LUMAT: International Journal on Math, Science and Technology Education https://journals.helsinki.fi/lumat <p>LUMAT publishes peer-reviewed research articles on math, science and technology education. Articles include research papers and perspective papers.</p> en-US editor@lumat.fi (Johannes Pernaa) editor@lumat.fi (Johannes Pernaa) Mon, 30 Mar 2020 14:19:39 +0300 OJS 3.1.2.0 http://blogs.law.harvard.edu/tech/rss 60 In-service Zimbabwean teachers’ views on the utility value of diagrams in the teaching and learning of geometry https://journals.helsinki.fi/lumat/article/view/1316 <p>Geometry is an essential component of mathematics which promotes the development of critical thinking and problem-solving skills. Geometry shapes are an integral part of our lives. This study focused on the teachers’ practices, specifically on how teachers ought to be equipped with a good understanding on the effectiveness of the use of use of diagrams in geometry teaching and learning. A mixed method approach comprising of questionnaires and interviews was used in this study. Ninety-one teachers participated in this study. The research findings were categorized using the four themes of utility, positive attitudes, negative attitudes, and teachers’ use of diagrams in geometry class.&nbsp; The study showed that diagrams are effective in the teaching and learning of geometry concepts. It is recommended that teachers could do well if they make use of technology in designing diagrams to be used in the teaching and learning of geometry.</p> Gladys Sunzuma, Cecilia Chando, Isaac Gwizangwe, Nicholas Zezekwa, Gracious Zinyeka Copyright (c) 2020 Gladys Sunzuma, Cecilia Chando, Isaac Gwizangwe, Nicholas Zezekwa, Gracious Zinyeka https://creativecommons.org/licenses/by/4.0 https://journals.helsinki.fi/lumat/article/view/1316 Mon, 30 Mar 2020 00:00:00 +0300 Understanding of learning styles and teaching strategies towards improving the teaching and learning of mathematics https://journals.helsinki.fi/lumat/article/view/1348 <p>This study was conducted to analyse the influence of learning styles and teaching strategies on academic performance in mathematics. Surveys were conducted to 277 randomly selected grade 9 students and five purposively sample mathematics teachers. Findings reveal that most of the student-respondents have a combination of dependent, collaborative and independent learning styles. Multiple regression analysis indicates that among the learning styles, only the independent style has a significant influence on the academic performance of grade 9 students. Four teaching strategies including cooperative learning, deductive approach, inductive approach, and integrative approach, were found to have a significant influence on academic performance. By understanding the learning styles of students, teachers will be guided in designing different strategies to help students enhance learning for their improved performance in mathematics.</p> Jose M. Cardino Jr., Ruth A. Ortega-Dela Cruz Copyright (c) 2020 Jose M. Cardino, Ruth A. Ortega-Dela Cruz https://creativecommons.org/licenses/by/4.0 https://journals.helsinki.fi/lumat/article/view/1348 Mon, 25 May 2020 00:00:00 +0300 Educators’ perceptions of mathematically gifted students and a socially supportive learning environment – A case study of a Finnish upper secondary school https://journals.helsinki.fi/lumat/article/view/1368 <p>This&nbsp;article explores five educators’ conceptions of the characteristics of mathematically gifted students and a social learning environment that supports their development in a school for mathematically gifted adolescents in Finland. We conducted this qualitative study through semi-structured interviews and participant observations in a Finnish upper secondary school with a special mathematics program. The research shows that gifted students and their educators form a tight community, the social learning environment of which supports shared motivation, healthy perfectionism, and practicing social skills. The results deepen the understanding of gifted education in the Finnish context and the significance of educators’ shared understanding of social activities as a basis for successful gifted education.