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Sand, Odd Petter; Lockwood, Elise; Caballero, Marcos & Mørken, Knut Martin
(2022).
Four Patterns in Students’ Connections Between Mathematics and Computing.
Vis 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.
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Mørken, Knut Martin
(2020).
IKT i alle fag.
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Mørken, Knut Martin
(2020).
Hvorfor programmering og algoritmer?
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Hodnebrug, Ina; Lingaas, Else Marie & Mørken, Knut Martin
(2019).
Samarbeid om utdanning mellom universiteter og høgskoler og næringslivet. Hvorfor? Hva fungerer? Hvor er utfordringene?
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Fyhn, Marianne; Malthe-Sørenssen, Anders; Mørken, Knut Martin; Nederbragt, Alexander Johan; Odden, Tor Ole & Sundnes, Joakim
(2019).
Beregningsorientering og utdanningsutvikling.
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Mørken, Knut Martin & Dæhlen, Morten
(2019).
Er frafallet i høyere utdanning et så stort problem som noen vil ha det til?
[Avis].
Khrono.
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Mørken, Knut Martin
(2019).
Hva er det egentlig studentene trenger for å lykkes?
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Mørken, Knut Martin
(2019).
Programmering for å styrke matematikken, er det mulig? .
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Mørken, Knut Martin
(2019).
Programmering for å styrke matematikken, er det mulig? .
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Mørken, Knut Martin
(2019).
Computing in Mathematics and Science Education.
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Tellefsen, Cathrine Wahlstrøm & Mørken, Knut Martin
(2019).
Programmering i naturfag.
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Tellefsen, Cathrine Wahlstrøm & Mørken, Knut Martin
(2018).
ProFag: realfaglig programmering.
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Tellefsen, Cathrine Wahlstrøm & Mørken, Knut Martin
(2018).
Programmering er mer enn koding.
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Tellefsen, Cathrine Wahlstrøm & Mørken, Knut Martin
(2018).
Programmering i naturfaget.
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Mørken, Knut Martin
(2018).
Computing in Science Education.
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Mørken, Knut Martin
(2018).
Emneutvikling og systematisk integrering av generiske ferdigheter i utdanningsprogrammene.
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Mørken, Knut Martin
(2018).
Utdanning og utveksling
.
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Mørken, Knut Martin
(2018).
Programmering i skolen: muligheter og utfordringer.
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Mørken, Knut Martin
(2018).
Programmering i alle fag!
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Mørken, Knut Martin
(2018).
Om fagfornyelsen i matematikk.
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Mørken, Knut Martin & Sølna, Hanne
(2018).
An Evolving Culture for Learning in Practice.
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Mørken, Knut Martin
(2018).
Educational Development: Computing in Science Education in a Wider Perspective.
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Mørken, Knut Martin
(2018).
Some reflections on how computing can enhance the learning of mathematics.
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Malthe-sørenssen, Anders; Henriksen, Ellen Karoline; Hjorth-Jensen, Morten; Mørken, Knut Martin; Sølna, Hanne & Tellefsen, Cathrine Wahlstrøm
(2017).
Center for computing in science education: fornyelse av utdanning ved integrasjon av beregninger.
Nordic Journal of STEM Education.
ISSN 2535-4574.
1(1),
s. 236–241.
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Mørken, Knut Martin; Runde, Ragnhild Kobro & Skramstad, Tone
(2017).
Det nasjonale kvalifikasjonsrammeverket og utdanningsutvikling.
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Fyhn, Marianne; Kristensen, Solveig; Mørken, Knut Martin; Sølna, Hanne; Tellefsen, Cathrine Wahlstrøm & Villanger, Ilan Dehli
(2017).
Helhetlig fokus på utdanningsutvikling.
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Mørken, Knut Martin
(2017).
Computing in Science Education (CSE).
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Mørken, Knut Martin
(2017).
Utdanningsutvikling på MN-fakultetet.
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Mørken, Knut Martin
(2017).
Utdanningsutvikling på MN-fakultetet ved UiO.
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Mørken, Knut Martin
(2017).
Kultur for kvalitet i høyere utdanning: Systematisk arbeid med utdanningskvaliteten med tanke på utvikling og forbedring.
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Mørken, Knut Martin
(2017).
InterAct at UiO: Good education is more than good lectures!
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Mørken, Knut Martin
(2017).
Computing in Science Education.
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Mørken, Knut Martin
(2017).
Utdanningsutvikling på MN-fakultetet ved UiO.
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Mørken, Knut Martin
(2017).
Computing in Science Education.
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Mørken, Knut Martin
(2017).
Computing in the undergraduate mathematics curriculum?
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Mørken, Knut Martin
(2017).
Reflections on mathematics and science education for the future.
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Mørken, Knut Martin
(2017).
Bioscience, chemistry, pharmacy or life science?
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Mørken, Knut Martin & Rasmussen, Live
(2016).
Skru av autopiloten!
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Mørken, Knut Martin
(2016).
How can computing assist in learning calculus?
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Sølna, Hanne & Mørken, Knut Martin
(2016).
How to radically change university education?
A joint venture between academics and administration.
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Mørken, Knut Martin; Hjorth-Jensen, Morten; Langtangen, Hans Petter & Malthe-Sørenssen, Anders
(2016).
How should computers influence the mathematics curriculum?
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Mørken, Knut Martin; Hjorth-Jensen, Morten; Langtangen, Hans Petter & Malthe-Sørenssen, Anders
(2016).
Computing across the curriculum.
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Mørken, Knut Martin
(2016).
Some reflections on the impact of computers in science education.
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Mørken, Knut Martin & Tellefsen, Cathrine Wahlstrøm
(2016).
Course alignment and a culture for quality.
