Pre-service teachers’ noticing: On the way to expert target

Unlike prevailing research focusing on what pre-service teachers attend to in a lesson and how they interpret it, the study investigates the content of their comments, knowledge-based reasoning and whether it agrees with experts’ views. Study 1 determined the dimensions of quality teaching pertinent to lessons in which a new subject matter is introduced and made a noticing target. In Study 2, pre-service teachers (n = 174) at the end of their university study made a written reflection of a video lesson, which was compared against the target. Most could not discern situations important for deep work with the content in the lesson. They failed to apply their theoretical knowledge in their interpretation of the ones they mentioned. Only half of their comments included knowledge-based reasoning, and their views were mostly partially consistent or inconsistent with the experts’ ones. This highlights the need to focus on content-related important situations in a lesson and their interpretation in teacher preparation and on developing the ability to discern the dimensions of instructional quality in concrete lessons

Different approaches to the teaching theorems on congruent triangles

summary:The article focuses on the approaches to the teaching of the same subject matter, namely the theorems for congruent triangles. The approaches mainly differ in the pupils' participation on the creation of new knowledge and are ordered on the scale instructional teaching - constructivist teaching. Three of the approaches have been tested in real classrooms and the trials are described in the article

Mathematics as a pedagogical problem or František as a living Czech legend of mathematics education

summary:V příspěvku je uveden upravený přepis projevu, který autorka přednesla na semináři Cesty a cestičky školské matematiky, který se konal 16. 9. 2022 na Přírodovědecké fakultě Univerzity Hradec Králové u příležitosti devadesátých narozenin prof. Františka Kuřiny. Příspěvek má neformální tón a soustřeďuje se na prof. Kuřinu jako člověka.

Teaching material “Comparison” as a tool developing pupils‘ ability to solve word problems

summary:This journal issue is devoted to teaching materials developed within a TAČR project Support of the integration of mathematical, reading and language literacy in primary school pupils. The introductory article by Havlíčková et al. introduces the main goals and theoretical background used when preparing the materials. Their purpose is to support teachers in developing pupils' ability to solve word problems by developing reading, language and metacognitive skills. Pupils are first guided by questions to analyse the word problem's text and become aware of the actors involved and the relationships between them. Language questions, which can be used by the mathematics teacher or the Czech language teacher to develop pupils' language skills, are also recommended. The paper by Vondrová presents materials based on inducing a comparison of two fictional children's word problem-solving strategies, correct or incorrect. Pupils are guided to understand the strategy and to be able to justify its steps and, for incorrect solutions, to identify the nature of the error. The paper by Slezáková and Jirotková presents teaching materials whose main goal is to enrich the range of pupils' problem-solving strategies and develop their ability to solve word problems and their metacognition. The paper by Havlíčková and Mottlová presents a non-traditional type of word problems, "Restless numbers", whose aim is to enhance pupils' need to argue and to use real experiences in solving them. They encourage pupils to experiment so that they discover new solving strategies. The paper by Sovič presents the materials called Varied word problems, whose aim is to develop problem-solving through the student's deeper understanding of the internal structure of word problems. Varied word problems consist of one basic task and two/three variations of the same context and different mathematical structures. The last paper by Páchová introduces an idea for teaching word problems in heterogeneous classrooms based on graded hints. Concrete examples illustrate all types of teaching materials

Causes of superficial solving strategies for word problems and how to prevent them

summary:Článek se zabývá povrchovými strategiemi řešení slovních úloh, tedy takovými, které nejsou založeny na matematické struktuře úlohy, ale jen na jejích povrchových rysech. Snahou je popsat různé příčiny, které mohou k používání těchto strategií žáky vést, včetně didaktických. Pozornost je věnována vlivu použitých čísel a tzv. signálních slov v zadání i strategii zařazení řešené úlohy do nějakého typu. Jsou naznačeny i psychologické příčiny, které jsou příslušné konkrétnímu žákovi. Ve druhé části článku jsou nastíněna didaktická doporučení. Účinnost některých z nich je dokumentována existujícím výzkumem. Vše je ilustrováno příklady z rozhovorů s žáky nad řešením slovních úloh.summary:The article focuses on such solving strategies for word problems which are only based on superfficial features of the problem and not on its complete situational model. Several possible causes of the use of these strategies are described and illustrated by examples from the author's research and interviews with pupils. These causes comprise the presence of cues in the word problem statement in the form of numbers and of words suggesting a mathematical operation, and the tendency to compare the solved problem with some prototypical word problems. Attention is devoted to didactic and psychological causes, too. In the second part of the article, some didactic recommendations are given, complemented with research results documenting their efficiency. For example, it is suggested to use word problems for which the strategy of signal words does not work, to develop pupils' metacognitive skills and to lead them towards using visualisation of the word problem structure

How is it actually? Numbers and sets

summary:Autoři se zamýšlejí nad pojmem číslo a nad číselnými obory, a to z hlediska didaktického. Blíže se věnují pojmu přirozené číslo, desetinné číslo a zlomek. S oporou o učebnice diskutují o vhodnosti vymezení těchto pojmů.

Future mathematics teachers noticing mathematics: Knowledge-based reasoning

International audienceThe article explores how future mathematics teachers (n = 26) at the end of their master studies notice moments in a lesson deemed important by experts and looks into their knowledge-based reasoning. A reflective task was given to the students and their written observation about the videoed mathematics lesson was compared against the expert analysis of the lesson. While all students commented on at least one important moment (the median was 3.5, expert rate 6), a third of their comments about these moments was of a subjective evaluation nature. They were mostly unable to provide a theoretical justification for their opinions. On the other hand, most students were able to suggest an alternative action to what they observed in the important moments of the lesson