This study presents research focusing on in-service mathematics teachers and their approach to tasks aimed at developing of functional thinking. The analysis is based on the model of The Mathematics Teachers' Specialised Knowledge -- model MTSK by Carrillo et al. (2018). The research question is the following: What ``specialised knowledge'', in the sense of the MTSK framework, is revealed when a~middle school teachers solve and discuss the selected tasks? The research was conducted with 9 teachers, who voluntarily participated in the professional development. The teachers solved a~set of 30 tasks that were selected with a~focus on 4 aspects of the concept of function, different representations and transitions between them and different actions that learners engage in the task solving. In this study, we analysed the teachers' written solutions and the discussion with the teachers about a~particular task. Reflecting on their work as learners was very important in moving from dealing with the mathematics itself to shifting to developing their knowledge of mathematics teaching (KMT) and knowledge of features of learning mathematics (KFLM) in terms of the MTSK framework. The results helped us to identify gaps in teachers' specialised knowledge and consequently will help us to improve professional development courses for both in-service and pre-service teachers.
{"title":"The specialized knowledge of middle school teachers concerning the concept of function","authors":"Matej Slabý, Ingrid Semanišinová, N. Climent","doi":"10.24917/20809751.14.5","DOIUrl":"https://doi.org/10.24917/20809751.14.5","url":null,"abstract":"This study presents research focusing on in-service mathematics teachers and their approach to tasks aimed at developing of functional thinking. The analysis is based on the model of The Mathematics Teachers' Specialised Knowledge -- model MTSK by Carrillo et al. (2018). The research question is the following: What ``specialised knowledge'', in the sense of the MTSK framework, is revealed when a~middle school teachers solve and discuss the selected tasks? The research was conducted with 9 teachers, who voluntarily participated in the professional development. The teachers solved a~set of 30 tasks that were selected with a~focus on 4 aspects of the concept of function, different representations and transitions between them and different actions that learners engage in the task solving. In this study, we analysed the teachers' written solutions and the discussion with the teachers about a~particular task. Reflecting on their work as learners was very important in moving from dealing with the mathematics itself to shifting to developing their knowledge of mathematics teaching (KMT) and knowledge of features of learning mathematics (KFLM) in terms of the MTSK framework. The results helped us to identify gaps in teachers' specialised knowledge and consequently will help us to improve professional development courses for both in-service and pre-service teachers.","PeriodicalId":33912,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84924133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper shows how technological devices can be integrated into the pupils’ use of four selected heuristic strategies in mathematical problem solving: Systematic experimentation, Introduction of an auxiliary element, Analogy, Solution drawing. Our research examined change in the pupils’ success rate and their attitude to problem solving as a consequence of being taught the four selected heuristic strategies while using technological devices actively. A statistically increased success rate of problem solving and a statistically significant decline in the frequency of the number of ‘no response’ cases (the solver does not start to solve the problem) were expected. The study was carried out about by 342 pupils from the 13-17 age group in the Czech Republic. The results of the study show the pupils’ success rate in the solution of problems effectively solvable using the strategies systematic experimentation and solution drawing improved significantly if the use of these strategies went hand in hand with the active use of technological devices. The number of ‘no response’ decreased significantly.
{"title":"Technological devices in the development of pupils’ expertise in the use of selected heuristic strategies","authors":"Petr Eisenmann, J. Novotná, J. Přibyl","doi":"10.24917/20809751.14.4","DOIUrl":"https://doi.org/10.24917/20809751.14.4","url":null,"abstract":"This paper shows how technological devices can be integrated into the pupils’ use of four selected heuristic strategies in mathematical problem solving: Systematic experimentation, Introduction of an auxiliary element, Analogy, Solution drawing. Our research examined change in the pupils’ success rate and their attitude to problem solving as a consequence of being taught the four selected heuristic strategies while using technological devices actively. A statistically increased success rate of problem solving and a statistically significant decline in the frequency of the number of ‘no response’ cases (the solver does not start to solve the problem) were expected.\u0000The study was carried out about by 342 pupils from the 13-17 age group in the Czech Republic. The results of the study show the pupils’ success rate in the solution of problems effectively solvable using the strategies systematic experimentation and solution drawing improved significantly if the use of these strategies went hand in hand with the active use of technological devices. The number of ‘no response’ decreased significantly.","PeriodicalId":33912,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78601550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study examines personalization from a personal autonomy, responsibility, and flexibility point of view. It is determined that personalization is one of the approaches which is utilized in a Montessori program, its principles, teachers' beliefs, and practices in the teaching of mathematics at a selected elementary school in the Czech Republic. The work explores if and how teachers implement personalization principles and strategies in the Montessori approach. Why some principles of personalized learning are not well incorporated in the Montessori approach is also noted. The reaserch findings show that the kinds of activities of teachers using the Montessori approach are in accordance with personalization.
