Towards a theory of mathematics homework as a social practice

This article presents a theoretical conceptualization of mathematics homework as a social practice. Rather than considering homework as a task or an artifact, this approach frames homework in terms of the social contexts in which students participate and how students participate in those contexts. This perspective has long been suggested by homework researchers but has not been developed as a framework for understanding homework. Drawing from Wenger’s (1998) social theory of learning and research grounded in sociocultural theory, this conceptualization makes central meaning making and identity development, and puts forth meaning and identity as lenses for understanding students’ participation in the practice of mathematics homework. To further develop this conceptualization of homework, I draw on data from an ethnographic study of the role and meaning of mathematics homework in the lives of middle school students. Case studies of two students are presented to demonstrate the relationships among the meaning of homework, students’ identities, and their participation in the practice of homework. One student’s experiences support him in identifying as a capable mathematics student who is bound for continued academic success through high school to college. Thus, he comes to take on mathematics homework as a means to learn and succeed. The other student’s experiences support him in building an identity that leads him to reject homework. This conceptualization of homework and the case study data have implications for the practice of homework and for theories of students’ motivational dispositions in the context of mathematics homework and learning in general.     

Does homework design matter? The role of homework's purpose in student mathematics achievement

This study used a randomized pretest–posttest clustered design to examine the effect of 3 homework purposes (i.e., practice, preparation, and extension) on 6th graders' mathematics achievement and how this relationship was modulated by the amount of completed homework. A total of 27 mathematics teachers and their 638 students participated in this study. Once a week for six weeks, the teachers assigned tasks that had a specific type of homework purpose according to their treatment condition. At the end of the six weeks, the students completed a non-standardized mathematics achievement test. The results of multilevel modeling showed that after controlling for student characteristics and class-level variables, extension homework positively impacted students' mathematics achievement, while practice and preparation homework did not. These findings were not related to the amount of homework that was completed by the students. The findings highlighted the importance of the teacher's role in the first phase of the homework process (i.e., designing homework with a specific purpose) and provide important data for teachers and school administrators to reflect upon when conducting actual homework practices.     

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.     

The relationship between homework time and achievement is not universal: evidence from multilevel analyses in 40 countries

Although homework is generally believed to be an important supplement to in-school learning, research has not yet fully clarified the relationship between homework and achievement. This cross-cultural study analyzed the relationship between homework time and mathematics achievement drawing on data from 231,759 students in 9,791 schools and 40 countries who participated in the Programme for International Student Assessment (PISA) 2003. Multilevel analyses found a positive association between school-average homework time and mathematics achievement in almost all countries, but the size of the association decreased considerably once socioeconomic background and school track were controlled. At the student level, no clear-cut relationship was established between homework time and achievement across the 40 countries. The results highlight the need to use multilevel analyses and to control for confounding variables in homework research.     

The relationship between homework and the academic progress of children in Spain during compulsory elementary education: A twin fixed-effects approach

Homework has traditionally been considered positive for students’ academic achievement, to the extent that it makes children more responsible while learning. Nevertheless, making students do a large amount of homework has been one of the most criticised practices in recent years. Parental associations have long held the view that Spanish elementary school pupils spend too much time on homework. This situation is so alarming that it has recently caused a ‘homework strike’, which has been supported by many children's parents. Furthermore, being assigned an excessive amount of homework is a serious problem which extends well beyond Spain. In light of this context, this article aims to provide new evidence on the relationship between homework and academic performance. To carry out this research, rich longitudinal census data, together with a twin fixed-effects approach and value-added models, have been used. In this way, we can control for variables that are the same within twins, allowing us to generate a better understanding of the association between homework time and primary children's academic achievement. Our main finding is that homework is not associated with young people's academic achievement (at least within this specific country context).     

The quality of secondary education in the Middle East and North Africa: what can we learn from TIMSS’ results?

Research on educational quality has been scarce in the Middle East and North Africa (MENA) region, whereas the debates over educational quality date from 1966 in the USA with the Coleman Report. Fortunately TIMSS (Trends in International Mathematics and Science Study) starts to fill this gap by providing data on students’ achievement and for many MENA countries this is the first time that such data are available. The paper gives an overview of the quality of education in MENA using TIMSS’ 2007 data. The research questions addressed here are why is achievement low? And why is the gap between the top‐performing countries and MENA countries large? In order to answer these questions, the paper focuses on several aspects: the first is the inefficiency of acquiring the language, the second is the inefficiency of time devoted to homework, the third is the meagre intended curriculum which is translated into a weaker implemented curriculum, the fourth aspect deals with the inefficiency of public resources devoted to the education sector. Finally, the paper highlights two other factors believed to affect students’ achievement: family background and students’ attitudes towards mathematics and science.     

