Self -regulated learning: The role of a journal in the learning process for students and teachers

A fundamental goal of education is to equip students with self-regulatory capabilities that enable them to educate themselves. Self directedness not only contributes to success in formal instruction but also promotes lifelong learning (Bandura, 1997). The area of research on self-regulated learning is well grounded within the framework of psychological literature attributed to motivation, metacognition, strategy use and learning. This study explored past research and established the purpose of teaching students to self-regulate their learning and highlighted the fact that teachers are expected to assume a major role in the learning process. A student reflective writing journal activity was sustained for a period of two semesters in two fourth-grade mathematics classrooms. The reflective writing journal was analyzed in search of identifying strategies reported by students. Research questions were analyzed using descriptive statistics, frequency counts, cross-tabs and chi-square analyses. ^ Results based on student-use of the journals and teacher interviews indicated that the use of a reflective writing journal does promote self-regulated learning strategies to the extent which the student is engaged in the journaling process. Those students identified as highly self-regulated learners on the basis of their strategy use, were shown to consistently claim to learn math “as well or better than planned” on a weekly basis. Furthermore, good self-regulators were able to recognize specific strategies that helped them do well and change their strategies across time based on the planned learning objectives. The perspectives of the participating teachers were examined in order to establish the context in which the students were working. The effect of “planned change” and/or the resistance to change as established in previous research, from the teachers point of view, was also explored. The analysis of the journal data did establish a significant difference between students who utilized homework as a strategy. ^ Based on the journals and interviews, this study finds that the systematic use of metacognitive, motivational and/or learning strategies can have a positive effect on student's responsiveness to their learning environment. Furthermore, it reflects that teaching students “how to learn” can be a vital part of the effectiveness of any curriculum. ^

The role of *language in early childhood mathematics

Math literacy is imperative to succeed in society. Experience is key for acquiring math literacy. A preschooler's world is full of mathematical experiences. Children are continually counting, sorting and comparing as they play. As children are engaged in these activities they are using language as a tool to express their mathematical thinking. If teachers are aware of these teachable moments and help children bridge their daily experiences to mathematical concepts, math literacy may be enhanced. This study described the interactions between teachers and preschoolers, determining the extent to which teachers scaffold children's everyday language into expressions of mathematical concepts. Of primary concern were the teachers' responsive interactions to children's expressions of an implicit mathematical utterance made while engaged in block play. The parallel mixed methods research design consisted of two strands. Strand 1 of the study focused on preschoolers' use of everyday language and the teachers' responses after a child made a mathematical utterance. Twelve teachers and 60 students were observed and videotaped while engaged in block play. Each teacher worked with five children for 20 minutes, yielding 240 minutes of observation. Interaction analysis was used to deductively analyze the recorded observations and field notes. Using a priori codes for the five mathematical concepts, it was found children produced 2,831 mathematical utterances. Teachers ignored 60% of these utterances and responded to, but did not mediate 30% of them. Only 10% of the mathematical utterances were mediated to a mathematical concept. Strand 2 focused on the teacher's view of the role of language in early childhood mathematics. The 12 teachers who had been observed as part of the first strand of the study were interviewed. Based on a thematic analysis of these interviews three themes emerged: (a) the importance of a child's environment, (b) the importance of an education in society, and (c) the role of math in early childhood. Finally, based on a meta-inference of both strands, three themes emerged: (a) teacher conception of math, (b) teacher practice, and (c) teacher sensitivity. Implications based on the findings involve policy, curriculum, and professional development.