{"title":"Personalisation in Montessori environments during mathematics lessons","authors":"M. Brozova","doi":"10.24917/20809751.14.8","DOIUrl":"https://doi.org/10.24917/20809751.14.8","url":null,"abstract":"This study examines personalization from a personal autonomy, responsibility, and flexibility point of view. It is determined that personalization is one of the approaches which is utilized in a Montessori program, its principles, teachers' beliefs, and practices in the teaching of mathematics at a selected elementary school in the Czech Republic. The work explores if and how teachers implement personalization principles and strategies in the Montessori approach. Why some principles of personalized learning are not well incorporated in the Montessori approach is also noted. The reaserch findings show that the kinds of activities of teachers using the Montessori approach are in accordance with personalization.","PeriodicalId":33912,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87516836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The article describes how to present vocal music in the most complete edition of Kronika of Marcin Bielski (1564). The view of the linguistic formation of this fragment of reality in an idiolectic approach from the 16th century confirms the use of several groups of words to describe this part of music that Bielski considers singing: the names of the melodic process of producing sound (śpiewać, odśpiewawać, przyśpiewawać, śpiewanie), what is sung (antyfona, cantica, gradał, hymn/hymna, kantyki, pienie, pieśń, proza, psalm, psałterz, responsyja, śpiewanie, żołtarz) and singers (psalterzysta, śpiewaczka, śpiewak). The conducted analyzes showed some features of Bielski’s lexical and research workshop and confirmed that his work is the beginning of perfecting the Polish language in many areas of its functioning.
{"title":"„Zawżdy usty śpiewali”, czyli o muzyce wokalnej w Kronice, to jest historyi świata Marcina Bielskiego (1564)","authors":"D. Kozaryn","doi":"10.24917/20831765.17.10","DOIUrl":"https://doi.org/10.24917/20831765.17.10","url":null,"abstract":"The article describes how to present vocal music in the most complete edition of Kronika of Marcin Bielski (1564). The view of the linguistic formation of this fragment of reality in an idiolectic approach from the 16th century confirms the use of several groups of words to describe this part of music that Bielski considers singing: the names of the melodic process of producing sound (śpiewać, odśpiewawać, przyśpiewawać, śpiewanie), what is sung (antyfona, cantica, gradał, hymn/hymna, kantyki, pienie, pieśń, proza, psalm, psałterz, responsyja, śpiewanie, żołtarz) and singers (psalterzysta, śpiewaczka, śpiewak). The conducted analyzes showed some features of Bielski’s lexical and research workshop and confirmed that his work is the beginning of perfecting the Polish language in many areas of its functioning.","PeriodicalId":33912,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84508551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the article, the subject of description included continuous and discontinuous auto-semantic lexical units used in the medieval language (until the end of the 15th century) which are a lexical representation of the concepts of Holy Mass in the Słownik pojęciowy języka staropolskiego online [Conceptual Dictionary of Old Polish online]. The result of onomasiological works on the vocabulary gathered within the concept of HOLY MASS in the Słownik pojęciowy języka staropolskiego [Conceptual Dictionary of Old Polish online] is the categorization of this lexis within subordinate concepts. They include lexical units referring to the name of the service, the maner of its celebration, sermon, sacrifice, rite of peace, holy communion, final blessing, and items related to the holy mass.
在这篇文章中，描述的主题包括中世纪语言(直到15世纪末)中使用的连续和不连续的自动语义词汇单位，这些词汇单位是Słownik pojęciowy języka staropolskiego在线[古波兰概念词典在线]中圣弥撒概念的词汇表示。对在Słownik pojęciowy języka staropolskiego[古波兰在线概念词典]中收集的神圣弥撒概念中的词汇进行的象形学工作的结果是在从属概念中对这些词汇进行分类。它们包括涉及服务名称的词汇单位，其庆祝方式，布道，牺牲，和平仪式，圣餐，最后的祝福，以及与神圣弥撒相关的项目。
{"title":"Reprezentacje leksykalne pojęcia MSZA ŚWIĘTA w średniowieczu. Analiza onomazjologiczna","authors":"Bożena Sieradzka-Baziur","doi":"10.24917/20831765.17.17","DOIUrl":"https://doi.org/10.24917/20831765.17.17","url":null,"abstract":"In the article, the subject of description included continuous and discontinuous auto-semantic lexical units used in the medieval language (until the end of the 15th century) which are a lexical representation of the concepts of Holy Mass in the Słownik pojęciowy języka staropolskiego online [Conceptual Dictionary of Old Polish online]. The result of onomasiological works on the vocabulary gathered within the concept of HOLY MASS in the Słownik pojęciowy języka staropolskiego [Conceptual Dictionary of Old Polish online] is the categorization of this lexis within subordinate concepts. They include lexical units referring to the name of the service, the maner of its celebration, sermon, sacrifice, rite of peace, holy communion, final blessing, and items related to the holy mass.","PeriodicalId":33912,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82517406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The article aims to recreate the tourist view based on the observation of the lexical layer of texts in quantitative terms. The subject of the research is the most frequent lexis excerpted in the form of an frequency list from Listy z podróży po Włoszech by Konstanty Gaszyński. The collected material consists of 300 words. The most common vocabulary was grouped into 9 semantic-lexical circles and analyzed using the research tools of cultural linguistics. The research has indicated that it is possible to reconstruct, on the basis of the analysis of the most common lexis, both the points of view in the texts and the correlated profiles of the Italian space.
