Tapaustutkimus 7.-luokkalaisten algebrallisesta yleistämisestä

Algebra on suomalaisten oppilaiden heikko alue. Toisaalta tutkimukset viittaavat siihen, että oppilaat voivat muodostaa algebrallisia ideoita tavanomaista aikaisemmin. Tämän tutkimuksen tavoitteena on selvittää, millaisia algebrallisia ideoita oppilaat muodostavat tutkiessaan funktioita 7. luokalla. Tutkimuksessa toteutettiin kahden oppitunnin opetusjakso lineaarisista ja epälineaarisista funktioista. Tunnit videoitiin, oppilaiden puhe nauhoitettiin ja oppilaiden kirjalliset tuotokset kerättiin. Tulosten mukaan oppilaat näyttivät olevan valmiita funktioiden käsittelyyn ja he muodostivat useita matemaattisia ideoita funktioista. Oppilaiden välillä oli kuitenkin eroja. Joillekin lineaariset f…

Differences in teacher telling according to students' age

Teacher telling can support but also hinder learning. In inquiry activities, telling that removes productive struggle may be problematic. In this study, different aged students experimented in a digital learning environment to build rules for a balance beam. We examined how the amount of teacher telling vary according to students’ age and the sophistication level of the rule. We collected video data from 21 pre-service teachers when each of them guided eight, 10, and 12 year old students. We found that the amount of teacher telling generally was not related to students’ age. However, when considering teacher guidance for more sophisticated rules, teacher telling was related to students’ age…

Analyzing science teachers’ support of dialogic argumentation using teacher roles of questioning and communicative approaches

The purpose of this study is to investigate how teachers use different types of discourse to support dialogic argumentation. Dialogic argumentation is a collaborative process in which students construct arguments together and examine arguments presented by their peers. Science teachers can use argumentation as a vehicle to help students gain a working understanding of science content and the nature of science and its practices. Whole-class closing discussions from video-recorded lessons are analyzed to study the discourse used to support argumentation by two physics teachers in lower secondary schools. Analysis of discourse includes coding of communicative approach at the episode level and …

Attending to and fostering argumentation in whole class discussion

Prior studies highlighted the importance of whole class discussion after student activities and have focused, for example, on teacher moves in supporting discussion. We characterize two processes in teacher-students interaction in argumentation discussions: attending to and fostering. These processes describe how student argumentation feeds teacher talk that in turn feeds student argumentation. We analysed video recordings of one whole class 7th grade lesson when students made geometric constructions and engaged in argumentation discussion. We elaborated on four themes in how the teacher talk attended to and fostered student argumentation. We argue that the concepts of attending to and fost…

Derivaatan ymmärtämiseen tähtäävä oppiminen ja opetus

Useissa ilmiöissä jokin suure riippuu toisesta suureesta. Esimerkiksi ilman lämpötila muuttuu ajan suhteen. Jonain hetkenä lämpötila muuttuu nopeasti ja jonain hetkenä hitaasti. Tällaisia tilanteita voidaan tarkastella muutosnopeuden eli derivaatan avulla. Muutosnopeus voidaan havaita erilaisista esitysmuodoista kuten kuvaajista, taulukoista tai funktioiden lausekkeista. Suureiden välisiä riippuvuuksia on tarkoitus harjaantua tarkastelemaan funktion avulla alakoulusta lähtien. Lukiossa tarkastelua syvennetään tutkimalla funktion arvojen muutosnopeutta eli derivaattaa. Yhtenä mahdollisuutena on edetä muutosnopeuden havaitsemisesta keskimääräisen muutosnopeuden laskemiseen ja hetkellisen muut…

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…

Comparing Guidance via Implicit and Explicit Model Progressions in a Collaborative Inquiry-Based Learning Environment with Different-Aged Learners

There is a need for research on the effect of different types of model progressions and learner age on learning and engagement in inquiry-based science settings. This study builds on the Scientific Discovery as Dual Search model to introduce less specific implicit model progression and compares them to the traditional explicit model progression. The data come from Finnish 8-, 10-, and 12-year-olds collaboratively using two different configurations of an inquiry-based learning environment about balance. Balance scale tasks were used to assess learning. Students also rated their situation-specific engagement. Both types of model progressions were beneficial for learning but there was no diffe…

Proceedings of the 2012 Annual Conference of Finnish Mathematics and Science Education Research Association = Matematiikan ja luonnontieteiden opetuksen tutkimusseuran konferenssijulkaisu 2012

Student teachers' questioning behaviour which elicit conceptual explanation from students

Getting students to explain their thinking is one of the big challenges in teachers’ work. Previous studies have analysed teacher questioning by focusing on amounts of different types of questions. In this study, I use questioning diagrams to see how questioning develops during the lessons. The data includes video recordings of student teachers’ mathematics lessons in secondary and upper secondary school. The data is analysed by constructing questioning diagram for each student teacher and locating conceptual explanations given by students. The lessons which included largest amount of conceptual explanations are further studied. In these lessons the student teachers had lengthy discussions …

Variation of student engagement between different algebra tasks

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 equa-tions 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 eng…

The role of representations in learning the derivative

How Do Lower-Secondary Students Exercise Agency During Formative Peer Assessment?

Exercising agency is an inherent component of peer assessment. However, the research on agency in peer assessment is scarce. This case study explored how seventh grade science students exercised agency during formative peer assessment. The data comprises audio recordings of students’ classroom discussions, written peer feedback, written work, student interviews, and the researcher’s field notes. With thematic analysis, we identified nine forms of agency as associated with three positions: group member, assessor, and assessee. An examination of student interactions revealed that peer assessment challenges students unequally. While some students exercised certain forms of agency without diffi…

Oppilaslähtöisyyden ja dialogisuuden ilmeneminen matematiikan opetuskeskusteluissa

Tässä tutkimuksessa tarkastellaan, miten oppilaslähtöisyys ja dialogisuus ilmenevät matematiikassa ja miten ne kytkeytyvät toisiinsa erityisesti oppilaiden näkökulmien, ajatusten ja kokemusten huomioimisen kautta. Tutkimuksen aineistoksi valittiin matematiikan aineenopettajaopiskelijoiden pitämiä oppitunteja, joissa havaittiin keskimääräisesti enemmän oppilaslähtöisyyden ja dialogisuuden ilmenemismuotoja. Keskustelunanalyysin keinoin osoitettiin, että oppilaslähtöisyyttä ja dialogisuutta voidaan edistää niin matematiikkaa kuin muitakin aiheita käsittelevissä opetuskeskusteluissa. Esimerkkien avulla pohditaan, miten vallitseva auktoritatiivinen ja oppiainekeskeinen opetusvuorovaikutus on haa…

Reflections on dialogicity : Challenges and suggestions by mathematics student teachers

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 tendency has bee…