Dimensions of learning mathematics via technology

Mathematics is a comprehensive, even esthetical experience, affecting a person intellectually, emotionally and physically. The purpose of this study is to determine and examine the dimensions of technology-enhanced mathematics learning. The three learning domains cognitive, psychomotor and affective, ranging from uncomplicated to more complex learning outcomes, as defined by Bloom, have been used a great deal in mathematics pedagogy (Krathwohl, Bloom, & Masia, 1964). This study goes deeper and also examines motivation theory and learning theories when applying technology to the teaching of mathematics. To get a broad picture of the impact of these dimensions on mathematics learning via technology, research was conducted in an array of contexts, including South Af-rica, Mozambique, Germany and Finland. The cross-cultural and cross-countries ap-proach was chosen to ensure wider generalizability of the research. The study invol-ved an action design research (ADR) approach of creating and evaluating artifacts; (i) a novel pedagogical INBECOM model for mathematics learning advocating both behavioristic and constructivist perspectives, and (ii) a newly designed and created story-based UFractions mobile game for learning of fractions incorporating tangible manipulatives. In particular, the affective domain of participants in the study was being studied throughout a ten-year research process from 2009 to 2019. The INBECOM pedagogical model was tested by organizing a fraction course for 21 grade 10 students. The development and evaluation of the pedagogical INBECOM model gives a concrete example of how two learning approaches, constructivism and behaviourism, can be combined in teaching fractions. Furthermore, the results of the qualitative evaluation confirm the view that successful instructional practices have features that are supported by both constructivism and behaviorism. The UFractions mobile game was evaluated with 305 grade 8 students and 12 teachers. Empirical tests indicate that combining concrete manipulatives and mobile phones is a meaningful way to learn the abstract concept of fractions, increasing active student participation. On the basis of the collected data, I initiated a taxonomy for the variety of play motivations in the UFractions game. The dynamics between game motivations and disturbance factors (DF) was analysed. Each motivation relates to a set of DFs typically affecting the player motivation negatively. By becoming aware of these relations, we are able to design more motivating educational games and give guidelines for game developers, users and educators. To explore the affective learning experiences of the three groups of research participants, the qualitative data was derived from the interviews with researchers, teachers and students, as well as from learning diaries, feelings blogs, observations (311 documents) and quantitized (Saldaña, 2009). All the data was explored from the affective perspective, by labelling the feelings the participants experienced according to the affective levels of the Krathwohl et al. (1964) framework. I concluded that affective learning at all five levels was recognized among the three groups of participants. However, the results show that affective learning mostly took place at the receiving level, indicating that the participants received more than they responded, valued, organized or internalized. There was also a significant effect of research participants pertaining to receive; students’ affective learning occurred more at the receiving level than that of the teachers; and teachers’ affective learning emerged more at the value level. Moreover, I define a dimension taxonomy of learning to be used as a framework in the design and implementation of technology-enhanced mathematics teaching and learning including the following three dimensions: (i) Domains of learning, (ii) Orientation of learning, and (iii) Motivation of learning. More precisely, the five domains of learning are cognitive, psychomotor, affective, interpersonal, and intra-personal. Considering orientation of learning, combining behaviorism and constructivism, would lead to more motivating and meaningful teaching and learning strategies. Furthermore, the level of technology integration, the level of students’ cognitive process, and the level of teachers’ knowledge, are intertwined. Motivational fac-tors are an essential part of learning, and it is important to acknowledge connections between motivations and disturbances, when using technology.