Students’ use of variables and multiple representations in generalizing functional relationships prior to secondary school

Wilkie, Karina Joyce

doi:10.1007/s10649-016-9703-x

Cited by 38 publications

(30 citation statements)

References 17 publications

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“…Expressing generality is a natural and rewarding part of how we, as people, make sense of the world around us. The ability to see the general in the special is fundamental and is a cornerstone of mathematics (Wilkie 2016). According to Mason et al (2005), algebra gives us a vocabulary of symbols that we can handle and a language to express and treat the general.…”

Section: Describing Patternsmentioning

confidence: 99%

Discovering key interactions. How student interactions relate to progress in mathematical generalization

2020

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This article presents a study of 8th grade students working in groups to solve a task about generalizing patterns. The study aimed to openly explore how progress in mathematical thinking might relate to the discourse. To do this, we first studied both separately. The progress in mathematical thinking was studied by inspecting how the groups progressed through different levels of generalization. The discourse was studied by characterizing each student interaction. When combining these, we realized that some specific types of interactions were related to students progressing to a higher level of generalization. We call these key interactions, and they were mainly of the types of advocating, locating, and reformulating. These seem clearly important for identifying evidence of progress during the discourses, but might also be helpful for understanding how specific types of interactions relates to sharing and growing mathematical thinking.

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Section: Describing Patternsmentioning

confidence: 99%

Discovering key interactions. How student interactions relate to progress in mathematical generalization

2020

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“…the previous calculation of the mean. In Pre-Algebra, recognizing growing patterns prepares for sequences, abstracted later as functions in Algebra [57,56]. It is axiomatic that sequences and their sums and series are iterative.…”

Section: Racketmentioning

confidence: 99%

Code ABC MOOC for Math Teachers

Niemelä

Partanen²,

Mannila

et al. 2018

Communications in Computer and Information Science

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Computing is the latest add-on to enhance the K-12 curricula of many countries, with the purpose of closing the digital skills gap. The revised Finnish Curriculum 2014 integrates computing mainly into math. Consequently, Finland needs to train math teachers to teach computing at elementary level. This study describes the Python and Racket tracks of the Code ABC MOOC that introduce programming basics for math teachers. Their suitability for math is compared based on the course content and feedback. The results show that conceptually the functional paradigm of Racket approaches math more closely, in particular algebra. In addition, Racket is generally regarded as more challenging in terms of syntax and e.g. for utilizing recursion as an iteration mechanism. Math teachers also rank its suitability higher because the content and exercises of the track are specifically tailored for their subject.

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“…Wilkie [44][45] [46] discusses the challenges of functional thinking and promotes gradual development by using multiple presentations and bridging arithmetic and procedural knowledge more cautiously. For the primary school, Wilkie has illustrated a pathway of generalizations of sequences as a preparation for algebra; these exercises are labelled pre-algebraic.…”

Section: ) Transfer Between Ict and Mathmentioning

confidence: 99%

K-12 Curriculum Research: The Chicken and the Egg of Math-aided ICT Teaching

Niemelä¹,

Helevirta²

2017

IJMECS

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Abstract-In this article, we examine the relationship in K-12 education between Mathematics and Information and Communication Technology (ICT). The topic is reviewed from various angles, based on both a literature study and by directly contrasting the Finnish National Curriculum (FNC) of 2014 (effective since autumn 2016) with the National Curriculums of the UK (UKNC) [3] and the US (USCC) [2].Finland has chosen a cross-curricular approach to developing the new curriculum for teaching ICT, which involves integrating it mainly with math, but also with handicraft, and various other subjects. This is in direct contrast to the UKNC, for example, which teaches ICT as its own field, to be taught through the Computing and Design/Technology syllabi. This poses a question for this research study, namely, how well do teaching math and ICT fit together? The first step towards answering this question is to establish which ICT concepts and domains are directly supported by math and which are left uncovered. As a theoretical research paper, the rationale for the inter-connectedness of math and ICT is based on the work of many researchers. To illustrate our comparison of the two subjects, in this article we concentrate on clarifying math's and ICT's shared concepts of variable and function.The results of this study indicate that transfer between the subjects happens bi-directionally, which might suggest that teaching ICT in combination with particular branches of math, notably algebra would be of benefit to our students. In order to pursue this approach, extra modules for logic, basic linear algebra and set theory would also be required. The fundamentals of basic algebra, the function and the variable, and their significance as synthesizers in both algebra and ICT are highlighted. In addition, the use of calculators as function tutors is explored in an instructional classroom setting. The conclusion of this study is that although there are certain benefits to the currently chosen approach of teaching ICT in combination with mathematics, these are not enough to outweigh the advantages of adopting a more versatile dedicated ICT syllabus, such as that provided by the UKNC.

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Students’ use of variables and multiple representations in generalizing functional relationships prior to secondary school

Cited by 38 publications

References 17 publications

Discovering key interactions. How student interactions relate to progress in mathematical generalization

Discovering key interactions. How student interactions relate to progress in mathematical generalization

Code ABC MOOC for Math Teachers

K-12 Curriculum Research: The Chicken and the Egg of Math-aided ICT Teaching

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