In recent decades, technology has influenced various aspects of assessment in mathematics education: (1) supporting the assessment of higher-order thinking skills in mathematics, (2) representing authentic problems from the world around us to use and apply mathematical knowledge and skills, and (3) making the delivery of tests and the analysis of results through psychometric analysis more sophisticated. We argue that these developments are not pushing mathematics education in the same direction, however, which creates tensions. Mathematics education—so essential for educating young people to be creative and problem solving agents in the twenty-first century—is at risk of focusing too much on assessment of lower order goals, such as the reproduction of procedural, calculation based, knowledge and skills. While there is an availability of an increasing amount of sophisticated technology, the related advances in measurement, creation and delivery of automated assessments of mathematics are however being based on sequences of atomised test items. In this article several aspects of the use of technology in the assessment of mathematics education are exemplified and discussed, including in relation to the aforementioned tension. A way forward is suggested by the introduction of a framework for the categorisation of mathematical problem situations with an increasing sophistication of representing the problem situation using various aspects of technology. The framework could be used to reflect on and discuss mathematical assessment tasks, especially in relation to twenty-first century skills.
DOCUMENT
We investigated whether Early Algebra lessons that explicitly aimed to elicit mathematical discussions (Shift-Problem Lessons) invoke more and qualitatively better mathematical discussions and raise students’ mathematical levels more than conventional lessons in a small group setting. A quasi-experimental study (pre- and post-test, control group) was conducted in 6 seventh-grade classes (N =160). An analysis of the interaction processes of five student groups showed that more mathematical discussions occurred in the Shift-Problem condition. The quality of the mathematical discussions in the Shift-Problem condition was better compared to that in the Conventional Textbook condition, but there is still more room for improvement. A qualitative illustration of two typical mathematical discussions in the Shift-Problem condition are provided. Although students’ mathematical levels were raised a fair amount in both conditions, no differences between conditions were found. We concluded that Shift-Problem Lessons are powerful for eliciting mathematical discussions in seventh-grade Shift-Problem Early Algebra Lessons.
DOCUMENT
It is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing the appearances of history of mathematics in curriculum materials. This framework consists of four formats that are entitled speck, stamp, snippet, and story. Characteristic properties are named for each format, in terms of size, content, location, and function. The formats are related to four ascending levels of cognitive demand. We describe how these formats, together with design principles that are also derived from the history of mathematics, can be used to raise the cognitive level of existing tasks and design new tasks. The combination of formats, cognitive demand levels, and design principles is called the 4S-model. Finally, we advocate that this 4S-model can play a role in mathematics teacher training to enable prospective teachers to reach higher cognitive levels in their mathematics classrooms.
DOCUMENT
