児童たちが算数を創り出すことを重視する算数教育において，統合的・発展的に考察することは大切な方法の一つである．本稿は，第6 学年の線対称と

の性質を発見する活動における実践授業を行い，単元を通して，中島健三が述べる「統合的，発展的な考察」の場面における児童の学びの様相を捉えることを目的とした．その結果，線対称とにおける「統合的，発展的な考察」は，単元を通した一連の考察として成立し，その中で，児童たちの線対称とを同じように見ようとする姿勢が向上していく様子を認めることができた．また，合同な図形に着目し，定義に関わる操作活動を通して性質を十分に確認させることや，性質をまとめた文章中の「対称の中心」と「対称の軸」を置き換えさせることによって，児童たちの「構造」に対する捉え方が変わっていく様子を認めることができた．

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   Diffusion microflames has potentials to be utilized as a point-symmetric one-dimensional flame to unveil detail structures of diffusion flame and as a heat source with high heat release density. The way to elevate those potentials is investigated in the present study. Thus, a microflame is established in the oxygen fraction controlled ambient coflow, where methane issues from the inner tube with 0.7 mm ID, whereas the coflow mixture of oxygen and nitrogen from the outer coaxial tube with 6.0 mm or 2.9 mm ID. The results show that increase of oxygen mole fraction in ambient flow makes a microflame close to the perfect point-symmetric one-dimensional flame. Specifically, increase of oxygen mole fraction from 0.21 to 0.49 reduces the difference from the perfect point-symmetric shape into half; this is considered because molecular diffusion becomes dominant owing to the decrease of Pe number resulting from the reduction of flame size. Increase of oxygen fraction is found to be quite effective to increase heat release density as it becomes 7 times larger by the increase of oxygen fraction from 0.21 to 0.49.

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A low-pass filter is almost always applied to data of finite length. Therefore, unexpected vibration occurs at the data end of the low-pass filter output. To solve this problem, the previous report of this paper has proposed that two types of low-pass filters (i.e. spacial and frequency) can be used in a point symmetric extension method. To make the above proposal more specific, a point symmetric extension method was applied to reduce an abnormal value occurring in the filtered data at the data end where the center of the point symmetric method is applied. Before that, the data end was replaced by the generalized low-pass filtered output. Consequently this paper proposes a method to determine the center point of this point symmetric extension based on the sum of squared errors between the primary and the filtered output. This new method also uses a spatial low-pass filter and a frequency low-pass filter. The method is applicable not only to a low-pass filter that uses a point symmetric extension method but also to all other types of low-pass filters for minimizing the sum of squared errors between primary and filtered data.

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前２報で、せん断と拡張、周期拡張を組み合わせることにより、ガウシアンフィルタとスプラインフィルタのエンド効果問題解決と振幅伝達特性保証を同時に満たすことに成功した。今回はその手法をロバストフィルタに適用し、エンド効果と振幅伝達特性保証が満たせるか検証を行なう。

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