Martin Carlsen

• Lorange, Carl Andreas; Sjaastad, Jørgen; Carlsen, Martin & Weingarden, Merav (2026). A commognitive lens on the transition from naive empiricism to the generic example: the case of figural patterns. Research in Mathematics Education. ISSN 1479-4802. p. 1–22. doi: 10.1080/14794802.2026.2691841. Full text in Research Archive Show summary

  The purpose of this article is to deepen our understanding of the transition from substantiating a formula for a figural pattern by naive empiricism to substantiation by a generic example. We conceptualise this transition using the commognitive constructs meta-rules, commognitive conflict, and reification. Our conceptualisation is exemplified by a description of the learning process of a group of four pre-service mathematics teachers (PSTs) engaged in justifying formulas for figural patterns. The PSTs initially substantiated the formula for a figural pattern by naive empiricism. After watching video-based suggested solutions, in which the structure of the figural pattern was made explicit by grouping the dots in the figural pattern, a commognitive conflict emerged. We show how this conflict was resolved in the next session, after the teacher initiated a plenary discussion on how a formula for a figural pattern should be substantiated. We demonstrate how the PSTs’ discourse developed during this process.

• Reinhardtsen, Jorunn & Carlsen, Martin (2025). A 6th grade teacher’s and students’ togethering in the algebra classroom: A process of overcoming emerging dialectical contradictions. In Bosch, Marianna; Bolondi, Giorgio; Carreira, Susana; Spagnolo, Camilla & Gaidoschik, Michael (Ed.), Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14), Free University of Bozen-Bolzano; ERME, Feb 2025, Bozen-Bolzano, Italy.. European Society for Research in Mathematics Education. ISSN 9791221086553. p. 486–493. Full text in Research Archive Show summary

  The aim of this paper is to shed light on the sociocultural process of togethering as a teacher and students in the middle-school classroom attune to each other as they generalize patterns. We address this issue through analyses of data from a Californian 6th grade algebra classroom. Learning algebra is multifaceted because the students are expected to shift their reasoning with respect to both form and function, i.e. from arithmetic to algebra syntax (form) and from calculational to analytical (function). It is crucial to the development of algebraic thinking that students shift from inductive work with numbers and manipulatives to the formulation of deductive arguments. In this paper we discuss how togethering manifests itself as dialectic contradictions in this shift, in terms of how emotions and meaning making permeate the space of joint action in the classroom.

• Breive, Svanhild & Carlsen, Martin (2025). Re-interpreting children’s initiatives in mathematical inquiry processes as distributed agency over human and non-human agents. Educational Studies in Mathematics. ISSN 0013-1954. doi: 10.1007/s10649-025-10462-5. Full text in Research Archive Show summary

  The point of departure for this article was our interest in how processes of mathematical inquiry (MI) unfold in kindergarten contexts, and their relations to play. In this study, we are scrutinising one specific aspect of mathematical inquiry, that is children’s initiatives when they participate in playful and inquiry-based mathematical activities in a Norwegian kindergarten context. The aim of this study is thus to scrutinize what characterises those events where mathematical initiatives seem to arise from a child. We consider the seeming initiatives as signs of freedom, eagerness and/or willingness, i.e., signs of agency. We draw on de Freitas and Sinclair’s (2014) inclusive materialist perspective to study embodied and material dimensions of the children’s mathematics learning processes. We, accordingly, conceptualise agency as a relational force that emerges from activity and is distributed between human and non-human agents. The analyses of videotaped and transcribed kindergarten events reveal, we argue, that the observed eagerness and willingness are emerging from the learning process, rather than being prerequisites initiating learning. The mathematical aesthetic serves as an essential force in the learning assemblages where disruption between what the children sense (perceive) and what is expected or accepted to sense seems to be an essential driving force for the further exploration. This has important implications for teaching. Kindergarten teachers may prompt MI by setting up mathematically conspicuous cruxes in the environment. That is, to establish opportunities for differences, paradoxes, etc. to emerge in mathematical activities.

• Lien, Beate; Sødal, Amalie; Reinhardtsen, Jorunn & Carlsen, Martin (2025). Pre-service teachers’ developing professional identity as mathematics teachers – a theoretical perspective. In Bosch, Marianna; Bolondi, Giorgio; Carreira, Susana; Spagnolo, Camilla & Gaidoschik, Michael (Ed.), Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14), Free University of Bozen-Bolzano; ERME, Feb 2025, Bozen-Bolzano, Italy.. European Society for Research in Mathematics Education. ISSN 9791221086553. p. 2816–2823. doi: https:/hal.science/hal-05334902/. Full text in Research Archive Show summary

  In this paper we will launch the theoretical perspective Patterns of Participation as a lens to study pre-service teachers’ developing professional identity as secondary mathematics teachers, through the notions of being, becoming, and belonging. It is documented in the research literature that pre-service teachers experience a gap between the university and the school as learning contexts. In our study we address tensions that manifest themselves in the development of professional identity, as the pre-service teachers participate in these two learning contexts. Furthermore, we introduce the idea of a resource bank, theorised as a boundary object between these contexts. Drawing on an example from another study, we argue that by reflecting on the content of a resource bank, one pre-service teacher testifies her being, becoming and belonging.

