Markku S. Hannula

Supporting emerging teacher identities: can we identify teacher potential among students?

The research focuses on Estonian university students’ emerging teacher identity and their interest in becoming teachers. Five hundred and sixty‐five first, third and fifth year students participated in the survey. The results suggest that pedagogical reasons for entering teacher education and clear motives for studying are significant indicators of teacher potential. Pedagogical reasons for entering teacher education or the teaching profession and the wish to function as a change agent in the society were related to academic self‐efficacy beliefs and the belief that the teacher expertise is mainly pedagogical in nature. However, at the point in their studies at which the students are able to choose their masters programme and entry into teacher education, their likelihood of choosing teacher education remains low, indicating that there is a need to develop pedagogical content, study counselling and career guidance services to encourage students’ continued interest in and entry to teacher education and the teaching profession.

Emotions in Problem Solving

Emotions are important part of non-routine problem solving. A positive disposition to mathematics has a reciprocal relationship with achievement, both enhancing the other over time. In the process of solitary problem solving, emotions have a significant role in self-regulation, focusing attention and biasing cognitive processes. In social context, additional functions of emotions become apparent, such as interpersonal relations and social coordination of collaborative action. An illustrative case study presents the role of emotions in the problem solving process of one 10-year old Finnish student when he is solving an open problem of geometrical solids. The importance of emotions should be acknowledged also in teaching. Tasks should provide optimal challenge and feeling of control. The teacher can model the appropriate enthusiasm and emotion regulation. Joking and talking with a peer are important coping strategies for students.

Mathematics-related emotions among Finnish adolescents across different performance levels

Abstract This study examined the relation of mathematics performance and gender with seven mathematics-related emotions (enjoyment, pride, anger, anxiety, shame, hopelessness and boredom) among adolescents. Using strict and lenient mathematics performance cut-off scores, respective groups of adolescents with mathematics difficulties (MD, n = 136), low (LA, n = 166) and typical mathematics performance (TA, n = 1056) were identified. Our results revealed that the MD group reported more shame than the LA group. The MD group also reported more negative emotions and less positive emotions than the TA group, with the exception of boredom, for which there was no statistically significant difference. The interaction effect between mathematics performance group and gender on emotions was significant. Only females with MD showed significantly higher levels of hopelessness and shame than females with LA, while males with LA even reported more boredom than males with MD. Concerning gender differences, males reported slightly more pride and enjoyment than females. However, the direction and magnitude of the gender differences showed great variance among mathematics performance groups. The practical implications of the results are discussed.

Studying the Factorial Structure of Ghanaian Twelfth-Grade Students’ Views on Mathematics

Researchers often import and adopt surveys from one cultural setting to another in order to collect comparative data or to simplify the laborious process of instrument development. Even when the instrument has been proven to have high reliability in the original setting, the reliability may prove to be much weaker in the new setting, especially when Western instruments are imported into non-Western countries. In this chapter, we discuss the problems of importing an instrument from one culture to another and associated methodological challenges. More importantly, we present a detailed account of using structural equation modeling (SEM) and MPlus software to validate a survey instrument imported to Ghana. The students’ Views of Mathematics (VOM) instrument is based on earlier Western research and was further developed in Finland, where it had been validated to have high reliability. First, we used confirmatory factor analysis to test whether the seven factors identified in Finland were identifiable in Ghana. As the original factor structure was found not to fit the Ghanaian data, we continued with an explorative approach to identify the Ghanaian factor structure, resulting in a four-factor structure. For cross-validation purposes, the sample was randomly split into two, one-half of the sample assigned as the calibration sample and the other half as the validation sample. Measurement invariance was established at the configural, metric and structural levels between the calibration and validation sample. We further discuss the measurement artifacts and cultural differences as possible causes for the observed differences in the factor structures between the Ghanaian and the Finnish sample.

Evaluating admission procedures for teacher education in Finland

In Finland the number of applicants for elementary teacher education is many times greater than the number of accepted persons. In this article we focus on the significance of the entrance examination procedures at three Finnish universities. Our findings imply that the differing admission procedures at the institutions yielded different student profiles. The test component “mathematics-science” used on the entrance examination in Turku was found to be a significant separating factor, but also the applicants’ mathematics achievement in upper secondary school seems to be an applicable criterion for developing admission procedures.