As compreensões do construtivismo de Ernst Von Glasersfeld e John Fossa: intermediando um diálogo em busca de novas significações

The present thesis, orientated by a letter sent by Ernst von Glasersfeld to John Fossa, is the product of a theoretical investigation of radical constructivism. In this letter, von Glasersfeld made three observations about Fossa’s understanding of radical constructivism. However, we limited our study to the second of these considerations since it de als with some of the core issues of constructivism. Consequently, we investigated what issues are raised by von Glasersfeld’s observation and whether these issues are relevant to a better understanding of constructivism and its implications for the mathema tics classroom . In order to realize the investigation, it was necessary to characterize von Glasersfeld’s epistemological approach to constructivism, to identify which questions about radical constructivism are raised by von Glasersfeld’s observation, to i nvestigate whether these issues are relevant to a better understanding of constructivism and to analyze the implications of these issues for the mathematics classroom. Upon making a hermeneutic study of radical constructivism, we found that what is central to it is its radicalism, in the sense that it breaks with tradition by its absence of an ontology. Thus, we defend the thesis that the absence of an ontology, although it has advantages for radical constructivism, incurs serious problems not only for the theory itself, but also for its implications for the mathematics classroom. The advantages that we were able to identify include a change from the usual philosophical paths to a very different rational view of the world, an overcoming of a naive way of thi nking, an understanding of the subject as active in the construction of his/her experiential reality, an interpretation of cognition as an instrument of adaptation, a new concept of knowledge and a vision of knowledge as fallible (or provisional). The prob lems are associated with the impossibility of radical constructivism to explain adequately why the reality that we build up is regular, stable, non - arbitrary and publicly shared. With regard to the educational implications of radical constructivism, the ab sence of an ontology brings to the mathematics classroom not only certain relevant aspects (or favorable points) that make teaching a process of researching student learning, empowering the student to learn and changing the classroom design, but also certa in weaknesses or limitations. These weaknesses or limitations of constructivism in the classroom are due to its conception of knowledge as being essentially subjective. This requires it to work with one - on - one situations and, likewise, makes the success of teaching dependent on the teacher’s individual skills. Perhaps the most important weakness or limitation, in this sense, is that it makes teaching orientated by constructivist principles unable to reach the goal of the formation of a community. We conclud e that issues raised by von Glasersfeld’s observation are absolutely relevant to the context of a better understanding of radical constructivism and its implications for education, especially for Mathematics Education.

'Sitting alone in the staffroom contemplating my future’ : communities of practice, legitimate peripheral participation and student teachers’ experiences of problematic school placements as guests

Peer reviewed

'Sitting alone in the staffroom contemplating my future’ : communities of practice, legitimate peripheral participation and student teachers’ experiences of problematic school placements as guests

Peer reviewed

THE EFFECT OF PURPOSEFUL MATHEMATICS DISCOURSE IN THE CLASSROOM ON STUDENTS’ MATHEMATICS LANGUAGE IN THE CONTEXT OF PROBLEM SOLVING

This study examines how one secondary school teacher’s use of purposeful oral mathematics language impacted her students’ language use and overall communication in written solutions while working with word problems in a grade nine academic mathematics class. Mathematics is often described as a distinct language. As with all languages, students must develop a sense for oral language before developing social practices such as listening, respecting others ideas, and writing. Effective writing is often seen by students that have strong oral language skills. Classroom observations, teacher and student interviews, and collected student work served as evidence to demonstrate the nature of both the teacher’s and the students’ use of oral mathematical language in the classroom, as well as the effect the discourse and language use had on students’ individual written solutions while working on word problems. Inductive coding for themes revealed that the teacher’s purposeful use of oral mathematical language had a positive impact on students’ written solutions. The teacher’s development of a mathematical discourse community created a space for the students to explore mathematical language and concepts that facilitated a deeper level of conceptual understanding of the learned material. The teacher’s oral language appeared to transfer into students written work albeit not with the same complexity of use of the teacher’s oral expression of the mathematical register. Students that learn mathematical language and concepts better appear to have a growth mindset, feel they have ownership over their learning, use reorganizational strategies, and help develop a discourse community.

