Communicating mathematics through images: A multimodal study of Year One students’ meaning-making when working with mathematics textbooks

This article focuses on how Swedish Year One students (age 7–8) make meaning when working with images in mathematics textbooks. Images include textbook images, but also students’ self-drawn images used as support for calculation. The focus was (1) what the images in the exercises were designed to offer (the designed affordance), and (2) what the students discovered when working with them. The data material consisted of video transcripts of 18 students working with subtraction exercises from mathematics textbooks. The results showed that the students sometimes discovered the designed affordance and sometimes did not. The students who discovered the designed affordance sometimes used the image when performing the calculations, while others did not. Some students expressed that images in mathematics textbooks are for those who find mathematics difficult, and that completing exercises without using the images was desired. The students’ approaches to images were discussed in two specific cases: First, the students’ desire to use mathematical symbols rather than images may lead to students not discovering the mathematics content that the exercise is designed to offer. Second, the use of mathematical symbols rather than images may lead to students not discovering themselves as mathematical individuals.

Effect of resource-based instructions on pre-service biology teachers’ motivation toward learning biology

Linking motivation and learning is central to understanding students’ motivation toward learning and learning itself as complex cognitive phenomena. Some studies focused on students’ motivation toward learning biology in general; however, the shortage of studies on the effect of animation-based instruction and small-group laboratory activities as Resource-based Instructions (RBIs) on pre-service biology teachers was realized. The present study aimed to determine the effect of resource-based Instructions on pre-service biology teachers’ academic motivation toward learning biology at private and public Universities in Rwanda. Pre-service biology teachers were grouped into three groups at a public teacher traning University and received a pre-and post-assessment. Quasi-experimental, pre and post-test control group design was used at a public university, while a repeated measures design was used at a private university. The standard academic motivation scale for learning biology (AMSLB) yielded a Cronbach alpha coefficient of 0.71 before use. The t-Test was computed to measure the statistically significant difference between the pre-and post-assessment scores and group of RBI interventions. Multivariate analysis (MANOVA) was computed to measure the effect of RBIs vis à vis the AMSLB factors. Findings revealed no statistically significant difference (df=18, p=.458) in the motivation of learning biology of pre-service teachers before and after learning via traditional instruction at a public university. However, a statistically signficant difference was found with animation instruction (df=18, p=.002) and lab instruction (df=18, p=.014). The motivation of learning biology increased at a public university than at a private university. However, animations and small-group lab activities increased pre-service biology teachers’ intrinsic and extrinsic—career motivation of learning biology at both universities. Therefore, the study recommends using RBIs to improve pre-service biology teachers’ motivation toward learning biology.

A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning

The concept of derivative is used in many areas including applied problems and requiring mathematical modelling in different disciplines. One of the most important approaches for teaching the derivative is to support students in visualizing the concept. Also, it is necessary to shift researchers and teachers’ focuses to students’ dynamic mental actions while learning derivative in order to conduct effective teaching process. With this necessity, I focused on the perspective of quantitative reasoning related to the graphical approach to the derivative. This study aims to reveal a calculus student’s mental actions related to the graphical approach to the derivative. The data were collected from a first-year calculus student engaged in the task requiring graphical interpretation of the derivative. Results showed that the student’s understanding of the slope shaped her inferences about the tangent line because the quantity of ratio is prior knowledge for learning the instantaneous rate of change. Besides, as the student had the idea of correspondence related to the concept of function, she had difficulties in interpreting the global view of the derivate. This result suggests that having global view of the derivative requires a strong understanding of function and rate.

Verkko-oppimisympäristöjen kehittäminen tekoälyn avulla: Tulevaisuusvisio matematiikan opetuksen täydennyskoulutuksesta

