Situation-specific diagnostic competence of mathematics teachers-a qualitative supplementary study of the TEDS-follow-up project

International audienceOne main facet of teachers' professional competences is diagnostic competence. While diagnostic competence of teachers becomes relevant in several situations within teaching and learning, this paper focuses on situation-specific diagnostic competence required by teachers within class. In a qualitative supplementary study of the TEDS-Follow-Up project, this situation-specific diagnostic competence is analysed using the video instrument of the TEDS-Follow-Up study. 131 primary level mathematics teachers participated in the primary study of this project and examined specific learning situations in the video instrument. These instances were analysed using qualitative text analysis (Mayring 2015). Results indicate that teachers notice very different aspects in those teaching situations. Two different diagnostic types can be differentiated: content-related and judging diagnostic type versus student-related and action-oriented diagnostic type

Preschool children estimating lengths - the role of standard units as relevant prior knowledge

International audienceLength estimation is a relevant ability in our everyday life. Especially during the Corona Pandemic, estimating a distance of 1.50 m is crucial for our health and social life. Standard units play a central role in many length estimation processes that occur in our everyday surrounding. However, standard units as well as approaches to length estimation are generally discussed with children in elementary school while children already face situations already in their preschool age. This research addresses the question of how preschool children deal with length estimation. In a study with 189 preschool children who were about to start elementary school, we assessed their length estimates and analyzed the role of standard units in this context. It shows that standard units are used by the majority of kids to estimate lengths. However, their estimates are far from precise but the relation between the measures they name is mostly correct

Preschool children estimating lengths -the role of standard units as relevant prior knowledge

International audienceLength estimation is a relevant ability in our everyday life. Especially during the Corona Pandemic, estimating a distance of 1.50 m is crucial for our health and social life. Standard units play a central role in many length estimation processes that occur in our everyday surrounding. However, standard units as well as approaches to length estimation are generally discussed with children in elementary school while children already face situations already in their preschool age. This research addresses the question of how preschool children deal with length estimation. In a study with 189 preschool children who were about to start elementary school, we assessed their length estimates and analyzed the role of standard units in this context. It shows that standard units are used by the majority of kids to estimate lengths. However, their estimates are far from precise but the relation between the measures they name is mostly correct

Langtidseffekter av skolegang og lærerutdanning på småskolelæreres kompetanseutvikling :

I denne longitudinelle studien ble 131 grunnskolelærere (1. til 4. trinn) fulgt opp fra det siste året i lærerutdanningen og gjennom de fire første årene i lærerjobb. Lærerne tok standardiserte tester i matematikk (matematikkunnskap) og matematikkdidaktikk (matematikkdidaktisk kunnskap) ved slutten av lærerutdanningen i 2008 og en gang til etter fire års arbeid som lærer, i 2012. I tillegg tok de etter fire år i jobb en standardisert videobasert test som måler ferdigheter i å oppdage og tolke situasjoner som oppstår under matematikkundervisning i klasserommet, samt evne til å ta avgjørelser om handling når det gjelder disse situasjonene (matematikkrelaterte praksisferdigheter). De målte kunnskapene og ferdighetene ble deretter relatert til grunnskolelærernes utdanningsløp ved hjelp av strukturelle ligningsmodeller med manifeste variabler (path analysis). Som forventet fant vi sterke langtidseffekter. Lærernes gjennomsnittskarakter fra avsluttende skoleeksamen predikerte sterkt deres matematikkrelaterte kunnskapsnivå og deres praksisferdigheter 10 til 12 år senere (etter fire år i jobb). Enda sterkere relatert til kunnskapsnivået i matematikk og matematikkdidaktikk etter fire år i jobb var typen matematikk-kurs de hadde tatt på videregående skole (avansert kurs vs. basiskurs). Derimot hadde typen skolematematikk-kurs ingen signifikant effekt på lærernes praksisferdigheter. Kunnskap i matematikk og matematikkdidaktikk ved slutten av lærerutdanningen korrelerte også signifikant med lærernes kunnskap fire år senere, mens effektene på praksisferdigheter var ubetydelig. Gjennomsnittskarakteren på den avsluttende brede lærerutdanningseksamenen hadde ingen signifikant effekt på lærernes matematikkrelaterte kunnskap eller ferdigheter. Alle langsiktige effekter av skolegang ble mediert gjennom lærerutdanningen. Når det gjelder videre forskning er en viktig konklusjon at det må undersøkes nøyere hva som påvirker praksisferdigheter. I tillegg er utvalgskriterier ved starten av lærerutdanningen et stikkord som burde diskuteres; et annet stikkord er hvilke muligheter studenter har til å lære seg matematikk og matematikkdidaktikk under grunnskolelærerutdanningen

Identifying and dealing with student errors in the mathematics classroom : Cognitive and motivational requirements