Promotion and diffusion of tha career Bachelor and Licenciature of Mathematics Teaching in rural areas of Costa Rica project: effects and results

This article describes the purpose and activities of the project Promoting Mathematics Education in Rural Areas of Costa Rica. The activity has focused on two objectives. First, supporting and monitoring students who have expressed interest in studying a mathematics teacher. To achieve this, it has been working with students who have an ideal profile for the career, mainly from rural areas. The second objective is to conduct training workshops for high school in-service teachers, to strengthen and improve their knowledge in the area of mathematics. Among the results of the project, it can be highlighted a significant increase in the enrollment of students in the career of Mathematics Education in 2010 and 2011, and the training processes in the field of Real Functions of Real Variable and Geometry at different regional areas mostly rural as Aguirre, Sarapiquí, Coto, Buenos Aires, Limón, Cañas, Pérez Zeledón, Nicoya, Los Santos, Turrialba, Puriscal, Desamparados, San Carlos, Puntarenas, Limón, Liberia, Santa Cruz y Upala.

Mieux connaître ses élèves à la formation générale des adultes pour mieux les accompagner

Résumé : La réussite et la persévérance des étudiants inscrits en formation générale adulte est un enjeu social et éducatif au Québec. La diversité et la fragilité de cette clientèle en est un second. Pour l’enseignant dans ce contexte, il est essentiel que des stratégies pédagogiques renforçant l’estime de soi et permettant la différenciation étayent son intervention. Cependant, celui-ci se sent parfois démuni. Des informations sur le parcours scolaire antérieur des étudiants qui lui sont confiés et sur les défis à relever pour chacun lui permettraient d’être plus proactif quant aux risques de décrochage. Un portrait-questionnaire a été élaboré pour répondre au besoin de ces enseignants qui veulent mieux connaître leurs élèves pour mieux les accompagner. Il peut devenir un point d’ancrage pour une relation éducative éclairée et collaborative. Des entrevues interrogeant des enseignants sur leurs perceptions avant l’élaboration de l’outil puis après sa mise à l’essai nous informent sur la pertinence et le gain possible de cette démarche.

Humor in mathematics teaching

HUMOR: OUR VIEW FOR MATHEMATICS TEACHING Our assumptions and context. Process humor and be able to produce is clearly a sign of intelligence, revealing, when done well, complex reasoning. Humor has an important social role, assuming as a cognitive experience that as well as creating a sense of well-being, predisposes people to work and can improve the productivity of that work. Mathematics is a discipline in which the reasoning occupies a very prominent place, both as a science as a school area. At the same time, students' interest for mathematics is not always the same and some have initially not very favorable feelings (Toh, 2009; Wanzer, Frymier & Irwin, 2010). Recent curriculum changes to the teaching of mathematics have been, in most countries of the world, showing the need for students to develop skills of critical nature, such as communication, thinking and problem solving along with the acquisition of mathematical knowledge. Also in Portugal, it is claimed the importance of promoting learning that combine the construction of mathematical knowledge with its use, when performing mathematical tasks and communicating mathematical ideas and mathematical reasoning. In the early years of schooling, corresponding to primary education in many countries, the use of texts such as short stories or comics, from which we can develop challenging mathematical tasks, is reported in the literature as having potential to promote learning specified in curricular documents (Wanzer, Frymier., & Irwin, 2010). In particular, some texts focus on mathematical topics in a humorous way and to be understood, students must develop their mathematical competence. The development of mathematical tasks from stories and other humorous presents big challenges to teachers (Flores & Moreno, 2011). Our questions. In this context, we put some questions: Primary teachers use in their classes tasks or situations that present, in a humorous way, mathematical ideas? What resources do they use? Also: How to select, adapt or build texts and tasks which have, in a humorous way, mathematical ideas with didactic potential for education in the early years of schooling? If the resources for this purpose have been produced and if teachers have been sensitized for their use, are they able to integrate them in their classes? Our intentions. This research project seeks to address these questions, focused on: (i ) assessment of teachers’ practices and underlying knowledge, resources available for the use of texts with mathematical ideas presented in a humorous way; (ii) selection, adaptation and construction of mathematical tasks from texts that present, in a humorous way, mathematical ideas with didactic potential in education for the early years of schooling; and ( iii ) integration and use, by primary school teachers, of texts that present , in a humorous way, contexts for the teaching of mathematics. So, the project is organized into three tasks and as a methodological design that combines qualitative elements with quantitative elements, the first one prevailing.

