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Student achievement in mathematics – the roles of attitudes, perceptions and family background
Student engagement in mathematics The December 2004 issue of Education Matters^{1} reported on the latest results from the Programme for International Student Assessment (PISA) for student achievement in mathematics. PISA 2003 found that, among the 41 participating countries, students in only two – Hong KongChina and Finland – performed better than Canadian students in math. Students in seven other countries performed as well as Canadian students, while students in the remaining countries performed less well. In fact, students in three provinces – Alberta, Quebec and British Columbia – ranked among the best in the world. Drawing on analysis of the PISA 2003 results,^{2} this article looks at two sets of factors that affect student achievement in mathematics. The first consists of the role played by student attitudes to, and perceptions of, mathematics. The second consists of the relationship between parental education and occupation and students’ math performance.Student engagement in mathematicsStudent engagement in mathematics refers to students’ motivation to learn mathematics, their confidence in their ability to succeed in mathematics and their emotional feelings about mathematics. Student engagement in mathematics plays a key role in the acquisition of math skills and knowledge – students who are engaged in the learning process will tend to learn more and be more receptive to further learning. Student engagement also has an impact upon course selection, educational pathways and later career choices.Canadian 15yearold students appear to be well motivated to learn mathematics. While they were just as interested in mathematics and enjoyed it as much as students in OECD countries as a whole, they believed more strongly in its usefulness to their future employment and education. The views that students form about their own competence in mathematics may affect the goals they set, as well as their achievement. Compared to the OECD average, Canadian students were more confident that they could succeed in mathematics. Canadian students reported aboveaverage levels of mathematics confidence and aboveaverage levels in their perceived ability in mathematics.Compared to the Canadian average, students in Quebec and Alberta reported higher levels of mathematics confidence; students in Newfoundland and Labrador and British Columbia did not differ significantly from the Canadian average; students in the remaining provinces reported lower levels of mathematics confidence compared to the Canadian average. Compared to the Canadian average, students in Alberta and Quebec reported aboveaverage levels in their perceived ability in mathematics while students in Ontario, Manitoba, and British Columbia reported belowaverage levels. Math anxiety may impede learning and lead to the avoidance of mathematics. Compared to the OECD average, 15yearold students in Canada reported slightly lower levels of anxiety in dealing with mathematics. Students in Newfoundland and Labrador, Prince Edward Island, and Nova Scotia reported levels of mathematics anxiety below the Canadian average. Students in Ontario reported levels of anxiety above the Canadian average. The level of anxiety reported by students in other provinces was not significantly different from the Canadian average.Both provincially and Canadawide, students with high levels of mathematics confidence performed the equivalent of two proficiency levels higher on the combined mathematics scale than did students with low levels. Students with high levels of math anxiety performed the equivalent of one proficiency level lower in mathematics than did students with low levels. Motivation to learn mathematics, as measured by interest and enjoyment in math and belief in its usefulness, was also positively related to achievement. Figure 1: Combined mathematics score for students with high mathematics engagement compared to students with low mathematics engagement* Students low on a given index are defined as those falling one standard deviation below the average, students high on a given index are defined as those falling one standard deviation above the average. Source: Human Resources and Skills Development Canada, Council of Ministers of Education, Canada and Statistics Canada, 2004, Measuring Up: Canadian Results of the OECD PISA Study: The Performance of Canada's Youth in Mathematics, Reading, Science and Problem Solving, 2003 , Vol. 2, Catalogue number 81590XIE2004001.. Girls generally reported less confidence in their ability to solve mathematical problems, lower levels of perceived ability to learn mathematics and higher levels of anxiety in dealing with mathematics. Girls were also less likely to believe that mathematics would be useful for their future employment and education and were more likely to report lower levels of interest and enjoyment in mathematics. These differences may play a role in shaping the educational and occupational choices made by boys and girls. The relationship between student engagement in mathematics and math achievement is complex and often circular. Which is cause and which is effect? For example, are high motivation and confidence and reduced anxiety the causes of strong performance or byproducts of doing well in mathematics? Regardless, the strong link between student engagement in mathematics and math performance suggests that high motivation and selfconfidence and low mathematics anxiety are important outcomes in themselves. The more students succeed in mathematics the more likely they are to believe that they can succeed; the more students believe they can succeed the more engaged they will become with learning mathematics.The relationship between parental educational attainment and student achievementParents play an important role in their children’s learning. Aside from being actively involved in their children’s education, parents also provide a home environment that can affect learning. Parents serve as a model for learning, determine the educational resources available in the home and hold particular attitudes and values towards education. Although it is difficult to examine the home environment of each student, the educational attainment and occupation of parents serve as an indicator of the values and resources with which parents create this environment.For Canada as a whole, the average math scores of students whose parents had high school or less were significantly lower than the average scores of students whose parents had college