A Cross-cultural Analysis of the Dimensions of Mathematics-related Affect : Assessing the psychometric properties and the relationship with achievement

The aim of the present set of studies in this dissertation was to examine the psychometric properties of measures of mathematics-related affect developed and normalized in one culture for use in another, how these properties transcend cross-culturally in an African context, and the methodological challenges associated with the process. Further aims were to examine the relationships between these constructs on a cross-cultural level, and to explore any associations be-tween students background variables and mathematics achievement. With these aims in mind, we conducted four original empirical studies based on different types of structural equation modeling. Studies I and II explored the problems of importing an instrument from one culture into another, and the associated methodological challenges. More specifically, Study I gives a detailed account of the processes involved in applying structural equation modeling to validate mathematics-related affective measures developed in one culture (Finland) for use in another (Ghana). Reliability estimates and confirmatory factor analyses indicated that the Ghanaian data set did not fit the original hypothesized model (seven-factor structure). A series of factor and confirmatory factor analyses indicated a four-factor structure for the Ghanaian sample. Study II examined the possible causes of the differences in the factor structures from a cross-cultural perspective. The results indicate that measurement artifacts, cultural differences, and construct validity and adaptability were possible causes of the observed differences in factor structure between the Ghanaian and the theoretical model. In conclusion, it is suggested that re-searchers should be aware of construct importation and adaptation, and of the fact that measurement errors, question order, negatively worded item, translation, and content overlap may influence the reliability and validity of survey measures. Moreover, it is necessary to consider cultural variation and the methodological approaches involved in the theoretical settings in order to make any meaningful comparative assessment. Researchers focusing on cross-cultural mathematics-related affect are recommended to acquire the theoretical and practical knowledge necessary to address these issues using appropriate tools such as structural equation modeling. Study III investigated the psychometric properties (factor structure, reliabilities, method effect, and measurement invariance country and gender) of the mathematics-related affective constructs used in the 2011 Trends in International Mathematics and Science Study (TIMSS 2011) across the five participating African countries. It also examined the relationship between these mathematically related affective constructs, as well as the associations amongst the constructs, and between the students background variables and mathematics achievement cross-culturally. The results empirically support the multidimensionality of the construct, and the measures were largely invariant across the five educational systems and gender. There was also some evidence to suggest that negatively worded items in a construct can attenuate the reliability and validity of the measures: a series of confirmatory factor analyses (CFAs) revealed the need to control for the method effects associated with such items. It seems that responses to negatively worded items differ systematically across countries and are systematically linked to students achievement. The analyses also covered the relationships between the student affect, achievement, and background variables such as parental education, gender and students educational aspirations. Lower mathematics achievement was associated with students from countries reporting higher motivational belief. On the association between students mathematics-related affect, achievement, parental education, educational aspirations and gender, it seems that there are culture-specific as well as cross-cultural universal outcomes. For instance, the relationship linking parental involvement, teacher responsiveness and mathematics achievement turned out to be culture-specific whereas, boys rated their mathematics competence more highly than girls did. Parental education, gender and long-term educational aspirations also influenced student achievement and motivation, but to different extents in different countries. Study IV, based on non-recursive structural equation models, tested theoretical and methodological models of the reciprocal relationship between mathematics-related affect (e.g., self-concept) and achievement using the TIMSS 2011 cross-sectional data set. The results in different countries support the existence of a unidirectional influence of affect on achievement and of achievement on affect, and a direct feedback-loop relationship between affect and achievement. According to the evidence, the reciprocal determinism between affect and achievement is dependent on the national context. Moreover, there was a cross-cultural universal pattern among males: reporting a stronger mathematics self-concept and higher long-term educational aspirations significantly predicted higher mathematics achievement. The effects of socioeconomic status on mathematics achievement and self-concept among the students