Abstract: The Influence of the number of Combinatorial Elements on Adolescents’ Combinatorial Performances in Sampling Combinatorial Problems Abstract Purposes The previous studies of sampling combinatorial problems indicate that adolescents at the formal operation stage show different performances in such tasks. We assume that it may be that the increase in the number of combinatorial elements reduces combinatorial performances. The present study examines the possible influence of the number of combinatorial elements on sampling combinatorial reasoning. Methods The present experiment investigated adolescents’ reasoning abilities in sampling combinatorial problems. Participants were 141 tenth graders from a middle school who had not learned the combinatorial knowledge in school instructions. Independent variables were the number of elements in a population and the number of elements in a sample in combinatorial problems. There were three conditions of combinatorial problems: C5,3, C7,3 and C7,4. Three classes’ students were respectively arranged to the three combinatorial problems. For example, a class’ students was arranged to the following C5,3 combinatorial problem. A sports team has five players. They are respectively represented by letter code A, B, C, D and E. Now three members are selected from the five players in the team to constitute a group to participate in a sports team competition project. Q. What are the possible group combinations? Please enumerate all the possible group combinations. Results Results showed that, as the number of elements in a population and the number of elements in a sample increased, participants’ combinatorial performances decreased, and the proportions of participants using the systematic variation method also decreased. The results supported the previous assumption. Conclusions Adolescents’ sampling combinatorial reasoning ability decreases as the number of combinatorial elements increases. It reveals that although the ability of sampling combinatorial reasoning is already acquired by adolescents, it doesn’t reach the level of generalization. It implies that there may be a distinction of a low level and advanced level in its development. Key words: adolescents，sampling combinatorial problems, number of elements, combinatorial strategy

Key words: adolescents, sampling combination, number of elements, combinatorial strategy

摘要： 先前抽样组合问题研究表明达到形式运算阶段青少年的抽样组合思维成绩表现并不一致，作者分析猜想可能的原因是组合元素数量增加会降低被试的抽样组合成绩。现在实验考察高中一年级学生的抽样组合思维能力，以组合问题中的总体元素数量和样本元素数量为自变量，设置了五选三、七选三和七选四的三种抽样组合问题条件。实验结果发现，随着总体元素数量和样本元素数量的增加，被试的组合成绩明显下降。这表明，青少年的抽样组合思维能力虽已获得，但随组合元素数量增加而表现出倒退，并没达到成熟的一般性；其发展水平可能存在初级水平到高级水平的区分。

关键词: 青少年, 抽样组合, 元素数量, 组合策略