Students' dialogic and justifying moves during dialogic argumentation in mathematics and physics
In this study, we focus on dialogic argumentation among students in a whole class setting in mathematics and physics in lower secondary school. By drawing on previous studies on the structure of argumentation and dialogic interactions, we suggest that transparency of student reasoning and students' engagement with each other's ideas are two key aspects in dialogic argumentation. We examine what levels might exist in these key aspects and how they can exist simultaneously. We collected data by video recording mathematics and physics lessons in lower secondary school, and created a coding scheme for students' dialogic and justifying moves. By using the coding scheme, we recognized different k…
Dialogista argumentaatiota matematiikkaan ja fysiikkaan
The development of secondary students’ feedback literacy: Peer assessment as an intervention
A growing body of research has recognized the importance of students’ having active roles in feedback processes. Feedback literacy refers to students’ understandings of and participation in feedback processes, and research on students’ feedback literacy has so far focused on higher education; secondary schools have not received attention. This case study investigates secondary students’ feedback literacy and its development in the context of formative peer assessment. From various data sources, three categories of students’ feedback literacy were identified, and criteria for the levels of literacy in each category were created. The criteria were used in the coding of seventh- and eighth-gra…
Guiding Student Thinking Through Teacher Questioning When Learning with Dynamic Representations
Dynamic representations (e.g., dynamic geometry software GeoGebra for mathematics learning and PhET simulations for science learning) offer excellent opportunities for students to conduct investigations and to formulate explanations for the visualized phenomena. In order for this to be effective, students need guidance, for example, for planning their investigations and reflecting on their actions. One way to support students is by prompting them by using questions that are adapted to the students’ current situation. This chapter focuses on how pre-service teachers provide guidance for students through questioning and by both structuring and problematizing student learning. Data comes from …
Argumentation in the Context of High School Mathematics : Examining Dialogic Aspects of Argumentation
In this chapter, I examine argumentation from the perspective of dialogic argumentation that highlights students’ engagement with each other’s ideas in the process of making mathematical claims and providing evidence to support them. I analyzed the provided data for students’ dialogic and justifying moves and investigated how the teacher supported argumentation. I found that the students’ dialogic moves included elaborating and commenting on peers’ ideas. Students’ justifying moves included one case of articulating reasoning and several instances of describing support. The teacher structured argumentation by sequencing it into steps so that each step established a new piece of information. …
Pathways Through Peer Assessment: Implementing Peer Assessment in a Lower Secondary Physics Classroom
AbstractPeer assessment has been shown to advance learning, for example, by improving one’s work, but the variance of learning benefits within or between studies has not been explained. The purpose of this case study was to examine what kinds of pathways students have through peer assessment and to study which factors affect them when peer assessment is implemented in the early stage of physics studies in the context of conducting and reporting inquiry. Data sources used include field notes, audio recordings of lessons, student lab reports, written peer feedback, and student interviews. We examined peer assessment from the perspective of individual students and found 3 profiles of peer asse…
Associative and reflective connections between the limit of the difference quotient and limiting process
Abstract This paper reports a study of how students may connect the limiting process inherent in the derivative to the limit of the difference quotient (LDQ) when solving problems. The data was collected mainly through task-based interviews with five eleventh grade students. It was found that the students used various kinds of limiting processes and connected them in different ways to LDQ. Some of them changed between these two representations, and some students explained one with the other. The two kinds of connections were, respectively, named as associative and reflective connections. One of the students, who made the associative connection, used LDQ skillfully. On the contrary, a studen…
Experimenting with the structured assessment dialogue in physics and mathematics classes
Teacher–student discussions are central in assessing students’ skills and knowledge. This study deals with formal, pre-planned discussions to assess students’ inquiry competences. The method is called the structured assessment dialogue (SAD) which combines formative and summative assessment. Six SAD sessions (4 lower secondary physics and 2 upper secondary math) were implemented at the end of inquiry lessons. The SAD sessions were video recorded and the discussions were analyzed using theory based categories and networks. The results showed that the truly novel SAD method in Finnish classrooms challenged teachers and students. For example, students usually gave lower order answers although …
Design Anamorphosis in Math Class
Many visual effects are based on mathematical, geometrical procedures. Creating visual illusions through playful activities hold exciting pedagogical opportunities for raising students’ interest towards mathematics and the technical aspects of visual arts. The Experience Workshop Math-Art Movement has a number of thematic workshops — developed through interdisciplinary collaborations between mathematics teachers, artists and scholars — that are connected to perspective illusions and visual paradoxes. In this paper we introduce classroom activities focusing on mathematical connections in anamorphosis, drawing inspiration from István Orosz’s anamorphic art. peerReviewed