Verkko-oppimisympäristöjen suosio kasvaa kiihtyvällä tahdilla maailman laajuisesti ja samaan aikaan tarve uusille lähestymistavoille verkko-oppimisen ja -opetuksen kehittämisessä ja tutkimuksessa on kasvanut. Vaikka lokitiedot mahdollistavat verkkokäyttäytymisen tutkimisen, on tätä mahdollisuutta hyödynnetty verkko-oppimisen ja -opetuksen tutkimuskontekstissa verrattain vähän. Tutkimuksessa hyödynnettiin lokitietoja verkkokurssin arvioinnissa ja kehittämisessä MOOC-ympäristössä. Tässä artikkelissa kuvataan oppimisprosessia lokitietojen avulla sekä pohditaan sitä, minkälaista ymmärrystä oppimisesta lokitiedot voivat tuottaa ja miten tällaisen tiedon voisi tulevaisuudessa valjastaa oppimisen tueksi. Tutkimusaineisto koostui matematiikan opettajien (N=58) täydennyskoulutusverkkokurssin lokitiedoista. Tutkimustulokset osoittavat, että syvällisemmät tai enemmän aikaa vaativat aktiviteetit keskeyttävät yhtenäisen opiskelun herkemmin kuin esimerkiksi videoluennot. Lyhytkestoiset videot ja nopeasti vastattavat kyselyt sen sijaan sitouttavat osallistujia yhtenäiseen opiskeluun. Vaikka suoristustavoissa on yksilöllisiä eroja, verkkokurssin kehittämistarvetta on mahdollista arvioida lokitietojen avulla. Esitämme artikkelissa vision siitä, kuinka tulevaisuudessa lokitiedot voisivat automaattisesti analysoitua, järjestelmä tunnistaisi oppimisprofiileja ja verkko-oppimisympäristö muokkautuisi automaattisesti tunnistettujen opiskelutaipumusten mukaan. Kun prosessiin yhdistetään tekoäly myös profilointialgoritmi kehittyisi automaattisesti käyttäjädatan kasvun myötä. In English Web-based learning enviroments have become increasingly popular world-wide. At the same time, the need for new approaches to both supporting and investigating teaching and learning have emerged. Although log information enables research of online behavior, this opportunity is not used to its full potential in the context of web-based teaching and learning. This research utilized log information in the assessment of a MOOC course and its development. This article describes the learning process with the help of log information. It also envisions what kind of understanding of the learning process log information can provide and how this understanding may be harnessed to support learning in the future. The data consisted of the log information of mathematic teachers (N=58) participating in an online continuing training course. The results show that in-depth time-consuming activities interrupt studying more easily than video lectures for example. Short videos and quick queries engage the participant in more coherent study. Although there are individual differences in the studying, less well-functioning teaching content and tasks can be recognized through log information. We present a vision of how log information can be automatically analyzed; the system would recognize learning profiles and the online environment would automatically modify itself according to the profile. When AI (artificial intelligence) is utilized the profiling algorithm would develop automatically as user data accumulates. Fulltext in Finnish.

Drawing out emotions in primary grade geometry: An analysis of participant-produced drawings of Grade 3–6 students

Research on psychosocial classroom learning environments has a strong tradition due to the early discovery of a relationship between positive classroom climate and academic performance and motivation, engagement, participation, and attitude towards school and teaching. Yet, more research is needed in this area due to the rich concept of classroom climate. In this paper, I focus on the emotional classroom climate in specific mathematics lessons, namely geometry lessons. The goals of this paper are threefold: (a) to present an analytical tool to determine the emotional classroom climate in geometry lessons using participant-produced drawings, (b) to provide insight into the emotional classroom climate in primary grade geometry lessons (Grades 3-6), and (c) to report on the differences and similarities between the grade levels regarding the emotional classroom climate. In total, 114 German primary grade students participated in the study. The emotional classroom climate was analyzed using participant-produced drawings. The results showed that the emotional classroom climate in all grades could be described as positive and relatively stable. However, positive emotional classroom climate dominated in Grade 3 geometry lessons only. Negative classroom climate was elicited in very few cases, if at all. Still, an ambivalent classroom climate (both positive and negative emotions) increased from the lower to the higher grades. Lastly, versatile implications for theory and practice are discussed regarding the methodology as well as possible future directions.

Att utveckla elevers förmåga att formulera undersökningsbara frågor i naturvetenskap: Mangling av en didaktisk modell

