Is procedure acquisition as unstable as it seems?

Are students’ mathematical procedures as unstable as they seem? Students often produce different errors in response to the same kind of problems on different testing occasions. This finding is puzzling. Past research has shown that students induce overly general procedures from worked-out examples during learning, which lead to a host of predictable errors on new problems. Do students create rule-based errors only to then switch between them at random? In this paper, we show that seemingly diverse errors on two different testing episodes may result from the same underlying stable procedure and are part of the same error category. These findings suggest that students’ errors are more stable on a category vs. on an individual level. The current study consists of teaching students addition in a new number system, called NewRoman, and analyzing students’ solution strategies in detail. Implications for teaching are discussed.     

Long-term Practicals in Chemistry in the First-cycle Engineering Curriculum

In 1974–75 at the K.U.Leuven Project Work as Practicals was started in the first-cycle engineering curriculum aiming at (1) the integration of separate teaching items and 7lpar;2) the integration of theoretical and practical or numerical aspects of those items. After 4 years the evaluation of it was more than satisfactory. The teaching team of the Chemistry course has integrated this system of practicals into their normal chemistry practicals. In this way more students 7lpar;currently only 20%) would be able to profit from the new education curriculum, now called ‘Long-term Practicals’. About 20%of the sophomore student volunteers are working for about 15 hours spread over 5 weeks at a mini-research subject in close contact with the members of the teaching team, using the instruments of the Chemistry Division, reading the literature, writing a report after the practical work, with discussion and evaluation of the work with their team-leader. To make it possible that all the sophomore students (400 students in 1987)could profit from this new education system, the physics, mechanics, mathematics, etc. practicals have to adapt to the same integrated practical system.     

A causal analysis relating previous achievement,attitudes, discourse,and intervention to achievement in biology and chemistry

This study described the relationship of 38 variates to achievement in high school biology and chemistry classes. Forty-four teachers prepared audio tape recordings of discussions throughout a nine-month period. Equal-sized groups received treatment consisting of wait time feedback and/or supportive intervention, a form of peer coaching. Other variables were initial measures, which included the variates of class size and previous science grade, pre- and posttest scores on student attitudes and perceptions, and prediscourse and discourse analyses, which included the variates of wait times, actions, and response durations. While previous research has shown that wait time feedback and supportive intervention are effective means of changing teacher behavior, the results of the present study revealed that previous student achievement and the attitudes of students accounted for 70% of the variation in the final examination scores (New York State Regents) on the basis of only the first three weeks of data collection on the variables assessed. Generally, little emphasis on higher-level thinking, wait time, or problem solving was found at the beginning of the school year, and only minimal changes resulted from the application of the treatment variables. Pressures for content coverage and preparation for externally imposed statewide examinations that emphasize memory-level learning augured against the changes that the independent variables were designed to produce.     

Some interesting mathematical gems

As the title of the article indicates, I am going to point out certain bright and beautiful pieces of mathematical work which can be treated as gems. Of course, choice of these pearl-like items is subjective depending on my understanding and appreciation (or lack of it) of the areas of mathematics in which I find interest.