• Karlsson, Lena; Palmér, Hanna & Carlsen, Martin (2025). Quality of preschool teachers’ mediation of early years mathematics in play-responsive teaching activities. Educational Studies in Mathematics. ISSN 0013-1954. doi: 10.1007/s10649-025-10470-5. Full text in Research Archive Show summary

  This study investigates the teaching of early years mathematics within an intervention using play-responsive teaching (PRT). It focuses on ways sequences characterized as play-responsive mathematics teaching (PRMT) and mathematics teaching (MT) address the nature of the mathematics that is made available to learn. A previous study revealed that when teachers and children engaged in play-responsive teaching (PRT) with an emphasis on mathematics, particularly cardinality, three distinct sequences were identified: play without mathematics, mathematics teaching without play (MT), and play-responsive mathematics teaching (PRMT). In this article, the two latter sequences are analyzed with a focus on teaching quality. In this context, the quality of teachers’ mediation refers to how preschool teachers make mathematical content accessible to children and how they support children’s meaningful participation in the learning sequences. The results indicate both advantages and disadvantages of play-responsive teaching. Specifically, MT sequences were rich in terms of the mathematics that was made available to learn, caused by a structured use of artifacts. In the PRMT sequence, however, children’s agency and responsiveness in mathematics were more prominent than the mathematics that was made available to learn. Thus, the content and scope of the two sequences complement each other by offering diverse learning opportunities. While mathematical content occasionally recedes in PRMT, the children remain engaged in the activities. Furthermore, integrating play with mathematics makes mathematics important and meaningful for the participating children.

• Erfjord, Ingvald; Carlsen, Martin & Hundeland, Per Sigurd (2025). Playful learning in mathematics in the first years of schooling: Opportunities and challenges. A theoretical contribution. In Skott, Charlotte Krog; Blomhøj, Morten; Eckert, Andreas; Elicer, Raimundo; Herheim, Rune; Kristinsdóttir, Bjarnheiður; Larsen, Dorte Moeskær; Nortvedt, Guri A.; Nyström, Peter; Sigurjónsson, Jóhann Örn & Tamborg, Andreas Lindenskov (Ed.), Interplay between research and teaching practice in mathematics education : Proceedings of NORMA24, The tenth Nordic Conference on Mathematics Education, Copenhagen, 2024. Svensk förening för MatematikDidaktisk Forskning - SMDF. ISSN 9789198402483. p. 112–119. Full text in Research Archive
• Reid, David Alexander & Carlsen, Martin (2025). Designing learning activities to promote algebraic thinking: Equation solving in Grade 5. In Skott, Charlotte Krog; Blomhøj, Morten; Eckert, Andreas; Elicer, Raimundo; Herheim, Rune; Kristinsdóttir, Bjarnheiður; Larsen, Dorte Moeskær; Nortvedt, Guri A.; Nyström, Peter; Sigurjónsson, Jóhann Örn & Tamborg, Andreas Lindenskov (Ed.), Interplay between research and teaching practice in mathematics education : Proceedings of NORMA24, The tenth Nordic Conference on Mathematics Education, Copenhagen, 2024. Svensk förening för MatematikDidaktisk Forskning - SMDF. ISSN 9789198402483. p. 104–111. Full text in Research Archive Show summary

  The aim of this study is to give insights into the design, implementation, and re-design of a teachinglearning activity on algebra at fifth grade. The mathematical topic was linear equations. Drawing on algebraic thinking as a theoretical construct, two progressions are analyzed, from arithmetic equations to algebraic equations and from actions on concrete objects to symbolic manipulations. The study reports design principles developed from a pilot study and theory, and the design-based research process in which an algebra learning-teaching activity (ALTA) was co-designed by mathematics teachers and researchers, through which the design principles were revised. The revised design principles are reported.

• Reinhardtsen, Jorunn; Opheim, Linda Gurvin & Carlsen, Martin (2025). Developing algebra learning-teaching activities in collaboration with teachers in middle school. In Skott, Charlotte Krog; Blomhøj, Morten; Eckert, Andreas; Elicer, Raimundo; Herheim, Rune; Kristinsdóttir, Bjarnheiður; Larsen, Dorte Moeskær; Nortvedt, Guri A.; Nyström, Peter; Sigurjónsson, Jóhann Örn & Tamborg, Andreas Lindenskov (Ed.), Interplay between research and teaching practice in mathematics education : Proceedings of NORMA24, The tenth Nordic Conference on Mathematics Education, Copenhagen, 2024. Svensk förening för MatematikDidaktisk Forskning - SMDF. ISSN 9789198402483. p. 297–305. Full text in Research Archive Show summary

  In this paper we outline the theoretical and methodological foundations for a research project that aims to develop algebraic learning-teaching activities in cooperation with teachers. We describe a vision of how strands of algebraic reasoning may be integrated across topics in grades 5-7. Drawing on the Vygotskian concept of sense making we formulate design principles for algebra learningteaching activities (ALTAs). We discuss the importance of collaborating with teachers in a colearning agreement to make an impact in schools. Through working together on concrete lesson plans we came to learn more about each other’s different worlds and over time our goals became more aligned. Through our collaboration we developed design principles, such as to include unit plans that are detailed but flexible to suit different classrooms and nurture teacher autonomy, and the ideas, representations, and solving methods ought to be relevant beyond the grade where introduced.

• Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2024). The Knowledge Quartet as a Theoretical Lens to Explore Kindergarten Teachers’ Teaching of Mathematics, Teaching Mathematics as to be meaningful – Foregrounding play and children’s perspectives: Results from the POEM5 Conference, 2022. Springer Nature. ISSN 9783031376634. p. 131–144. doi: 10.1007/978-3-031-37663-4. Full text in Research Archive
• Kaloutsi, Konstantina; Reinhardtsen, Jorunn & Carlsen, Martin (2023). Designing mathematical tasks to promote preservice teachers’ algebraic reasoning and argumentation. In Drijvers, Paul; Csapodi, Csaba; Palmer, Hanna; Gosztonyi, Katalin & Kónya, Eszter (Ed.), Proceedings of the thirteenth Congress of the European Society for Research in Mathematics Education (CERME13). European Society for Research in Mathematics Education. ISSN 9789637031045. p. 568–575. Full text in Research Archive
• Maj-Tatsis, Bozena; Tzekaki, Marianna; Carlsen, Martin; Maffia, Andrea & Levenson, Esther (2022). Introduction to the papers of TWG 13: Early Years Mathematics. In Hodgen, Jeremy; Geraniou, Eirini; Bolondi, Giorgio; Feretti, Federica & Ferretti, Federica (Ed.), Proceedings of the 12th Congress of the European Society for Research in Mathematics Education (CERME12). European Society for Research in Mathematics Education. ISSN 9791221025378. p. 2124–2127. Full text in Research Archive
• Erfjord, Ingvald; Hundeland, Per Sigurd & Carlsen, Martin (2022). An analysis of a kindergarten teacher’s choices and justifications regarding teaching of a mathematical activity. In Hodgen, Jeremy; Geraniou, Eirini; Bolondi, Giorgio; Feretti, Federica & Ferretti, Federica (Ed.), Proceedings of the 12th Congress of the European Society for Research in Mathematics Education (CERME12). European Society for Research in Mathematics Education. ISSN 9791221025378. p. 2168–2175. Full text in Research Archive Show summary

  This paper aims to increase the insight into kindergarten teachers’ justification of their teaching. The study was done in a context with mathematical activities developed by the researchers in collaboration with the teachers. This is a context we consider as rich to reveal their choices and justifications made in advance of and during the teaching of a mathematical activity. Data from a semi-structured, post-teaching stimulated recall interview based on an activity with 5-year-old children was analysed employing the Knowledge Quartet proposed by Rowland et al. (2005). We identify seven choices made by the kindergarten teacher that reveal aspects of the kindergarten teacher’s knowledge-in-action and knowledge-in-interaction. She adapts the activity through questions, comments, particularities within the activities, and use of artefacts. Thus, she nurtures the children in their mathematical learning process.

• Reinhardtsen, Jorunn & Carlsen, Martin (2022). Calculational and analytical perspectives in introductory algebra: a theoretical contribution. In Hodgen, Jeremy; Geraniou, Eirini; Bolondi, Giorgio; Feretti, Federica & Ferretti, Federica (Ed.), Proceedings of the 12th Congress of the European Society for Research in Mathematics Education (CERME12). European Society for Research in Mathematics Education. ISSN 9791221025378. p. 596–603. Full text in Research Archive
• Lorange, Carl Andreas; Sjaastad, Jørgen & Carlsen, Martin (2022). Affordances and constraints of the Dragonbox School teaching material. In Hodgen, Jeremy; Geraniou, Eirini; Bolondi, Giorgio; Feretti, Federica & Ferretti, Federica (Ed.), Proceedings of the 12th Congress of the European Society for Research in Mathematics Education (CERME12). European Society for Research in Mathematics Education. ISSN 9791221025378. p. 2793–2800. Full text in Research Archive Show summary

  The aim of this paper is to analyze the affordances and constraints of the way dynamic representations are used in the digital learning lab 'The set line' from the Dragonbox School teaching material. The learning lab is designed for second graders. The starting point of our analysis is the task 18 + 6. Our analysis shows that 'The set line' offers affordances for the users' learning of addition and other aspects of the number concept because the regrouping involved in the addition of 18 and 6 is explicitly displayed by the dynamic representations in the learning lab. 'The set line' may also cause constraints for students' opportunities to learn the inherent mathematical concepts and relations because several operations are carried out automatically by the learning lab.

• Lorange, Carl Andreas; Sjaastad, Jørgen & Carlsen, Martin (2022). Grunnskolelærerstudenters erfaring med eBok-basert undervisning i matematikk. Uniped - Tidsskrift for universitets- og høgskolepedagogikk. ISSN 1500-4538. 45(3), p. 219–232. doi: 10.18261/uniped.45.3.6. Full text in Research Archive Show summary

  I denne artikkelen analyserer vi grunnskolelærerstudenters respons på en eBok-basert undervisningsform i matematikk. Denne eBoka besto av oppgaver med både skriftlige og videobaserte løsningsforslag. Oppgavene ble hentet fra tidligere gitte eksamensoppgaver knyttet til nasjonal deleksamen i matematikk. Formålet var å undersøke: a) hvordan studentene benyttet de ulike læringsressursene i eBoka, og b) på hvilke måter studentens bruk av læringsressursene hadde pragmatisk og epistemisk verdi (Artigue, 2002). Analysene bygger på kvantitative og kvalitative data fra en spørreundersøkelse (N = 60) om bruk av eBoka og viser at nesten alle studentene benyttet de videobaserte løsningsforslagene, mens litt under halvparten benyttet de skriftlige løsningsforslagene. Studentenes respons gir uttrykk for den pragmatiske verdien av bruken av læringsressursene. De fikk tips både i begynnelsen av løsningsprosessen og underveis om hvordan oppgavene kan løses, samt en sjekk på om de hadde løst oppgavene korrekt. Studentenes respons gir også uttrykk for den epistemiske verdien av bruken av læringsressursene. De fikk hjelp til å forstå hva oppgavene spurte om, de fikk hjelp til å forstå sin egen løsningsprosess, og de oppdaget andre måter å løse oppgavene på. Dette viser at eBoka ga grunnlag for matematisk meningsskaping blant grunnskolelærerstudentene.

