|Li Jun (China)||email@example.com|
|Lionel Pereira-Mendoza (Singapore)||firstname.lastname@example.org|
Researchers who have investigated probability have identified many misconceptions, such as representativeness, availability, outcome approach, equiprobability, and so on. The results of the research show that the use of some misconceptions decreases with age, while others are very stable and even grow stronger with age. The research has usually been undertaken in Western countries.
This study investigated the following three questions: What are the Chinese students main misconceptions of probability? What is the developmental structure of students' understanding of probability? Can an activity-based short-term teaching programme improve ordinary grade 8 students' understanding of probability?
The first two questions were answered in the first part, referred to as the main study. The sample was 567 Chinese students from three grades (6, 8 and 12) and two school streams (ordinary and advanced). The second part is referred to as the teaching intervention. Six activity-based lessons which focused on empirical probability were given to two grade 8 classes (each with about 25 students) in an ordinary school. The approaches were parallel except that one class had the opportunity to see computer simulations of a long series of experiments, while the other class was given the data in written form. During most of the teaching time the two classes did the same activities. All the students were tested and interviewed both prior to and after the teaching intervention.
Fourteen groups of misconceptions were observed in this study. The outcome approach, chance cannot be measured mathematically, compound approach and equiprobability were the main misconceptions for each grade and each stream of students. The context and data used in an item were found to play a role in eliciting some misconceptions.
The SOLO taxonomy was used in this study to describe students' hierarchical understanding levels on the concept of probability. It was found that, generally, there was no improvement in developmental level at grades 6 and 8, the two grades without any formal probability training. Grade 12 students have a better understanding than the younger students.
The results of this activity-based short-term teaching programme show that even a short intervention can help students overcome some of their misconceptions, such as chance cannot be measured mathematically. However, in this particular teaching experiment there was little change in the students use of the outcome approach and equiprobability, but it is possible that an alternative teaching experiment designed specifically to overcome these misconceptions might have a positive impact. Students in the two classes, one class with and one class without computer simulations, improved substantially in their answers and reasoning but no statistically significant difference was found between the classes.
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