Cristin-resultat-ID: 2006000
Sist endret: 22. juni 2022, 08:58
Resultat
Poster
2022

Four Patterns in Students’ Connections Between Mathematics and Computing

Bidragsytere:
  • Odd Petter Sand
  • Elise Lockwood
  • Marcos Caballero og
  • Knut Martin Mørken

Presentasjon

Navn på arrangementet: Conference on Research in Undergraduate Mathematics Educaton
Sted: Boston, Massachusetts
Dato fra: 24. februar 2022
Dato til: 26. februar 2022

Arrangør:

Arrangørnavn: SIGMAA on RUME

Om resultatet

Poster
Publiseringsår: 2022

Klassifisering

Vitenskapsdisipliner

Matematikk • Matematikk og naturvitenskap

Emneord

Matematikkutdanning • Utdanningsutvikling • Beregningsorientert matematikk

Beskrivelse Beskrivelse

Tittel

Four Patterns in Students’ Connections Between Mathematics and Computing

Sammendrag

Computers and programming have become important in science and mathematics in the last few decades, and this has also affected the ways in which students and teachers interact with mathematics (see for instance Broley et al., 2018). For this reason, there have been calls for more attention to be paid to computing in mathematics education research. For instance, how does integrating computing into mathematics classrooms affect students’ understanding (Lockwood & Mørken, 2021)? One way in which students generalize is by relating knowledge, situations, techniques, or problems; what we often call forming connections (Ellis et al., 2017, Lobato, 2012). When students work with the domains of mathematics and computing, it is therefore likely that they will see similarities between situations across domain boundaries (we call such connections cross-domain connections). Greeno et al. (1993) discussed the affordances of such connections in terms of reasoning, which they defined as activities that transform representations. Importantly, the representations themselves afford particular transformations. Therefore, transforming a mathematical representation to a computational one (or vice versa) allows students to reason in ways that they might not otherwise. Our research questions are “1) which patterns of such connections emerge in the students’ work, and 2) what do these patterns afford the students?” To answer these questions, we interviewed first-year students in twos and threes as they worked with tutorials designed by the authors to support the forming of mathematical-computational connections. We instructed the students to work as they would in class, using the interviewer as a TA when needed. Using thematic analysis, we identified the themes that emerged in the data. In addition to students’ verbal utterances, we classified connections by looking at the medium they used, how they structured the information they worked with, and the notation or syntax they employed for individual pieces of information. While our study is an exploratory case study and as such not comprehensive, we found interesting examples of four distinct patterns in the connections that students formed. Students would (a) use mathematics to retrace the steps of a program, (b) use mathematics to interpret output, which inspired revisions to the code (which then produced new output, forming a cycle), (c) use mathematics and code together to design a program, and (d) use mathematics and output together to make refinements to a working program. The affordances evident in our data were, respectively, (a) understanding a program’s purpose or creating a formal proof, (b) explaining how a program works, as well as improving it, (c) confidence in a program’s correctness and organizing mathematical knowledge, and (d) producing results closer to standards and being able to explain these results. In our final poster, we will provide illustrative examples of each of the four patterns and use these to highlight the affordances (and limitations) of integrating computing in mathematics classrooms.

Bidragsytere

Odd Petter Sand

  • Tilknyttet:
    Forfatter
    ved Computing in Science Education ved Universitetet i Oslo

Elise Lockwood

  • Tilknyttet:
    Forfatter

Marcos Caballero

  • Tilknyttet:
    Forfatter
    ved Computing in Science Education ved Universitetet i Oslo

Knut Martin Mørken

  • Tilknyttet:
    Forfatter
    ved Fakultetsadministrasjonen ved Universitetet i Oslo
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