were dependent on the national context.Tämän väitöskirjan tavoitteena oli selvittää matematiikan asennemittareiden psykometrisiä ominaisuuksia, kun niitä käytettiin toisessa kulttuurisessa kontekstissa kuin missä ne alun perin oli kehitetty, miten nämä ominaisuudet eroavat afrikkalaisten maiden välillä, sekä prosessiin liittyviä menetelmällisiä haasteita. Tavoitteena oli myös vertailla miten asennetekijöiden väliset suhteet erosivat eri maiden välillä sekä selvittää oppilaan taustamuuttujien yhteyksiä hänen matematiikan osaamisensa. Näiden tavoitteiden saavuttamiseksi teimme neljä empiiristä tutkimusta käyttäen erilaisia rakenneyhtälömallintamisen menetelmiä. Tutkimuksissa I ja II selvitimme mittarin siirtämistä kulttuurista toiseen sekä siirtoon liittyviä menetelmällisiä haasteita. Tutkimuksessa I selvitettiin yksityiskohtaisesti miten rakenneyhtälömallintamisella voidaan validoida Suomessa kehitetyn matematiikka-asennemittarin käyttöä Ghanassa. Reliabiliteetin estimaatit ja konfirmatorinen faktorianalyysi osoittivat, että Suomessa löydetty seitsemän faktorin malli ei sopinut ghanalaiseen aineistoon. Sarja exploratiivisia ja konfirmatorisia faktorianalyysejä osoitti, että neljän faktorin malli sopii ghanalaiseen aineistoon. Tutkimuksessa II selvitimme kulttuurien välisenä vertailuna faktorirakenteiden erojen mahdollisia syitä. Tulokset osoittavat, että mittarivirheet, kulttuurierot sekä mittarin heikko käsitevaliditeetti sekä heikko käännös ja sovittaminen olivat mahdollisia syitä alkuperäisen mallin ja ghanalaiseen aineistoon pohjautuvan mallin välillä havaittuihin eroihin. Johtopäätöksenä ehdotamme, että tutkijoiden tulee huomioida käsitteiden alkuperä ja mittarin kääntäminen ja sovittaminen uuteen kontekstiin. Kun mittari siirretään kulttuurista toiseen, on huomattava mittausvirheiden, väittämien järjestyksen, väittämien negatiivisen muotoilun, käännöksen ja sisällöllisten päällekkäisyyksien mahdolliset vaikutukset kyselymittareiden luotettavuuteen ja pätevyyteen. Tämän lisäksi on otettava huomioon tutkimuksen teoreettisen viitekehyksen tunnustama kulttuurien välinen vaihtelu, mikä pitää huomioida valituissa menetelmissä, jotta voidaan tehdä kulttuurien välistä vertailua. Suosittelemme, että tutkijat, jotka paneutuvat matematiikka-asenteiden kulttuurien välisiin eroihin, hankkivat teoreettisen ja käytännöllisen tiedon käsitellä näitä ongelmakohtia rakenneyhtälömallintamisella tai muilla soveltuvilla työkaluilla. Tutkimuksessa III selvitettiin vuoden 2011 Trends in International Mathematics and Science Study (TIMSS 2011) tutkimuksessa käytettyjen matematiikan asennetekijöiden psykometrisiä ominaisuuksia (faktorirakenne, luotettavuus, metodiefekti ja mittarin invarianssi maan ja vastaajan sukupuolen suhteen) viidessä tutkimukseen osallistuneessa Afrikan maassa. Tutkimuksessa selvitettiin myös matematiikkaan liittyvien eri asennetekijöiden välisiä yhteyksiä sekä oppilaan matematiikan osaamisen ja taustamuuttujien vaikutusta asennetekijöihin ja niiden välisiin yhteyksiin. Kulttuurien välinen vertailu tukee olettamusta asenteiden moniulotteisuudesta. Mittarit olivat pääsääntöisesti invariantteja viiden tutkitun koulutusjärjestelmän sekä vastaajien sukupuolen suhteen. Havainnot viittaavat siihen, että negatiivisesti muotoillut väittämät saattavat heikentää käsitteen mittaamisen luotettavuutta ja pätevyyttä. Tehdyt konfirmatoriset faktorianalyysit vahvistivat että negatiivisiin väittämiin liittyvä metodiefekti tulee huomioida. Maiden välillä oli systemaattisia eroja negatiivisiin väittämiin vastaamisessa ja negatiivisilla väittämillä havaittiin myös systemaattinen yhteys oppiaan osaamiseen. Analysoimme myös oppilaiden asenteiden, osaamisen sekä sukupuolen, koulutustavoitteiden ja vanhempien koulutuksen kaltaisten taustamuuttujien väliset yhteydet. Mitä parempi matematiikan osaaminen kussakin maassa oli, sen heikompi oli oppilaiden keskimääräinen motivaatio. Oppilaiden matematiikka-asenteiden, matematiikan osaamisen, vanhempien koulutuksen, koulutustavoitteiden sekä sukupuolen välillä havaitsimme sekä kulttuurispesifejä että kulttuurisesti universaaleja yhteyksiä. Esimerkiksi vanhempien tuen, opettajakontaktin ja matematiikan osaamisen väliset yhteydet osoittautuivat kulttuurispesifeiksi. Sen sijaan poikien käsitys omista matemaattisista kyvyistään vaikuttaa olevan universaalisti myönteisempi kuin tytöillä. Vanhempien koulutustaso sekä oppilaan sukupuoli ja koulutustavoitteet vaikuttivat oppilaan osaamiseen ja motivaatioon, mutta vaikutuksen voimakkuus vaihteli tutkittujen maiden välillä. Tutkimuksessa IV testasimme matematiikka-asenteiden (mm. minäkuva) ja osaamisen välisiä teoreettisia ja menetelmällisiä vastavuoroisen riippuvuuden malleja käyttäen TIMSS 2011 tutkimuksen poikittaisaineistoa. Eri maissa saadut tulokset antavat tukea kaikille mahdollisille eri malleille: yksisuuntaiselle vaikutukselle asenteista osaamiseen, vastakkaissuuntaiselle yksisuuntaiselle vaikutukselle, sekä myös suoralle takaisinkytkennälle asenteiden ja osaamisen välillä. Tulosten valossa asenteen ja osaamisen välisen suhde on luonteeltaan kulttuurispesifi. Miesten osalta havaitsimme kulttuurien rajat ylittävänä universaalina piirteenä, että myönteinen matemaattinen minäkuva ja korkeammat koulutustavoitteet ennustivat merkittävästi parempaa matematiikan osaamista. Sosioekonomisen taustan vaikutukset matematiikan osaamiseen ja matemaattiseen minäkuvaan puolestaan olivat erilaiset eri maissa

