本研究探討在數學課室討論文化中，社會常規以及社會數學常規之形成與相互關係。並進一步比較二年級不同成就學童在常規形成前後，提供正整數乘法的學習機會以及所產生的數學學習。
對22堂數學課進行質性分析，發現在師生與同儕互動中，呈現四個社會常規：1.解題紀錄之社會常規，2.提問題與建議適切性之社會常規，3.小組討論之社會常規，4.說明之社會常規。而社會數學常規在可接受的數學解釋和質疑辯證包含：1.回到題目說明解題紀錄，2.提出和數學意義相關之問題；數學的相同性與相異性包含，1.算式填充題意思的相同處，2.做法意義的同異處；數學的複雜性包含解題策略之多樣性。數學的有效性包含解題紀錄的有效性；數學的精緻性包含解題紀錄之完整性。
除此之外，本研究還發現：
1.社會常規以及社會數學常規的形成歷程是相互支撐；
2.社會數學常規會隨著數學內容不斷演化；
3.社會數學常規會衍生出另一個社會數學常規；
4.社會常規會影響學童的學習，而社會數學常規的形成，更是影響學童數學學習的重要因素；
5.社會數學常規對不同成就學童其需求性不相同；
6.「數學的有效性」與「數學的複雜性」對學童而言，為較高層次的社會數學常規。
對於未來的研究，建議可以探討不同數學內容的社會數學常規之同異處以及探討在課室討論中，有關學童問題解決、溝通、表徵、評析等方面的能力。

The purpose of this research was to investigate evolution of social norms and sociomathematical norms and the relationship between two these items in the discussion culture of mathematics classroom. Moreover, the study compared the different achievements of the second-grade students’ learning opportunities in multiplication, and the mathematical learning that arose before with after evolution of norms.
The study utilized qualitative methodology to analyze 22 mathematics classes videotaped. Consequently, the study obtained that there are four social norms emerging in the interaction of teacher-students and students-students: 1. the social norms of problem solving records, 2. the social norms of asking a question and a suggestion appropriately, 3. the social norms of the small-group interaction, 4. the social norms of explanation. Furthermore sociomathematical norms in acceptable mathematical explanation and justification include: 1. to explain the problem solving records by being back to the word problems, 2. to probe questions correlated with mathematical meaning. Mathematical sameness and difference norms include: 1. the sameness of meaning of fill-in the blank problems, 2. the sameness and difference of the meaning of solving ways. Mathematically sophisticated norms include variety of the strategies that solve a problem. Mathematical efficient norms include effectiveness of problem solving records. Mathematically elegant norms include integrality of problem solving records.
In addition, this study also has following conclusion:
1. Social norms and sociomathematical norms are interwoven and supported each other in the forming process.
2. Sociomathematical norms evolve with the mathematics content constantly.
3. Sociomathematical norms derive out other social sociomathematical norms.
4. The social norms affect the students’ learning, as for the influence of students’ mathematics learning processes, the formation of sociomathematical norms are more important the social norms.
5. Based on students’ various mathematics achievements, the need of the sociomathematical norms will be different as well.
6. For students, mathematically sophisticated norms and mathematically efficient norms are the higher level of the sociomathematical norms.
Regarding future researches, this study suggests that they can investigate the sameness and differences of sociomathematical norms in different mathematical contents, and to explore abilities of students’ problem solving, communication, representation, evaluation and analysis in the mathematical classroom discussion.

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