The impacts of student-, teacher- and school-level factors on mathematics achievement: an exploratory comparative investigation of Singaporean students and the USA students

Reports from the Trends in International Mathematics and Science Study (TIMSS) consistently show that there is a substantial gap in average mathematics achievement between Singapore and the USA. This study conducts an exploratory comparative investigation on the multilevel factors influencing the mathematics achievement of students from these two countries. A conceptual framework together with an integrated model is proposed for the analysis. The TIMSS 2011 eighth grader mathematics data were chosen for this study. Results reveal that the common features influencing mathematics achievement for the students of both countries are student self-confidence, school composition by student background and teacher confidence in teaching mathematics. The cause of the different effects of American students’ mathematics achievement is more associated with resources, whereas the effects of Singaporean students’ mathematics achievement are more related to attitudes, expectations and motivations. The major elements that affect Singaporean student mathematics performances are at the teacher level. Suggestions for future research are discussed.     

Relationship between affect and achievement in science and mathematics in Malaysia and Singapore

Background : The Trends in International Mathematics and Science Study (TIMSS) assesses the quality of the teaching and learning of science and mathematics among Grades 4 and 8 students across participating countries.

Purpose : This study explored the relationship between positive affect towards science and mathematics and achievement in science and mathematics among Malaysian and Singaporean Grade 8 students.

Sample : In total, 4466 Malaysia students and 4599 Singaporean students from Grade 8 who participated in TIMSS 2007 were involved in this study.

Design and method : Students’ achievement scores on eight items in the survey instrument that were reported in TIMSS 2007 were used as the dependent variable in the analysis. Students’ scores on four items in the TIMSS 2007 survey instrument pertaining to students’ affect towards science and mathematics together with students’ gender, language spoken at home and parental education were used as the independent variables.

Results : Positive affect towards science and mathematics indicated statistically significant predictive effects on achievement in the two subjects for both Malaysian and Singaporean Grade 8 students. There were statistically significant predictive effects on mathematics achievement for the students’ gender, language spoken at home and parental education for both Malaysian and Singaporean students, with R ² = 0.18 and 0.21, respectively. However, only parental education showed statistically significant predictive effects on science achievement for both countries. For Singapore, language spoken at home also demonstrated statistically significant predictive effects on science achievement, whereas gender did not. For Malaysia, neither gender nor language spoken at home had statistically significant predictive effects on science achievement.

Conclusions : It is important for educators to consider implementing self-concept enhancement intervention programmes by incorporating ‘affect’ components of academic self-concept in order to develop students’ talents and promote academic excellence in science and mathematics.     

“Did you do your homework?” Mathematics teachers’ homework follow‐up practices at middle school level

Teachers’ homework follow‐up practices, the in‐class strategies teachers use to monitor their students’ homework assignments, have an impact on their students’ homework behaviors and academic achievement. The current study explored the perspectives of middle school mathematics teachers on the three domains of homework follow‐up: the practices used in class, the purposes of each practice, and the aspects that may influence this process. Data were collected from two data sources (i.e., focus groups and classroom observations) and were analyzed using thematic analysis. The findings showed that teachers monitored homework either using a single strategy or a combination of strategies (e.g., checking homework completion and providing individual feedback) linked to a specific purpose (e.g., promote students’ involvement). The teachers also reported that they were under certain constraints when they delivered homework follow‐up practices (e.g., pressure to follow the curriculum), so their practices’ effectiveness sometimes can be compromised. Implications for practice are discussed.     

Student perceptions of the classroom environment: Relations to motivation and achievement in mathematics

This study examined the relationship of 979 middle school students’ perceptions of their mathematics classroom environment to their motivation and achievement. Structural equation modeling indicated that motivational variables (utility, personal achievement goals, efficacy) mediated the influence of perceived teacher expectations, teacher support and use of reform practices on mathematics standardised test scores. Our study provides empirical evidence that students’ perceptions that their teachers believe that they are capable of learning and understanding mathematics positively relate to their Mastery and Performance Goal orientations and mathematics Utility. Further, we found an interaction between students’ perceptions of the frequency of reform practice use in their mathematics classroom and mathematics efficacy. For students with lower mathematics efficacy, their perceptions of more frequent use of reform practices in their mathematics class related to higher standardised test performance. For students with higher mathematics efficacy, perceived use of reform practices did not significantly relate to standardised test performance. These data suggest that frequent exposure to reform practices is especially critical for students who judge themselves as being less capable in mathematics and who are lower performers. This finding differs from prior research that has suggested that reform practice use benefits higher achievers but not lower achievers. An important implication of our study is the need for coordinated, ongoing professional development that highlights reform pedagogy and beliefs while also focusing on student motivation theories and strategies.     

