results indicated that children’s perceptions of both parent and teacher mastery and performance goal emphases predicted children’s personal goals. Further, children’s personal goals mediated the relation between perceived parent and teacher goal emphases and children’s efficacy beliefs and coping strategies. Children’s perceptions of parent and teacher emphasis on performance goals varied slightly by gender but not ethnic background, whereas variance across groups in perceptions of mastery emphases did not reach practical significance. Relations between goal perceptions, personal goals, efficacy and coping strategies also did not vary by gender or ethnic background. Implications for future research regarding the goals children perceive to be emphasized in home and school contexts, and their importance for children’s adaptive beliefs and behaviors in mathematics, are discussed.     

Teachers, equity, and computers for secondary mathematics learning

The findings presented in this article were derived from a 3- year study aimed at examining issues associated with the use of computers for secondary mathematics learning in Victorian (Australia) schools. Gender and other equity factors were of particular interest. In this article, the focus is on the participating mathematics teachers. Data on their perceived competence levels with technology, and their use of and beliefs about computers for their male and female students’ mathematics learning were gathered. A clear majority of teachers felt comfortable about, and did use, computers for teaching mathematics, and believed that computers helped students’ mathematical learning. Generally, the teachers considered boys to be more confident and capable than girls with computers. The results have implications for pre-service education programs and for the professional development of practicing secondary mathematics teachers.Various findings included in this article have been presented at a range of mathematics education conferences including: AAMT (2003), MAV (2003), and ICME 10 (2004).     

MOTIVATION AND ACHIEVEMENT: IS THERE AN EAST ASIAN MODEL?

The importance of motivation in learning has been widely recognized. However, due to its multidimensional and complex nature, it appears difficult to synthesize research findings on motivation across studies. Heated debates about the effects of intrinsic and extrinsic motivation on learning and their interaction have been going on since the terms started to be used. Moreover, cultural difference acts as another crucial factor in the field. Using the Trends in International Mathematics and Science Studies 2003 eighth grade mathematics data, this study scrutinized the relationship between pleasure-oriented (intrinsic-related) and productivity-oriented (extrinsic-related) motivation and how they collectively affect students’ academic performance in East Asian education systems compared with those from Australia, England, The Netherlands, and the USA. The study found that both types of motivation contributed to East Asian students’ mathematics achievement in an additive fashion, whereas extrinsic-related motivation appeared to have a detrimental effect on their Western counterparts’ learning. Possible reasons were explored from a cultural perspective.     

Connected and culturally embedded beliefs: Chinese and US teachers talk about how their students best learn mathematics

This study compares US and Chinese elementary mathematics teachers' beliefs about how students learn mathematics. Interviews with teachers in each country revealed that Chinese and US teachers have distinct ways of thinking about how mathematics should be taught and how students learn. Many Chinese teachers talked about developing students’ interest in mathematics and relating the content of mathematics lessons to real-life situations. The US teachers talked about students' learning styles and using hands-on approaches to learning mathematics. Furthermore, these beliefs may be widespread and persistent within each country because the set of ideas among teachers appear to be internally consistent. Implications for teacher change and the study of teachers' beliefs are discussed.     

The role of students’ interests in self-regulated learning: The relationship between students’ interests, learning strategies and causal attributions

The purpose of this research was to examine the relationship between students’ interests, their use of certain specific learning strategies and causal attributions which they made for their academic achievement. In this manner, we attempted to explore the relationships between some important variables from three different, but connected phases of self-regulated learning: the forethought phase (interests), the performance control phase (learning strategies) and the self-reflective phase (causal attributions). Results confirmed the presumption that learning strategies could be a potential mediator in the relationship between students’ interests and their academic achievement. Also, results indicate that the causal dimension of controllability could have a partial mediating role between students’ academic achievement and their interests. Generally, our findings indicate a dynamic and cyclical nature of learning process — interest is an integral part of this process and it could be conceptualized as both a consequence and an antecedent of cognitive aspects of learning.     

Dealing with errors in mathematics classrooms: Structure and relevance of perceived error climate

Errors are often perceived by students as self-threatening and not as learning opportunities. The present work focuses on contextual influences on reactions to errors and learning processes. Based on prior research, a conceptualization of perceived error climate in the classroom with eight subdimensions and one superordinate uniform factor is proposed and a newly developed student questionnaire for its assessment is presented. Results of a study with N = 1116 students from 56 mathematics classrooms in German secondary schools indicated the validity of the error climate conceptualization and the suitability of the questionnaire. Moreover, the results showed that perceived error climate in the classroom predicted the adaptivity of students’ individual reactions to errors above and beyond perceived classroom goal structures and personal achievement motivation (academic self-concept, mastery goal orientation). In addition, the study provided evidence that perceived error climate affects – partially mediated through students’ individual reactions to errors – the quantity and self-regulation of students’ effort.     

The effects of cooperative learning on Turkish elementary students’ mathematics achievement and attitude towards mathematics using TAI and STAD methods

This study was designed to compare the effects of Team Assisted Individualization (TAI) and Student Teams-Achievement Divisions (STAD) on fourth grade students’ academic achievement in and attitudes towards mathematics. Seven classes of a school were randomly selected for this experimental study. Two of these were given instruction through TAI; two through STAD, and the remaining three were treated as a control group. For the purpose of the data analysis regarding academic achievement, the 3 X 1 covariance analysis was used to compare the groups. As a result of this comparison, both the TAI and STAD methods were found to have positive effects (d = 1.003 for TAI and d = 0.40 for STAD) on students’ academic achievement in mathematics. The pairwise comparisons showed that the TAI method had a more significant effect than the STAD method. The scores for the attitude towards mathematics were analyzed by using non-parametric statistics. As a result of this analysis, no significant difference was observed regarding students’ attitudes towards mathematics.     

Students’ emotions during homework in mathematics: Testing a theoretical model of antecedents and achievement outcomes

The experience of pleasant and unpleasant emotions in academic situations is known to affect students’ learning. The aim of the present study was to extend previous research by examining the antecedents and consequences of student emotions in the homework context. Multilevel analyses of a longitudinal dataset containing 3483 grade 9 and grade 10 students in 155 classes showed that the perceived quality of the homework tasks assigned by the teacher affected students’ experience of unpleasant homework-related emotions. Moreover, the experience of unpleasant emotions during homework sessions was negatively related to homework effort and negatively predicted later achievement in mathematics.