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Kluge, Anders & Mørken, Knut Martin
(2016).
Nytt skolefag nødvendig.
Dagens næringsliv.
ISSN 0803-9372.
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Mørken, Knut Martin
(2015).
MNs utdanningssatsing.
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Mørken, Knut Martin & Sølna, Hanne
(2015).
Strategisk blikk på utdanning.
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Mørken, Knut Martin; Hjorth-Jensen, Morten; Langtangen, Hans Petter & Malthe-Sørenssen, Anders
(2015).
Tanker om digital realfagsundervisning.
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Mørken, Knut Martin; Hjorth-Jensen, Morten; Langtangen, Hans Petter & Malthe-Sørenssen, Anders
(2015).
Some reflections on the impact of computers in science education.
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Mørken, Knut Martin
(2015).
Utdanning, utdanningsroller
og læringsmiljø.
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Mørken, Knut Martin; Sølna, Hanne & Villanger, Ilan Dehli
(2015).
Hvordan skaper vi gode betingelser for læring?
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Bruvoll, Solveig; Lyche, Tom Johan & Mørken, Knut Martin
(2015).
Uniformly stable wavelets on nonuniform triangulations.
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Mørken, Knut Martin
(2014).
Hva er digital kompetanse i matematikk?
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Mørken, Knut Martin
(2014).
Fra Computing in Science Education (CSE) til generell utdanningsutvikling.
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Mørken, Knut Martin
(2014).
Fra Computing in Science Education (CSE) til generell utdanningsutvikling.
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Mørken, Knut Martin
(2014).
Computational Science & Engineering infusion in general undergraduate education.
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Mørken, Knut Martin
(2014).
InterAct — Kultur for læring.
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Mørken, Knut Martin
(2014).
Fagfornyelse i matematikk.
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Mørken, Knut Martin & Sølna, Hanne
(2014).
Computing in Science Education.
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Mørken, Knut Martin
(2014).
Reforming mathematics and science education.
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Floater, Michael S.; Lyche, Tom; Mazure, Marie-Laurence; Mørken, Knut Martin & Schumaker, Larry L.
(2014).
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface.
Lecture Notes in Computer Science (LNCS).
ISSN 0302-9743.
8177 LNCS.
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Mørken, Knut Martin
(2013).
Reforming Mathematics and Science Education.
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Bruvoll, Solveig; Lyche, Tom & Mørken, Knut Martin
(2012).
Uniformly stable linear wavelets on nonuniform triangulations.
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Mørken, Knut Martin
(2012).
Estetikk, kreativitet og modeller i matematikk.
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Mørken, Knut Martin
(2012).
FoU-basert utdanning i realfag: Computing in Science Education (CSE).
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Mørken, Knut Martin & Sølna, Hanne
(2012).
KUPP: Kulturkompetanse og personlig utvikling. Trenger vi et nytt perspektiv i utdanningene?
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Mørken, Knut Martin & Sølna, Hanne
(2012).
Framtidas teknologiutdanning.
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Mørken, Knut Martin
(2012).
Realfagsutdanning og læring når rammene endrer seg.
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Mørken, Knut Martin
(2012).
Integrating computational methods throughout the bachelor education.
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Mørken, Knut Martin; Sveinsson, Henrik Andersen & Dahl, Lars Oswald
(2012).
Computing in Science Education (CSE): Numeriske metoder i tverrfaglig og FoU-basert undervisning – gevinster for utdanningen, kandidatene og arbeidslivet.
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Mørken, Knut Martin & Sølna, Hanne
(2012).
IT i moderne forskningsbasert undervisning: CSE — hva er nøkkelen?
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Mørken, Knut Martin & Sølna, Hanne
(2012).
Mathematics and science education in a world with computers: Computing in Science Education (CSE).
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Mørken, Knut Martin
(2012).
Mathematics and science education in a world with computers: Computing in Science Education (CSE).
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Mørken, Knut Martin & Sølna, Hanne
(2012).
Hvorfor beregningsorientert matematikk, og hvordan?
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Mørken, Knut Martin & Sølna, Hanne
(2011).
Hvordan kan IKT bidra til mer relevant opplæring?
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Mørken, Knut Martin
(2011).
Beregningsorientert ingeniørutdanning?
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Mørken, Knut Martin
(2011).
Beregningsperspektiv i ingeniørutdanningen?
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Mørken, Knut Martin & Sølna, Hanne
(2011).
Hvorfor beregningsorientert matematikk og hvordan?
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Mørken, Knut Martin & Sølna, Hanne
(2011).
Hvorfor beregningsorientert matematikk og hvordan?
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Mørken, Knut Martin
(2011).
Hvorfor beregningsorientert matematikk og hvordan?
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Mørken, Knut Martin & Sølna, Hanne
(2011).
Hvorfor beregningsorientert matematikk og hvordan få det til?
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Mørken, Knut Martin
(2011).
Realfagsundervisning med beregninger.
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Mørken, Knut Martin
(2011).
Beregninger i realfagsutdanningen.
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Mørken, Knut Martin
(2011).
Status for CSE-prosjektet.
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Mørken, Knut Martin & Sand, Ingrid
(2019).
Spørreundersøkelse MN nye laveregradsstudenter høsten 2019.
Universitetet i Oslo.
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Bersvendsen, Jørn; Samset, Eigil; Mørken, Knut Martin & Reimers, Martin
(2016).
Segmentation of cardiac structures in 3-dimensional echocardiography.
Universitetet i Oslo.
ISSN 1501-7710.
Fulltekst i vitenarkiv
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Mørken, Knut Martin; Bruvoll, Solveig & Lyche, Tom
(2011).
Uniformly stable wavelets on nonuniform triangulations.
CMA.