Got math attitude? (In)direct effects of student mathematics attitudes on intentions,behavioral engagement,and mathematics performance in the U.S. PISA

Academic performance is predicted by a multitude of demographic, contextual, cognitive, and noncognitive factors. The noncognitive factors predicting achievement in mathematics that have previously been investigated in depth are study skills, confidence, self-efficacy, and personality traits (Kyllonen, 2012). Limited applied research has explored the predictive value of attitudes and beliefs in mathematics achievement using representative data of U.S. students. The current study uses the theory of planned behavior (TPB) to explain high school students’ performance in mathematics in large-scale assessment data by using the PISA 2012. Along with key demographic factors, results indicated that students’ attitudes, subjective norms, and perceived behavioral control beliefs explained 21.1% of the variability in intentions to pursue and major in mathematics in the future, 59.4% of the variability in behavioral engagement with mathematics learning, and 30.7% of the variability in mathematics performance.The study results have implications on: (1) the applicability of an attitude-behavior framework in educational research for understanding academic performance, (2) the importance of perceived control and self-efficacy beliefs for predicting behavioral engagement in mathematics (e.g., paying attention in class, completing homework, studying for exams) and subsequent mathematics performance, and (3) the practical significance of students’ attitude towards mathematics on their intentions to pursue mathematics coursework in post-secondary education and possess math-relevant career aspirations.     

Parental influences on primary school children's mathematics achievement: insights from the Longitudinal Study of Australian Children

Results from international mathematics tests are focussing the attention of national leaders on the learning of mathematics in the primary years. With this attention, comes the need to explore the factors that contribute to and impede this learning. Though much of this focus is on classroom practices, it is timely to examine the important influence that parents have on their children's achievement. This paper reports on a secondary analysis of data from a large longitudinal study in Australia; in particular, the effectiveness of Australian parents’ involvement in their children's homework. The results suggest that the actual help with homework has, on average, a negative effect on children's achievement even after controlling for earlier achievement. Significantly, however, the other types of involvement, such as provision of a good home environment, have positive effects on achievement. The implications of these findings are also discussed.     

What Can Mathematics Educators in England Learn from TIMSS?

In most of the countries taking part in TIMSS, students scored at similar levels for mathematics and science. England was one of the few countries where the results did not conform to this pattern. The key question for mathematics educators in England is: why did students in England perform relatively well in science but relatively badly in mathematics? The results for 9-year-olds were particularly intriguing since the majority of students at this age in England were taught mathematics and science by their class teacher. In order to seek answers to the question posed above, this article compares the responses to the TIMSS context questionnaires made by 9-year-olds and their teachers in the 13 European countries taking part in the TIMSS survey of that age group (Population 1). Issues examined include: curriculum content; lesson time; homework; class size; use of calculators in mathematics; practical activities in science; classroom organisation and students’ attitudes.     

优化作业设计提高数学教学效率探研

数学作业是数学教学的重要组成部分,是对数学课堂的拓展和延伸,能够让学生对课堂所学知识进行巩固和吸收。有效的作业布置,不仅能促进学生更好地学习数学知识,还能减轻学生的学习负担,提高教学效率和教学质量,提升学生数学核心素养。文章结合教学实践,对优化作业设计提高数学教学效率进行探研。     

Evidence-based decision making or a tunnel vision effect? TIMSS,problem definition and policy change in Israeli mathematics education

ABSTRACT

This study examines the influence of the Trends in International Mathematics and Science Study (TIMSS) 1999 results on mathematics education policy in Israel. Analyzing various documents, the study shows how these results transformed policymakers’ discourse regarding mathematics education. In order to achieve improvement in Israel’s ranking, the middle school mathematics curriculum was aligned with the TIMSS test. Following this change, the scores of Israeli students rose considerably in TIMSS 2011. Parallel results from Programme for International Student Assessment (PISA) and Israeli internal standardized tests, however, do not show comparable improvement in mathematics achievement. High school matriculation data for the same period of time show a decline in the percentage of students who took the most advanced mathematics courses. Furthermore, none of these data sources show any noticeable reduction in social inequality in mathematics achievement. On the basis of theoretical insights from political science, it is argued that international tests influence the way educational problems are framed and defined. Thus, instead of enriching educational decision-making processes, these tests can create a tunnel vision effect that restricts policymakers’ attention to ‘problems’ and ‘solutions’ defined by the tests themselves.     