Behavioral Executive Functions Among Adolescents With Mathematics Difficulties

This study investigates behavioral executive functions (EFs) in the mathematics classroom context among adolescents with different mathematics performance levels. The EF problems were assessed by teachers using a behavioral rating inventory. Using cutoff scores on a standardized mathematics assessment, groups with mathematics difficulties (MD; n = 124), low mathematics performance (LA; n = 140), and average or higher scores (AC; n = 355) were identified. Results showed that the MD group had more problems with distractibility, directing attention, shifting attention, initiative, execution of action, planning, and evaluation than the LA group, whereas the differences in hyperactivity, impulsivity, and sustaining attention were not significant. Compared to the AC group, the MD group showed more problems with all behavioral EFs except hyperactivity and impulsivity, while the LA group showed more problems only with shifting attention. Male adolescents showed more behavioral EF problems than female adolescents, but this gender difference was negligible within the MD group. The practical implications of the results are discussed.

A Comparative Study of Finland and Chile: the Culture-Dependent Significance of the Individual and Interindividual Levels of the Mathematics-Related Affect

Mathematics-related affect is established regarding both individual and interindividual levels. However, the interaction between the levels has not been elaborated. Furthermore, it is known that people may draw either from intrinsic or extrinsic experiences to construct their identities depending on their cultural environment. Thus, affective individual and interindividual levels seem to interact with culture. In this study we focus on the significance of and the interaction between the individual and the interindividual levels of affect. This is done with respect to 2 different types of countries (Finland and Chile) to include cultural effect. We use questionnaire-based data and pupils’ drawings of their mathematics class to find out about their individual and interindividual experiences. By using mixed data, we are not only getting a wider picture of pupils’ affect but we can also avoid the most typical errors made in the cross-cultural comparisons as the pupils’ own voice is strengthened. The main finding in the study is that the 2 affective levels are not congruent and that the incongruence appears differently in different types of cultures.

Research on Mathematics-Related Affect

In the first Handbook of Research on the Psychology of Mathematics Education (Gutierrez & Boero, 2006) Gilah Leder and Helen Forgasz began the chapter on Affect and Mathematics Education with an overview of research on affect outside and before PME.

Developing a method to determine teachers’ and pupils’ activities during a mathematics lesson

Third-graders from nineteen classrooms (N = 316) were asked to draw a picture on a mathematics lesson. Based on these drawings we have developed a data analysing method that allows us to find out how pupils present both their teacher’s and their classmates’ activities in their drawings. Two inventories were formed that contain, respectively, teachers’ and pupils’ activities during a mathematics lesson as seen in the pupils’ drawings. The first inventory contains 14 separate items organized into six groups that contain teacher activities like asking questions and giving feedback on mathematics. Ten of the items are related to teaching and the rest contain items like keeping order in addition to the teacher’s location in the classroom. Respectively, pupils’ activities are organized into five groups that contain altogether 22 items. These contain the activities of a single pupil, and also pupil-teacher and pupil-pupil discussions on mathematics.

Affective Factors and Beliefs About Mathematics of Young Chilean Children: Understanding Cultural Characteristics

Understanding the affective factors and beliefs of young students about mathematics is a complex task. This is especially important in the framework of problem solving where these kinds of beliefs are related to various learning processes and influence achievement. In this work, we present the analysis of a questionnaire regarding beliefs about self-competence, self-confidence, mastery goal orientation, effort, difficulty of mathematics, and enjoyment of mathematics applied to Chilean third graders. Exploratory factor analysis leads us to the conclusion that it is possible to measure these kinds of beliefs with a Likert-type questionnaire and that there is an inverse item effect. We tested two confirmatory factor analysis models that allowed us to understand the behavior of inverse items in relation to the mathematics-related affect traits. These models suggest that the inverse item effect is a response style of Chilean children and the affect structure is consistent with the theoretical one considering this effect.