or university. For example, the gap in average performance between students who had at least one parent with a university degree compared to those whose parents had no more than a high school education was about twothirds of a proficiency level. However, while there is a positive relationship between the educational level of the parents and student performance in mathematics, there also is considerable overlap in the performance of students from different educational backgrounds. In fact, many students whose parents had a high school education or less scored higher than students whose parents had a university degree. For example, onequarter of the students who scored in the top 15% of students had parents who had at most a high school education. Similarly, onequarter of those in the bottom 15% of students had at least one parent with a university degree.Given the wide range of student performance within each group, it is clear that the success of many students appears to be dependent on factors other than their parents’ level of education. Parental occupation and rolemodellingParental occupation may influence student performance in various ways. For example, occupationrelated income may determine access to learning opportunities and resources and so play a role in learning outcomes. The education and types of skills associated with different occupations and modeled by parents may motivate students to develop their own skills in particular ways. Parental occupation may also influence how students perceive the value of mathematics learning, their beliefs about the usefulness of mathematics and the learning environment at home.If occupation is considered as an indicator of parental skill use, it appears that students whose parents worked in occupations with greater skill requirements also performed better in mathematics. However, the large overlap between groups also indicates that there are still large differences within occupational categories. Some of these differences may be explained by the specific skills parents use in their occupations. Looking only at students whose parents were in professional or managerial occupations – occupations that typically require at least a college education and higherthanaverage incomes – considerable differences were found in student mathematics achievement. Students whose parents had occupations that specifically required strong math skills – that is, physical, mathematical and engineering science professionals – tended to have higher math scores than other students. Students whose parents were in the occupational category that includes legislators, senior officials, executives and managers in fact performed almost one proficiency level lower than students whose parents worked in the mathematicsintensive occupational group.Family socioeconomic status and student performanceSocioeconomic status (SES) is a term used to summarise a variety of factors, including parental education and occupation, that influence student performance. In PISA 2003, SES is measured by an index that includes information describing family structure, parental education and occupation, parental labour market participation, and whether a student’s family has specific educational and cultural possessions at home.Analysis of the PISA 2000 results, which focussed mainly on literacy, found that students from higher socioeconomic families tended to show stronger literacy skills.^{3} The same result is found for PISA 2003 – students from families with higher socioeconomic status also tended to perform better in mathematics. However, compared to the OECD countries as a whole, differences in socioeconomic status had a smaller impact on student achievement in Canada. Furthermore, differences in socioeconomic status among Canadian students also were smaller than in most OECD countries.Both theory and evidence suggest that students’ knowledge and behaviour, including academic outcomes, are influenced by the characteristics of the schools they attend. Schools may have higher or lower average SES, depending on whether their students are predominantly from low or high SES families. The socioeconomic background of a school population may reflect the socioeconomic conditions of the community where the school is located and thus be a community characteristic as well as a school characteristic. Schools can play an important role in moderating the effects of individual socioeconomic status. Students tended to perform better, on average, in schools with higher average SES, regardless of their socioeconomic backgrounds. In other words, students are not only affected by the socioeconomic circumstances of their own parents, but by those of their peers as well. This may have a positive effect for students surrounded by positive peer influences and role models. It may also doubly disadvantage students from lower SES families attending schools that consistent predominantly of students with similar backgrounds.ConclusionThe results summarized here highlight the link between student engagement in mathematics and math achievement. In fact, students with high mathematics confidence performed about two proficiency levels higher than did students with low confidence. Furthermore, students with high math anxiety performed the equivalent of one proficiency level lower than students with low anxiety. These results suggest that high mathematics confidence and low mathematics anxiety may be important outcomes on their own.Family background was also related to student performance in mathematics. Students whose parents were universityeducated performed about twothirds of a proficiency level higher than those whose parents had no more than a high school education. However, there is an important nuance to add to this finding. Students whose parents worked in an occupation that required advanced mathematics skills in fact performed almost one proficiency level higher than students whose parents had similar education levels and income but whose occupation did not require advanced mathematics. This raises a number of research questions. For example, is this the result of parents passing on innate ability to their children? To what extent does rolemodelling and creating a home environment that is oriented to mathrelated activities play a role? Are children in these households more likely to receive assistance from parents in their quest to master mathematical concepts? PISA collected a wide range of information about the students, their parents, their home environments and their schools. Research that further explores the connections among these can help us to answer such questions.Notes