--- Matematiikka on moniulotteinen kokemus vaikuttaen henkilöön älyllisesti ja tunnetasolla samalla kytkeytyen myös fyysiseen ulottuvuuteen. Tämä tutkimus määrittää ja tarkastelee teknologia-avusteisen matematiikan oppimisen dimensioita. Bloomin määrittämät kolme oppimisen osa-aluetta, kognitiivinen, psykomotorinen ja affektiivinen, jotka etenevät yksinkertaisista monimutkaisempiin oppimisen tasoihin, ovat olleet laajasti käytössä matematiikan pedagogiikassa (Krathwohl, Bloom & Masia, 1964). Tämä tutkimus laajentaa käsitystä oppimisesta tutkimalla motivaatio ja oppimisteorioita sekä niiden käytännön soveltamista matematiikan opetuksessa teknologian avulla. Laajan ymmärryksen saavuttamiseksi siitä, miten nämä tekijät vaikuttavat matematiikan oppimiseen teknologian avulla, tutkimusta toteutettiin monissa eri ympäristöissä, mukaan lukien EteläAfrikka, Mosambik, Saksa ja Suomi. Tutkimuksessa huomioitiin kulttuuriset ja kansainväliset näkökulmat tulosten laajemman yleistettävyyden varmistamiseksi. Tutkimus hyödynsi suunnittelutoimintatutkimuksen (Action Design Research, ADR) menetelmää artefaktien luomiseksi ja evaluoimiseksi: (i) uudenlaista behavioristisia ja konstruktivistisia näkökulmia yhdistävää pedagogista INBECOM-mallia matematiikan oppimiseen, ja (ii) käsinkosketeltavia matematiikan apuvälineitä hyödyntävää UFractions-mobiilipeliä murtolukujen oppimiseen. Erityisesti osallistujien affektiivista oppimista tutkittiin kymmenen vuoden tutkimusprosessin aikana vuosina 2009–2019. INBECOM-pedagogista mallia testattiin järjestämällä murtolukukurssi kansanopiston 10luokalle, jolla oli 21 oppilasta. Pedagogisen INBECOMmallin kehitys ja arviointi antavat konkreettisen esimerkin siitä, miten kahden oppimisteorian, konstruktivismin ja behaviorismin, voi yhdistää murtolukujen opetuksessa. Lisäksi laadullisen arvioinnin tulokset vahvistavat käsitystä siitä, että menestyksellisillä opetusmenetelmillä on piirteitä, jotka hyödyntävät sekä konstruktivistisia että behavioristisia periaatteita. UFractions-mobiilipeli arvioitiin 305 8-luokan opiskelijan ja 12 opettajan avulla. Empiiriset testit osoittavat, että konkreettisten apuvälineiden ja matkapuhelimien yhdistäminen on mielekäs tapa oppia abstrakti murtoluvun käsite ja edistää opiskelijoiden aktiivista osallistumista. Kerätyn datan perusteella kehitettiin taksonomia UFractions-pelin pelimotivaatioista. Pelimotivaatioiden ja häiriötekijöiden (Disturbance Factors, DF) välistä dynamiikkaa analysoitiin. Jokainen motivaatio liittyy tiettyihin häiriötekijöihin, jotka yleensä vaikuttavat pelaajan motivaatioon negatiivisesti. Näiden suhteiden tiedostaminen auttaa suunnittelemaan motivoivampia opetuspelejä ja antaa suuntaviivoja pelikehittäjille, käyttäjille ja opettajille. Affektiivisen oppimisen kokemusten tutkimiseksi tutkimukseen osallistuneiden kolmen ryhmän dataa tarkasteltiin laadullisen tutkimuksen keinoin; tutkijoiden, opettajien ja opiskelijoiden haastattelut, oppimispäiväkirjat, tunneblogi sekä havainnot (311 asiakirjaa) kvantifioitiin (Saldaña, 2009). Kaikki data analysoitiin affektiivisesta näkökulmasta merkitsemällä osallistujien kokemat tunteet Krathwohlin ym. (1964) viitekehyksen affektiivisten tasojen mukaisesti. Tutkimus osoitti, että affektiivista oppimista tunnistettiin kolmen osallistujaryhmän keskuudessa kaikilla viidellä tasolla. Tulokset osoittavat kuitenkin, että affektiivinen oppiminen tapahtui pääasiassa vastaanottotasolla, mikä viittaa siihen, että osallistujat vastaanottivat enemmän kuin he vastasivat, arvostivat, järjestivät tai sisäistivät. Myös osallistujaryhmien affektiivista oppimista koskevat tulokset vaihtelivat merkittävästi: opiskelijoiden affektiivinen oppiminen tapahtui enemmän matalammalla vastaanottotasolla kuin opettajien, ja opettajien affektiivinen oppiminen ilmeni enemmän korkeamman, arvotason oppimisena. Lisäksi tutkimuksessa määritellään oppimisen ulottuvuuksien taksonomia, jota käytetään teknologia-avusteisen matematiikan opetuksen ja oppimisen suunnittelussa ja toteutuksessa. Tähän kuuluu seuraavat kolme ulottuvuutta: (i) Oppimisen osa-alueet, (ii) Oppimisen orientaatio ja (iii) Oppimisen motivaatio. Tarkemmin sanottuna viisi oppimisen osa-aluetta ovat kognitiivinen, psykomotorinen, affektiivinen, interpersonaalinen ja intrapersonaalinen. Yhdistämällä behavioristisia ja konstruktivistisia elementtejä saadaan innostavia ja merkityksellisiä opetus ja oppimisstrategioita. Motivaatiotekijät ovat olennainen osa oppimista, ja teknologiaa käytettäessä on tärkeää tunnistaa yhteydet motivaation ja erilaisten häiriötekijöiden välillä. Lisäksi teknologian integraation taso, opiskelijoiden kognitiivinen prosessi ja opettajien tietotaso ovat kietoutuneet toisiinsa

