4 Mathematics Self-Beliefs And Participation In .
42Mathematics Self-Beliefs andParticipation in Mathematics-RelatedActivitiesThis chapter examines several ways in which students’ beliefs in their ownmathematics skills manifest themselves: self-efficacy (the extent to whichstudents believe in their own ability to solve specific mathematics tasks),self-concept (students’ beliefs in their own mathematics abilities), anxiety(feelings of helplessness and stress when dealing with mathematics),students’ engagement in mathematics activities at and outside school,and students’ intentions to pursue mathematics-related studies or careersin the future. These are analysed in relation to mathematics performance,gender and socio-economic status. Trends in students’ mathematics selfbeliefs since 2003 are also examined.READY TO LEARN: STUDENTS’ ENGAGEMENT, DRIVE AND SELF-BELIEFS – VOLUME III OECD 201379
4Mathematics Self-Beliefs and Participation in Mathematics-Related ActivitiesHow students think and feel about themselves shapes their behaviour, especially when facing challenging circumstances(Bandura, 1977). Education systems are successful when they equip students with the ability to influence their own lives(Bandura, 2002). Mathematics self-beliefs have an impact on learning and performance on several levels: cognitive,motivational, affective and decision-making. They determine how well students motivate themselves and persevere in theface of difficulties, they influence students’ emotional life, and they affect the choices students make about coursework,additional classes, and even educational and career paths (Bandura, 1997; Wigfield and Eccles, 2000).In 2012 PISA investigated a range of self-beliefs: mathematics self-efficacy (the extent to which students believe in theirown ability to handle mathematical tasks effectively and overcome difficulties), mathematics self-concept (students’beliefs in their own mathematics abilities), mathematics anxiety (thoughts and feelings about the self in relation tomathematics, such as feelings of helplessness and stress when dealing with mathematics), and student engagement inmathematics activities at and outside school. Results confirm previous evidence that different mathematics self-beliefsare related, but are conceptually distinct (see Pajares and Kranzler, 1995; Pajares and Miller, 1994; Lent, Lopez andBieschke, 1991; Lee, 2009).What the data tell us Some 30% of students reported that they feel helpless when doing mathematics problems: 25% of boys, 35% ofgirls, 35% of disadvantaged students, and 24% of advantaged students reported feeling that way. On average across OECD countries, greater mathematics anxiety is associated with a 34-point lower score inmathematics – the equivalent of almost one year of school. Countries in which mathematics anxiety decreased or did not change are more likely to be those where students’mathematics self-concept or self-efficacy improved. Figure III.4.1 Mathematics self‑beliefs, dispositions and participation in mathematics‑related activitiesMathematics self-efficacyConstructed index based on students’ responses abouttheir perceived ability to solve a range of pure andapplied mathematics problemsMathematics self-conceptConstructed index based on students’ responses abouttheir perceived competence in mathematicsMathematics anxietyConstructed index based on students’ responses about feelingsof stress and helplessness when dealing with mathematicsDispositions towards mathematics (Mathematics intentionsand Subjective norms in mathematics)Constructed indices based on students’ responses about whetherthey intend to use mathematics in their future and whetherstudents’ parents and peers enjoy and value mathematicsMathematics behavioursConstructed indices based on students’ responses abouttheir participation in a range of mathematics-related activities80 OECD 2013 READY TO LEARN: STUDENTS’ ENGAGEMENT, DRIVE AND SELF-BELIEFS – VOLUME III
Mathematics Self-Beliefs and Participation in Mathematics-Related Activities4Mathematics self-beliefs illustrate students’ subjective convictions. While they are built into how well students perform inmathematics over the course of their lives, once established, they play a determining and independent role in individuals’continued growth and in the development of their mathematical skills and competencies (Bandura, 1997; Markusand Nurius, 1986). While they are partly the product of a students’ past performance in mathematics, mathematicsself-beliefs influence how students function when confronted with mathematical problems. In addition, they have anindependent effect on life choices and decisions. Students who perform similarly in mathematics usually choose differentcourses, educational pathways and ultimately different careers, in part depending on how they perceive themselves asmathematics learners (Bong and Skaalvik, 2003; Wang, Eccles and Kenny, 2013).MATHEMATICS SELF-EFFICACYThe term “self-efficacy” is used to describe students’ belief that, through their actions, they can produce desired effects,which, in turn, is a powerful incentive to act or to persevere in the face of difficulties (Bandura, 1977). Mathematicsself-efficacy refers to students’ convictions that they can