Abstract
From a system theoretically grounded point of view, a hierarchy of primary and secondary impact factors influencing the mathematics teacher’s choice to use practical activities in mathematics teaching is suggested initially in the article. A study, based on qualitative responses from mathematics teachers, then gives grounds for suggesting that a hierarchy of impact factors regarding the choice to use a practical activity in mathematics teaching must include more than just a binary clustering of primary and secondary impact factors. The teacher’s everyday life experience, knowledge of pupils’ everyday life experience, and the teacher’s conscience are suggested examples of impact factors that might call for the introduction of a new level, as they are primary impact factors that seem to depend on adaptation to responses at the secondary impact factor level. This coincides with demands for strengthening of mathematical literacy in school mathematics and more independence for the teacher when it comes to teaching of mathematics.
Highlights
Practical activities, here defined to include all forms of engagement where the pupil uses physical concretes while carrying out the activity at hand (Haara & Smith, 2009), for visualization, investigation and application of mathematics, are considered integral to school mathematics (OECD; 2013; Haara, 2011)
What may make the mathematics teacher choose to make use of a leek to concretize geometrically the algebraic deduction of the area of a circle or the essence of integration? The essence of integration can be concretized by showing how the almost rectangular areas of the rings that make up the cross section of the vegetable, are the area between the curve of the circumference of the circle with a variable radius and the “radius‐ axis”
The analysis showed that in addition to impact factors already labelled as primary or secondary, the teachers put emphasis on some impact factors that are neither solely primary nor solely secondary impact factors
Summary
Here defined to include all forms of engagement where the pupil uses physical concretes while carrying out the activity at hand (Haara & Smith, 2009), for visualization, investigation and application of mathematics, are considered integral to school mathematics (OECD; 2013; Haara, 2011). Handal & Lauvås, 1987; Shulman, 1987), and on teaching of mathematics in particular (Franke, Kazemi & Battey, 2007; Koehler & Grouws, 1992) All these influential elements, circumstances and qualities are hereafter referred to as impact factors. Examples of what is comprised by this definition are brought up explicitly later in the article The influence from such impact factors on the teacher’s choice of using a practical activity in the teaching, is less explained. The essence of integration can be concretized by showing how the almost rectangular areas of the rings that make up the cross section of the vegetable, are the area between the curve of the circumference of the circle with a variable radius and the “radius‐ axis” (the first‐axis). Impact factors of the latter kind, are for instance expectations from the pupils or teacher colleagues, the textbook or the national curriculum
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