L'évaluation de l'autonomie fonctionnelle des personnes âgées : contribution de la didactique professionnelle à la formation des travailleuses et travailleurs sociaux au Québec

Résumé : Le vieillissement démographique est statistiquement indiscutable au Québec. Ce singulier trompeur masque les différentes manières de vieillir. Pour ceux qui ne parviennent pas à vieillir en santé, les solidarités familiales, comme les solidarités institutionnelles, c’est à dire publiques viennent en principe compenser ce qu’il est convenu de désigner de perte d’autonomie. Les politiques de santé publique au Québec organisent les services de soutien à domicile sous condition d’avoir estimé la situation de la personne avec l’outil d’évaluation multiclientèle (OEMC). Il est en usage dans l’ensemble du réseau de la santé et des services sociaux, et utilisé par les professionnels dont les travailleuses et les travailleurs sociaux (TS). Or, la gérontologie est peu soutenue dans la formation initiale des TS. Nous nous sommes interrogée sur les savoirs mobilisés par les TS quand ils évaluent. S’agissant des savoirs inscrits dans la pratique, nous avons orienté la recherche dans les théories de l’activité, la didactique professionnelle et le cadre conceptuel de la médiation. Nous avons étudié l’activité de professionnels en travail social expérimentés afin d’identifier certains des savoirs mobilisés pour les rendre disponibles à la formation des étudiant (e)s en travail social au Québec. Cent-cinquante heures d’observations et vingt-deux entretiens individuels et collectifs ont été réalisés avec des intervenants volontaires du service de soutien à domicile. Les résultats préliminaires de la recherche ont été présentés lors de groupes de discussion avec les TS ayant participé à la recherche, puis avec des enseignants en travail social. Nos résultats permettent de décrire les procédures de l’évaluation dans l’organisation du service d’aide à domicile et d’en différencier le processus de l’activité par laquelle le TS évalue l’autonomie fonctionnelle de la personne. Nous constatons que les savoirs mobilisés par les TS reposent premièrement sur une connaissance fine du territoire, de l’outil d’évaluation et des institutions. Un deuxième registre de savoir concerne la conceptualisation de l’autonomie fonctionnelle par l’outil OEMC comme objet et domaine d’intervention des TS. Enfin, un troisième registre se réfère aux savoirs mobilisés pour entrer en relation avec les personnes âgées, avec leur entourage. Or, ces trois registres de savoir n’apparaissent pas dans le discours des TS et résultent de notre propre analyse sur leur pratique. L’évaluation de l’autonomie fonctionnelle analysée par le concept de médiation est révélatrice du rapport aux savoirs du TS. S’agissant de savoirs de la pratique, nous constatons que leur classification entre les catégories usuelles de savoirs théoriques ou pratiques était inopérante. Nous empruntons le vocabulaire de la didactique professionnelle : celui des invariants opératoires reliés à l’autonomie fonctionnelle et celui des schèmes d’activité reliés à l’activité d’évaluation. C’est ainsi que nous avons identifié deux moments dans l’évaluation. Le premier assemble la collecte des informations et l’analyse des données. L’autonomie fonctionnelle se décline dans des conditions d’existence de la personne sur l’axe allant de la mobilité à la cognition avec comme balises d’intervention la sécurité et l’intégrité de la personne. Dans ce processus itératif, le TS identifie avec la personne ce qui nuit à son quotidien. L’évaluation formule comment résoudre cette incidence, comment la perte d’autonomie pourrait être compensée. La collecte d’information et le raisonnement du TS est alors un mouvement itératif, les deux éléments du processus sont liés et en continu. Le second moment de l’évaluation apparait si, dans le processus itératif, le TS perçoit une dissonance. Il est essentiel d’en identifier la nature pour la prendre en compte et maintenir la finalité de l’activité qui consiste à évaluer l’autonomie fonctionnelle à des fins compensatrices. Le TS doit identifier l’objet de la dissonance pour pouvoir cerner avec la personne le besoin inhérent à la perte d’autonomie et envisager d’y remédier. La prise en compte de cette dissonance vient ralentir le déroulement de l’activité. Le raisonnement qui, jusque-là, était relié à la collecte d’informations s’en dissocie pour analyser ce qui vient faire obstacle à l’activité d’évaluation à partir de la situation. Les composantes qui génèrent la dissonance paraissent reliées à la quotidienneté, aux conditions de vie à domicile de la personne (cohérence/incohérence, refus de services, autonégligence, maltraitance, agressivité). La dissonance génère une activité plus complexe pour évaluer la situation. L’autonomie fonctionnelle se décline toujours sur l’axe mobilité/cognition avec comme balises d’intervention la sécurité et l’intégrité de la personne. Or, pour ce faire, les TS raisonnent selon trois schèmes. Dans les situations où, pour décider de la suite du dossier, il faut en référer à une norme (de service, de profession, etc.) le raisonnement est déontologique. Il est aussi des situations où le TS agit au regard de valeurs et de représentations qui relèvent de sa sphère personnelle. Nous désignons ce raisonnement d’instinctuel. Enfin, le TS peut naviguer entre ces deux orientations et choisir la voie du raisonnement clinique que nous qualifions d’éthique et se rapproche alors des pratiques prudentielles qui sont marquées par l’incertitude.