En viktig målsättning för naturvetenskaplig undervisning är att utveckla förmågan att formulera undersökningsbara frågor. Syftet med den här studien är att undersöka hur undervisning som utformats med hjälp av metoden Question Formulation Technique (QFT) kan stödja utveckling av elevers förmåga att formulera naturvetenskapligt undersökningsbara frågor. QFT är en modell för att utveckla elevers förmåga att formulera och värdera sina egna frågor i allmänhet. I studien prövas QFT i en svensk skolkontext och inom ramen för naturvetenskaplig undervisning. Studien genomfördes som en interventionsstudie i gymnasieskolan och inom ramen för kursen Gymnasiearbete. I kursen ska eleverna genomföra en egen naturvetenskaplig undersökning. QFT användes för att utforma undervisning som del av introduktionen till kursen. Data består av videoinspelningar av elevsamtal från undervisning som har analyserats utifrån ett pragmatiskt ramverk med organiserande syften och praktisk epistemologisk analys. Resultaten visar vilka närliggande syften som etableras i elevernas samtal om undersökningsbara frågor i undervisningen: (A) att producera så många frågor som möjligt, (B) att bedöma vilka frågor som är mest relevanta, (C) att kategorisera frågor, (D) att hitta och specificera ett undersökningsobjekt och (E) att planera för att genomföra en undersökning. Slutsatsen är att QFT kan fungera som stöd för lärares planering av undervisning om naturvetenskapligt undersökningsbara frågor under förutsättning att läraren aktivt stödjer eleverna i att uppmärksamma centrala kvaliteter avseende undersökningsbarhet och genom att binda samman närliggande syften med det övergripande syftet. In English An important goal for science education is to develop students’ ability to formulate questions of inquiry. The aim of this study is to investigate if science teaching designed from the method “Question Formulation Technique” (QFT) can support the development of this ability. QFT is a model for developing students' ability to phrase and evaluate questions in general which has been developed in a US context. In this study QFT is used in a Swedish context and within upper secondary school science education. The study is an intervention study where QFT was used as part of the introduction to Diploma work in the final year of upper secondary school. During the diploma work students are expected to conduct their own scientific investigations. The data consists of video recordings of student conversations while working with the formulation of questions for inquiry as part of a research lesson designed using QFT. Data was analyzed using a pragmatic approach of combining practical epistemological analysis (PEA) and organising purposes. The results show that five proximate purposes were established in the student conversations while the students engaged in formulating and refining questions of inquiry based on the QFT model. The five proximate purposes were: (A) to produce as many questions as possible, (B) to assess which questions are most relevant, (C) to categorize questions, (D) to find and specify the object of inquiry and (E) plan to conduct an inquiry. In conclusion, QFT can support the planning of teaching in relation to the ultimate purpose regarding how to formulate and refine questions of inquiry provided that the teacher actively participates to support students in connecting the established proximate purposes with the ultimate purpose. Fulltext in Swedish.

Matematiikan parhaat osaajat lukion lopussa ja heidän matematiikka-asenteissaan tapahtuneet muutokset

Tutkimus perustuu Opetushallituksen ja Kansallisen koulutuksen arviointikeskuksen keräämään pitkittäisaineistoon. Samaan ikäluokkaan kuuluvat oppilaat ovat osallistuneet kansallisiin matematiikan kokeisiin ja matematiikka-asenteita kartoittaviin kyselyihin vuosien 2005–2015 aikana neljällä eri mittauskerralla perusopetuksen kolmannelta vuosiluokalta toisen asteen loppuun. Tutkimusaineiston kokonaisotos käsittää yhteensä 3896 oppilasta. Tutkimuksessa keskitytään tarkastelemaan matematiikassa parhaiten menestyneitä opiskelijoita. Matematiikan parhaiksi osaajiksi määritetään kansalliseen matematiikan kokeeseen osallistuneet lukiolaiset, jotka saivat pitkän matematiikan ylioppilaskokeesta arvosanan laudatur tai eximia cum laude approbatur (n = 146). Ensin tutkimuksessa selvitetään, miten parhaiden osaajien matematiikka-asenteet muuttuivat perusopetuksesta lukion loppuun ja toiseksi, miten opetuksen pedagogiset ratkaisut yläkoulussa ja lukiossa selittävät osaamiseltaan parhaiden tyttöjen ja poikien asenteissa tapahtuneita muutoksia. Selittävien tekijöiden analyysissa käytetään päätöspuuanalyysia (DTA) ja lineaarista regressioanalyysia. Matematiikan parhaiden osaajien matematiikasta pitäminen kasvoi lukio-opintojen aikana, mutta minäkäsitys ja kokemus matematiikan hyödyllisyydestä laskivat. Matematiikassa parhaiten menestyneiden tyttöjen asenteissa tapahtuneet muutokset poikkesivat asenteiden yleisestä muutossuunnasta. Parhaiden tyttöjen minäkäsitys kasvoi yläkoulun ja lukion aikana lähes parhaiten menestyneiden poikien tasolle ja tytöt pitivät matematiikasta lukion lopussa poikia enemmän. Matematiikassa parhaiten menestyneiden tyttöjen ja poikien asenteiden kehittymistä selittivät erilaiset opetuksen pedagogiset ratkaisut. Molemmilla myönteisiä asenteita vahvistivat yleisesti oppilaskeskeisyyteen, yhteistoiminnallisuuteen ja oppijoiden tarpeiden huomioimiseen liittyvät pedagogiset ratkaisut. In English The study is part of a longitudinal research. Students belonging to the same age group were followed from the third grade of primary education to the end of upper secondary level. The data was collected by EDUFI and FINEEC during 2005–2015. The data consists of 3896 students. The target group consists of mathematically high-achieving students at the end of their studies in upper secondary school. The definition of high-achieving students based on success in matriculation examination of advanced math (n = 146). First we examine how high-achieving students’ attitudes towards mathematics change from primary education to the end of upper secondary level and then how pedagogical solutions in grades 7–9 and in upper secondary level explain boys’ and girls’ changes in attitudes. Decision tree analysis (DTA) and regression analysis were used to analyse the data. The results indicated that high-achieving students liked more mathematics during upper secondary school but self-concept and experience of usefulness of mathematics decreased. The changes of high-achieving girls’ attitudes differed from the general trend of change. High-achieving girls’ self-concept increased almost to the same level than high-achieving boys’ during grades 7–9 and in upper secondary school. Additionally, girls liked mathematics more than boys at the end of upper secondary level. The development of high-achieving girls’ and boys’ attitudes was explained by different pedagogical solutions. Both girls’ and boys’ positive attitudes were generally reinforced by pedagogical solutions related to student-centeredness, cooperative learning and paying attention to students’ needs. Fulltext in Finnish.