Utilizing Informal Formative Assessment and Dialogicity During Reflections on Educational Dialogue in Mathematics
In this study, educational dialogue is explored through informal formative assessment and dialogicity. We enhance the understanding of informal formative assessment and dialogicity by considering their relationship. Even though the interconnection of informal formative assessment and dialogicity is acknowledged, it has not been explicitly examined in research on educational dialogue. The data consists of video-stimulated joint reflections between mathematics student teachers and a teacher educator. The reflections were part of a teacher education program integrated in a mathematics pedagogic course. Conversational analysis was conducted to detect interactional patterns and indicators that e…
Enhancing Dialogic Argumentation in Mathematics and Science
This paper reports on a teacher professional development (PD) programme addressing dialogic argumentation in mathematics and science classrooms. While argumentation skills are becoming more and more important in an increasingly polarised society, the social aspect of argumentation is often neglected in secondary education. Moreover, it is agreed that genuine argumentation requires time and space in classroom dialogue. There have been calls for research delving into how teachers could be familiarised with dialogic argumentation so that they could foster such dialogue in students. The described PD programme features versatile and continuous cooperation between scholars and participating teach…
Kohti ilmiölähtöistä matematiikan oppimista : matemaattista ongelmanratkaisua taiteeseen yhdistäen
Ilmiölähtöistä matematiikan oppimista tuetaan ja edistetään sellaisten ongelmanratkaisutehtävien avulla, joissa oppilaat saavat itse suunnitella ratkaisuaan ja tehdä sitä koskevia valintoja. Matemaattista ongelmanratkaisua voidaan tukea eri tavoin, kuten taiteen avulla. Pohdimme tässä artikkelissa ilmiölähtöistä matematiikan oppimista yleisesti sekä erityisesti pohjautuen toteuttamaamme matematiikan pedagogiikan opintojaksoon. Matematiikan pedagogiikan opintojaksolla luokanopettajaopiskelijat perehtyivät itse matemaattiseen ongelmanratkaisuun taiteen viitekehyksessä sekä suunnittelivat ja toteuttivat oppimaansa hyödyntäen kokeilutunnin perusopetuksessa. peerReviewed
Forms and functions of on-the-fly formative assessment conversations in physics inquiry lessons
This case study examined teachers’ on-the-fly formative assessment conversations, that is, how teachers collect information from students’ thinking and use that information to support their learnin...
Assessment On-the-Fly: Promoting and Collecting Evidence of Learning Through Dialogue
International audience; Inquiry activities generate rich opportunities for STEM learning and for assessment. When teachers pay attention to assessment information collected during the course of learning, they are able to interpret and make decisions about such assessment data in a timely fashion that can drive future planning and support student learning, for example through feedback. This chapter focuses on how classroom talk can generate evidence of learning and how teachers can utilise this to enable assessment to guide inquiry learning. It looks at several vignettes from different countries of on-the-fly interactions in inquiry settings and unpacks how teachers organised, facilitated an…
Student teachers’ types of probing questions in inquiry-based mathematics teaching with and without GeoGebra
Previous studies have produced several typologies of teacher questions in mathematics. Probing questions that ask students to explain are often included in the types of questions. However, only rare studies have created subtypes for probing questions or investigated how questioning differs depending on whether technology is used or not. The aims of this study are to elaborate on different ways of asking students to give explanations in inquiry-based mathematics teaching and to investigate whether questioning in GeoGebra lessons differs from questioning in other lessons. Data was collected by video recording 29 Finnish mathematics student teachers’ lessons in secondary and upper secondary sc…
Complementing the Guidance Provided by a Simulation through Teacher Questioning
The interaction between the teacher and the learners when using simulations is in need of research. This study concentrates on two questioning approaches, series of probing and series of guiding questions that teachers use to guide learning with simulations. These two approaches are contrasted with non-directive and directive guidance provided by the simulation. The data was collected through screen capture videos of pre-service primary teachers teaching physics with a PhET simulation. Two cases were selected for further analysis of teacher questioning and its adaptation to the learners. Even though teachers might use the spaces for explanations created by the simulation to probe for learne…
Recognising Articulated Reasoning in Students' Argumentative Talk in Mathematics Lessons
Previous studies have reported difficulties in analysing students’ argumentation. Especially the warrant, which connects data with claims, is found to be problematic to recognise. Weexamine how specific criteria for different forms of reasoning could decrease this difficulty. Instead of identifying warrants, we recognise whether students’ argumentation contains explicitly stated reasoning. We have developed an analysis method for recognising reasoning in argumentative talk. We collected video data from two mathematics lessons where students had to state claims about a mathematical situation and build convincing justification for their claims. The focus of analysis is in how the students art…
The interplay between the guidance from the digital learning environment and the teacher in supporting folding back