Investigating problem-based learning in Saudi Arabian mathematics education: a TIMSS-related study

The aim of this study is to investigate the effectiveness of problem-based learning (PBL) on students’ mathematical performance. This includes mathematics achievement and students’ attitudes towards mathematics for third and eighth grade students in Saudi Arabia. Mathematics achievement includes, knowing, applying, and reasoning domains, while students’ attitudes towards mathematics covers, ‘Like learning mathematics’, ‘value mathematics’, and ‘a confidence to learn mathematics’. This study goes deeper to examine the interaction of a PBL teaching strategy, with trained face-to-face and self-directed learning teachers, on students’ performance (mathematics achievement and attitudes towards mathematics). It also examines the interaction between different ability levels of students (high and low levels) with a PBL teaching strategy (with trained face-to-face or self-directed learning teachers) on students’ performance. It draws upon findings and techniques of the TIMSS international benchmarking studies. Mixed methods are used to analyse the quasi-experimental study data. One -way ANOVA, Mixed ANOVA, and paired t-tests models are used to analyse quantitative data, while a semi-structured interview with teachers, and author’s observations are used to enrich understanding of PBL and mathematical performance. The findings show that the PBL teaching strategy significantly improves students’ knowledge application, and is better than the traditional teaching methods among third grade students. This improvement, however, occurred only with the trained face-to-face teacher’s group. Furthermore, there is robust evidence that using a PBL teaching strategy could raise significantly students’ liking of learning mathematics, and confidence to learn mathematics, more than traditional teaching methods among third grade students. Howe ver, there was no evidence that PBL could improve students’ performance (mathematics achievement and attitudes towards mathematics), more than traditional teaching methods, among eighth grade students. In 8th grade, the findings for low achieving students show significant improvement compared to high achieving students, whether PBL is applied or not. However, for 3th grade students, no significant difference in mathematical achievement between high and low achieving students was found. The results were not expected for high achieving students and this is also discussed. The implications of these findings for mathematics education in Saudi Arabia are considered.