Introduction: Mathematics classrooms are typically characterized by considerable heterogeneity with respect to students’ knowledge and skills. Mathematics teachers need to be highly attentive to students’ thinking, learning difficulties, and any misconceptions that they may develop. Identification of potential errors and appropriate ways to approach them is crucial for attaining positive learning outcomes. This paper explores which knowledge and affective-motivational skills teachers most require to effectively identify and approach students’ errors. Methods: To address this research question within the German follow-up study of the Teacher Education and Development Study in Mathematics (TEDS-M), 131 primary school mathematics teachers’ ability to identify students’ errors was assessed based on (a) a digitalized speed test showing different students’ solutions in a written notation and (b) three video vignettes that showed different scenes from mathematics classes. These scenes dealt, among other things, with children who struggled with the lesson’s mathematical content. Teachers were asked to analyze students’ thinking and to determine how best to react. In addition, teachers’ mathematics pedagogical content knowledge, mathematical content knowledge, and beliefs were assessed in separate tests and served as predictors for teachers’ abilities to identify, analyze, and deal with students’ errors. Results: The results indicate that all components are interrelated. However, path analysis reveals that teachers’ ability to deal with students’ errors is mainly predicted by their constructivist beliefs while their ability to quickly identify typical students’ errors is largely dependent on their mathematics content knowledge. Discussion: The results show the central filtering function of beliefs. Teachers who believe that students must shape and create their own learning processes are more successful in perceiving and analyzing student errors in classroom situations. They may understand errors as learning opportunities and - thus - pay specific attention to these occurrences.publishedVersio

About the Complexities of Video-Based Assessments: Theoretical and Methodological Approaches to Overcoming Shortcomings of Research on Teachers’ Competence

Research on the evaluation of the professional knowledge of mathematics teachers (comprising for example mathematical content knowledge, mathematics pedagogical content knowledge and general pedagogical knowledge) has become prominent in the last decade; however, the development of video-based assessment approaches is a more recent topic. This paper follows the call for more situated and performance-related ways to assess teacher competence. We discuss the theoretical and methodological challenges connected to the development of such instruments and exemplify these by an instrument developed within the follow-up study of the international “Teacher Education and Development Study in Mathematics (TEDS-M)”, called TEDS-FU. Drawing on the novice-expert framework from cognitive psychology allows analysing the structure and development of mathematics teachers’ professional competence. More recent concepts on teacher noticing of classroom situations and students’ activities are incorporated into this video-based evaluation instrument, which is described in detail in this paper, by assessing perceptual, interpretative and decision-making skills. Reliability and validity concerns remain an issue of such assessments for which solutions are proposed. Overall, the paper shows that a more comprehensive evaluation of teachers’ competence comprising cognitive-affective and situated facets is possible and has been achieved

Wie situationsbezogen ist die Kompetenz von Lehrkräften? Zur Generalisierbarkeit der Ergebnisse von videobasierten Performanztests

Untersucht wird die Situationsabhängigkeit der Performanz von Lehrkräften mithilfe eines videobasierten Assessments, das im Rahmen von TEDS-FU, einer Follow-up-Studie zur Teacher Education and Development Study: Learning to Teach Mathematics (TEDS-M), entwickelt wurde. Dabei werden zwei Anforderungen betrachtet: pädagogische Aufgaben des Klassenmanagements und fachdidaktische Aufgaben des Unterrichtens von Mathematik. Ob und - wenn ja - wie stark die Umsetzung der dafür benötigten situationsbezogenen Fähigkeiten von den jeweiligen Unterrichtssituationen des Assessments abhängig ist, wird dabei mit denselben Videos erfasst, sodass sich Unterschiede zwischen pädagogischen und mathematikdidaktischen Fähigkeiten herausarbeiten lassen. Als konkurrierende Hypothesen werden keine, teilweise oder vollständige Situationsabhängigkeit der Itembearbeitung angenommen. Die durchgeführten Modellvergleiche zeigen, dass die intraindividuelle Variation von Lehrerperformanz in den verschiedenen Situationen im Bereich Pädagogik stärker ausgeprägt ist als im Bereich Mathematikdidaktik. (DIPF/Orig.)Using a video-based assessment developed in the follow-up study of the Teacher Education and Development Study: Learning to Teach Mathematics (TEDS-M), the authors examine whether and to what extent teacher performance depends on differences in classroom situations. Two teaching challenges are focused upon: general pedagogical tasks related to classroom management and subject-specific tasks related to teaching mathematics. The assessment of situation-specific skills necessary to master these two tasks is done with video-vignettes. Since each time the same video-vignettes are used, differences between general pedagogical and subject-specific skills can be examined. The authors test competing hypotheses of having no, partial, or complete item-dependency on classroom situations. Findings reveal that intra-individual variation of teacher performance is more pronounced in the area of general pedagogy than in the area of mathematics pedagogy. (DIPF/Orig.