• Wathne, Unni & Carlsen, Martin (2022). Third grade students’ multimodal mathematical reasoning when collaboratively solving combinatorial problems in small groups. Mathematical Thinking and Learning. ISSN 1098-6065. doi: 10.1080/10986065.2022.2099611. Full text in Research Archive Show summary

  The aim of this study is to investigate Norwegian primary school students’ multimodal mathematical reasoning when solving combinatorial problems. The data collection took place in four small groups of altogether thirteen 8–9 years old third-graders. Our study shows a variety of approaches used to solve the given combinatorial problems, such as count-all and grouping. These approaches were characterized by the students’ use of inscriptions that displayed all combinations and inscriptions that did not display all combinations. Moreover, the students used gestures such as pointing and sliding. The students’ multimodal reasoning was characterized by the ways their utterances, inscriptions, and gestures emerged and supplemented each other. The students’ pointing gestures mediated the intended mathematical meaning solely when combined with inscriptions displaying all possible combinations. Sliding gestures, on the other hand, did mediate the intended mathematical meaning when their inscriptions were not displaying all possible combinations. In this latter case, the shortcomings of their inscriptions were complemented and compensated by the sliding gestures. The students’ multimodal mathematical reasoning made explicit their combinatorial thinking, mediated the intended mathematical meaning, and facilitated their solving of the given combinatorial problems.

• Rege, Mari; Størksen, Ingunn; Solli, Ingeborg Caroline Foldøy; Kalil, Ariel; M., McClelland Megan & Braak, Dieuwer Ten [Show all 12 contributors for this article] (2021). The Effects of a Structured Curriculum on Preschool Effectiveness A Field Experiment. The Journal of human resources. ISSN 0022-166X. 59(2), p. 576–603. doi: 10.3368/jhr.0220-10749R3. Full text in Research Archive Show summary

  Abstract: This study tests an intervention that introduces a structured curriculum for five-year-olds into the universal preschool context of Norway, where the business as usual is an unstructured curriculum. We conduct a field experiment with 691 five-year-olds in 71 preschools and measure treatment impacts on children’s development in mathematics, language, and executive functioning. The nine-month intervention has effects on child development at post-intervention and the effects persist one year following the end of the treatment. The effects are mainly driven by the preschools identified as low-quality at baseline, indicating that a structured curriculum can reduce inequality in early childhood learning environments.

• Carlsen, Martin & Breive, Svanhild (2021). The nature of mathematical inquiry amongst kindergarten children: more than questioning and verbalisations. In Nortvedt, Guri A.; Buchholtz, Nils; Fauskanger, Janne; Hreinsdottir, Freyja; Hähkioniemi, Marcus; Jessen, Britta Eyrich; Kurvits, J.; Liljekvist, Yvonne; Misfeldt, Morten; Naalsund, Margrethe; Nilsen, Hans Kristian; Palsdottir, Gudbjørg; Portaankorva-Koivisto, Päivi; Radišić, Jelena & Werneberg, A. (Ed.), Bringing Nordic mathematics education into the future : Preceedings of Norma 20 : The ninth Nordic conference on mathematics education Oslo, 2021. SMDF, Swedish Society for Research in Mathematics Education. ISSN 9789198402438. Full text in Research Archive Show summary

  This volume presents Nordic mathematics education research, which will be presented at the Ninth Nordic Conference on Mathematics Education, NORMA 20, in Oslo, Norway, in June 2021. The theme of NORMA 20 regards what it takes or means to bring Nordic mathematics education into the future, highlighting that mathematics education is continuous and represents stability just as much as change.

• Hundeland, Per Sigurd; Carlsen, Martin & Erfjord, Ingvald (2020). Qualities in mathematical discourses in kindergartens. ZDM: Mathematics Education. ISSN 1863-9690. 52(4), p. 691–702. doi: 10.1007/s11858-020-01146-w. Full text in Research Archive Show summary

  In this study we investigated qualities of the mathematical discourse in four kindergarten classes in which kindergarten teachers and 5-year-old children engaged in mathematical learning activities. We analysed differences in the mathematical discourses in two experimental kindergarten classes and two control kindergarten classes, in a research and development project. The overarching research question guiding our study was as follows: what characterises the mathematical discourse unfolding in kindergarten classes? In our study we drew on the theoretical framework Mathematical Discourse in Instruction coined by Adler and Ronda, as we quantified the collected qualitative data. Our analyses identified significant characteristics of mathematical discourse with respect to the children’s opportunities to contribute with ideas and arguments. The discourse in the kindergartens differed both with respect to the extent and nature of verbal utterances among the participants, as well as the mathematical engagement nurtured amongst the children. Moreover, the mathematical discourse within the experimental kindergarten classes, to a greater extent than that in the control kindergarten classes, initiated opportunities for the participating children’s mathematical learning.