Predictors of Socio-economic Profiles and Mathematics Achievement in Grade Eight Students’ in Ghana

This study used the Trends in International Mathematics and Science Study (TIMSS 2011) dataset for Ghana, which measures the trends in Mathematics and Science Achievement at the fourth and eighth grades. The focus of the present study is on the eighth grade Ghanaian students’ with a sample size 7323 (47% girls) who participated in TIMSS2011. The mean age was 15.81 with standard deviation of 1.50. This paper first addresses the issue of measuring socio-economic background in the context of the TIMSS 2011 data set using students’ home resources. This is based on the fact that the literature indicates that data on home possessions/resources collected from young children are much more reliable compared to the information they provide about their parents’ education, jobs, and income as such this study uses data on home resources as a measure of students Socio-Economic Status (SES). Applying a two-level mixture modeling technique by accounting for the clustering in the data set, the study explored the profiles of students’ (SES). Latent class analysis was used for the profiling. The two-level latent class analysis takes into account the measurement error and the variation of the latent class indicators across different class/schools. The detail process involved in obtaining the index of students’ socio-economic profiles from home possessions/resources items using latent class analysis is described. Once the SES measure was obtained, a discriminant analysis was used to validate the students SES. The relationship between the demographic variables (e.g., parental education, language spoken at home, parental involvement and gender) and students’ SES were examined. The analysis identified three latent classes of students based on reported home resource namely: the high SES, the intermediate SES, and the low SES group. The discriminant analysis based on the eleven household items was able to correctly classify 92.2% of the individual students into their appropriate SES group. Furthermore, the variables that had the most significant association with students socio-economic profile were investigated. Multinomial logit latent-class regression models were posited. The final analysis used the hierarchical regression analysis to access the clusters of variables to evaluate the relative importance of the predictors for students’ mathematics achievement. The results indicated that gender, parental education, SES, students’ educational aspiration, language spoken at home, and parental involvement variables significantly predict students’ mathematics achievement. When the variables were entered as six blocks, students’ educational aspirations were found to have the greatest variance explained for mathematics achievement. Gender and parental education explained additional 2% and 2.9% respectively of the variance in mathematics achievement. Speaking English always at home and being in the low SES group did not have any significant effect on students’ mathematics achievement. The findings of this study provide information to educators, researchers, parents, teachers, and policy makers about the effect of home resources on students’ academic achievement. This thesis advocates that governments should provide financial support for students from low SES. In addition, financial incentives to schools in low income areas should be increase to help close the achievement gap between students’ from the low-SES and high-SES

