Kognitive krav og forståelse av funksjoner : En studie av oppgaver i to lærebøker i Matematikk 1P

Abstract

The purpose of this study is to investigate how demanding tasks given in schooltextbooks and written exam in the subject Matematikk 1Pare. I havestudied tasks given within the subject of functions, andhow the tasks allowfor a rich understanding of functions. Mathematics is a subjectwhere the textbook is an important source ofboth information and tasks. It is therefore importantthat these tasks are adapted to the students’different levels,and that they provide theopportunity for good understanding. This study aims to give an answer to the following research questions: -AT which cognitive levels are the students challenged in the textbooks’tasks in Matematikk 1P-How is the difficulty level of tasks in textbooks compared to tasks given ina written exam in Matematikk 1P?-What opportunitiesfor a rich understanding of functions in Matematikk 1Pare given by the tasks in two different textbooks. This was studied by looking at tasks in two different textbooks, Sinus 1Pand Matematikk 1P, and tasks given in written exams in 1P over the last four years.I have categorized the tasks according tothe cognitive demands they give students, andby which transformations of semiotic representations that are used in the tasks. My analysis is based on an already existing model of analysis presented by Brändström (2005)anddeveloped a model that fits my research questions. The results from this study show that the students work a lotusing procedures in tasks, both in textbooks and written exams. Among these tasks aretypical algorithmic tasks wherethe focus isgetting the right answer, but for the most tasksthe students need to understand the meaning behind the procedure. The analyzed tasks use many conversions between different forms of representatio ns for functions, with fewerconversionsto or from a numerical table.From a teacher’s point of view this study can make you more aware of what challenges students face with different tasks, and what type of understanding the tasks can give. You can also become more aware of the types of tasks you find in textbooks in 1P. It is then importantfor teachersto be able to give all students challenges at their level and be critical tothe tasks theygive to the students. This study also provides insight into different ways of categorizing tasks, which can be used to get an overview of different aspects of the tasks.