• Bruns, Julia; Carlsen, Martin; Eichen, Lars; Erfjord, Ingvald & Hundeland, Per Sigurd (2020). Situational perception in mathematics (SPiM) – Results of a cross-country study in Austria and Norway. In Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (Ed.), Mathematics education in the early years : Results from the POEM4 conference, 2018. Springer Nature. ISSN 9783030347758. p. 317–332. doi: 10.1007/978-3-030-34776-5_19. Full text in Research Archive
• Erfjord, Ingvald; Carlsen, Martin & Hundeland, Per Sigurd (2019). Characterising the mathematical discourse in a kindergarten. In Jankvist, Uffe Thomas; Heuvel-Panhuizen, Marja Van den & Veldhuis, Michiel (Ed.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education. European Society for Research in Mathematics Education. ISSN 9789073346758. p. 2257–2264. Full text in Research Archive
• Carlsen, Martin (2018). Upper secondary students’ mathematical reasoning on a sinusoidal function. Educational Studies in Mathematics. ISSN 0013-1954. 99(3), p. 277–291. doi: 10.1007/s10649-018-9844-1. Full text in Research Archive
• Breive, Svanhild; Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2018). Designing playful inquiry-based mathematical learning activities for kindergarten. In Benz, Christiane; Steinweg, Anna S; Gasteiger, Hedwig; Schöner, Priska; Vollmuth, Helene & Zöllner, Johanna (Ed.), Mathematics education in the early years. Results from the POEM3 conference 2016. Springer Publishing Company. ISSN 9783319782201. p. 181–205. doi: 10.1007/978-3-319-78220-1_10. Full text in Research Archive
• Hundeland, Per Sigurd; Erfjord, Ingvald & Carlsen, Martin (2017). A kindergarten teacher’s revealed knowledge in orchestration of mathematical activities. In Dooley, Thérèse & Gueudet, Ghislaine (Ed.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10). European Society for Research in Mathematics Education. ISSN 9781873769737. p. 1853–1860. Full text in Research Archive
• Carlsen, Martin (2016). Matematiske samtaler i barnehagen: Utfordringer og muligheter. In Herheim, Rune & Johnsen-Høines, Marit (Ed.), Matematikksamtaler. Undervisning og læring - analytiske perspektiv. Caspar Forlag. ISSN 9788290898736. p. 221–239. Full text in Research Archive
• Carlsen, Martin; Erfjord, Ingvald; Hundeland, Per Sigurd & Monaghan, John David (2016). Kindergarten teachers’ orchestration of mathematical activities afforded by technology: agency and mediation. Educational Studies in Mathematics. ISSN 0013-1954. 93(1), p. 1–17. doi: 10.1007/s10649-016-9692-9. Full text in Research Archive
• Erfjord, Ingvald; Carlsen, Martin & Hundeland, Per Sigurd (2015). Distributed authority and opportunities for children’s agency in mathematical activities in kindergarten. In Krainer, Konrad & Vondrova, Nada (Ed.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education. European Society for Research in Mathematics Education. ISSN 9788072908448. p. 1918–1924. doi: 10.1007/s10649-016-9692-9. Full text in Research Archive
• Carlsen, Martin (2015). Upper secondary students appropriating the tool of harmonic oscillation: The issue of resistance. In Silfverberg, Harry; Kärki, Tomi & Hannula, Markku S. (Ed.), Nordic research in mathematics education – Proceedings of NORMA14, Turku, June 3-6, 2014. The Finnish Research Association for Subject Didactics. ISSN 9789525993172. p. 267–276. Full text in Research Archive
• Isabwe, Ghislain Maurice Norbert; Reichert, Frank; Carlsen, Martin & Lian, Thomas Andreé (2014). Using Assessment for Learning Mathematics with Mobile Tablet Based Solutions. International Journal of Emerging Technologies in Learning (iJET). ISSN 1868-8799. 9(2). doi: 10.3991/ijet.v9i2.3219. Full text in Research Archive Show summary

  This article discusses assessment for learning in mathematics subjects. Teachers of large classes face the challenge of regularly assessing students’ ongoing mathematical learning achievements. Taking the complexity of assessment and feedback for learning as a background, we have developed a new approach to the assessment for learning mathematics at university level. We devised mobile tablet technology supported assessment processes, and we carried out user studies in both Rwanda and Norway. Results of our study indicated that students found it fruitful to be involved in assessing other students’ mathematics work, i.e. assessing fellow students’ answers to mathematical tasks. By being involved in the assessment process, the students expected mathematical learning gains. Their providing and obtaining of feedback to/from their fellow students using technology supported tools were highly appreciated as regards their own mathematical learning process.

