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Exploring and deriving proofs of closed-form expressions for series can be fun for students. However, for some students, a physical representation of such problems is more meaningful. Various approaches have been designed to help students visualize squares of sums and sums of squares; these approaches may be arithmetic-algebraic or combinatorial in nature, or they may involve mathematical induction. In the activity described in this article, students use balls and disks to prove the general formulas for sums of squares and cubes. (Contains 2 tables and 6 figures.)

The classroom-friendly ABO blood type kit was developed by combining advantages of modelling and a simulation laboratory to teach the topics of ABO blood types and blood transfusion. Teachers can easily simulate the agglutination reaction on a blood type testing plate in the classroom, and show the students how this reaction occurs by using the models. Simple materials are used to help teachers prepare for daily teaching. The kit can be used to engage students in hands-on and minds-on activities. There were some positive preliminary results reported after using the kit with Thai high-school students. (Contains 2 tables and 6 figures.)

A diagnostic instrument consisting of 18 items was developed to evaluate students' understandings about mechanics. The instrument was administered to 240 eleventh grade students attending four typical public high schools in Thailand. Analysis of the students' responses identified the existence of patterns of reasoning that are common to conceptions in different areas of mechanics involving the direction of force acting on a moving object, objects moving under the sole influence of gravity, motion involving mechanical energy and momentum. Reliability proved sufficient (Cronbach's alpha equals .7). The study revealed students held a difficulty in understanding why and when to use force, motion, energy and momentum concepts, and especially the qualitatively interpreting basic principle related to conservation laws. Their skills of problem analysis and judgment on the efficiency of a given solution to a problem were poor . We also found a mismatch between students' confidence in answering the items and their correct responses through the correlation between the students' confidence of being correct on each item and the actual correct responses being significantly less than 0.278. Thus this instrument is a convenient diagnostic tool that any teacher could use to identify students' perceptions to the introduction of the topic and students' alternative conceptions during classroom instruction. [ABSTRACT FROM AUTHOR]

Quantitative chemistry has a considerable importance in chemistry curricula both in the high school and university levels. Research suggested that students faced difficulty in learning quantitative chemistry and that the concepts were difficult to teach. This study was designed to indicate how students learn and how teacher teach quantitative chemistry in Thai high schools, and explore Thai high school students' attitudes toward quantitative chemistry learning. There were 603 students and 53 teachers that participated in the study. The Quantitative Chemistry Learning Questionnaires (QCLQ) were used as a data collection instrument, one for teachers, and another for students. The results indicated that both students and teachers agreed that the curriculum focused more on conceptual understanding rather than problem solving. However , in teaching quantitative chemistry, the teachers focused more on teaching how to solve algorithmic problems rather than teaching the concepts, and they did not often let students do experiments which students like the most. When solving algorithmic problems, students preferred to the use of formulae method rather than using proportional method that most teachers taught. Students thought that quantitative chemistry was difficult to learn and only about a quarter of the students liked to study it. The three topics that students felt most difficult were stoichiometry, acid-base, and rate of the reactions. The possible effective strategies for teaching quantitative chemistry from students' views were also discussed. [ABSTRACT FROM AUTHOR]

One important component of pedagogical content knowledge (PCK) is knowledge of strategies and representations for teaching particular topics. Aimed to enhance this component of pre-service mathematics teachers, the abstract and symbolic concept of series is used as a learning context of a learning unit which is called "PCK+series unit", which was developed. The teaching and learning process of this unit was based on the constructivist approach to foster atmospheres of mathematics learning through key features of a constructivist view of learning, and was implemented while enhancing pre-service teachers' PCK in instructional designs and teaching of series. The unit was implemented (8 weeks) with 23 pre-service mathematics teachers in the third year of attending selected topics in a mathematics instruction course. The collection of data involved a pre-post questionnaire, weekly journals, and video recording of series lesson plan presentation sessions with their respective mentors. At the beginning of the PCK+series unit implementation, most pre-service teachers were unable to employ appropriate teaching strategies required to explain series concepts. Most of them planned to teach by showing various series formulas and giving some examples of problem solving through a traditional teaching approach. After the implementation, learning components of PCK and several activities including brief hands-on activities helped pre-service teachers to realize that moving from the constructivist learning theory into classroom practice is necessary for their future students. The results support a growing awareness among pre-service teachers concerning the need to understand students' prior knowledge and relate it with new learning experiences provided in teaching and learning situation; for example using guided questions and designing series models to help students comprehend and build series' formulas from their own ideas. [ABSTRACT FROM AUTHOR]