Have the quantity and quality of papers on tertiary mathematics education in Australasia changed? Are researchers going over the same ground, or are they venturing into new areas and exposing a vista ...not previously seen? This review of research found indications of improved quality as well as some repetitive work. The authors state that new directions are being opened up. Compared with the last review, the numbers of refereed papers increased 12%. and shows the same natural cyclic variation. This chapter, unlike the corresponding chapters in previous reviews, adds consideration of papers on statistics in tertiary education. The majority of the papers in this area deal with statistics as a service subject rather than post-secondary statistics majoring courses. In mathematics, nearly half of the papers reviewed for this chapter were published in journals, compared with one quarter in the previous four-year period. Such figures probably reflect both an increasing quantity and quality of manuscripts, and in all likelihood, increased production that has been driven by the demand from university employers for fully refereed research outputs. The increase may also be stimulated by an increasing need to address pedagogical issues in the tertiary sector as governments and students demand higher quality teaching. The authors hope that the growing variety and depth of research over the last four years, documented in this chapter, will lead to stronger publications in the near future. Author abstract, ed
In the context of mathematics education research the concept ‘opportunity to Learn’ has been used in international comparative studies as a measure to judge whether the student test items will be ...fair and appropriate, and as a mean to explain differences in performance. In the report of the first IEA study (FIMS) ‘opportunity to learn’ is related to whether students have been exposed to the topic or problems in question (Husén, 1967).
Troubles with mathematical contents Facchin, Marco
Philosophical psychology,
09/2022, Volume:
ahead-of-print, Issue:
ahead-of-print
Journal Article
Peer reviewed
Open access
To account for the explanatory role representations play in cognitive science, Egan's deflationary account introduces a distinction between cognitive and mathematical contents. According to that ...account, only the latter are genuine explanatory posits of cognitive-scientific theories, as they represent the arguments and values cognitive devices need to represent to compute. Here, I argue that the deflationary account suffers from two important problems, whose roots trace back to the introduction of mathematical contents. First, I will argue that mathematical contents do not satisfy important and widely accepted desiderata all theories of content are called to satisfy, such as content determinacy and naturalism. Secondly, I will claim that there are cases in which mathematical contents cannot play the explanatory role the deflationary account claims they play, proposing an empirical counterexample. Lastly, I will conclude the paper highlighting two important implications of my arguments, concerning recent theoretical proposals to naturalize representations via physical computation, and the popular predictive processing theory of cognition.
Paweł Gładziejewski has recently argued that the framework of predictive processing (PP) postulates genuine representations. His focus is on establishing that certain structures posited by PP ...actually play a representational role. The goal of this paper is to promote this discussion by exploring the contents of representations posited by PP. Gładziejewski already points out that structural theories of representational content can successfully be applied to PP. Here, I propose to make the treatment slightly more rigorous by invoking Francis Egan’s distinction between mathematical and cognitive contents. Applying this distinction to representational contents in PP, I first show that cognitive contents in PP are (partly) determined by mathematical contents, at least in the sense that computational descriptions in PP put constraints on ascriptions of cognitive contents. After that, I explore to what extent these constraints are specific (i.e., whether PP puts unique constraints on ascriptions of cognitive contents). I argue that the general mathematical contents posited by PP do not constrain ascriptions of cognitive content in a specific way (because they are not relevantly different from mathematical contents entailed by, for instance, emulators in Rick Grush’s emulation theory). However, there are at least three aspects of PP that constrain ascriptions of cognitive contents in more specific ways: (i) formal PP models posit specific mathematical contents that define more specific constraints; (ii) PP entails claims about how computational mechanisms underpin cognitive phenomena (e.g. attention); (iii) the processing hierarchy posited by PP goes along with more specific constraints.
This article seeks to show that learning environments centered on an everyday or professional topics, usually in the interest of students and supported by technology, contribute favorably to minimize ...the feeling of irrelevance of mathematical contents, common among students. The problems proposed were based on work carried out in Linear Programming discipline from an Information Systems Course in which many of the students involved also execute professional activities, making it difficult to dedicate to the studies. Through the experience, it was possible to observe that the use of everyday or professional subjects contribute to minimize the sense of irrelevance of the discipline and, in addition, the students became more critical and involved with the information received.
