Synergies between theoretical approaches to mathematics education with technology: A case study through a cross-analysis methodology

Mathematics education as a research domain is characterized by a plurality of theoretical approaches. Acknowledging the existence of such diversity and the risks of an excessive theoretical fragmentation does not mean to search for a unifying theory but to urge the community to develop strategies for coping with this diversity. This article is meant to show the potential of a “cross-analysis” methodology for establishing connections between different theoretical approaches to mathematics education with technology. Within the frame of the ReMath European Project, two Teaching Experiments were realized, centred on the use of a same ICT tool—Casyopée. Two distinct theoretical approaches shaped both the Teaching Experiments design and their enactments: the Theory of Didactical Situations and the Theory of Semiotic Mediation. The two Teaching Experiments have then been analysed from both theoretical points of view. In this article we will provide some examples drawn from this cross-analysis that show the synergy which can be established between the aforementioned theoretical approaches. Beyond contributing to a deeper understanding of the observed “didactical phenomena”, that synergy allows establishing connections between the two approaches that lead to their reciprocal enrichment.     

Representations over the Earth’s shape and the process of day and night from Nahua indigenous schoolchildren / Representaciones sobre la forma de la Tierra y del proceso día y noche en niños de escuelas indígenas Nahuas

This research presents the way in which children from a Nahua indigenous community build representations of the Earth’s shape, as well as the process that causes day and night. Concepts from school and local culture were studied. For the first case, a questionnaire was applied to 331 children, out of which 38 children were then interviewed on the topics from the questionnaire. For the cultural ideas, three teachers from the region and 30 children from the sample were interviewed. The results show that the representations depend on the form of questioning and the existence of three models: a flat structure with a celestial dome and mechanisms that hide or remove the Sun or the Moon in order to create day and night; a spherical structure with a surrounding sky, where the Sun and Moon rise and set; and a transitional model with a hollow sphere, flat surface and celestial dome. Cultural ideas do not appear to have any influence over these models, probably due to a loss of the community’s cosmogonic knowledge and the age of the children.     

Perceptions of Portuguese undergraduate students about assessment: a study in five public universities

This paper draws upon a broader piece of research on assessment in higher education, particularly focusing on issues regarding the fairness and effectiveness of the assessment methods and their implications for the learning process. The perceptions of undergraduate students are analysed taking into account the effectiveness and fairness of both traditional and learner-centred assessment methods, as well their influence on the learning process. In total, 624 students participated in this study in five Portuguese Public Universities in different areas of knowledge and programmes. Data were collected through questionnaires. Findings suggest that assessment is seen as more effective and fairer when it is done through the use of learner-centred assessment methods rather than by traditional assessment (e.g. written tests or exams). The students also claim that they devote more time to study when assessment is performed through learner-centred assessment methods than by traditional ones. The most used assessment methods are written tests and oral presentations in group. However, differences in the programmes were identified as well as differences according to gender. Implications of the findings for assessment and for the teaching and learning process are discussed.     

Learning to live together. The contribution of school

The paper we present is a biographical qualitative study on the school experience and its repercussions on the lives of young people. The paper has two aims: (1) to understand the repercussions of school experiences on the construction of personal identity, and (2) to incorporate the voices of alumni into a reflection on the present and future challenges facing primary education. The study is framed by the movement known as student voice. For this purpose, the interpretations ex-students were collected through in-depth interviews. The conclusions reveal the persistent effects of the school experience over the years as young people establish a sense of identity. The young people explain the attitudes and abilities that make up their way of living, and they relate this to what they learned in their early childhood and primary education.     

Distinct Influences of Mothers and Fathers on Kindergartners’ Numeracy Performance: The Role of Math Anxiety,Home Numeracy Practices,and Numeracy Expectations

The current study analyzed maternal and paternal differential influences on numeracy performance in kindergarten children. Participants were 180 Chilean children from backgrounds of low and high socioeconomic status (SES), their mothers, and their fathers. A path analysis was used to explore the influences of both maternal and paternal numeracy practices on children’s numeracy performance and the influences of maternal and paternal expectations and anxiety on those activities. Research Findings: Results showed that mothers and fathers who endorse higher numeracy expectations for their children and who report lower levels of math anxiety also report engaging more frequently in advanced numeracy practices with their children. Mothers’—but not fathers’—engagement in numeracy practices at home predicted children’s numeracy performance. Also, low-SES mothers engaged more frequently in numeracy practices with their children, and mothers in general engaged more often in numeracy activities with girls than with boys. Practice or Policy: These findings improve understanding of how maternal and paternal processes relate differently to numeracy performance in kindergarten children. Moreover, these results highlight the need to take into account parents’ numeracy attitudes and practices, as well as their SES, when designing interventions directed at increasing family support for math achievement.     

Changes in involvement in homework throughout compulsory secondary education / Cambios en la implicación en los deberes escolares a lo largo de la Educación Secundaria Obligatoria

This paper analyses the changes found in students’ involvement in homework throughout the four grade levels of compulsory secondary education in Spain (ages 12–15). It also analyses the relationship between the changes in students’ involvement in homework throughout schooling and motivational and emotional variables related to homework. Findings indicated that: (a) the amount of homework completed and homework time management diminished slightly throughout the grade levels researched; however, this result is clearer in terms of the amount of homework completed; (b) prior academic achievement is significantly related to the variables associated with students’ involvement in homework; (c) the motivational and affective variables researched explained statistically significant variance related to two of the three dependent variables associated with involvement in homework; and (d) the association between the motivational and affective variables and involvement in homework is lower.     

How to promote conservation behaviours: the combined role of environmental education and commitment

This study tested the influence of both environmental education (EE) and commitment interventions among teenagers for promoting energy and water conservation at home. Conservation behaviours were measured in two ways – directly and through questionnaires – prior to and after the interventions. Results indicate (1) EE participants may have saved more energy than non-participants and (2) those signing a public commitment saved more energy and water than those who did not. Results from the questionnaire measures demonstrated the importance of EE for promoting ecological self-identity and a personal norm for energy conservation. Based on these results the use of commitment interventions in EE initiatives for promoting conservation behaviours among teenagers is proposed.     

Achieving scientific excellence: An exploratory study of the role of emotional and motivational factors

This study investigates the perceived role of psychological factors in achieving excellence in scientific research. Six outstanding scientists aged 33–42 were interviewed. Data were analyzed inductively resulting in three main dimensions: personality traits and characteristics, psychological skills and processes, and task-specific strategies. Researchers highlighted the importance of emotional factors and motivational processes to achieve and sustain scientific excellence. Flexible coping, emotion regulation, and goal setting were emphasized and described as particularly important in dealing with rejections, setbacks, and team management issues. Persistence and adaptive perfectionism were key individual characteristics which helped participants in nurturing and sustaining motivation. This study suggests that the specific impact of emotional, motivational, and other psychological skills at different stages of excellence development is relevant; yet, further investigation is needed.