• The Mathematical Education
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• v.62 no.4
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• pp.473-490
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• 2023

Previous studies from domestic and abroad are accumulating information on how to reason students' continuous changes through teaching experiments. These studies deal with scenes in which students who make 'smooth reasoning' and 'chunky reasoning' construct mathematical results together in teaching experiments. However, in order to analyze their results in more detail, it is necessary to check what kind of results a student reasoning in a specific way constructs for the tasks of previous studies. According to the need for these studies, the researcher conducted a total of 14 teaching experiments on one first-year high school student who was found to make 'chunky reasoning'. In this study, it was possible to observe a scene in which a student who makes 'chunky reasoning' constructs an output similar to 'a mathematical result constructed by students with various reasoning methods(smooth reasnoning or chunky reasoning) in previous studies.' In particular, the student who participated in this study observed a consistent construction method of constructing the function of 'time-speed' from the function of 'time-distance'. The researcher expected that information on this student's distinctive construction methods would be helpful for subsequent studies.

• School Mathematics
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• v.18 no.3
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• pp.457-478
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• 2016

The purpose of this study is to investigate middle school students' understanding and development of function graphs. We collected the data from the teaching experiment with two middle school students who had not yet received instruction on linear function in school. The students participated in a 15-day teaching experiment(Steffe, & Thompson, 2000). Each teaching episode lasted one or two hours. The students initially focused on numerical values rather than the overall relationship between the variables in functional situations. This study described meaning, role of and students' responses for the given tasks, which revealed the students' understanding and development of function graphs. Especially we analyzed students' responses based on their methods to solve the tasks, reasoning that derived from those methods, and their solutions. The results indicate that their continuous reasoning played a significant role in their understanding of function graphs.

• The Korean Journal of Nuclear Medicine
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• v.32 no.3
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• pp.225-237
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• 1998

Purpose: We investigated the statistical methods to compose the functional brain map of human working memory and the principal factors that have an effect on the methods for localization. Materials and Methods: Repeated PET scans with successive four tasks, which consist of one control and three different activation tasks, were performed on six right-handed normal volunteers for 2 minutes after bolus injections of 925 MBq $H_2^{15}O$ at the intervals of 30 minutes. Image data were analyzed using SPM96 (Statistical Parametric Mapping) implemented with Matlab (Mathworks Inc., U.S.A.). Images from the same subject were spatially registered and were normalized using linear and nonlinear transformation methods. Significant difference between control and each activation state was estimated at every voxel based on the general linear model. Differences of global counts were removed using analysis of covariance (ANCOVA) with global activity as covariate. Using the mean and variance for each condition which was adjusted using ANCOVA, t-statistics was performed on every voxel To interpret the results more easily, t-values were transformed to the standard Gaussian distribution (Z-score). Results: All the subjects carried out the activation and control tests successfully. Average rate of correct answers was 95%. The numbers of activated blobs were 4 for verbal memory I, 9 for verbal memory II, 9 for visual memory, and 6 for conjunctive activation of these three tasks. The verbal working memory activates predominantly left-sided structures, and the visual memory activates the right hemisphere. Conclusion: We conclude that rCBF PET imaging and statistical parametric mapping method were useful in the localization of the brain regions for verbal and visual working memory.