In the last 25 years, a small collection of reports of studies focused on gaining insight into prospective teachers' knowledge of decimals has been published. Three themes are used to frame findings ...from papers published prior to 1998. Additional findings from papers published between 1998 and 2011 are discussed. Direction for future research that can contribute to the development of curriculum and instruction in mathematics teacher education is shared.
The mathematics textbook is, in France, a central object to teachers’ professional practices (and more markedly among beginners), and in students’ daily work, whether in class or in their personal ...work.
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.
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