</p> Eeva Haataja, Anu Laine, Markku Hannula Copyright (c) 2020 Eeva Haataja, Anu Laine, Markku Hannula https://creativecommons.org/licenses/by/4.0 https://journals.helsinki.fi/lumat/article/view/1368 Mon, 01 Jun 2020 12:24:05 +0300 Planning in mathematics teaching – a varied, emotional process influenced by others https://journals.helsinki.fi/lumat/article/view/1326 <p class="Abstract"><span lang="EN-US">Plan</span>ning is an essential part of teachers’ work that has consequences for students’ learning. However, previous research shows that what it means to plan vary. To explore the meaning of planning from teachers’ point of view, and to open up for planning as a situated and emotional process, an interview study with Swedish mathematics teachers was conducted. In the analysis, the theoretical concepts, meaning, and emotions were used as analytical tools to fill the gap identified in the review of previous research about planning.&nbsp; Findings reveal planning as a varied process in which teachers draw on different resources. Actors other than teachers influence both how planning is done and the mathematics teaching that is planned for. Findings also reveal that feelings, such as joy, shame, and insufficiency, are present in the process of planning. These feelings sometimes have consequences for decisions teachers make about their mathematics teaching.</p> Helena Grundén Copyright (c) 2020 Helena Grundén https://creativecommons.org/licenses/by/4.0 https://journals.helsinki.fi/lumat/article/view/1326 Mon, 01 Jun 2020 12:23:25 +0300 The three-factor model: A study of common features in students' attitudes towards studying and learning science and mathematics in the three countries of the North Calotte region https://journals.helsinki.fi/lumat/article/view/1369 <p>This study investigated common features of students' attitudes towards studying science and mathematics in comprehensive and secondary schools in three countries. Data were obtained by conducting a survey (N = 581) in Norway, Finland and Russia. A Confirmatory factor analysis (CFA) provided a model with a three-factor solution consisting of factors: the perception of the teacher, anxiety towards science and mathematics, and motivation. The results suggest that most students are motivated to study sciences and mathematics. Data analysis indicate gender differences in attitudes to students' future studies and career plans.&nbsp; Most girls recognized the importance of these subjects for their future studies and careers, while boys showed more interest than girls in local career opportunities in industry. Teachers have a significant role in directing students' attitudes toward science and mathematics. Students experienced that the teachers who use innovative teaching approaches, both motivate and reduce anxiety, in their learning process.</p> Päivi Tomperi, Inna Ryzhkova, Yulia Shestova, Oleg Lyash, Irina Lazareva, Asya Lyash, Mona Kvivesen, Saeed Manshadi, Stig Uteng Copyright (c) 2020 Johannes Pernaa https://creativecommons.org/licenses/by/4.0 https://journals.helsinki.fi/lumat/article/view/1369 Mon, 01 Jun 2020 00:00:00 +0300 Learning mathematics by project work in secondary school https://journals.helsinki.fi/lumat/article/view/1372 <p>In project-based learning, pupils have two central learning objectives: to understand the content of the subject and to develop their twenty-first-century skills. This article concerns the use of project work in mathematics learning, considered here in the context of the Finnish national core curriculum, mathematical proficiency, and pupils’ previous level of attainment. The research consisted of two case studies in which a coordinate system project and a statistics project were tested with secondary school pupils (N=59+58). The main findings show it is possible to study the mathematics of the curriculum and to develop all types of mathematical proficiency using project work. Additionally, the pupils’ grades on the project work correlate positively with their overall grades in mathematics.&nbsp;</p> Elina Viro, Jorma Joutsenlahti Copyright (c) 2020 Elina Viro, Jorma Joutsenlahti https://creativecommons.org/licenses/by/4.0 https://journals.helsinki.fi/lumat/article/view/1372 Mon, 01 Jun 2020 12:25:17 +0300 Scrutinizing two Finnish teachers’ instructional rationales and perceived tensions in enacting student participation in mathematical discourse https://journals.helsinki.fi/lumat/article/view/1329 <p>This study employs interviews and observations to investigate instructional rationales of two purposefully sampled teachers with divergent classroom discourse practices in Swedish-speaking Finnish lower secondary mathematics classrooms. Studies on classroom discourse often point to beliefs and contextual factors shaping teachers’ discourse practices. Less is known