AbstractPrevious studies have proposed that students’ mathematical understanding develops dynamically through the process known as folding back, in which learners revisit earlier forms of understanding and use them to build even deeper levels of mathematical understanding. Digital learning environments, where students can manipulate representations, are often used to enable students to notice properties, patterns, or rules. When working in such an environment, students usually receive support from the environment and the teacher. The interplay between these different sources of support is important according to previous studies. In this study, we examine this interplay in the case of foldin…
Reflections on dialogicity: Challenges and suggestions by mathematics student teachers
Abstract Research related to dialogic teaching has been gaining ground in recent decades. On a theoretical level, researchers have described how sociocultural approaches are linked to dialogic teaching. In addition, empirical studies have explained how dialogic teaching manifests itself in educational dialogue and classroom interactions. However, studies addressing how the dialogic theory and practice could be linked meaningfully in teacher education and professional development programs in subject teacher education and related praxis are still limited. Especially in the case of math teacher education, the reported professional development programs are limited in number. Whereas the tendenc…
Teacher's reflections on experimenting with technology-enriched inquiry-based mathematics teaching with a preplanned teaching unit
Abstract According to previous studies, inquiry-based mathematics teaching enhances learning. However, teachers need support in implementing this type of teaching. In this study, a high school teacher was given a short preplanned inquiry-based mathematics teaching unit that included activities with GeoGebra. The teacher was interviewed after every lesson to explore her reflections after teaching. I analyzed how the teacher described the differences between her regular teaching style and the teaching unit and the pros and cons of the teaching unit. The teacher reflected on the roles of the teacher and students, depth of students’ knowledge, her stance toward the teaching unit, constraints fo…
Teacher orchestration of classroom interaction in science: exploring dialogic and authoritative passages in whole-class discussions
Whereas science is fundamentally a result of a dialogic debate, the authoritative approach has been conceived of as a fundamental part of school science. Dialogic interactions encompass the mutual appreciation of different ideas manifested in teacher supportiveness toward students and, in authoritative interactions, the focus is more on the science’s or teacher’s point of view. Whereas dialogic and authoritative interactions have been viewed as oppositional in recent educational research, authoritative interactions could well be the seed for and give strength and meaning to dialogic interactions, and thus, to the overall dialogue. The focus in this study is on the interplay between authorit…
Three Dimensions of Dialogicity in Dialogic Argumentation
Three dimensions of dialogicity are emphasised in the literature: dialogic teacher talk, students' dialogic moves and organising for dialogic teaching. In this article, we examine these dimensions and the interplay between them in supporting dialogic argumentation in the context of whole-class discussions in mathematics and physics. Three seemingly different seventh-grade lessons were selected for further analysis from the database of a research project on dialogic argumentation. In this paper, we focus on whole-class discussions after a group assignment. The lessons were video recorded with multiple cameras and transcribed. We characterised dialogic features of teacher talk, more general t…
Mathematics Learning through Arts and Collaborative Problem-Solving : The Princess and the Diamond-Problem
In this paper, we examine a mathematics education course which focused on collaborative mathematical problem solving in art topics. The students of the course were Finnish primary school pre-service teachers. During the course students investigated tessellations, reflected on their experiences and designed workshops for pupils. The course meetings were video recorded. Students’ work contained elements of mathematical problem solving and gave them experiences of working collaboratively. The topic of tessellation was found suitable for this purpose. peerReviewed
Teacher Guidance in Mathematical Problem-Solving Lessons: Insights from Two Professional Development Programs
When implementing a problem-solving lesson, the teacher needs to provide students appropriate guidance during problem solving. This demanding task requires understanding students’ work in progress and giving them necessary help without constraining their thinking. In this article, we share insights from two professional development programs on how teachers guided students’ problem solving and how they reflected on these instances. One of the programs included Finnish pre-service teachers, while the other program included US in-service teachers. We analyzed video-recorded problem-solving lessons from 16 Finnish and 2 US teachers in grades 6–9. We found two themes about teacher guidance of st…
PRIMARY SCHOOL STUDENT TEACHERS´ CLASSROOM TALK DURING INQUIRY-BASED BIOLOGY LESSONS
Article
Geogebra-avusteinen tutkiva matematiikka opetusharjoittelussa : tutkimuksia opettajan ja oppilaiden toiminnasta
Tässä artikkelikokoelmassa julkaistavat tutkimusraportit syntyivät osana johtamaani ”Tutkiva matematiikka opetusharjoittelussa” -projektia. Projektin tavoitteena on tarkastella tekijöitä, joista tutkiva matematiikan oppiminen muodostuu sekä kehittää ohjeistusta tutkivan matematiikan käytännön toteutukseen. Opetin matematiikan aineenopettajiksi opiskeleville kahdeksan 45 minuutin oppituntia tutkivan matematiikan periaatteita kurssilla ”OPEA411 Syventävä ainepedagogiikka”. Lisäksi kurssin ”OPEA611 Aineenopettaja työnsä tutkijana” 10 oppitunnin aikana perehdyimme tutkivaa matematiikkaa käsitteleviin tutkimuksiin, opetusta kehittämään pyrkiviin tutkimusmenetelmiin ja videoanalyysiin. Näistä 18 …