| dc.description.abstract | Over the decades, the probability curriculum at junior high stage in Taiwan has been characterized exclusively by ＂classical probability＂ which misses the richness of probability concepts. Comparing with the national curricular plan of peer countries, the introduction of probability in Taiwan is scheduled relatively late. Therefore, this research proposes to design a new probability course for the secondary stage. The research team will compile textbooks ＂Hsu′s probability I＂ and ＂ Hsu ′s probability II＂ and conduct teaching experiments, so as to test the students′ learning effectiveness and suitability of the new course.
This study is a two-year longitudinal study justified by self-examinations. Junior high school students received experimental teaching according to the forementioned texts from grade 8th to grade 9th, followed by a performance test and a delay test. The results verified that students in grades 8th and 9th can understand the subjective, classical, and frequency probabilistic viewpoints. They can also deal with advanced probabilistic concepts such as independent events. The research also found that with the tree diagram, students can understand and use the principles of adding branches at the same level and multiplying branches on a path of different levels from the tree diagram. In addition, from interpretive structural modeling, it can be seen that tree diagram and independence are the basis for learning advanced concepts in probability.
However, from the students′ texts, this study found that students learning tree diagrams might have two types of difficulties. (1) The confusion between probability value misplacement and operational rules: Students fail to connect the relationship between literal meaning and probability when interpreting the meaning of the question, resulting in probability value misplacement and misuse of addition and multiplication principles. (2) Graph-text conversion of drawing multiple independent and paired sample tree diagrams: Students have difficulties in identifying and classifying multiple independent and paired samples, resulting in the inability to draw correct tree diagrams.
Finally, this study suggests that the curriculum design of junior high school mathematics can be adjusted to include probability content. In the design of teaching materials, the concept of ＂daily experience＂ is often used to link the concept of probability and design examples of different situations. In the design of teaching method, the concept of tree diagram can be established and the algorithm can be developed consistently. In the design of teaching activities, it is advisable to allow students to practice oral interpretation of the probability concepts, so as to improve students′ probability of thinking. The experimental texts designed for this study also proposes a basic design plan for the connection between the concept of probability and graphical thinking, and the prevention of the misconceptions of probability. | en_US |