Letní semestr 2018/2019


7. 3. 2019

Using puzzle-based activities to develop aspects of algebraic thinking
Johanis Papadopolous (Aristotle University of Thessaloniki, Greece)

Helping students succeed in algebra is a worldwide challenge for the mathematics education community. During the last 20 years a growing concern for developing students’ algebraic thinking in earlier grades has been noticed. In this presentation an effort to shift the focus towards puzzle-based activities and their contribution is made. Findings of a study with primary school students will be presented aiming to show how such experiences prepare the students for their formal introduction to algebra and their transition from arithmetic to algebra. A series of example will be used to show how certain mathematical puzzles can support algebraic reasoning, arithmetic facility and perseverance in problem solving. ‘Mobile-puzzles’ (multiple balanced collections of objects whose weights must be determined) are solved by the students. In their effort to solve them, the students exhibit certain algebraic habits of mind and demonstrate symbol-sense.

21. 3. 2019

Proč funguje Hejného metoda
Ladislav Kvasz (PedF UK)

V příspěvku se pokusím použít výsledky teorie změn vědeckých teorií („patterns of theory change“) pro zdůvodnění jednak toho, proč Hejného metoda funguje u dětí, a také na vysvětlení toho, proč jí mnoho matematiků a didaktiků matematiky nedůvěřuje.

4. 4. 2019

Výzkum kulturního obsahu učebnic matematiky
Hana Moraová (PedF UK)

Na semináři bude představena dizertační práce, ve které se její autorka věnovala zkoumání učebnic matematiky z hlediska jejich kulturního obsahu. Ve výzkumu autorka vycházela z toho, že učebnice matematiky není jen pedagogický dokument, ale také kulturní artefakt, který vzniká v konkrétní společnosti s konkrétními společenskými normami. V učebnicích matematiky se žáci setkávají s celou řadou obrazů každodennosti. Přitom vzhledem k hlavnímu cíli učebnice matematiky, tj. rozvíjet dovednosti a znalosti žáků v matematice, se textovým (nematematickým, kulturním) obsahům věnuje poměrně málo pozornosti. Žáci se tak v hodinách matematiky téměř denně setkávají se světem, který má vyvolávat dojem reálného světa, normy. Jak přesně ale tento svět odráží dění v dnešní společnosti? Na semináři budou představena teoretická východiska výzkumu i jeho výsledky. V rámci výzkumu bylo analyzováno pět sad učebnic pro 6. ročník základní školy (primu nižšího gymnázia) a dále čtyři učebnice pro 9. ročník (část zaměřená na finanční matematiku, která je úzce spjata s každodenností), a to z hlediska nematematického, kulturního.

18. 4.2019

Trails, congresses and gallery walk: Active strategies for teaching and learning mathematics
Isabel Vale, Ana Barbosa (School of Education of the Polytechnic Institute of Viana do Castelo, Portugal)

People are no longer rewarded only for what they know, but for what they can do with what they know. So, school must develop students‘ skills to be creative, to think critically, to solve problems, to communicate and to collaborate. In particular, math class should create an environment that leads students to guess, generalize, prove, question, discuss, collaborate, explain and communicate their thinking, creating a sense of community. On the other hand, our young students are increasingly inactive in classrooms, which goes against their nature. Studies recommend that children need to move around because an active body energizes the brain, making students engaged and more open to learning. In this scenario, students should be confronted with challenges that excite them to learn and encourages them to work with each other, moving around, inside or outside the classroom. So, in this scope, trails, congresses and gallery walk emerge as potential instructional strategies. A mathematical trail is a sequence of stops along a pre-planned route, in which students solve mathematical tasks in the surrounding environment; a congress consists of the presentation of problem resolutions, previously worked on, in pairs or groups, by the students, in an auditorium to their colleagues, allowing to discuss their ideas with the audience; the gallery walk is a strategy that allows students to work collaboratively by solving tasks, presenting them in posters, located around the classroom or outside, in a similar perspective to artworks displayed in a gallery, and still have the opportunity to share ideas and receive feedback. In this session, we will discuss some theoretical ideas about these strategies and some studies developed by future teachers and students of basic education that address these non-conventional instructional strategies (in Portugal) and where conventional programmatic themes have been worked on. These approaches have been accepted with enthusiasm and involvement by both future teachers and basic education students, giving them a different perspective about mathematics, above all, that we can do mathematics without being stuck to a chair, working collaboratively and learning in a meaningful way.

