Motivational and affective determinants of self-regulatory strategy use in elementary school mathematics

The aim of the study was to investigate the relationships between elementary students’ reported use of self-regulatory strategies in mathematics and their motivational and affective determinants. Participants of the study were 344 fifth- and sixth-grade Greek students. Students were asked to complete self-reported measures regarding the strategies they use to self-regulate mathematics learning, their achievement goals in relation to mathematics, their self-efficacy concerning mathematics learning and achievement, the value they attribute to mathematics as a subject domain and their enjoyment of mathematics learning. Structural equation modelling confirmed a mediation model, that is, students’ mathematics self-efficacy, value beliefs about mathematics and enjoyment mediated the effects of achievement goals on reported strategy use. Results are discussed in terms of implications for elementary students’ self-regulated learning skills.     

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.     

Children's self‐regulated learning profile in language and mathematics: The role of task value beliefs

This study explored the self‐regulated learning (SRL) profile of upper elementary (fifth and sixth grade) school children who were differentiated in their task value beliefs (low and high) in language and mathematics. Students' SRL profile involved their teachers' ratings of achievement outcomes and SRL behaviors. The subscale of task value beliefs from the Motivational Self‐Regulated Learning Questionnaire (MSLQ) was administered to the children, and their teachers completed a battery of scales and measurements concerning students' achievement and SRL behaviors. The results confirm previous evidence indicating that SRL involves high levels of motivation, metacognition, and strategic action. Furthermore, the results support the domain‐specific character of task value beliefs. Differences in teachers' evaluations about the achievement outcomes and SRL behaviors regarding the two groups of students (low and high in task value beliefs) were found significant mostly in the domain of mathematics. Students with high value beliefs in mathematics were described as more cognitively, metacognitively, and motivationally competent learners as compared to students with lower value beliefs. The results suggest that future intervention studies should focus on strengthening task value beliefs in “threatening” school subjects, such as mathematics, from the elementary school years. © 2010 Wiley Periodicals, Inc.     

Students’ conceptions of assessment: Links to outcomes

Students conceive of assessment in at least four major ways (i.e., assessment makes students accountable; assessment is irrelevant because it is bad or unfair; assessment improves the quality of learning; and assessment is enjoyable). A study in New Zealand of 3469 secondary school students’ conceptions of assessment used a self‐report inventory and scores from a standardised curriculum‐based assessment of reading comprehension. Four inter‐correlated conceptions based on 11 items were found with good psychometric properties. A path‐model linking the four correlated conceptions with student achievement in reading, while taking into account student ethnicity, student sex, and student year, had good psychometric properties. The conception that assessment makes students accountable loaded positively on achievement while the three other conceptions (i.e., assessment makes schools accountable, assessment is enjoyable, and assessment is ignored) had negative loadings on achievement. These findings are consistent with self‐regulation and formative assessment theories, such that students who conceive of assessment as a means of taking responsibility for their learning (i.e., assessment makes me accountable) will demonstrate increased educational outcomes.     

An Empirical Study of Gender Difference in the Relationship between Self‐Concept and Mathematics Achievement in a Cross‐Cultural Context

The reciprocal relationship between mathematics achievement and self‐concept is examined in this study to expand the existing knowledge to a cross‐cultural setting. Based on analyses of educational data two years before and after Hong Kong’s sovereignty switch in 1997, this investigation shows a weak reciprocal relationship among the eighth‐grade students across gender categories. With the introduction of a new policy to promote Chinese instruction, changes in the perceived importance of English have been assessed by education stakeholders, and the results are used to indicate a latent factor of “English push” behind the learning process. In the context of cross‐cultural transition, gender differences have been found in path coefficients toward mathematics achievement and self‐concept. Limited by the four‐year research period, one may speculate whether it would take longer to demonstrate a large effect size in the reciprocal relationship.     

Outcomes of schooling: Mathematics achievement and attitudes towards mathematics learning in Hong Kong

High achievement of cognitive skills and the formation of favourable attitudes towards learning are universally acclaimed outcomes of schooling. The present study utilised the Second IEA Mathematics Study data (N=5644) to examine which of the ten measured attitude dimensions are pertinent in explaining mathematics achievement variance of Form One students in Hong Kong. Correlational and commonality analysis revealed that students' perception of their ability to do mathematics, the importance of mathematics to society and the concept of mathematics being a creative subject are the most pertinent attitude dimensions. In particular, the perception of students' estimated abilities to do mathematics made a substantial, unique and common contribution to the explained mathematics achievement variance.     