Drawing out classroom social climate: The use of participant-produced drawings in research on psychosocial classroom learning environment in the context of school mathematics

Over the last twenty years, visual methods in childhood research have become more mainstream across social science research. Through this paradigm shift, children became active agents in the research process. Participant-produced drawings in particular allow a constructive process of thinking in action, rather than seeing drawings as simple representations of the participants’ worldviews. In this paper, we use participant-produced drawings as a window into students’ perceptions of the mathematics classroom learning milieu from a social perspective. The goals of this report are threefold: (1) to conceptualize the complex and multifaceted construct of classroom social climate from the standpoint of primary grade students by using a qualitative research approach (i.e., participant-produced drawings), (2) to evaluate the extent to which participant-produced drawings can be used when researching the construct of classroom social climate, and (3) to provide two analytical tools that can be used in qualitative inquiry on classroom social climate in different mathematics lessons. To conclude, versatile recommendations for theory and practice are discussed regarding the employed methodology (i.e., participant-produced drawings as a visual research method) as well as some possible future directions.

Enhancing the performance of students in chemistry through flipped classroom with peer instruction teaching strategy

This study examines the implementation of flipped classroom with peer instruction teaching strategy to Grade 7 public high school students in Laguna, Philippines. To analyze the effect of flipped classroom with peer instruction on Chemistry achievement, a two-group quasi-experimental pretest-posttest research design was used. In addition, student perception and participation were conducted using a post-implementation survey. In the flipped classroom with peer instruction, the students were introduced to the lesson using the science courseware developed by the Department of Science and Technology and YouTube videos as pre-class activities. The in-class activity was focused on answering concept questions through peer instruction. Findings show that the two groups of students significantly increased their Chemistry achievement after the implementation of the teaching strategies. However, the students in the flipped classroom with peer instruction had higher Chemistry achievement, high level of participation, and wide acceptance of the teaching strategy than the control group. With this teaching strategy, the students were able to complete their assigned tasks on time, show cooperative and supportive attitude during classroom discussion and activities, share ideas in class, and show respect for the opinion of others. On the contrary, students in the traditional classroom with peer instruction setup performed poorly on these aspects of classroom participation.

Effect of the REACT strategy on senior high school students’ achievement in molecular genetics

Molecular genetics, a key concept in biology, is found to be very difficult for students at the senior high school level. A situation largely blamed on teachers' instructional approaches. Since the Relating, Experiencing, Applying, Cooperating and Transferring (REACT) strategy is reported to be an effective pedagogical approach for improving students' understanding of science concepts, in this paper, we sought to explore its effectiveness on Senior High School students' achievement in molecular genetics in Ghana. To do this, the embedded mixed methods research design was employed. Two intact biology classes selected through simple random sampling were assigned as experimental and control groups and taught with the REACT strategy and the conventional approach respectively. Quantitative data were obtained with pre-test-post-test control group design and analysed with Independent sample t-test and ANOVA. The qualitative data on students’ perception of learning with the REACT strategy was obtained through interviews and analysed thematically. The findings showed that the REACT strategy was more effective for teaching molecular genetic compared with the conventional approach. Although REACT could not bridge the gap between low and high achievers in that group, the performance of low achievers in the REACT group was at par with high achievers in the conventional group. Students perceived the opportunity to search and share information as well as relate new concepts to prior learning provided by the REACT strategy to have facilitated their understanding of concepts in molecular genetics. It is recommended that biology teachers use the REACT strategy to teach concepts students find problematic.