25. 4. 2019

Cooperative learning in the mathematics classroom

Lambrecht Spijkerboer, STA-international, Amersfoort, the Netherlands STA@Lambrechtspijkerboer.nl, www.Lambrechtspijkerboer.nl

The seminar will start with the presentation of the differences between deep approach and surface approach. What is learned by the instruction of the teacher (reproduction) , and what is learned in challenging motivational questions to invite students to think themselves and solve problems by using their knowledge, skills and interest (insight). If the learning is organised in groups of 3-4 students together, the chance to do deep learning is improved. What is the difference between sitting together and doing mathematical tasks, and cooperative learning for problem solving? Not only the kind of exercises can change the pupils behaviour, also the way the exercises are supposed to be handled and discussed with classmates. Different invitations for learning are guided by different collaborative ways of working. The focus is on motivational lessons, inviting tasks and active participation of students in your classroom. The proposed cooperative learning methods are experienced during this seminar by doing ourselves. We will reflect on the ways of lesson organisation and also the teachers role is taken into account. You are invited to make a choice for one of the cooperative learning methods to practice the next day in your lessons. It will not take much extra time to practice in your future lessons one or two of the alternative methods, the only challenge is to change your own behaviour with small changes of the way you handle lesson time, the book, and the grouping of students, etc. Small changes can cause big effects. The seminar will have an English instruction, (with translation if necessary). Because participants work together in small groups, part of the communication can be carried out in Czech language. References: Bellanca J. & Fogarty R. (1994). Blueprints for Thinking in the Cooperative Classroom. Australia: Hawker Brownlow Education. Hill, S. & Hill, T. (1990). The Collaborative Classroom: A Guide to Cooperative Learning. South Yarra, Victoria: Eleanor Curtain. Maréchal, J. & Spijkerboer, L (2017 Leerlingen AANzetten tot leren, Pica, Huizen, the Netherlands Reid, J. (2002). Managing small group Learning. Newtown, NSW: Primary English Teaching Association (PETA). Spijkerboer, L. & Santos, L. (2015). Organising dialogue and Enquiry in Gellert, U e.o Educational Paths to Mathematics, Springer, Swiss. Spijkerboer, L. (2015). Math that matters, CIEAEM 67, Aosta, Italy.

2. 5. 2019

Exploring the Impact of Sequences of Connected and Challenging Tasks on Primary Students and their Teachers

Janette Bobis (University of Sydney, Australia)

Student learning is “greatest in classrooms where the tasks consistently encourage higher-level student thinking and reasoning” (National Council of Teachers of Mathematics, 2014, p.17). Unfortunately, many teachers are reportedly hesitant to integrate such tasks into their classrooms, raising concerns about some teachers’ capacities to activate higher-level thinking in their students. The need to encourage all teachers to implement such experiences prompted Sullivan, Borcek, Walker and Rennie (2016) to explore an approach that initiated learning through challenging tasks. They found that student learning is facilitated when a particular lesson structure is enacted. This structure involves initiating learning through an appropriate challenging task, differentiating that challenge, and “consolidating the learning through task variations” (p.159). While higher-level student thinking can be activated within thoughtfully constructed lessons involving challenging tasks, the potential of implementing structured sequences of challenging mathematics experiences remains underexplored. This presentation will outline the rationale and theoretical underpinnings of a research project that aims to explore the impact of sequences of connected, cumulative, and challenging tasks on early years students’ learning and their teachers’ knowledge of mathematics and pedagogy. Data from the first phases of this study will provide the stimulus for discussion.

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