• Hundeland, Per Sigurd; Carlsen, Martin & Erfjord, Ingvald (2014). Children’s engagement with mathematics in kindergarten mediated by the use of digital tools. In Kortenkamp, Ulrich; Brandt, Birgit; Benz, Christiane; Krummheuer, Götz; Ladel, Silke & Vogel, Rose (Ed.), Early mathematics learning. Selected papers of the POEM 2012 conference. Springer Science+Business Media B.V.. ISSN 9781461446774. p. 207–221. doi: 10.1007/978-1-4614-4678-1_13. Full text in Research Archive

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• Størksen, Ingunn; Braak, Dieuwer ten; Breive, Svanhild; Lenes, Ragnhild; Lunde, Svanaug & Carlsen, Martin [Show all 9 contributors for this article] (2024). Lekbasert læring - ressursbok for barnehage, skole og SFO. Cappelen Damm Akademisk. ISBN 9788202833763. 223 p. Full text in Research Archive
• Bjerre, Mette; Carlsen, Martin & Sunde, Pernille Bødtker (2024). Det ved vi om. Matematisk opmærksomhed i dagtilbud. Dafolo Forlag. ISBN 9788772343136. Full text in Research Archive
• Carlsen, Martin; Wathne, Unni & Blomgren, Gro (2024). Matematikk for barnehagelærere (4. utg.). Cappelen Damm Akademisk. ISBN 9788202792374. Full text in Research Archive
• Størksen, Ingunn; Braak, Dieuwer ten; Breive, Svanhild; Lenes, Ragnhild; Lunde, Svanaug & Carlsen, Martin [Show all 9 contributors for this article] (2020). Legebaseret læring: et forskningsbaseret førskoleoplæg. Akademisk Forlag, Danmark. ISBN 9788723541338. 232 p. Full text in Research Archive Show summary

  Alle børn skal have de bedste forudsætninger for at starte i skole. Det er derfor vigtigt at stimulere de områder, som baner vejen for en vellykket skolestart. Legebaseret læring er udviklet med netop dette formål. Materialet bygger på den nyeste internationale forskning inden for tidlig stimulering af sociale kompetencer, selvregulering, sprogudvikling og matematisk forståelse, og det indeholder et væld af aktiviteter, som understøtter børns udvikling inden for disse områder. Med Legebaseret læring får du helt konkrete anvisninger til, hvordan du kan understøtte læring gennem leg. Materialet rummer også ideer til, hvordan du kan sammensætte aktiviteter til sammenhængende forløb, udforme dagsplaner, årshjul mv. Legebaseret læring er udviklet og afprøvet i et tæt samarbejde mellem forskere og pædagoger fra mere end 80 daginstitutioner.

• Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2020). Mathematics education in the early years : Results from the POEM4 conference, 2018. Springer Nature. ISBN 9783030347758. 448 p. Full text in Research Archive
• Størksen, Ingunn; Braak, Dieuwer ten; Breive, Svanhild; Lenes, Ragnhild; Lunde, Svanaug & Carlsen, Martin [Show all 9 contributors for this article] (2019). Lekbaserat Lärande. Bonnierförlagen Lära. ISBN 9789178230594. 208 p. Full text in Research Archive
• Størksen, Ingunn; Braak, Dieuwer ten; Breive, Svanhild; Lenes, Ragnhild; Lunde, Svanaug & Carlsen, Martin [Show all 9 contributors for this article] (2018). Lekbasert læring - et forskningsbasert førskoleopplegg fra Agderprosjektet. Aschehoug & Co. ISBN 9788249219636. 231 p. Full text in Research Archive
• Carlsen, Martin; Wathne, Unni & Blomgren, Gro (2017). Matematikk for barnehagelærere (3. utgave). Cappelen Damm Akademisk. ISBN 9788202482671. 325 p. Full text in Research Archive
• Størksen, Ingunn; Braak, Dieuwer Ten; Breive, Svanhild; Lenes, Ragnhild; Lunde, Svanaug & Carlsen, Martin [Show all 9 contributors for this article] (2016). Lekbasert læring i barnehagen - Et forskningsbasert førskoleopplegg fra Agderprosjektet. Aschehoug & Co. ISBN 9788249218523. 227 p. Full text in Research Archive Show summary

  Forlag: GAN Aschehoug, H. Aschehoug & Co. (W. Nygaard) AS

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• Eliassen, Marie Winther; Hundeland, Per Sigurd & Carlsen, Martin (2024). MatteLandia - Lekbasert læring. Tangenten - Tidsskrift for matematikkundervisning. ISSN 0802-8192. Full text in Research Archive
• Carlsen, Martin; Wathne, Unni & Blomgren, Gro (2024). Matematikk for barnehagelærere - En lærebokpresentasjon. Full text in Research Archive
• Carlsen, Martin; Skreland, Lisbeth Ljosdal & Brodal, Per Alf (2024). Hva skjer med leken i den «lekbaserte læringen»? Full text in Research Archive
• Carlsen, Martin & Kristensen, Heidi (2024). Matematisk opmærksomhed i dagtilbud. Full text in Research Archive
• Larson, Niclas & Carlsen, Martin (2023). En kompleks episode. [Internet]. Apple Podcasts. Full text in Research Archive Show summary

  I sesongens 9. episode av Spøkelser etter avdøde størrelser har Niclas Larson og Martin Carlsen en semistrukturert samtale om utviklingen av de komplekse tallene. Episoden tar deg med tilbake til Cardano på 1500-tallet, og på reisen mot 2000-tallet støter vi på mange store matematikere som Euler og Gauẞ. Den store norske stjernen, Niels Henrik Abel, blir også nevnt, men mer sentral i episoden er en annen nordmann, nemlig Caspar Wessel. På slutten av 1700-tallet var Wessel den som introduserte den geometriske tolkningen av de komplekse tallene som i dag tilsvarer det komplekse tallplanet.