Students' views on mathematics in single-sex and coed classrooms in Ghana

In this study, we investigated students’ views on themselves as learners of mathematics as a function of school-by-sex (N = 2034, MAge = 18.49, SDAge = 1.25; 12th-grade; 58.2% girls). Using latent variable Structural Equation Modeling (SEM), the measurement and structural equivalence as well as the equality of latent means of scores across single-sex and coed schools were tested. Findings regarding the latent mean differences revealed that girls in single-sex schools had significantly higher mathematics self-confidence than did students’ in coed schools. Girls in coed schools had significantly lower mathematics self-concepts than did boys in single-sex, girls in single-sex and boys in coed schools. Girls in single-sex schools had significantly higher family encouragement than students’ in all other school types. Moreover, a more complex dynamics were found on the teacher quality variate. This paper argues for a deeper understanding of sex-school interaction and of possible causes of students’ views on mathematics.Peer reviewe

TIMSS data in an African comparative perspective : Investigating the factors influencing achievement in mathematics and their psychometric properties

Relationships among motivational constructs from the 2011 Trends in International Mathematics and Science Study (TIMSS 2011) were investigated for eight-graders in all the five participating African countries, representing 38,806 (49 % girls). First, we investigated the psychometric properties (factor structure, reliabilities, method effect, and measurement invariance---country and gender) of the mathematics motivational constructs across the five educational systems. There was empirical support for the multidimensionality of the construct and the TIMSS 2011 motivational construct was largely invariant across cultures. Furthermore, a series of confirmatory factor analyses revealed that there is a need to control method effects associated with negatively worded items in the measurement model. There was support suggesting that in many cultures responses to negatively worded items are systematically different. The factor structures and reliabilities (i.e., confidence and the like mathematics scales) were affected by negatively worded items. Second, the relationships between the constructs, achievements and background variables such as parental education, gender and students' educational aspirations were investigated. We identified several significant relationships between self-belief and mathematics achievement. Differences in the latent mean achievement and the motivational construct were similar to those that have been described in the literature as "paradoxical" and "perplexing". Nations with high mathematics achievement seem to have students with more negative mathematics self-belief. Some results extend, whereas others refute the findings of previous research. For instance, the relationship between students' mathematics confidence and mathematics achievement was lower than the relationship between the value of mathematics and achievement in some countries and it was the reverse in others. However, consistent with cultural stereotypes, boys rated their mathematics competence higher than girls. The findings are discussed with reference to implications for cross-cultural research and practice.Peer reviewe

Home Resources as a Measure of Socio-economic Status in Ghana

Peer reviewe

Reciprocal determinism between students' mathematics self-concept and achievement in an African context

International audienceThe study tests the theoretical and methodological models of the direct feedback loop in which mathematics self-concept and achievement are specified as both causes and effects of each other using the TIMSS–2011 cross-sectional data set. The participants were students in grades 8–9 from five African countries participating in TIMSS–2011 (N=38,806, MAge =15.42, SD =1.37). Using nonrecursive structural equation models, the author examined the reciprocal-effects model indicating that achievement has an effect on self-concept (skill-development model) and that mathematics self-concept has an effect on achievement (self-enhancement model). There was support for the skill-development, self-enhancement as well as direct feedback loop models. Discussion centres on the theoretical, methodological, and practical implications of the results

Internal/external frame of reference: exploring the paradoxical relations between mathematics and self-concept across 29 countries: Internal/external frame of reference: exploring the paradoxical relations between mathematics and self-concept across 29 countries

Students’ self-concept is an important construct in explaining achievement-related outcomes. The study examined the theoretical and methodological issues underpinning the Internal/External (I/E) frame of reference model. This model posits a paradoxical relation between “distinct” school subjects, for example, mathematics and verbal. Also, achievement in each domain is deemed to positively affect self- concept in the matching domain but negatively in the nonmatching domain. The investigation is based on 29 countries (N= 181,745) using the TIMSS–2011 data set. The data supported the assumptions associated with the I/E model. Result indicates a negative achievement effect on non-corresponding self-concepts (internal) and positive effects achievement on the corresponding self-concepts (external). The findings contribute to a better understanding of how students form self-concept across domains cross-culturally