successfully perform given academic tasks at designated levels(Schunk, 1991). While better performance in mathematics leads to higher levels of self-efficacy, students who have lowlevels of mathematics self-efficacy are at a high risk of underperforming in mathematics, despite their abilities (Bandura,1997; Schunk and Pajares, 2009). If students do not believe in their ability to accomplish particular tasks, they will notexert the effort needed to complete the tasks successfully, and a lack of self-efficacy becomes a self-fulfilling prophecy.While other factors apart from self-efficacy can guide and motivate students, when students do not believe in their abilityto succeed in a given task, they need to have much higher levels of self-control and motivation in order to succeed.Unfortunately, students who have low self-efficacy are less likely to regulate their achievement behaviors or be motivatedto engage in learning (Klassen and Usher, 2010; Schunk and Pajares, 2009). Figure III.4.2 Students’ mathematics self‑efficacyPercentage of students across OECD countries who reported feeling confident or very confident about doing thefollowing tasks%10080604020Calculating the petrol-consumptionrate of a carSolving an equationlike 2(x 3) (x 3)(x-3)Finding the actual distance betweentwo places on a map witha 1:10 000 scaleSolving an equation like 3x 5 17Understanding graphspresented in newspapersCalculating how many square metresof tiles you need to cover a floorCalculating how much cheaper a TVwould be after a 30% discountUsing a train timetable to work outhow long it would take to getfrom one place to another0Note: Results for each participating country and economy can be found in Table III.4.1a.Source: OECD, PISA 2012 Database, Table III.4.1a.1 2 http://dx.doi.org/10.1787/888932963844READY TO LEARN: STUDENTS’ ENGAGEMENT, DRIVE AND SELF-BELIEFS – VOLUME III OECD 201381
4Mathematics Self-Beliefs and Participation in Mathematics-Related ActivitiesPISA 2012 asked students to report on whether they would feel confident doing a range of pure and appliedmathematical tasks involving some algebra, such as using a train timetable to work out how long it would take to getfrom one place to another; calculating how much cheaper a TV would be after a 30% discount; calculating how manysquare meters of tiles would be needed to cover a floor; calculating the petrol-consumption rate of a car; understandinggraphs presented in newspapers; finding the actual distance between two places on a map with a 1:10 000 scale; andsolving equations like 3x 5 17 and 2(x 3) (x 3)(x-3). Students’ responses to questions about whether they feel veryconfident, confident, not very confident or not at all confident were used to create the index of mathematics self-efficacy,which identifies students’ level of self-efficacy in mathematics. The index was standardised to have a mean of 0 anda standard deviation of 1 across OECD countries (see Box III.2.1 for a detailed description of how PISA indices wereconstructed and how they should be interpreted).Tables III.4.7a and III.4.7b show that girls and socio-economically disadvantaged students are more likely to havelow levels of self-efficacy than boys and socio-economically advantaged students. A detailed analysis of gender andsocio-economic differences in students’ responses to questions about their level of confidence in tackling a number of Figure III.4.3 Gender and socio‑economic differences in mathematics self‑efficacyAll studentsBoysGirlsStudents in bottom quarter of ESCSStudents in top quarter of ESCSMean index1.501.000.500.00-0.50Chinese Poland*Korea*New Zealand*Singapore*France*Greece*United ak Republic*United Kingdom*Ireland*Japan*Russian Federation*Slovenia*OECD average*Sweden*Czech Republic*Denmark*Finland*Spain*Hong *Estonia*United Arab *Malaysia*Italy*Viet sta esia*Colombia*Thailand*-1.00Mean stria*Luxembourg*Switzerland*New Zealand*Australia*France*Hong Kong-China*Denmark*Netherlands*Finland*United Kingdom*Czech Republic*Iceland*Belgium*Israel*Japan*OECD a*Qatar*Costa Rica*Sweden*Chile*Italy*Lithuania*United States*Chinese Tunisia*Slovenia*United Arab Emirates*Serbia*Singapore*Argentina*Russian gal*Slovak et khstanAlbaniaMalaysia-1.00Notes: Countries/economies where the gender/socio-economic gap is significant are indicated with an asterisk.ESCS refers to the PISA index of economic, social and cultural status.Countries and economies are ranked in descending order of gender differences (bottom panel) and socio-economic differences (top panel) on the indexof mathematics self-efficacy.Source: OECD, PISA 2012 Database, Tables III.4.1c and III.4.1d.1 2 http://dx.doi.org/10.1787/88893296384482 OECD 2013 READY TO LEARN: STUDENTS’ ENGAGEMENT, DRIVE AND SELF-BELIEFS – VOLUME III