• Carlsen, Martin (2023). Playful learning of mathematics in the transition from kindergarten to school: Opportunities and challenges. Full text in Research Archive
• Reid, David Alexander & Carlsen, Martin (2023). An ALTA for Grade 5 Equation Solving. Full text in Research Archive
• Lorange, Carl Andreas; Sjaastad, Jørgen & Carlsen, Martin (2022). Affordances and constraints of the Dragonbox School teaching material. Full text in Research Archive
• Larson, Niclas & Carlsen, Martin (2022). Toppen av et toppforskningssenter. [Internet]. Apple Podcasts. Full text in Research Archive Show summary

  I 12. episode av Spøkelser etter avdøde størrelser får vi endelig svaret på spørsmålet som var tittel til 11. episode, nemlig om M. Carlsen spiser mye ris. Men framfor alt får vi vite mer om det prioriterte forskningssenteret MERGA og om den nye nasjonale forskerskolen. I episoden har Niclas Larson en semistrukturert samtale med Martin Carlsen, som er professor ved Institutt for matematiske fag på UiA og dessuten er leder for MERGA. Martin er også dedikert frisbeegolfspiller, så på slutten av episoden får vi vite litt mer om koblingen mellom matematikk og frisbeegolf.

• Reinhardtsen, Jorunn & Carlsen, Martin (2022). Calculational and analytical perspectives in introductory algebra: a theoretical contribution. Full text in Research Archive
• Carlsen, Martin (2022). Tenk på et tall. Full text in Research Archive
• Carlsen, Martin (2022). Matematisk oppmerksomhet i barnehagen. Full text in Research Archive
• Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2022). The Knowledge Quartet as a theoretical lens to explore kindergarten teachers’ teaching of mathematics. Full text in Research Archive
• Carlsen, Martin (2022). Masteroppgaven i GLU - Innledning til diskusjon. Full text in Research Archive
• Lorange, Carl Andreas; Sjaastad, Jørgen & Carlsen, Martin (2022). Grunnskolelærerstudenters erfaring med eBok-basert undervisning i matematikk. Full text in Research Archive
• Erfjord, Ingvald; Hundeland, Per Sigurd & Carlsen, Martin (2022). An analysis of a kindergarten teacher’s choices and justifications regarding teaching of a mathematical activity. Full text in Research Archive
• Lorange, Carl Andreas & Carlsen, Martin (2022). Grunnskolelærerstudenters erfaring med eBok-basert undervisning i matematikk. Full text in Research Archive
• Lorange, Carl Andreas & Carlsen, Martin (2022). DragonBox Skole: muligheter og begrensninger. Tangenten - Tidsskrift for matematikkundervisning. ISSN 0802-8192. 33(3), p. 39–44. Full text in Research Archive
• Ebbesen, Solfrid Øvrebø; Lorange, Carl Andreas & Carlsen, Martin (2022). Skal du bli mattelærer og strever med matematikken? Nå er det hjelp å få. [Journal]. Forskning.no. Full text in Research Archive
• Carlsen, Martin (2022). My experience from attending the same TWG at the CERME conferences – and why this is a good idea. Full text in Research Archive
• Carlsen, Martin (2021). Designing playful inquiry-based mathematical learning activities for kindergarten in Norway. Full text in Research Archive
• Carlsen, Martin (2021). Matematikkdidaktisk forskning på barnehagebarn - Hva vet vi? hva har vi funnet ut på UiA. Full text in Research Archive
• Carlsen, Martin (2021). Grunnleggende matematikkompetanse - essensielt for danning og sosioøkonomisk utvikling. In Nielsen, May-Brith Ohman & Høeg, Ida Marie (Ed.), Agder Vitenskapsakademi - Årbok 2020. Novus Forlag. ISSN 9788283900774. Full text in Research Archive
• Carlsen, Martin (2021). Designing playful inquiry-based mathematical learning activities for kindergarten in Norway. Full text in Research Archive
• Carlsen, Martin (2020). Grunnleggende matematikkompetanse - essensielt for danning og sosioøkonomisk utvikling. Full text in Research Archive
• Carlsen, Martin (2020). Early years mathematics education. Research at UiA - Contributions from the last decade. Full text in Research Archive
• Erfjord, Ingvald; Carlsen, Martin & Hundeland, Per Sigurd (2019). Characterising the mathematical discourse in a kindergarten. Full text in Research Archive
• Rege, Mari; Størksen, Ingunn; Solli, Ingeborg Caroline Foldøy; Kalil, Ariel; McClelland, Megan & Braak, Dieuwer ten [Show all 12 contributors for this article] (2019). Promoting Child Development in a Universal Preschool System: A Field Experiment. CESifo Working Papers. ISSN 1617-9595. p. 1–41. Full text in Research Archive
• Carlsen, Martin (2019). Lekende matematikkundervisning gir bedre læring. p. 22–23. Full text in Research Archive
• Bruns, Julia; Carlsen, Martin; Eichen, Lars; Erfjord, Ingvald & Hundeland, Per Sigurd (2018). Situational perception in mathematics (SPiM) – Results of a cross-country study in Austria and Norway. Full text in Research Archive
• Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2018). An analysis of two kindergarten teachers’ orchestration of mathematical activities: Choices and reasons. Full text in Research Archive
• Rege, Mari; Størksen, Ingunn; Solli, Ingeborg Foldøy; Kalil, Ariel; McClelland, Megan & Lenes, Ragnhild [Show all 11 contributors for this article] (2018). Effects of Childcare Quality on Child Development in a Generous Welfare State. Full text in Research Archive
