Odd Petter Sand

• Sand, Odd Petter; Lockwood, Elise; Caballero, Marcos & Mørken, Knut Martin (2022). Three cases that demonstrate how students connect the domains of mathematics and computing. Journal of Mathematical Behavior. ISSN 0732-3123. 67. doi: 10.1016/j.jmathb.2022.100955. Fulltekst i vitenarkiv Vis sammendrag

  This study uses actor-oriented transfer perspective to investigate different ways in which students make connections across the domains of mathematics and computing. We interview first-year students at the University of Oslo as they work with a set of tutorials that we designed to integrate knowledge from both domains. The cases we present here demonstrate four different types of cross-domain connections: (a) mathematically reproducing the work of a computer program, (b) cyclically improving a program to produce better output, (c) coupling math to output to justify program improvements and (d) coupling math to code to justify program design. We provide rich examples of the ways in which students make these connections and discuss affordances for mathematical learning in this context.

• Sand, Odd Petter; Lockwood, Elise; Caballero, Marcos & Mørken, Knut Martin (2022). Students’ Development of a Logarithm Function in Python Using Taylor Expansions: a Teaching Design Case Study. Digital Experiences in Mathematics Education. ISSN 2199-3246. doi: 10.1007/s40751-022-00104-3. Vis sammendrag

  We present here the lessons learned by iteratively designing a tutorial for first-year university students using computer programming to work with mathematical models. Alternating between design and implementation, we used video-taped task interviews and classroom observations to ensure that the design promoted student understanding. The final version of the tutorial we present here has students make their own logarithm function from scratch, using Taylor polynomials. To ensure that the resulting function is accurate and reasonably fast, the students had to understand and apply concepts both from computing and from mathematics. We identify three categories of such concepts and identify three design features that students attended to when demonstrating such understanding. Additionally, we describe four important take-aways from a teaching design point of view that resulted from this iterative design process.

• Sand, Odd Petter; Odden, Tor Ole; Lindstrøm, Christine & Caballero, Marcos Daniel (2018). How computation can facilitate sensemaking about physics: A case study. Physics Education Research Conference Proceedings. ISSN 1539-9028. s. 1–4. doi: 10.1119/perc.2018.pr.Sand. Fulltekst i vitenarkiv

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• Løken, Trygve Kvåle & Sand, Odd Petter (2024). Ungdomsskoleelevers spontane bruk av programmeringskonsepter for å løse sammensatte geometriske problemer. Vis sammendrag

  I vårt foredrag tar vi for oss en case-studie gjort på ungdomstrinnet hvor vi observerer hvordan elevgrupper løser sammensatte geometriske problemer ved hjelp av Python-programmering. Vi vil presentere et undervisningsopplegg og oppgaver som stimulerer til matematisk refleksjon og samarbeid. Ut fra videoopptak av elevgrupper har vi foretatt en tematisk analyse av datamaterialet. Foreløpige resultater viser at elevene spontant tar i bruk programmeringskonsepter for å kunne løse matematiske problemer, og at de uoppfordret generaliserer det de jobber med til å utforske grensetilfeller for mangekanter med egenprodusert Python-kode. I tillegg har vi observert at selv om elevene har lav eller ingen formell kunnskap om begreper som variabler og verdier, tar de disse aktivt i bruk for å løse det presenterte problemet. Dette gir innsikt i hvordan elevene forstår variabler i henholdsvis matematikk og programmering, og i hvilken grad de klarer å koble disse sammen på tvers av kontekst.

• Sand, Odd Petter (2023). Seminar: Integrating Computing with Mathematics and Science Education. Vis sammendrag

  Computing (such as programming) has revolutionised the way mathematicians and scientists work, and has also changed the way we teach mathematics and science. However, relatively little is known about how the changes to teaching impact students' understanding. To learn more, we designed teaching experiments and interviewed first-year university students. In these interviews, we found rich examples of the ways in which students use mathematics and computing together, including what helps and hinders them in making sense of what they do. One of our main findings is that we saw certain patterns in students’ use of mathematics and computing that may support their understanding. Additionally, we present three tutorials that we designed for this purpose, and share what we learned in the process.

• Sand, Odd Petter (2022). Leveraging the Potential of Abstraction in Programming Education. Vis sammendrag

  Abstraction is a fundamental part of computer science, but it is also challenging, especially for novice learners. Part of this difficulty is that experts and teachers often unconsciously operate on several levels of abstraction at once, without being conscious of or explicit about this fact. This lightning talk suggests ways to overcome this potential disconnect between teachers and learners, and discusses the need for more research into the ways in which Python makes abstraction more visible and explicit to students.

• 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.

• Sand, Odd Petter (2018). How to get students to engage in computational sensemaking.
• Sand, Odd Petter; Odden, Tor Ole; Lindstrøm, Christine & Caballero, Marcos Daniel (2018). How computation can facilitate sensemaking about physics.
• Sand, Odd Petter (2021). Integrating Computing with Mathematics and Science Education. Universitetet i Oslo. ISSN 1501-7710.
• Sand, Odd Petter (2021). Integrating Computing with Mathematics and Science Education: Case Studies of Student Understanding and Teaching Design. Universitetet i Oslo. ISSN 1501-7710. Fulltekst i vitenarkiv Vis sammendrag

  Computing (such as programming) has revolutionised the way mathematicians and scientists work, and has also changed the way we teach mathematics and science. However, relatively little is known about how the changes to teaching impact students’ understanding. To learn more, we designed teaching experiments and interviewed first-year university students. In these interviews, we found rich examples of the ways in which students use mathematics and computing together, including what helps and hinders them in making sense of what they do. One of our main findings is that we saw certain patterns in students’ use of mathematics and computing that may support their understanding. Additionally, we present three tutorials that we designed for this purpose, and share what we learned in the process.

• Sand, Odd Petter & Elgarøy, Øystein (2016). Massive neutrinos and spherical collapse in LCDM and DGP gravity. Universitetet i Oslo.

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