An Analysis of Interactive Learning Environments for Arithmetic and Algebra Through an Integrative Perspective

International audienceThe analysis presented in this article tries to obtain a global view of the field of interactive learning environments (ILE) dedicated to arithmetic and algebra. As preliminaries, a brief overview of evaluation methods focusing on educational software is given and a short description of ten ILEs concerned by the study is provided as a kind of a state-of-the-art. Then the methodology of ILEs analysis developed in the TELMA project is explained consisting in the design and the refinement of an analysis grid and its use on the ten ILEs is mentioned. Next, a first level analysis of results leading to a compiled, analytic and synthetic view of the ILEs available and/or missing functionalities is given. A second level of the analysis is also proposed, with two concise representations of the ILEs, composed of graphical representations of the previous results, leading to a 3D map of ILEs dedicated to arithmetic and algebra. This map provides, as promised, a global view of the field and permits to define five sorts of ILEs according to two criteria: the first one is teacher-oriented and concerns usages enabled by the ILE; the second one is student-oriented and concerns control provided by the ILE to accomplish such usages

An Analysis of Interactive Learning Environments for Arithmetic and Algebra Through an Integrative Perspective

International audienceThe analysis presented in this article tries to obtain a global view of the field of interactive learning environments (ILE) dedicated to arithmetic and algebra. As preliminaries, a brief overview of evaluation methods focusing on educational software is given and a short description of ten ILEs concerned by the study is provided as a kind of a state-of-the-art. Then the methodology of ILEs analysis developed in the TELMA project is explained consisting in the design and the refinement of an analysis grid and its use on the ten ILEs is mentioned. Next, a first level analysis of results leading to a compiled, analytic and synthetic view of the ILEs available and/or missing functionalities is given. A second level of the analysis is also proposed, with two concise representations of the ILEs, composed of graphical representations of the previous results, leading to a 3D map of ILEs dedicated to arithmetic and algebra. This map provides, as promised, a global view of the field and permits to define five sorts of ILEs according to two criteria: the first one is teacher-oriented and concerns usages enabled by the ILE; the second one is student-oriented and concerns control provided by the ILE to accomplish such usages

Quantitizing Affective Data as Project Evaluation on the Use of a Mathematics Mobile Game and Intelligent Tutoring System

Technology-echnology-enhanced learning generally focuses on the cognitive rather than the affective domain of learning. This multi-method evaluation of the INBECOM project (Integrating Behaviourism and Constructivism in Mathematics) was conducted from the point of view of affective learning levels of Krathwohl et al. (1964). The research questions of the study were: (i) to explore the affective learning experiences of the three groups of participants (researchers, teachers and students) during the use of a mobile game UFractions and an intelligent tutoring system Active Math to enhance the learning of fractions in mathematics; and (ii) to determine the significance of the relationships among the affective learning experiences of the three groups of participants (researchers, teachers and students) in the INBECOM project.This research followed a sequential, equal status, multi-mode research design and methodology where the qualitative data were derived from the interviews with researchers, teachers and students, as well as from learning diaries, feelings blogs, and observations (311 documents) across three contexts (South Africa, Finland, and Mozambique). The qualitative data was quantitized (Saldana, 2009), i.e. analysed deductively in an objective and quantifiable way as instances on an Excel (TM) spreadsheet for statistical analyses. All the data was explored from the affective perspective by labelling the feelings participants experienced according to the affective levels of the Krathwohl et al. (1964) framework.The researchers concluded that: (i) the research participants not only received information, but actively participated in the learning process; responded to what they learned; associated value to their acquired knowledge; organised their values; elaborated on their learning; built abstract knowledge; and adopted a belief system and a personal worldview; and (ii) affirmation of affective learning at all five levels was recognised among the three groups of participants. The study raised a number of issues which could be addressed in future, like how affective levels of learning are intertwined with cognitive levels of learning while learning mathematics in a technology-enhanced learning environment; and how pedagogical models which take into account both cognitive and affective aspects of learning support deep learning

