need to know how to assess practical geometry
Answers
A lot of research has indicated that the way students are taught has a strong influence and impact on their ideas about the subject and how the subject should be taught. In 1908 at the International Congress of Mathematicians in Rome the great mathematician Felix Klein (1849 - 1925) talked about the paradox of double forgetting. The essence of the paradox is the life experience of young teachers who have to forget about a lot of university training and its scientific thinking to successfully teach mathematics. This phenomenon currently persists at Slovak primary and secondary schools. The problem is especially striking in teaching geometry. Many Slovak and Czech teachers agree that geometry has many applications in everyday life, but there is not enough “real-life” everyday problems in Slovak mathematics textbooks which are structured according to the deductive approach to teaching and learning. Based on the concept of realistic mathematics education, we deal with the implementation of special geometrical tasks called topographical tasks in teacher training. Our findings are based on real experiences teaching through workshops devoted to topographical tasks which were realized during two school lessons. In the conclusion we analysed the benefits of this new approach to active teaching. The studentś solutions to the tasks and their methodological analysis are included, too.
Assessment should enhance mathematics learning and support good instructional practice.
This principle has important implications for the nature of assessment. Primary among them is that assessment should be seen as an integral part of teaching and learning rather than as the culmination of the process.1 As an integral part, assessment provides an opportunity for teachers and students alike to identify areas of understanding and misunderstanding. With this knowledge, students and teachers can build on the understanding and seek to transform misunderstanding into significant learning. Time spent on assessment will then contribute to the goal of improving the mathematics learning of all students.
The applicability of the learning principle to assessments created and used by teachers and others directly involved in classrooms is relatively straightforward. Less obvious is the applicability of the principle to assessments created and imposed by parties outside the classroom. Tradition has allowed and even encouraged some assessments to serve accountability or monitoring purposes without sufficient regard for their impact on student learning.