André Heck

Mathematics on the threshold

Lowering the dropout rate of incoming mathematics and science students, and enhancing the provision of mathematics support for freshmen are two important aims of the University of Amsterdam. The approach recently adopted to support first year students is to set up a diagnostic pretest and posttest and use these tests to identify students being at risk of failing their mathematics courses and other modules in the first year. Follow-up procedures are implemented and computer algebra based assessment and practise of mathematics skills play an important role in it. In this paper we describe this approach and its success.

In a hurry to work with high-speed video at school?

Casio Computer Co., Ltd., brought in 2008 high‐speed video to the consumer level with the release of the EXILIM Pro EX‐F1 and the EX‐FH20 digital camera.® The EX‐F1 point‐and‐shoot camera can shoot up to 60 six‐megapixel photos per second and capture movies at up to 1200 frames per second. All this, for a price of about US

Giving students the run of sprinting models

1000 at the time of introduction and with an ease of operation that allows high school students to work in 10 minutes with the camera. The EX‐FH20 is a more compact, more user‐friendly, and cheaper high‐speed camera that can still shoot up to 40 photos per second and capture up to 1000 fps. Yearly, new camera models appear and prices have gone down to about US

Gait analysis by high school students

250–300 for a decent high‐speed camera. For more details we refer to Casios website.1

BIRD'S-EYE VIEW OF GROBNER BASES

A biomechanical study of sprinting is an interesting task for students who have a background in mechanics and calculus. These students can work with real data and do practical investigations similar to the way sports scientists do research. Student research activities are viable when the students are familiar with tools to collect and work with data from sensors and video recordings and with modeling tools for comparing simulation and experimental results. This article describes a multipurpose system, named COACH, that offers a versatile integrated set of tools for learning, doing, and teaching mathematics and science in a computer-based inquiry approach. Automated tracking of reference points and correction of perspective distortion in videos, state-of-the-art algorithms for data smoothing and numerical differentiation, and graphical system dynamics based modeling are some of the built-in techniques that are suitable for motion analysis. Their implementation and their application in student activities in...

Understanding the Physics of Bungee Jumping

Human walking is a complicated motion. Movement scientists have developed various research methods to study gait. This article describes how a high school student collected and analysed high quality gait data in much the same way that movement scientists do, via the recording and measurement of motions with a video analysis tool and via electromyography, i.e., the measurement of muscle activity. Physics, biology, and mathematics come together in this practical investigation work at a rather high level. It shows that science learning at school can resemble science practice in research laboratories, provided that students have adequate tools.

The Role of Digital, Formative Testing in e-Learning for Mathematics: A Case Study in the Netherlands

In this expository chapter we give a short introduction to Grobner basis theory and its main applications. It is a long write-up of the overview paper [127]. Quite a few books [3, 16, 37, 66, 85, 91, 98, 156] and overview articles [5, 35, 36, 61, 105, 175] on Grobner basis theory already exist. This one differs in style and in choice of examples. The style is concrete: examples illustrate the main techniques and the use of a computer algebra system, in our case Maple, is not shunned. Most examples are taken from the science literature and illustrate the Grobner basis techniques on real applications.

Introduction to Computer Algebra

Changing mass phenomena like the motion of a falling chain, the behaviour of a falling elastic bar or spring, and the motion of a bungee jumper surprise many a physicist. In this article we discuss the first phase of bungee jumping, when the bungee jumper falls, but the bungee rope is still slack. In instructional material this phase is often considered a free fall, but when the mass of the bungee rope is taken into account, the bungee jumper reaches acceleration greater than g. This result is contrary to the usual experience with free falling objects and therefore hard to believe for many a person, even an experienced physicist. It is often a starting point for heated discussions about the quality of the experiments and the physics knowledge of the experimentalist, or it may even prompt complaints about the quality of current physics education. But experiments do reveal the truth and students can do them supported by information and communication technology (ICT) tools. We report on a research project done by secondary school students and use their work to discuss how measurements with sensors, video analysis of self-recorded high-speed video clips and computer modelling allow study of the physics of bungee jumping.

Ramp it up and down

Repeated formative, diagnostic assessment lies at the heart of student-centred learning, providing students with a continuous stream of information on the mastery of different topics and making suggestions to optimize the choice of subsequent learning activities. When integrated into a system of e-learning, formative assessment can make that steering information instantaneous, which is a crucial aspect for feedback in student-centred learning. This empirical study of the role of formative assessment in mathematics e-learning focuses on the important merit of integrating these assessments into a system of state or national testing. Such tests provide individual students with crucial feedback for their personal learning, teachers with information for instructional planning, and curriculum designers with information on the strengths and weaknesses in the mastery states of students in the program and the need to accommodate any shortcomings. Lastly, they provide information on the quality of education at state or national level and a means to monitor its development over time. We shall provide examples of these merits based on data from the national project ONBETWIST, part of the Dutch e-learning program Testing and Test-Driven Learning.ResumenLa repetida evaluación diagnóstica y formativa es uno de los elementos clave del aprendizaje centrado en el alumno, ya que ofrece a los estudiantes un flujo continuo de información sobre su nivel de conocimientos en distintas materias y permite optimizar la posterior elección de actividades de aprendizaje. Cuando se integra en un sistema de aprendizaje virtual, la evaluación formativa puede convertir esta información en instantánea, lo que constituye un aspecto crucial para el retorno de información en un aprendizaje centrado en el alumno. Este estudio empiríco sobre el papel de la evaluación formativa en el aprendizaje virtual de matemáticas se centra en la ventaja de integrar estas evaluaciones en un sistema national o estatal de exámenes. Estos exámenes proporcionan a los estudiantes una información crucial para su aprendizaje personal; suministran a los profesores los datos necesarios para llevar a cabo la planificación docente; y ofrecen a los encargados de elaborar los planes de estudio la información necesaria sobre las fortalezas y las debilidades de los estudiantes de cada programa y la necesidad de solucionar cualquier deficiencia. En último lugar, ofrecen información sobre la calidad de la enseñanza a escala national o estatal y son un medio para controlar su desarrollo a través del tiempo. Daremos ejemplos de todas estas ventajas según los datos del proyecto nacional ONBETWIST, que forma parte del programa de aprendizaje virtual holandés «Los exámenes y el aprendizaje basado en exámenes».

Using SOWISO to realize interactive mathematical documents for learning, practising, and assessing mathematics

The goal of this chapter is to briefly describe what computer algebra is about, present a little history of computer algebra systems, give some examples of computer algebra usage, and discuss some advantages and limitations of this new technological tool. We end with a sketch of the design of the Maple system.