about how tensions perceived by teachers can influence the instructional rationale in a context such as Finland, known for traditional and teacher-centered mathematics instruction. Findings of this study suggest that these Finnish teachers’ instructional rationales for differently enacted classroom-discourse practices are grounded in similar concerns of student needs, related to student learning, well-being, and equity. One of the teachers perceived a tension between these concerns and mathematics education literature’s ideals of classroom discourse and avoided engaging students in discussions other than in tightly teacher-led format. The other embraced the idea of discourse as facilitating learning and created methods for giving all students equal access to the perceived benefits of mathematical discussions. The identified tensions of student learning, well-being, and equity can be used as guiding principles in developing teachers’ discourse practices in professional development in Finland and beyond.</p> Jennifer Luoto Copyright (c) 2020 Jennifer Luoto https://creativecommons.org/licenses/by/4.0 https://journals.helsinki.fi/lumat/article/view/1329 Mon, 15 Jun 2020 14:36:13 +0300 The Finnish matriculation examination in biology from 1921 to 1969 – trends in knowledge content and educational form https://journals.helsinki.fi/lumat/article/view/1376 <p>The history and evolution of science assessment remains poorly known, especially in the context of the exam question contents. Here we analyze the Finnish matriculation examination in biology from the 1920s to 1960s to understand how the exam has evolved in both its knowledge content and educational form. Each question was classified according to its topic in biology, and its cognitive level by Bloom’s taxonomy. Overall, the exam progressed from a rather dichotomous test of botany and zoology to a modern exam covering biology from biochemistry to environmental science, reflecting the development of biology as a scientific discipline. The contribution of genetics increased steadily, while ecology witnessed a decline and a renaissance during the same time period. The biological profile of the questions was established by the 1950s. The educational standard and cognitive demand of the questions was always high and established by the 1940s.</p> <p><strong>Tiivistelmä</strong></p> <p>Luonnontieteellisten koekysymysten historiaa ja kehitystä on tutkittu hyvin vähän. Biologian ylioppilaskokeen kysymyksiä tarkasteltiin 1920-luvulta 1960-luvulle koekysymysten sisällöllisen ja opetuksellisen kehityksen selvittämiseksi. Kysymykset luokiteltiin biologisiin sisältöluokkiin, kun taas kognitiivinen taso arvioitiin Bloomin asteikolla. Tarkastelujakson aikana koe kehittyi kaksijakoisesta kasvi- ja eläintiedettä käsittelevästä kuulustelusta uudenaikaiseksi kokeeksi, joka tarkasteli biologiaa biokemiasta ympäristötieteeseen, heijastaen biologian kehitystä tieteenalana. Perinnöllisyystieteen osuus kokeessa kasvoi tasaisesti, kun taas ekologia koki jonkinasteisen taantuman ja uudelleentulemisen samalla aikavälillä. Kysymysten biologinen profiili vakiintui 1950-luvulla. Kysymysten opetuksellinen taso ja kognitiivinen vaatimustaso oli korkea alusta saakka ja vakiintui jo 1940-luvulla.</p> Jakke Neiro, Niko Johansson Copyright (c) 2020 Jakke Neiro, Niko Johansson https://creativecommons.org/licenses/by/4.0 https://journals.helsinki.fi/lumat/article/view/1376 Mon, 22 Jun 2020 10:16:46 +0300 Learning Study och kollegial CoRe stimulerar lärares professionella utveckling inom naturvetenskaplig undervisning https://journals.helsinki.fi/lumat/article/view/1393 <p>Syftet med studien är att klargöra hur lärares professionella utveckling stimuleras då de planerar och genomför en Learning Study (LS) kombinerad med verktyget Content Representation (CoRe). Data består av sex erfarna lärares inspelade diskussioner under åtta träffar då de planerar och analyserar en LS bestående av två lektioner i årkurs 6 inom kemi, samt tre CoRe som lärarna skriver. I början av studien talar lärarna mest om undervisning som att fakta ska förmedlas till eleverna. När de sedan planerar första lektionen övergår deras diskussioner till hur de kan stimulera eleverna till diskussion och reflektion. Lärarna planerar både lektion 1 och 2 utifrån ett variationsteoretiskt perspektiv, men lektion 1 genomförs inte i enlighet med vad de planerat. Det är först i lektion 2 som läraren behåller fokus på lärandeobjektet och dess kritiska aspekter. Resultatet av studien visar även att en Learning Study kombinerad med CoRe stimulerar lärares professionella utveckling och ämnesdidaktiska kompetens i form av lärande nätverk enligt Clarkes och Hollingsworths (2002) modell ”interconnected model of professional growth”.