Enhancing student achievement through computer-generated homework

The purpose of this study was to investigate the effects of interactive computer-generated homework on student achievement. Of two sections of Physical Science I, one received homework via the computer; the other received printed, equivalent homework assignments. The results of this study indicate that the use of drill-and-practice computer homework minimizes differences among students with a corresponding decrease in the correlation between posttest scores and entry-level combined ACT science and mathematics scores. The results also support the basic assumption of mastery learning that appropriate instruction will decrease the relationship between aptitude and achievement.     

Relationship between Science Teaching Practices and Students’ Achievement in Singapore,Chinese Taipei,and the US: An Analysis Using TIMSS 2011 Data

The assumption that inquiry-based instruction is more effective in influencing student science achievement than traditional didactic teaching has been the driving force of science education reform in recent decades and in many countries. However, the empirical relationship between these two kinds of science teaching and student science performance is not soundly established, which is worth a careful examination. Framed through the theoretical perspectives of inquiry-based instruction and culturally relevant pedagogy, using a two-level hierarchical linear modeling (HLM) approach and simultaneous multiple regression, this study examines the above relationship using the Trends in International Mathematics and Science Study (TIMSS) 2011 8th grade dataset from Singapore, Chinese Taipei, and the US. The study found that for the low-performing students, none of the inquiry-based teaching practice items measured had a significant relationship with the science achievements at any performance levels of students in any country/region except for the case of two inquiry-based teaching practice items that were positively related to Chinese Taipei students’ achievements. No didactic teaching practice items were associated with the Singapore students’ science achievement, three of these practice items were found negatively related to Chinese Taipei students’ science achievement, and one traditional didactic teaching practice was negatively related to the science achievement of U.S. students. However, for medium- and high-performing students, none of these inquiry-based or traditional didactic science-teaching practices were found to be positive predictors of science performance in all three countries/regions. However, in the case of Chinese Taipei, one didactic teaching practice item was negatively related with the medium level performing students’ achievement and two didactic teaching practices were found to hinder high-performing students’ science achievements.     

数学作业的布置与批改探析

作业是数学教学中的关键环节,通过作业能够检验学生的课堂学习效果,但当前学生数学作业的完成效率不高。数学教师只有在作业中体现趣味性、层次性和差异性,与生活相结合,并在数学作业批改时坚持及时性、启发性原则,做到多种批改、分项评价、一题多改,采用多样化作业批改方式,才能引导学生在完成作业的过程中提高数学素养。     

Learning environment and students’ mathematics attitude

This study investigated the association between students’ perception of the learning environment and three aspects of their mathematics attitude: ‘mathematics academic self-concept’, ‘enjoyment of mathematics’ and ‘perceived value of mathematics’. The focus was on the association of students’ mathematics attitude with four dimensions in the learning environment: the extent to which the teacher ‘motivates to exert learning effort’, ‘activates towards self-regulated learning’, ‘gives feedback and coaches’, and ‘structures and steers’. Data were obtained from an extended version of the international Trends in Mathematics and Science Study (TIMSS) of 2003. Multilevel analysis on a sample of 4354 eighth grade students in 228 classes in 119 schools in Flanders (Belgium) indicated that the learning environment plays a significant role in the enjoyment of mathematics. This while the mathematics academic self-concept and the perceived value of mathematics are insensitive for aspects in the learning environment.     

Investigating Flipped Learning: Student Self-Regulated Learning,Perceptions, and Achievement in an Introductory Biology Course

In flipped classrooms, lectures, which are normally delivered in-class, are assigned as homework in the form of videos, and assignments that were traditionally assigned as homework, are done as learning activities in class. It was hypothesized that the effectiveness of the flipped model hinges on a student’s desire and ability to adopt a self-directed learning style. The purpose of this study was twofold; it aimed at examining the relationship between two variables—students’ perceptions of the flipped model and their self-regulated learning (SRL) behaviors—and the impact that these variables have on achievement in a flipped class. For the study, 76 participants from a flipped introductory biology course were asked about their SRL strategy use and perceptions of the flipped model. SRL strategy use was measured using a modified version of the Motivated Strategies for Learning Questionnaire (MSLQ; Wolters et al. 2005), while the flipped perceptions survey was newly derived. Student letter grades were collected as a measure of achievement. Through regression analysis, it was found that students’ perceptions of the flipped model positively predict students’ use of several types of SRL strategies. However, the data did not indicate a relationship between student perceptions and achievement, neither directly nor indirectly, through SRL strategy use. Results suggest that flipped classrooms demonstrate their successes in the active learning sessions through constructivist teaching methods. Video lectures hold an important role in flipped classes, however, students may need to practice SRL skills to become more self-directed and effectively learn from them.