Informal formative assessment in inquiry-based science lessons

This paper is focused on the characterization of informal formative assessment conversations (i.e., interactions on-the-fly) from a methodological perspective. Interactions on-the-fly are unexpected teachable moments in which the teacher tries to probe students’ understanding and use that information to support their inquiry process. One of the coding systems used (ESRU framework) was adopted from the research literature (Ruiz-Primo & Furtak, 2007). Two other systems described here were developed and previously reported in two papers written by the authors (Correia, Nieminen, Serret, Hähkiöniemi, Viiri, & Harrison, in press; Nieminen, Hähkiöniemi, Leskinen, & Viiri, 2016). This paper presents these three coding systems together and discusses their features to characterize interactions on-the-fly. Examples for coding interactions on-the-fly from Finnish and English physics lessons are presented. For example, on the one hand, on-the-fly discussion proceeds as follows: The teacher initiates an on-the-fly episode by eliciting information using an open-ended (divergent) question, as the discussion progresses the teacher starts narrowing down the discussion using a closed-ended question (convergent), and closes the discussion by giving a short mini lecture. On the other hand, when guiding students’ inquiry, the teacher can collect information rapidly (quick interpretation) or he/she can use series of probing questions (further probing). In the former, the guidance is more authoritative as it is based on correspondence of the students’ and the teacher’s ideas. In the latter, guidance is based more on the student’s ideas representing more dialogic way to support learning

Variation of student engagement between different algebra tasks

Abstract In this study, we analyse how 7th grade students’ engagement during small group work differed in two consecutive algebra lessons: in the first lesson students solved equations and in the second lesson they created equations for other small groups to solve. Data was collected by videorecording the work of two groups in both lessons. Through directed content analysis, categories indicating student engagement were formed based on previous research and refined during analysis. The analysis revealed a change from individual engagement to collaborative engagement between lessons and an increase in many passive students engagement. Task characteristics which may affect the type and amount of engagement are discussed

Research on the teaching and learning of geometry

The chapter provides a comprehensive review of recent research in geometry education, covering geometric and spatial thinking, geometric measurement, and visualization related to geometry, as well as encompassing theoretical developments and research into teaching and teacher development. Studies examining the uses of forms of digital technology are addressed in every section. The content of the chapter reflects the main emphases of research in geometry education as presented at PME conferences over the period 2005–2015. The synthesis is presented in the form of the following sections: spatial reasoning, geometric visualization, geometric measurement, geometric reasoning and proving, students’ knowledge, teachers’ knowledge and development, and teaching geometry and the design and use of geometric tasks. While some topics of research are under-represented (including the topics of congruency and similarity, transformation geometry, analytic/ coordinate geometry, vector geometry), research in geometry education is embracing the use of more recent discursive, embodied and eco-cultural perspectives, and is also employing new methods such as eye-tracking. As research develops further, the affordance of digital technologies is enriching approaches to geometric and spatial teaching and learning by providing new ways of apprehension and representation, new manipulation and processes, wider and deeper conceptual understanding and linking of different meanings and treatments