Torulf Palm

Mathematical reasoning requirements in Swedish upper secondary level assessments

We investigate the mathematical reasoning required to solve the tasks in the Swedish national tests and a random selection of Swedish teacher-made tests. The results show that only a small proportion of the tasks in the teacher-made tests require the students to produce new reasoning and to consider the intrinsic mathematical properties involved in the tasks. In contrast, the national tests include a large proportion of tasks for which memorization of facts and procedures are not sufficient. The conditions and constraints under which the test development takes place indicate some of the reasons for this discrepancy and difference in alignment with the reform documents.

Features and Impact of the Authenticity of Applied Mathematical School Tasks

In this paper the issue of the authenticity of applied mathematical school tasks is discussed. The paper includes a description of a framework for reflection, analysis and development of authentic tasks. Its possible uses are exemplified by two studies. One of the studies is an analysis of in what way and to what extent the applied tasks included in the national assessments in Finland and Sweden are, or are not, authentic. In the second example the framework is used in a study of the impact of authenticity on the students’ sense making in word problem solving.

Assessing mathematical competencies : an analysis of Swedish national mathematics tests

ABSTRACT Internationally, education reform has been directed towards describing educational goals that go beyond topic and content descriptions. The idea of mathematical competencies describes such goals. National tests have been seen as one way of communicating these goals and influence teaching. The present study analyses Swedish national tests in mathematics, and seeks evidence about the extent to which they represent these competencies and may play a role in reforming teaching. The results show that the national tests assess all competencies. However, the study also shows a limited focus on the competencies’ interpretation and evaluation aspects. Thus, the tests do not fully capture the complex nature of the competencies. This may cloud the reform message and restrict the possibilities for the tests to function as levers for reform.

Characteristics of improved formative assessment practice

ABSTRACTAn earlier study showed that the changes in teachers’ classroom practice, after participation in a professional development program in formative assessment, significantly improved student achievement in mathematics. The teachers in that study were a random selection of Year 4 teachers in a Swedish mid-sized municipality. In the present study, we analyse and describe the characteristics of these changes in classroom practice, which were based on a combination of various strategies for formative assessment. Data were collected through teacher interviews and classroom observations. The teachers implemented many new activities that strengthened a formative classroom practice based on identifying student learning needs and modifying the teaching and learning accordingly. The characteristics of the changes the teachers made reveal the complexity of this formative assessment practice and why such developments of practice are likely to require major changes in most teachers’ practices. We also discuss how...