Mathematics Self-Beliefs and Participation in Mathematics-Related Activities4mathematical tasks reveal that across OECD countries 75% of girls feel confident or very confident about calculatinghow much cheaper a TV would be after a 30% discount, compared to 84% of boys. No gender differences in confidenceare observed when students are asked about doing tasks that are more abstract and clearly match classroom content,such as solving a linear or a quadratic equation. However, gender differences are striking when students are asked toreport their ability to solve applied mathematical tasks, particularly when the mathematics problem is presented in termsof tasks that are associated with stereotypical gender roles (such as calculating the petrol-consumption rate of a car). Onaverage across OECD countries, 67% of boys but only 44% of girls reported feeling confident about performing such acalculation (Table III.4.1b).While gender differences in mathematics self-efficacy and related beliefs about competence have long been a subject ofstudy (Eccles, 1984; Jacobs et al., 2002; Pajares and Miller, 1994), differences in self-efficacy related to socio-economicstatus are just as pervasive (Figure III.4.3). Disadvantaged students are generally less likely to feel confident about theirability to tackle specific mathematics tasks than advantaged students (Table III.4.7b). While these differences partly reflectdifferences in mathematics performance related to socio-economic status, these differences remain large and statisticallysignificant even when comparing students who perform similarly in mathematics (see Table III.7.3b and Chapter 7 moregenerally for a detailed discussion of differences in self-reported self-efficacy related to gender and socio-economic statusamong students with similar mathematics performance).Between 2003 and 2012, students’ mathematics self-efficacy increased slightly across OECD countries as studentsbecame more likely, for example, to report feeling confident about using a train timetable to work out how long itwould take to get from one place to another. However, this general trend masks the fact that students’ mathematicsself-efficacy decreased in New Zealand, Hungary, the Slovak Republic and Uruguay. In the Slovak Republic, Hungaryand New Zealand, for example, the percentage of students who reported that they feel confident in calculating howmany square metres of tiles are required to cover a floor dropped by at least eight percentage points during the period.Students’ reported mathematics self-efficacy increased in 21 countries and economies. Increases in mathematics selfefficacy were notable in Portugal, Germany, Thailand, Turkey and Spain where the index of mathematics self-efficacygrew by more than 0.2 units. Reflecting the increase in the mathematics self-efficacy, the share of students who reportedfeeling confident in calculating the price of a TV that has been discounted by 30%, for example, increased by more thanfive percentage points in Thailand, Greece, Portugal, Turkey, Germany, the Russian Federation and Japan between 2003and 2012 (Table III.4.1f) (Portugal’s improvement in PISA and recent educational policies and programmes is outlinedin Box III.4.1).Mathematics self-efficacy tended to increase among countries that show reduced levels of mathematics anxiety(correlation at the country level of -0.4, Table III.4.10). Such is the case in Portugal and Iceland where steep drops inmathematics anxiety coincided with increases in students’ mathematics self-efficacy. The relationship between students’mathematics self-efficacy and their mathematics performance was strong in 2003 and remained strong in 2012 (acorrelation of 0.5), on average across OECD countries and for 23 countries and economies.Boys’ and girls’ mathematics self-efficacy improved slightly between 2003 and 2012. On average across OECD countries,boys’ mathematics self-efficacy improved by 0.08 units, with a similar improvement observed among girls (0.06 units),maintaining the gender gap in mathematics self-efficacy in favour of boys at over 0.3 points. Despite this average trend,the gap in mathematics self-efficacy widened in favour of boys in France, Hong Kong-China, Iceland, New Zealand andAustralia. In France, Hong Kong-China, Iceland and Australia, mathematics self-efficacy increased more among boys thangirls; in New Zealand, the decrease in self-efficacy was greater among girls than boys. In Iceland, for example, boys in2012 were 5 percentage points less likely than boys in 2003 to feel confident about solving an equation like 3x 5 17,but girls were no more likely to feel such confidence. The gender gap in mathematics self-efficacy narrowed in MacaoChina, the Slovak Republic, Greece and Finland (Figure III.4.4a and Table III.4.1g).In 2012, socio-economically disadvantaged students reported lower levels of mathematics self-efficacy when comparedto their advantaged counterparts, and on average across OECD countries these differences remained similar to thosein 2003. Socio-economic disparities in mathematics self-efficacy widened in Portugal and Luxembourg due to a largerincrease in mathematics self-efficacy among advantaged students than among disadvantaged students, and in Latvia andCanada due to an increase in mathematics self-efficacy among advantaged students concurrent with no change amongdisadvantaged students. Differences in mathematics self-efficacy related to socio-economic status narrowed between2003 and 2012 in Thailand, the Slovak Republic, Uruguay, Sweden and Belgium. In Thailand, Sweden and Belgium thiswas mostly due to an increase in mathematics self-efficacy among disadvantaged students (Figure III.4.4b).READY TO LEARN: STUDENTS’ ENGAGEMENT, DRIVE AND SELF-BELIEFS – VOLUME III OECD 201383