EXAMINING SECONDARY MATHEMATICS TEACHER CANDIDATES’ LEARNING AND ENACTMENT OF MATHEMATICS TEACHING PRACTICES: A MULTIPLE CASE STUDY

This qualitative case study explored three teacher candidates’ learning and enactment of discourse-focused mathematics teaching practices. Using audio and video recordings of their teaching practice this study aimed to identify the shifts in the way in which the teacher candidates enacted the following discourse practices: elicited and used evidence of student thinking, posed purposeful questions, and facilitated meaningful mathematical discourse. The teacher candidates’ written reflections from their practice-based coursework as well as interviews were examined to see how two mathematics methods courses influenced their learning and enactment of the three discourse focused mathematics teaching practices. These data sources were also used to identify tensions the teacher candidates encountered. All three candidates in the study were able to successfully enact and reflect on these discourse-focused mathematics teaching practices at various time points in their preparation programs. Consistency of use and areas of improvement differed, however, depending on various tensions experienced by each candidate. Access to quality curriculum materials as well as time to formulate and enact thoughtful lesson plans that supported classroom discourse were tensions for these teacher candidates. This study shows that teacher candidates are capable of enacting discourse-focused teaching practices early in their field placements and with the support of practice-based coursework they can analyze and reflect on their practice for improvement. This study also reveals the importance of assisting teacher candidates in accessing rich mathematical tasks and collaborating during lesson planning. More research needs to be explored to identify how specific aspects of the learning cycle impact individual teachers and how this can be used to improve practice-based teacher education courses.

Teaching Through Technology – the Experience of Bulgarian Teachers

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

The pedagogical content knowledge of Danish geography teachers in a changing schooling context

This study examines the self-reported, topic-specific professional knowledge (TSPK) of Danish geography teachers seen as an aspect of their pedagogical content knowledge (PCK) when teaching weather formation and climate change. This topic is considered representative of geography teaching in Denmark. In the last ten years Danish primary and lower-secondary schooling has undergone several significant changes, including the introduction of a final multiple-choice exam in geography in 2007, and a fundamental reconstruction of the curriculum in 2014. These changes are expected to influence the TSPK of geography teachers in ways that potentially have an impact on their classroom practice. Teachers´ responses to specific questions relating to their choice of learning goals and the content and organisation of their lessons show that geography teachers take into account not only the knowledge aspects which point to the final multiple-choice exam, but also the ‘bildung’ perspectives of the subject equipping students to develop their own opinions when dealing with socio-scientific issues (SSI).

Knowledge and writing in school mathematics : a communicational approach

This thesis is about young students’ writing in school mathematics and the ways in which this writing is designed, interpreted and understood. Students’ communication can act as a source from which teachers can make inferences regarding students’ mathematical knowledge and understanding. In mathematics education previous research indicates that teachers assume that the process of interpreting and judging students’ writing is unproblematic. The relationship between what students’ write, and what they know or understand, is theoretical as well as empirical. In an era of increased focus on assessment and measurement in education it is necessary for teachers to know more about the relationship between communication and achievement. To add to this knowledge, the thesis has adopted a broad approach, and the thesis consists of four studies. The aim of these studies is to reach a deep understanding of writing in school mathematics. Such an understanding is dependent on examining different aspects of writing. The four studies together examine how the concept of communication is described in authoritative texts, how students’ writing is viewed by teachers and how students make use of different communicational resources in their writing. The results of the four studies indicate that students’ writing is more complex than is acknowledged by teachers and authoritative texts in mathematics education. Results point to a sophistication in students’ approach to the merging of the two functions of writing, writing for oneself and writing for others. Results also suggest that students attend, to various extents, to questions regarding how, what and for whom they are writing in school mathematics. The relationship between writing and achievement is dependent on students’ ability to have their writing reflect their knowledge and on teachers’ thorough knowledge of the different features of writing and their awareness of its complexity. From a communicational perspective the ability to communicate [in writing] in mathematics can and should be distinguished from other mathematical abilities. By acknowledging that mathematical communication integrates mathematical language and natural language, teachers have an opportunity to turn writing in mathematics into an object of learning. This offers teachers the potential to add to their assessment literacy and offers students the potential to develop their communicational ability in order to write in a way that better reflects their mathematical knowledge.