• Rege, Mari; Størksen, Ingunn; Solli, Ingeborg Foldøy; Kalil, Ariel; McClelland, Megan & Lenes, Ragnhild [Show all 12 contributors for this article] (2018). Effects of Childcare Quality on Child Development in a Generous Welfare State. Full text in Research Archive
• Carlsen, Martin (2018). Problemløsning som arbeidsmåte i matematikk. Full text in Research Archive
• Solli, Ingeborg Foldøy; Rege, Mari; Størksen, Ingunn; Braak, Dieuwer ten; Lenes, Ragnhild & Lunde, Svanaug [Show all 11 contributors for this article] (2018). Effects of Childcare Quality on School Readiness Skills in a Generous Welfare State. Full text in Research Archive
• Rege, Mari; Størksen, Ingunn; Solli, Ingeborg Foldøy; Lenes, Ragnhild; Braak, Dieuwer ten & Breive, Svanhild [Show all 12 contributors for this article] (2018). Effects of Childcare Quality on Child Development in a Generous Welfare State. Full text in Research Archive
• Solli, Ingeborg Foldøy; Rege, Mari; Størksen, Ingunn; Kalil, Ariel; McClelland, Megan & Lenes, Ragnhild [Show all 12 contributors for this article] (2018). Effects of Childcare Quality on Child Development in a Generous Welfare State. Full text in Research Archive
• Carlsen, Martin & Wathne, Unni (2017). Primary students’ reasoning when collaboratively solving combinatorial problems in small groups. Full text in Research Archive
• Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2017). Agderprosjektet - Lekbasert læring av matematikk i barnehagen. Full text in Research Archive
• Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2017). Agderprosjektet - Lekbasert læring av matematikk i barnehagen. Full text in Research Archive
• Hundeland, Per Sigurd; Erfjord, Ingvald & Carlsen, Martin (2017). A kindergarten teacher’s revealed knowledge in orchestration of mathematical activities. Full text in Research Archive
• Carlsen, Martin (2017). Å forske på fagdidaktikk i barnehagen - Eksempler fra egen forskning. Full text in Research Archive
• Birkeland, Per Arne; Carlsen, Martin; Erfjord, Ingvald; Hundeland, Per Sigurd & Wathne, Unni (2016). Matematikklærere må kunne mer enn faget. p. 38–38. Full text in Research Archive
• Birkeland, Per Arne; Carlsen, Martin; Erfjord, Ingvald; Hundeland, Per Sigurd & Wathne, Unni (2016). Må kunne mer enn matte. 142(151), p. 20–20. Full text in Research Archive
• Hundeland, Per Sigurd; Wathne, Unni; Carlsen, Martin; Birkeland, Per Arne & Erfjord, Ingvald (2016). Mattelærere må kunne mer enn matte. Full text in Research Archive
• Birkeland, Per Arne; Carlsen, Martin; Erfjord, Ingvald; Hundeland, Per Sigurd & Wathne, Unni (2016). Mattelærere må kunne mer enn matte. p. 11–11. Full text in Research Archive
• Carlsen, Martin (2016). Antall, rom og form - et fagområde for alle !? Full text in Research Archive
• Breive, Svanhild; Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2016). Designing playful inquiry based mathematical activities for kindergarten. Full text in Research Archive
• Breive, Svanhild; Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2015). Lek og utforskning i matematikk i barnehagen - Arbeid med inquiry i barnehager i Vest-Agder. Full text in Research Archive
• Breive, Svanhild; Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2015). Tall og telling. Arbeid med tallbegrepet i barnehager i Aust-Agder. Full text in Research Archive
• Breive, Svanhild; Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2015). Tall og telling. Arbeid med tallbegrepet i barnehager i Vest-Agder. Full text in Research Archive
• Breive, Svanhild; Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2015). Lek og utforskning i matematikk i barnehagen - Arbeid med inquiry i barnehager i Aust-Agder. Full text in Research Archive
• Breive, Svanhild; Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2015). Matematikkaktiviteter og deres implementering i barnehager i Aust-Agder. Full text in Research Archive
• Breive, Svanhild; Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2015). Matematikkaktiviteter og deres implementering i barnehager i Vest-Agder. Full text in Research Archive
• Carlsen, Martin (2015). Tommel opp for digitale verktøy i undervisning. [Internet]. sornett.no. Full text in Research Archive
• Carlsen, Martin (2015). Et matematikkeventyr. [Journal]. Vetuva. Forskning og ny kunnskap om barnehage. Full text in Research Archive
• Carlsen, Martin (2015). Matematikk i barnehagen. Hvordan skape et godt læringsmiljø for ett- og toåringene? Full text in Research Archive
• Carlsen, Martin (2014). Fireåringer lærer matematikk med et museklikk. Full text in Research Archive
• Hundeland, Per Sigurd; Carlsen, Martin & Erfjord, Ingvald (2014). Kan man lære matematikk i barnehagen? 140(183), p. 22–22. Full text in Research Archive
• Carlsen, Martin; Erfjord, Ingvald & Hundeland, Per Sigurd (2014). Takk for Sørlandets kompetansefonds populærvitenskapelige pris. In Jahr, Ernst Håkon; Nossum, Rolf Tomas & Storesletten, Leiv (Ed.), Agder Vitenskapsakademi Årbok 2013. Portal forlag. ISSN 9788283140200. p. 140–142. Full text in Research Archive
• Carlsen, Martin (2014). Om bruk av nettbrett i undervisning på skolen. [Radio]. NRK. Full text in Research Archive

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