Quality in Icelandic mathematics teaching: Cognitive activation in mathematics lessons in a Nordic context

The thesis is published openly. Paper I is published openly in an English translation. Paper II is published openly in the publisher's version. Paper III is uploaded as an accepted manuscript, but not published openly as a modified version will be published in Nordic Studies in Mathematics Education (NOMAD). Its main results are presented in the thesis.
The doctoral research project underpinning this dissertation was aimed at developing a deeper understanding of cognitive activation in mathematics teaching in Iceland and in a Nordic context through classroom video observations and student perceptions. Ten mathematics teachers in Iceland participated. Three to four consecutive lessons in grade 8 were video-recorded. In total, 34 lessons in Iceland were analysed using the observation system PLATO. Mathematical tasks were identified and analysed using the Task Analysis Guide. The students, aged 13–14 (N = 217), responded to the Tripod student perception survey and their responses were compared to the PLATO observation scores. Specific lessons where cognitive activation scored high were selected for further analysis, two from each country: Iceland, Denmark, Norway, and Sweden. These eight lessons were analysed qualitatively in terms of teacher-student interactions and instructional format. The findings show limited evidence of cognitive activation in a majority of mathematics lessons in Iceland. Lesson time was primarily used for students’ individual work and the way teachers implemented tasks commonly resulted in low observation scores. The task analysis showed that most tasks were aimed at procedural fluency with limited connections to understanding mathematical concepts. The connection between the observation scores and student perceptions as indicators of cognitive activation was weak. Variance in student ratings was generally greater within classrooms than between them. The qualitative analysis of the outstanding Nordic mathematics lessons showed a variety of topics and instructional formats. Group-work and whole-class discussions were dominant, but all lessons included brief intervals of whole-class direct instruction. Many of these lessons had short sprints of “traditional” individual work. The teaching in these lessons was exemplified by an emphasis on student understanding through mathematical connection-making, frequent shifts between types of interactions, use of explicit student roles in the classroom to facilitate student engagement, and formative feedback.
Í rannsókninni sem þessi doktorsritgerð byggir á var miðað að því að þróa skilning á hugrænni virkjun í stærðfræðikennslu á Íslandi og á Norðurlöndum með því að rýna kerfisbundið í myndbandsupptökur úr kennslustundum og greina nemendakönnun. Tíu stærðfræðikennarar á Íslandi tóku þátt. Þrjár til fjórar aðliggjandi kennslustundir í 8. bekk voru teknar upp á myndband. Í heild voru 34 kennslustundir greindar með greiningarrammanum PLATO. Stærðfræðileg viðfangsefni voru greind með The Task Analysis Guide. Nemendur á aldrinum 13-14 ára (N = 217) svöruðu Tripod nemendakönnuninni og svör þeirra voru borin saman við athugunargildi út frá myndbandsgreiningu með PLATO. Til nánari greiningar voru valdar kennslustundir þar sem hugræn virkjun var metin á háu stigi, tvær frá hverju landi: Íslandi, Danmörku, Noregi og Svíþjóð. Þessar átta kennslustundir voru greindar eigindlega út frá bæði samskiptum kennara við nemendur og kennslusniði. Niðurstöðurnar sýna að athugunargildi fyrir hugræna virkjun voru lág í meirihluta kennslustundanna frá Íslandi. Tíminn í kennslustundunum var að mestu notaður til einstaklingsvinnu nemenda og útfærsla kennarans á verkefnum leiddi oft til þess að gildi voru lág. Greining stærðfræðilegu viðfangsefnanna sýndi að flest verkefni miðuðu að færni nemenda í að beita aðferðum á meðan tengsl við skilning á stærðfræðilegum hugtökum voru takmörkuð. Tengslin milli athugunargilda og skynjun nemenda sem mælinga á hugrænni virkjun voru veik. Dreifni í svörum nemenda var almennt meiri innan nemendahópa en á milli þeirra. Eigindleg greining á norrænu kennslustundunum sem metnar voru á háu stigi sýnir bæði fjölbreytt stærðfræðileg efnistök og kennslusnið. Hópvinna og bekkjarumræða voru fyrirferðarmikil snið, en allar kennslustundir innihéldu beina kennslu yfir stuttan tíma. Margar kennslustundir höfðu „hefðbundna“ einstaklingsvinnu í stuttum sprettum. Kennslan í þessum kennslustundum einkenndist af áherslu á stærðfræðilegan skilning nemenda í gegnum tengsl stærðfræðilegra hugtaka, tíðar breytingar á tegundum samskipta, skýr hlutverk nemenda í skólastofunni til að stuðla að þátttöku þeirra, og endurgjöf til leiðsagnar.
The Icelandic Research Fund (Rannsóknasjóður Grant 206754-051 through University of Iceland, School of Education), QUINT (Nordforsk Grant 87663 through University of Oslo, Department of Teacher Education and School Research, and the QUINT mobility fund), University of Iceland’s Doctoral Student Travel Fund (Ferðasjóður doktorsnema), and the Steingrímur Arason Memorial Fund (Styrktarsjóður Steingríms Arasonar)