</p> <p><strong>In English:</strong> The aim of this study is to explore science teachers’ professional development when they perform a Learning Study (LS), using the tool Content Representations (CoRe). The empirical data consists of six experienced teachers’ audio recorded discussions during eight meetings when they plan and analyse two lectures in chemistry for year 6 (age 12-13 years), and three written CoRe. In the beginning of the study, the teachers talk about teaching and learning mainly as transformation of facts. However, when they plan the first lecture, they discuss how to stimulate students’ discussions and reflections. The teachers planned both lectures according to variation theory. However, only the second lecture is also implemented according to their plan, with a focus on the object of learning. The results show that the combination of CoRe and LS stimulate also experienced teachers’ professional development, through growth networks according to the model "interconnected model of professional growth" (Clarke and Hollingsworth, 2002).</p> Niclas Åhman, Gunilla Gunnarsson, Inger Edfors Copyright (c) 2020 Niclas Åhman, Gunilla Gunnarsson, Inger Edfors https://creativecommons.org/licenses/by/4.0 https://journals.helsinki.fi/lumat/article/view/1393 Thu, 20 Aug 2020 12:26:33 +0300 Promoting learning with understanding: Introducing languaging exercises in calculus course for engineering students at the university level https://journals.helsinki.fi/lumat/article/view/1412 <p>The study of mathematics at the university level requires logical thinking and strong mathematical skills. Contemporary first-year students are not prepared for these demands and end up failing their courses. This study aims to present an instrument for enhancing mathematics teaching and promoting learning with understanding in higher education by a combination of symbolic, natural, and pictorial languages in different tasks. We analyze the 17 solutions of four languaging exercises administered in a basic calculus course for engineering students at the University of Costa Rica. The results suggest that these exercises promote the acquisition of skills necessary to be mathematically proficient and are a useful tool for revealing students’ mathematical thinking and misconceptions.</p> Helen Alfaro Viquez, Jorma Joutsenlahti Copyright (c) 2020 Helen Alfaro Viquez, Jorma Joutsenlahti https://creativecommons.org/licenses/by/4.0 https://journals.helsinki.fi/lumat/article/view/1412 Thu, 24 Sep 2020 00:00:00 +0300 University mathematics students' study habits and use of learning materials https://journals.helsinki.fi/lumat/article/view/1317 <p><span lang="EN-GB">In this article, we study a group (N=98) of students from two campuses of one Finnish university and their responses to a questionnaire that surveyed the respondents' study habits and how they use different kinds of learning materials in university mathematics courses. Our results show that the grades in the national matriculation exams in mathematics and mother tongue do not play a significant role in one's study habits or use of learning materials. The older students are more communicative with their teachers, whereas the younger students ask for help more often from fellow students. The sociomathematical norms that constitute the local study culture have a larger impact on the study habits and on the use of learning materials. For example, the use of videos and studying lecture materials before the lectures were clearly more usual at one campus than at the other. We also found some significant differences between the groups that are based on the study programmes. The students of mathematics without an intention to become a teacher were most traditional in their study habits, whereas the students of applied physics were most active to participate in teaching. The student teachers most often lie in the middle in the issues where the other groups differ from one another.</span></p> Timo Tossavainen, Janne Gröhn, Lasse Heikkinen, Anna Kaasinen, Antti Viholainen Copyright (c) 2020 Timo Tossavainen, Janne Gröhn, Lasse Heikkinen, Anna Kaasinen, Antti Viholainen https://creativecommons.org/licenses/by/4.0 https://journals.helsinki.fi/lumat/article/view/1317 Mon, 05 Oct 2020 10:55:46 +0300