The Role of Intuitive Rules in Science and Mathematics Education

During the last two decades many researchers in mathematics and science education have studied students’ conceptions and ways of reasoning in mathematics and science. Most of this research is content‐specific. It was found that students hold alternative ideas that are not always compatible with those accepted in science. It was suggested that in the process of learning science or mathematics, students should restructure their specific conceptions to make them conform to currently accepted scientific ideas. In our work in mathematics and science education it became apparent that some of the alternative conceptions in science and mathematics are based on the same intuitive rules. We have so far identified two such rules: “More of A, more of B”, and “Subdivision processes can always be repeated”. The first rule is reflected in subjects’ responses to many tasks, including all classical Piagetian conservation tasks (conservation of number, area, weight, volume, matter, etc.) in all tasks related to intensive quantities (density, temperature, concentration, etc.) and in all tasks related to infinite quantities. The second rule is observed in students’, preservice and inservice teachers’ responses to tasks related to successive division of material and geometrical objects and in seriation tasks. In this paper, we describe and discuss these rules and their relevance to science and mathematics education.     

The relation between classroom management and mathematics achievement: A multilevel structural equation model

The impact of teachers on their students’ academic achievement continues to be an area of inquiry. One area not fully explored is the relation between teachers’ behavior and classroom management (CM) skills, student motivation, and student achievement. We examined these relations using a multi‐level structural equation model. Data included Behavior Management subscale scores of the Classroom Assessment Scoring System for 247 fourth and fifth grade teachers, indicators of academic motivation, and end‐of‐year state standardized mathematics assessment results for 4,847 students from the National Center of Teacher Effectiveness Main Study. The results indicate teachers’ CM skills have a significant direct effect on student motivation and a significant indirect effect on students’ math achievement, suggesting that students in classrooms of teachers with better CM are more motivated to learn math and have higher math achievement scores. This underscores the importance of helping teachers increase their use of evidence‐based classroom management techniques.     

Collective Effects of Individual,Behavioral, and Contextual Factors on High School Students’ Future STEM Career Plans

This study explored the structural relationships among secondary school students’ conceptions, self-regulation, and strategies of learning science in mainland China. Three questionnaires, namely conceptions of learning science (COLS), self-regulation of learning science (SROLS), and strategies of learning science (SLS) were developed for investigating 333 Chinese high school learners’ conceptions, metacognitive self-regulation, and strategies in science. The confirmatory factor analysis results verified the validity of the three surveys. Moreover, the path analyses revealed a series of interesting findings. Learners with lower-level COLS, namely “memorizing,” “testing,” and “practicing and calculating,” tended to use surface learning strategies such as “minimizing scope of the study” and “rote learning.” However, learners’ higher-level COLS, namely “increase of knowledge,” “applying,” “understanding,” and “seeing in a new way,” had complicated connections with their SROLS and SLS. On the one hand, learners’ higher-level COLS had negative relations to “minimizing scope of the study” and “rote learning.” On the other hand, their higher-level COLS were powerful predicators for their metacognitive self-regulation and further affected their use of “deep strategy” and “rote learning.” Though Chinese secondary students with higher-level COLS usually have a negative view of “rote learning,” the functioning of their metacognitive self-regulation may change their initial attitudes towards the surface strategy. Learners with higher-level COLS still used “rote learning” as a prior step for achieving deep learning. Therefore, we concluded that the SROLS played an important mediating role between the COLS and SLS and may change learners’ original intention to utilize learning strategies.     

Facilitating self-directed learning (SDL) and satisfaction with SDL among pre-university students

The aim of the study was to evaluate our practice of self-directed learning (SDL) among pre-university students in Malaysia. Respondents provided data on their previous school learning experiences besides present SDL experiences in college. We carried out exploratory factor analysis based on the school data. We did a confirmatory factor analysis using College SDL experiences of students. Given high similarities between the measurement models, we decided to use the original structure of the instrument. Students provided feedback using a questionnaire based on Prociuk’s. A large majority declared that they needed SDL experiences which they lacked while at school. The study also showed that students had rated their SDL experiences in college more positively than in school, on four factors of SDL experiences. Pearson correlations showed that “knowledgeable and organised teachers” and “promotion of active learning” correlated significantly with students’ current satisfaction with SDL in college.     