4Mathematics Self-Beliefs and Participation in Mathematics-Related Activities Figure III.4.4a Change between 2003 and 2012 in the gender gap in mathematics self‑efficacyChange between 2003 and 2012 in the gender gap(boys–girls) on the index of mathematics self-efficacy0.3Boys’ advantage on the index of mathematicsself-efficacy has increased0.20.10-0.1Boys’ advantage on the index of mathematicsself-efficacy has decreased-0.2-0.3Macao-ChinaTurkeySlovak RepublicGreeceFinlandNetherlandsRussian lPolandThailandSpainOECD average 2003SwedenAustriaDenmarkLuxembourgCzech nited StatesKoreaNew ZealandIcelandFranceHong Kong-China-0.4Notes: Statistically significant changes at the 5% level (p 0.05) between PISA 2003 and 2012 are marked in a darker tone.Only countries and economies with comparable data from PISA 2003 and PISA 2012 are shown.OECD average 2003 compares only OECD countries with comparable indices of mathematics self-efficacy since 2003.Countries and economies are ranked in descending order of the change in the gender gap on the index of mathematics self-efficacy between PISA 2003 and PISA 2012.Source: OECD, PISA 2012 Database, Table III.4.1g.1 2 http://dx.doi.org/10.1787/888932963844 Figure III.4.4b Change between 2003 and 2012 in socio-economic disparities in mathematics self-efficacyChange between 2003 and 2012 in socio-economicdisparities (advantaged–disadvantaged) on theindex of mathematics self-efficacy0.30.2Advantaged students’ edge on the index of mathematicsself-efficacy has increased0.10-0.1-0.2-0.3ThailandSlovak sNorwayBelgiumCzech RepublicJapanMexicoSwitzerlandGermanyUnited StatesAustriaKoreaOECD average relandAustraliaGreeceFinlandNew ZealandCanadaIndonesiaHong Kong-ChinaRussian gItalyAdvantaged students’ edge on the index of mathematicsself-efficacy has decreased-0.4Notes: Statistically significant changes at the 5% level (p 0.05) between PISA 2003 and 2012 are marked in a darker tone.Advantaged/disadvantaged students are students in the top/bottom quarter of the PISA index of economic, social and cultural status.Only countries and economies with comparable data from PISA 2003 and PISA 2012 are shown.OECD average 2003 compares only OECD countries with comparable indices of mathematics self-efficacy since 2003.Countries and economies are ranked in descending order of the change in socio-economic disparities on the index of mathematics self-efficacy betweenPISA 2003 and PISA 2012.Source: OECD, PISA 2012 Database, Table III.4.1g.1 2 http://dx.doi.org/10.1787/88893296384484 OECD 2013 READY TO LEARN: STUDENTS’ ENGAGEMENT, DRIVE AND SELF-BELIEFS – VOLUME III
Mathematics Self-Beliefs and Participation in Mathematics-Related Activities4At the country level, mathematics self-efficacy is strongly associated with mathematics performance. Figure III.4.5 shows thatcountries with higher mean performance in mathematics are those where students are more likely to report feeling confidentabout being able to solve a range of pure and applied mathematics problems. When comparing PISA 2003 and PISA 2012results, Indonesia and Thailand are the only countries where the correlation between students’ mathematics self-efficacy andtheir mathematics performance was weak
mathematics – the equivalent of almost one year of school. Countries in which mathematics anxiety decreased or did not change are more likely to be those where students’ mathematics self-concept or self-efficacy improved. Figure III.4.1 Mathematics self‑beliefs, dispositions and partici
Beliefs The first component is beliefs. A consumer may hold both positive beliefs toward an object (e.g., coffee tastes good) as well as negative beliefs (e.g., coffee is easily spilled and stains papers). In addition, some beliefs may be neutral (coffee is black), and some may be differ in valance depending on the person or the
4.7.1 Andrew’s Beliefs about Mathematics Pedagogy 143 4.7.2 Andrew’s Beliefs about Learning Mathematics 143 4.7.3 Andrew’s Emotions during Mathematics Reform 145 4.7.4 Andrew’s Experiences with Coaching 146 4.8 Teacher Beliefs, Emotions and Coaching Experiences during Mathematics Reform 147 4.9 Chr
Liking mathematics affects student interest, boredom, self-efficacy beliefs and task value beliefs related to mathematics.Significant more number of students who feel mathematics as difficult tends to dislike mathematics (93%) than those who feel mathematics as easy (59%) [F 2 (1, N 51) 9.37, p .01]. Also, significant more number of students who
Understanding school principal self-efficacy beliefs and supporting the development of these beliefs is one way supervisors can help the future effectiveness of school principals. There are four main sources of information used to develop self-efficacy beliefs. These four sources of information are: mastery learning, vicarious learning,
On Computable Beliefs of Rational Machines IBM Research Division, Almaden Research Center, San Jose, California 95120-6099, and . beliefs may be determined by the basic beliefs but the program cannot even approximate them. It should be noted that in this paper we do not . beliefs, so a pair (Mi, Mj) entails a complete description of the .
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