Background: Sequencing contents is of great importance for instructional design within the teaching planning processes. We believe that it is key for a meaningful learning. Material and methods: ...Therefore, we propose to formally establish a partial order relation among the contents: the relation: “to be a prerequisite”. We have applied this approach to the mathematical contents of the compulsory Secondary Education of the Spanish educational system. This information has been modeled as a graph. The amount of contents considered (814) and the number of ordered pairs in the order relation considered (17,782) has produced a big graph. In order to work effectively with that amount of data, we have used software specialized in network analysis. More precisely, we have used the software packages Pajek and Gephi. Results: This software, together with the use of techniques borrowed from graph theory, has allowed providing a tool for debugging curriculum developments (similar to rule based expert systems verification). Conclusions: This is a contribution to the processes of sequencing contents and, therefore, to the processes of planning teaching and instructional design.
In the first part, the article presents a series of theoretical aspects about interdisciplinarity, a concept which under the present conditions of the new curriculum for preschool education, requires ...a new approach of mathematical contents and particularly another modality of using didactic strategies. The second part of the article focuses on the presentation of two models of interdisciplinary activities, which are meant to emphasize those methodical aspects, which should be taken into account by the teacher, in approaching mathematical contents and in correlating them by means of the other experiential fields. In the end, the stress is laid on some conclusions regarding the use of interdisciplinarity in approaching mathematical contents at the level of preschool education.
Razvoj misaonih struktura djeteta utječe na uspješnost u savladavanju matematičkih pojmova. Pojava konkretnog logičkog mišljenja i njegovi indikatori (pojmovi konzervacije) značajni su za pozitivno ...školsko postignuće učenika u okviru matematičkih sadržaja. Oblikovanjem formalnih operacija, kao posljednjom najsavršenijom fazom razvoja mišljenja, omogućuju se najsloženiji vidovi konzervacije. Kombinatorika predstavlja generalizaciju operacija stečenih u stadiju konkretnih operacija i obilježje posljednje faze razvoja mišljenja.
Cilj ovog rada usmjeren je na procjenu razvoja misaonih struktura konkretnih logičkih operacija (ostvarivanjem konzervacije broja, duljine, mase i volumena) i formalnih operacija (ostvarivanjem kombinatorike), kao i njihovu povezanost s matematičkim postignućem učenika s blažim intelektualnim teškoćama starije školske dobi.
U istraživanju je sudjelovalo 120 učenika oba spola (43,3% djevojčica i 56,7% dječaka), kronološke dobi od 12 do 15 godina. Sudionici su učenici od V do VIII razreda beogradskih osnovnih škola za djecu s blažim intelektualnim teškoćama.
Za procjenu operativnosti mišljenja korišteni su standardni Piagetovi zadaci za procjenu konzervacije (broja, duljine, mase i volumena) i kombinatorike, a za procjenu usvajanja matematičkih sadržaja korišten je kriterijski test znanja, posebno konstruiran za potrebe ovog istraživanja.
Rezultatima istraživanja je utvrđena povezanost između stupnja misaone razvijenosti na svim primijenjenim zadacima i razine savladavanja gradiva matematike.
Imajući u vidu loša postignuća ispitanika našeg istraživanja u svim segmentima rada, naglašavamo značaj prezentiranja Piagetovih i matematičkih zadataka kroz igru, kao što i Piagetova teorija zastupa stav o primjeni igara kojima se potiču reverzibilnost, identitet i konzervacija te kojima se matematičko mišljenje čini gipkijim, aktivnijim, širim, dubljim i originalnijim.
U radu se iznose rezultati istraživanja do kojih se došlo ispitivanjem stavova učitelja razredne nastave u pogledu učenikova poznavanja matematičkih sadržaja, razvijenosti matematičkog jezika i ...matematičkih vještina, stupnju kognitivnog razvoja, kao i razvijenosti matematičkih osobnosti kod učenika.
Istraživanje je provedeno na uzorku od 156 ispitanika, učitelja razredne nastave u osnovnim škola. Provedeno je tijekom mjeseca veljače 2007. godine.
Dobiveni su sljedeći rezultati:
Ispitanici ističu: 1. da je stupanj poznavanja matematičkih sadržaja njihovih učenika dobre razine (prosječna aritmetička sredina iznosi: = 3.10); 2. da je matematički jezik učenika dobro razvijen ( = 3.01); 3. da su matematičke vještine učenika dobro razvijene ( = 3.02); 4. da je stupanj kognitivnog razvoja učenika dobre razine ( = 3.03); 5. da je kvalitativna osobina (geometrijski tip) gotovo dvaput prisutnija od kvantitativne osobine (algebarski tip).
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