Constructive Use of Errors in Teaching the UML Class Diagram in an IS Engineering Course

A class diagram is one of the most important diagrams of Unified Modeling Language (UML) and can be used for modeling the static structure of a software system. Learning from errors is a teaching approach based on the assumption that errors can promote learning. We applied a constructive approach of using errors in designing a UML class diagram in order to (a) categorize the students’ errors when they design a class diagram from a text scenario that describes a specific organization and (b) determine whether the learning-from-errors approach enables students to produce more accurate and correct diagrams. The research was conducted with college students (N = 45) studying for their bachelor’s degree in engineering. The approach is presented, and the learning-from-errors activity is illustrated. We present the students’ errors in designing the class diagram before and after the activity, together with the students’ opinions about applying the new approach in their course. Twenty errors in fundamental components of the class diagram design were observed. The students erred less after the activity of learning from errors. The displayed results show the relevance and potential of embedding our approach in teaching. Furthermore, the students viewed the learning-from-errors activity favorably. Thus, one of the benefits of our developed activity is increased student motivation. In light of the improved performance of the task, and the students’ responses to the learning-from-errors approach, we recommend that information systems teachers use similar activities in different fields and on various topics

Desenvolvimento e Avaliação de Material Web para o Ensino de Decimais Utilizando Exemplos Incorretos

O uso de exemplos incorretos como ferramenta pedagógica ainda é um assunto controverso. Muitos professores são ambivalentes e, até mesmo, hostis quanto ao seu uso. No ensino de matemática, este sentimento persiste. Poucos professores ensinam utilizando exemplos incorretos. Contudo, pesquisadores na área de educação matemática vêm demonstrando que a discussão de conceitos utilizando erros incentiva a reflexão e a construção do conhecimento. Devido a esta polêmica, existe uma lacuna de material didático que utiliza esta abordagem. Dessa forma, este trabalho possui dois objetivos principais. O primeiro é desenvolver material Web que utiliza exemplos incorretos para ensinar matemática; com foco no conceito de decimais. O segundo é investigar os benefícios (ou malefícios) deste material. Foi conduzido um estudo com 429 alunos do ensino fundamental de duas escolas públicas dos EUA para avaliar o impacto deste material na aprendizagem de decimais. Os resultados indicam um significativo aumento na aprendizagem dos alunos, dando mais evidências a favor do uso de exemplos incorretos para ajudar a aprendizagem de matemática

Development of an Attitude Scale of Mathematics and Science Teachers towards Mistake and Instant Feedback to the Mistake: A Validity and Reliability Study

The purpose of the research is to develop a valid and reliable attitude scale that can measure the attitudes of math and science teachers (315) and teacher candidates (105) towards mistakes and instant feedback. In the validity studies, the exploratory factor analysis was made with the SPS1S 8.0 package program after that the confirmatory factor analysis was made with Lisrel 8.8 software. To develop the scale; 1. Creation of Item Pool 2. Obtaining Expert Opinion, 3. Creation of Pre-Trial Form 4. Factor Analysis is made. According to factor analysis; Kaiser Meyer Olkin (KMO) rate; .808; Bartlett test result: 2148,354; Cronbach alpha reliability coefficient for the whole scale: .829. According to confirmatory factor analysis: Root Mean Square Error of Approximation (RMSEA) .022 (<.05); p-Value for Test of Close Fit .00 (<.05), standardized root mean square residual (SRMR) .014, Goodness of Fit Index (GFI) .75, Adjusted Goodness of Fit Index (AGFI) .69; Normed Fit Index (NFI) .91; Relative Fit Index (RFI) .78; Incremental Fix Index (IFI): .83; Parsimony Goodness of Fit Index (PGFI): .62; Degrees of Freedom: 760; Root Mean Square Residual (RMR): 2.07 and NonNormed Fit Index (NNFI): .88. According to research findings, attitude scale is valid and reliable so it can be used to determine math and science teachers and teacher candidates positive and negative attitudes toward mistake and giving instant feedback to mistake