On measuring and theorising mathematical identity

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An assessment of non-standardized tests of mathematical competence for Norwegian secondary school using Rasch analysis

International audienceDo non-standardized, publisher-provided tests for lower secondary school provide valid and reliable measures of mathematical competence? We analysed a sample of items pooled from tests accompanying three different Norwegian textbooks using Rasch analysis. The pooled sample of items was found to be sufficiently unidimensional for measuring function competence, with four strands of sub-competencies in accordance with theory. The competence associated with an increasing difficulty of items could be qualitatively characterised by shifts from a) identifying through constructing to reasoning about representations, b) using visual to using algebraic representations, and c) local to global interpretations of functions. While the individual tests differed substantially in the distribution of items across strands of mathematical competence, minor adjustments to the combined instrument were sufficient for providing a valid and reliable measure of mathematical competence

Measuring Mathematical Identity, 2018

Survey measuring mathematical identity. The study was conducted among secondary school students, teacher students and graduate engineering students in Norway

Stereotypes in a polarised world and how they relate to mathematical identity

International audiencePrevious studies have indicated that men are stereotyped as more mathematical than women. Since these stereotype images have shown psychological effects-particularly for negatively stereotyped groups-it is relevant to ask how variables other than gender relate to mathematics. In this study, we examined how stereotype characteristics of gender, occupation, political views, and personality relate to mathematical identity. From statistical analyses of Comparative Judgement data, we show significant associations between mathematical identity and extreme stereotypes (related to occupation, political views, and personality). No significant association was found between mathematical identity and gender

Measuring mathematical identity in lower secondary school

The authors examined whether we can use the same instrument for measuring and comparing the mathematical identities of lower secondary school students and those of university students in science, technology, engineering, and mathematics (STEM). Specifically, Rasch measurement techniques were used on items from an instrument that was earlier validated for measuring mathematical identities in STEM contexts to assess the psychometric properties of the instrument in lower secondary school. Moreover, data from the two contexts were merged to assess the invariance of the instrument. The results indicate that the same instrument can measure mathematical identity in STEM contexts and lower secondary school contexts. Also, evidence is provided that the instrument is practically invariant. Implications and suggestions for further research are provided

Concurrent Design og Programvareutvikling

Hensikten med denne oppgaven er å få et innblikk i, og kartlegge hvordan utviklingen av programvare foregår i dag og om metoden Concurrent Design (strukturert metode basert på tverrfaglig samarbeid i sanntid) kan tilføre noe av verdi på dette området. Problemstillingen vi har brukt lyder som følger: “Hvordan egner Concurrent Design (CCD) seg som prosjektmetode i utvikling av programvare?”. Resultatene av denne studien bygger på et teoretisk grunnlag av programvareutvikling og CCD, etterfulgt av syv kvalitative semistrukturerte dybdeintervjuer med en representativ gruppe sentrale deltakere i prosessen innen utvikling av digitale produkter og tjenester. Disse er hovedsakelig ressurser knyttet til konsulentvirksomhet og med bakgrunn fra forskjellige sektorer (privat og offentlig). Konklusjonen vår fra dette arbeidet viser at såkalt smidige utviklingsmetoder i stor grad foretrekkes, og er den “de facto” fremgangsmåten for utviklingen av programvare i dag. Det er en del fellesnevnere mellom arbeidsprosessene for CCD og utviklingen av programvare, som for eksempel workshops. CCD er imidlertid karakterisert av en mer rigid og systematisk struktur i forhold til det vi ser i de smidige metodene. Vår oppfatning er at CCD kan bli for omfattende til direkte bruk i programvareutviklingsprosjekter i forhold til dagens praksis, som har vist seg å dra nytte av mer fleksibilitet

The association between engineering students’ self-reported mathematical identities and average grades in mathematics courses

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Measuring student teachers’ practices and beliefs about teaching mathematics using the Rasch model

Several attempts have been made to measure and categorize beliefs and practices of mathematics teachers [Swan, M. 2006. “Designing and Using Research Instruments to Describe the Beliefs and Practices of Mathematics Teachers”. Research in Education 75 (1): 58–70]. One of the reasons for measuring both beliefs and practices is to characterize teachers in terms of the relationship between their beliefs and practices. However, the practice-instruments and the beliefs-instruments discussed in the literature are predominately based on differing constructs. Consequently, it is challenging to compare the relationship between beliefs and practices solely based on these instruments. As such, we argue that practice- and beliefs-instruments based on the same construct would be desirable when both beliefs and practices are at stake. This paper presents two Rasch-calibrated instruments that measure the level of teacher-centredness with respect to student teachers’ practices and beliefs about teaching mathematics. From a sample of 160 student teachers, 15 items have been established as being beneficial for measurement, both when the items are translated as practice items and when translated as beliefs items. By studying the invariance between both translations, we conclude that measures from both instruments can be directly compared

The transition from higher education to the world of work: Measuring student teachers' beliefs and practices for purposeful sample selection

International audienceThis paper reports on methodological results from an ongoing project investigating student transition from teacher education to the world of work. We argue that research benefits from purposeful sampling, and we present two Rasch-calibrated instruments that aim at finding participants with particular characteristics. With items from existing instruments, one practice instrument is calibrated on Norwegian student teachers. Furthermore, these items are rephrased to fit a second instrument measuring beliefs about teaching mathematics. Finally, 'virtual equating' is used to align items so that measures can be compared across instruments

The association between engineering students’ self-reported mathematical identities and average grades in mathematics courses

Arguments have been made that one purpose of learning mathematics successfully is for students to develop mathematical identities. Thus, since students are frequently evaluated with grades in university mathematics courses, a relevant question is how mathematical identities are associated with average grades. This study has measured engineering students’ mathematical identities and compared these measures with grades in university mathematics courses, and a Welch’s ANOVA conclude that the mean average grade amongst students with high mathematical identities is significant, and about one grade higher than students with low mathematical identities. Moreover, the variance is greater amongst students with low mathematical identities, which indicates a strong association between mathematical identity and average grade only when mathematical identities are high