本文旨在通过对语篇词汇层的定量观察，重建旅游观。本次研究的主题是Konstanty Gaszyński以频率列表的形式从Listy z podróży po Włoszech中摘录的最频繁的词汇。收集的材料有300字。将最常见的词汇分为9个语义-词汇圈，并运用文化语言学的研究工具进行分析。研究表明，在分析最常见词汇的基础上，重构文本中的观点和意大利语空间的相关轮廓是可能的。
{"title":"Dziewiętnastowieczne impresje z podróży do Włoch w perspektywie analizy kwantytatywnej leksyki wobec językowego obrazu świata (na przykładzie Listów z podróży po Włoszech Konstantego Gaszyńskiego)","authors":"Agnieszka Jedziniak","doi":"10.24917/20831765.17.6","DOIUrl":"https://doi.org/10.24917/20831765.17.6","url":null,"abstract":"The article aims to recreate the tourist view based on the observation of the lexical layer of texts in quantitative terms. The subject of the research is the most frequent lexis excerpted in the form of an frequency list from Listy z podróży po Włoszech by Konstanty Gaszyński. The collected material consists of 300 words. The most common vocabulary was grouped into 9 semantic-lexical circles and analyzed using the research tools of cultural linguistics. The research has indicated that it is possible to reconstruct, on the basis of the analysis of the most common lexis, both the points of view in the texts and the correlated profiles of the Italian space.","PeriodicalId":33912,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80675592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Already in the oldest cultures, numbers were used not only for counting, but humans used them to tame and organise the world and attributed to them magical, mystical and causative powers. It is difficult to characterise all cultural and linguistic areas in which the number three plays a very important role and performs many functions. Out of necessity, this article will limit itself to selected ones: various contemporary and past religions; folk culture; sports; children’s rhymes and counting books; phraseological idioms, proverbs and maxims. Triads occur extremely often in the physical and mental world of many societies, because the number three is considered lucky, perfect, often even sacred, basic in many areas of life (among others in folklore, in fairy tales, in literature, in games and plays, spells, aphorisms, wishes).
{"title":"Liczba trzy w kulturze i języku","authors":"M. Ruszkowski","doi":"10.24917/20831765.17.16","DOIUrl":"https://doi.org/10.24917/20831765.17.16","url":null,"abstract":"Already in the oldest cultures, numbers were used not only for counting, but humans used them to tame and organise the world and attributed to them magical, mystical and causative powers. It is difficult to characterise all cultural and linguistic areas in which the number three plays a very important role and performs many functions. Out of necessity, this article will limit itself to selected ones: various contemporary and past religions; folk culture; sports; children’s rhymes and counting books; phraseological idioms, proverbs and maxims. Triads occur extremely often in the physical and mental world of many societies, because the number three is considered lucky, perfect, often even sacred, basic in many areas of life (among others in folklore, in fairy tales, in literature, in games and plays, spells, aphorisms, wishes).","PeriodicalId":33912,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86285574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Claire Kramsch, Language as Symbolic Power, Cambridge University Press, 2021, pp. 279","authors":"J. Jakubík","doi":"10.24917/20831765.17.21","DOIUrl":"https://doi.org/10.24917/20831765.17.21","url":null,"abstract":"<jats:p>brak</jats:p>","PeriodicalId":33912,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","volume":"118 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85387508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This draft is dedicated to the warunek sine qua non expression, which is pervasive in modern Polish language (both in scientific and sensu largo journalistic sources). The draft’s author explains in detail the mechanism of error of this popular lingual hybrid and reflects on the causes for the several decade-long popularity of this structure, notabene sanctionaed in normative linguistic compendiums, as well as numerous lexicons and dictionaries. The issue of this unfortunate error in this case has been silhouetted against the issue of awareness on proper and subtle use of Latin expressions, phrases, and idioms in scientific dissertations and media publications. This issue is extremely important in modern culture and fades in a terrifyingly fast manner.
{"title":"Łacina po polsku, czyli glosa o niefortunnej hybrydzie \"warunek sine qua non\"","authors":"A. Gorzkowski","doi":"10.24917/20831765.17.4","DOIUrl":"https://doi.org/10.24917/20831765.17.4","url":null,"abstract":"This draft is dedicated to the warunek sine qua non expression, which is pervasive in modern Polish language (both in scientific and sensu largo journalistic sources). The draft’s author explains in detail the mechanism of error of this popular lingual hybrid and reflects on the causes for the several decade-long popularity of this structure, notabene sanctionaed in normative linguistic compendiums, as well as numerous lexicons and dictionaries. The issue of this unfortunate error in this case has been silhouetted against the issue of awareness on proper and subtle use of Latin expressions, phrases, and idioms in scientific dissertations and media publications. This issue is extremely important in modern culture and fades in a terrifyingly fast manner.","PeriodicalId":33912,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82561789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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