A selection from Stockholm University publication database

• Mean, median, and mode in school years 4–6: A study about aspects of statistical literacy

  2023. Karin Landtblom.

  Thesis (Doc)

  This thesis explores different aspects of statistical literacy such as mathematical knowledge, context knowledge, use of words, and conceptions. The focus is on measures of central tendency: mean, median, and mode, and school years 4–6 (ages 10–13). The thesis contains of five papers and the phenomenon is studied in different contexts. In the first three papers, data is generated through a questionnaire answered by prospective teachers, teachers, and students in grade 6. In papers 4–5, second hand data is generated through textbook analysis where all tasks about the measures in seven different textbook series were analysed.

  Papers 1–3 showed that all respondent groups, primarily express procedural knowledge. They sometimes mix up the definitions of mean and median. Mean appears to be the most familiar measure and different contexts appropriate for mean are suggested. Median and mode appear to be less familiar, especially median which according to the students only exists in a school context. All respondent groups show several ways to express the mean using different colloquial connotations. Median and mode on the other hand do not bring any connotations, leading to difficulties to express explanations. For mode, some students used a homonym that gives a wrong meaning to the concept.  This implies that the support for understanding mean, based on colloquial words, is not available for median or mode. 

  The results from paper 4 show a high proportion of procedural tasks dealing with above all quantitative values for mode. Only one textbook definition of mode exemplified with qualitative values. In paper 5, tasks were examined out of mathematical properties related to input object, transformation, and output object. Here, tasks about both mean, median, and mode were examined. The results show that the distribution of the tasks was skew, meaning that students have different opportunities to learn various mathematical properties of the three concepts, something that was even more complex given that in many tasks, the mathematical properties in focus were implicit. 

  Overall, statistical literacy according to the results generated in the five different studies, appear to be pre-dominantly about numbers and procedures. Very little attention seems to be on contextual knowledge, something that is crucial in statistical literacy.  

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• Teachers and prospective teachers’ conceptions about averages

  2019. Karin Landtblom, Lovisa Sumpter. Journal of Adult Learning, Knowledge and Innovation

  Article

  In this paper, we explore prospective teachers and teachers’ conceptions about averages. The results show that when talking about which of the averages that is easiest and hardest to explain, respectively, the two groups differ in their responses. When teachers’ motivations most often are based on pedagogical explanations, the prospective teachers indicate conceptions based on personal experiences, often linked to procedures. When studying the conceptions about which of the averages that is most and least useful, the results indicate that there is no difference between the two groups. Mean is considered most useful, similar to what has been reported in previous studies, and mode is considered least useful by both groups. Few of the respondents recognize the mathematical properties of averages, particularly that “usefulness” is linked to which data that is in focus. The implications of the results are discussed.

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• Is data a quantitative thing? An analysis of the concept of the mode in textbooks for grade 4-6

  2018. Karin Landtblom. Looking back, looking forward

  Conference

  This paper presents analyses of seven popular Swedish textbooks for grades 4-6 examined for their presentation of statistics, focusing on average mode. Since textbooks in mathematics have great impact on both teaching and content in Swedish classrooms, it is of interest to examine both definitions and tasks. Tasks and definitions were analysed to identify quantitative or qualitative context. Tasks were also analysed whether they evoke procedural or conceptual knowledge. Findings suggest an excess of quantitative data in the context of the tasks and definitions, which may be a consequence of the ambiguity of vocabulary used. Findings also show an overwhelming focus on procedural knowledge and, in some cases, doubtful use of levels of measure in the tasks. These findings have implications for future understanding.

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• Prospective Teachers’ Conceptions of the Concepts Mean, Median and Mode

  2018. Karin Kihlblom Landtblom. Students' and Teachers' Values, Attitudes, Feelings and Beliefs in Mathematics Classrooms, 43-52

  Chapter

  This paper examines the conceptions of mean, median and mode expressed by prospective teachers. A constant comparative method was used to analyse responses to a questionnaire. The results identified prospective teachers to express procedural knowledge rather than conceptual knowledge. Their descriptions resonate with definitions of the averages, with very few comments on how to teach average and statistical literacy. The results of this research have implications to inform essential course content in teaching statistics on teacher education programmes in the future.

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• Elevers agerande och kommunikation i IKT -stödda aktiviteter

  2012. Karin Kihlblom Landtblom, Kerstin Pettersson, Lisa Björklund Boistrup.

  IKT (informations- och kommunikationsteknologi) används i allt högre omfattning i undervisningen. Frågan är om och hur undervisningen förändras i och med detta. I denna studie har syftet varit att studera hur användningen av IKT inverkar på elevernas agerande i några olika aktiviteter i matematik, vissa utförda med stöd av IKT. Aktiviteterna har studerats utifrån hur eleverna har agerat samt hur de har kommunicerat i dessa aktiviteter. Situationerna har varit multimodala vilket gör att eleverna fått tillgång till olika representationer av funktioner, vilket utgör det matematiska innehållet för studien.

  Elevers agerande och kommunikation har dokumenterats i tre olika aktiviteter med videokamera. Datamaterialet har transkriberats och analyserats genom interaktionsanalys. Vid analysen har ett ramverk bestående av socialsemiotik och affordance använts.

  Resultaten visar att elever söker efter liknande sätt att agera oavsett om de använder IKT eller inte, framförallt att hitta vägar för att kontrollera sina svar. Resultaten visar även att eleverna använder olika semiotiska resurser i sin kommunikation samt att de tillgängliga representationerna påverkar valet av semiotisk resurs. Det är sällan som en talad mening ger hela budskapet, meningsutbyten sker i regel genom en interaktion mellan olika resurser. Videofilmning har varit en användbar metod för att dokumentera olika semiotiska resurser.

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• OPPORTUNITIES TO LEARN MEAN, MEDIAN, AND MODE AFFORDED BY TEXTBOOK TASKS

  2023. Karin Landtblom. Statistics Education Research Journal 22 (3)

  Article

  This research paper examines tasks related to mean, median, and mode in seven Swedish textbook series for students aged between 10–13 years. The tasks were analysed based on context, mathematical properties, input and output objects, and transformations. These categories allowed for a thorough analysis of the opportunities afforded to students to understand these measures. The analysis revealed that most tasks focus on the mean and on procedural transformations with quantitative values. The findings suggested that the textbooks do not afford enough explicit context for students to develop a deep understanding of the mathematical properties of different measures of central tendency. By analysing various textbooks, a broader understanding of the learning opportunities afforded to students was gained. The discussion includes the implications of these results for task design.

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Show all publications by Karin Kihlblom Landtblom at Stockholm University