Abstrakta och konkreta ting i geometrilandskapet : Varför elever i årskurs 7-9 har lätt och svårt i geometriområdet samt vad läraren gör för att underlätta elevernas förståelse

Sammanfattning: Geometry is an area in mathematics that is considered not abstract, on the contrary from other areas in mathematics. As geometry is considered an unabstracted area in mathematics, why has students around the world difficulties with geometry? TIMSS (Trends in International Mathematics and Science Study) has shown that Swedish students in 8th grade has difficulties in algebra and geometry. The study focuses on why secondary school students’ have easy to understand some parts in geometry and why they have difficulties in other parts. Furthermore the study focuses on strategies teachers use to facilitate understanding in geometry. The study is carried out by interviewing six teachers in secondary school. The interviews are recorded and transcribed for enabling thematic analysis. The result shows that teachers experiences that students have easy to understand the first dimension (length and perimeter) and easy to understand geometrical objects as for example rectangular shapes. The reason behind the easiness is that these elements in geometry is known for the students, easy for the teachers to explain and not abstract. The students have difficulties comprehending two and especially three dimensional objects, difficult geometrical objects as circular objects, objects where the height is “situated” outside the object and irregular figures, unit conversions and concepts in geometry. The reasons behind these difficulties are mainly: the elements and methods are unfamiliar and abstract to the students. The abstraction in geometry are shown as comprehending how big or small sizes are in two and three dimensions and difficulties to comprehend the big discrepancy between the numbers in unit conversion, Teachers also observe that students have difficulties in visualizing and manipulating objects. These results show that what is known and not abstract are the opposite for what students have difficulties with, i.e. unknown and abstract. The strategies the teachers use are mostly to concretize the difficulties in geometry and in that way show students why it is valid. Other strategies are concerning with building a strong foundation in geometry, to combine geometry with other subjects in school and using students prior knowledge to build new knowledge. The red articles agrees with the result from the study.