Modelling of factors influencing gender difference in mathematics achievement using TIMSS 2011 data for Singaporean eighth grade students

Numerous studies have attributed gender difference in mathematics achievement to various sociocultural influences. Singapore is a country of higher gender equality as represented in the Global Gender Gap Index and Singaporean girls perform as well or higher than boys in international mathematics assessments. This study develops a conceptual model to examine the relationship and effects of parental involvement in education, teacher efficacy, and students’ attitudes towards mathematics on mathematics achievement for Singaporean eighth grade students using Trends in International Mathematics and Science Study (TIMSS) 2011 data. The study finds that there is no significant gender difference in parental involvement in education and teacher efficacy and there is no gender difference in the attitude of like learning mathematics among Singaporean eighth grade students. The attitude of confidence in mathematics has positive and significant effect on mathematics achievement and the effect is greater for girls than boys. Parental involvement in education and teacher efficacy were found to have greater effect on girls’ confidence in mathematics than on boys’. As such, increasing involvement in mathematics education and providing positive reinforcement to raise girls’ self-confidence in mathematics by parents and teachers should be an integral part of any initiative to reduce gender gap in mathematics achievement.     

Secondary school students' conceptions of learning and their relationship to achievement

Conceptions of learning were investigated in three studies. Study 1 piloted a modified version of Purdie and Hattie's (2002) Conceptions of Learning Inventory (COLI-I) with 236 secondary students. Multilog analysis was used to remove items with poor measurement characteristics. Study 2 used a nationally representative sample of 701 New Zealand secondary school students who completed the COLI-II. The measurement model had marginally acceptable fit. Study 3 consisted of 608 secondary students who completed a slightly revised COLI-III and provided standardised academic reading and mathematics achievement data. The Study 2 and 3 samples were found to have configural invariance and the structural model mapping students' conceptions of learning onto their academic achievement had acceptable fit. The conception that learning is a duty predicted lower achievement and the conception of learning as continuous predicted higher achievement. This is the first study to empirically demonstrate a direct relationship between learning conceptions and academic outcomes in the secondary sector.     

Investigating the link between self directed learning readiness and project-based learning outcomes: the case of international Masters students in an engineering management course

Modern learning approaches increasingly have fewer structured learning activities and more self-directed learning tasks guided through consultation with academics. Such tasks are predominately project-/problem-based where the student is required to follow a freely guided road map to self discovery while simultaneously achieving desired learning outcomes for a particular course. However, many international students struggle to adjust to an Australian higher learning environment where they are being increasingly encouraged to undertake self directed learning (SDL). Thus, this paper proposes the concept that international students who have higher readiness for SDL gain greater learning outcomes from project-based learning (PBL) approaches. To achieve this objective, a questionnaire survey of 26 students (65% of class) completing an engineering management course was conducted. Linear regression analysis provided evidence that SDL readiness was a key enabler for achieving learning outcomes from PBL. In particular, having high self-management skills was shown to be the most significant and reliable predictor for achieving learning outcomes from PBL. Through understanding students SDL readiness at the commencement of their engineering programmes, academics can better tailor PBL support mechanisms to achieve desired learning outcomes.     

Tablet-based AR technology: Impacts on students’ conceptions and approaches to learning mathematics according to their self-efficacy

Most studies of Augmented Reality (AR) in education have considered students’ learning outcomes and motivation. Previous studies have revealed that AR has the potential to help students learn abstract conceptions in mathematics. In this paper, a series of statistics and probability lessons using AR installed on tablets was designed and developed to examine the effect of the AR technology by comparing the conceptions and learning approaches of junior high school students with different levels of self-efficacy. A total of 101 students were divided into two groups based on their mathematics learning self-efficacy. The analysis of the results shows that AR applications in mathematics courses can help students with higher self-efficacy to pay closer attention to higher level conceptions. It can also help higher self-efficacy students to apply more advanced strategies when learning mathematics.     

Variation in Student Reflections on their Conceptions of and Approaches to Learning Biochemistry in a First‐year Health Sciences’ Service Subject

Many factors affect students’ learning approaches, including topic conceptions and prior study. This research, undertaken after a first‐semester compulsory subject, explores students’ conceptions of biochemistry and how they approached their studies. Students (n=151) completed an open‐ended survey analysed phenomenographically. Those with cohesive conceptions were found to be more likely to adopt deeper approaches to study than those with fragmented conceptions, a result unaffected by various demographic parameters. Compared with earlier research, a semester of study increased the percentage of students with a cohesive view, with no concomitant change in learning approaches, suggesting that cohesive conceptions are a necessary but not sufficient criterion for deep learning outcomes. Compared with results for a science major subject, more of the students with cohesive conceptions used surface approaches. This may reflect a regression to safe surface approaches when faced with an unfamiliar topic or high total workload driving a strategic approach to learning. It could also reflect a perception that this material is only a tool for later application. The present findings indicate the crucial importance, when university studies begin, of enabling students to build an overarching conception of the topic’s place in professional practice. This concept building should be applied across the entire curriculum to emphasize application and integration of material (key graduate attributes). Improved conceptions may provide crucial motivation for students to achieve deeper learning, especially in these foundation service subjects. These essential changes to the learning context may also better prepare students for increasing self‐directed/life‐long learning.     

Resisting reductionism in mathematics pedagogy

Although breaking down a mathematical problem into smaller parts can often be an effective solution strategy, when the same reductionist approach is applied to mathematics pedagogy the effects are far from beneficial for students. Mathematics pedagogy in UK schools is gaining an increasingly reductionist flavour, as seen in an excessive focus on bite-sized learning objectives and a tendency for mathematics teachers to path-smooth their students’ learning. I argue that a reductionist mathematics pedagogy severely restricts students’ opportunities to engage in authentic mathematical thinking and deprives them of the enjoyment of solving richer, more worthwhile problems, which would forge connections across diverse areas of the subject. I attribute the rise of a reductionist mathematics pedagogy partly to an assessment-dominated curriculum and partly to a systemic de-professionalisation of teachers through a performative accountability culture in which they are constantly required to prove to non-specialist managers that they are effective. I argue that pedagogical reductionism in mathematics must be resisted in favour of a more holistic approach, in which students are able to bring a variety of mathematical knowledge and skills to bear on rich, challenging and non-routine mathematical tasks. Some principles for achieving this are outlined and some examples are given.     

Researching research: mathematics education in the Political

We discuss contemporary theories in mathematics education in order to do research on research. Our strategy consists of analysing discursively and ideologically recent key publications addressing the role of theory in mathematics education research. We examine how the field fabricates its object of research by deploying Foucault’s notion of bio-politics—mainly to address the object “learning”—and ?i?ek’s ideology critique—to address the object “mathematics”. These theories, which have already been used in the field to research teaching and learning, have a great potential to contribute to a reflexivity of research on its discourses and effects. Furthermore, they enable us to present a clear distinction between what has been called the sociopolitical turn in mathematics education research and what we call a positioning of mathematics education (research) practices in the Political.     

Relational Analysis of College Science‐Major Students’ Epistemological Beliefs Toward Science and Conceptions of Learning Science

In recent years, there has been an increasing interest among educational researchers in exploring the relationships between learners’ epistemological beliefs and their conceptions of learning. This study was conducted to investigate these relationships particularly in the domain of science. The participants in this study included 407 Taiwanese college science‐major students. All of them responded to two major questionnaires, one assessing their scientific epistemological beliefs (SEBs) and the other one probing their conceptions of learning science (COLS). The SEB questionnaire included four factors: “certainty,” “source,” “development,” and “justification” of science knowledge. The COLS survey consisted of six factors in a hierarchical order, that is, learning science as “memorizing,” “preparing for tests,” “calculating and practicing,” “increasing one’s knowledge,” “application,” and “understanding and seeing in a new way.” The students’ confidence and interest toward learning science were also assessed by additional questionnaire items. Stepwise regression analyses, in general, showed coherence between students’ SEBs and their COLS, indicating that the sophistication of SEBs was consistent with less agreement with lower‐level COLS (such as “memorizing” and “preparing for tests”) as well as more agreement with higher‐level COLS (such as “understanding and seeing in a new way”). However, the SEB’s “justification” factor was positively related to almost all of COLS factors from the lower‐level to higher‐level. This study finally found that among all of the SEB and COLS factors, the “preparing for tests” factor in COLS was the solely significant variable for predicting students’ interest in science and confidence toward learning science.     

Student engagement and mathematics achievement: Unraveling main and interactive effects

The present study explored the relationships between student engagement and mathematics achievement for 295,416 15‐year‐old students from 11,767 secondary schools in 34 countries who participated in the Program for International Student Assessment (PISA) 2012. Affective engagement was measured by students’ mathematics interest (InterestMath) and perceived usefulness of schooling (PerceptionSch), behavioral engagement by behaviors facilitating mathematics learning (BehaviorMath) and participation in mathematics learning activities (ActivitiesMath), and cognitive engagement by openness (Openness) and perseverance (Perseverance) in problem‐solving. Results showed that students who were more engaged had higher levels of academic achievement, with cognitive engagement having the strongest association with achievement. Results also showed that students who were highly engaged in two domains had higher achievement levels than peers who were engaged in only one domain in six pairwise comparisons (InterestMath‐BehaviorMath, InterestMath‐Openness, InterestMath‐Perseverance, PerceptionSch‐BehaviorMath, PerceptionSch‐Openness, PerceptionSch‐Perseverance). These results highlighted the importance of a whole‐school based approach in enhancing student achievement.