Ostad S A
Institute of Special Education, University of Oslo, Norway.
Br J Educ Psychol. 1997 Sep;67 ( Pt 3):345-57. doi: 10.1111/j.2044-8279.1997.tb01249.x.
Several studies concerned with task-specific strategies in addition have suggested that, when compared with the performance of mathematically normal peers (MN pupils), the performance of mathematically disabled pupils (MD pupils) is characterised by frequent use of inefficient problem-solving strategies. These studies, however, have focused more or less exclusively on single age-groups and on the youngest age-groups in particular. What characterises strategy use, as this develops year by year during the primary school stage, has not been adequately studied.
The major purpose of the present study was to investigate the character and extent of differences between the MD pupils and the MN pupils as reflected in the use of task-specific strategies for solving elementary addition problems as the pupils move up through primary school, i.e., from grade 1 to grade 7. Particular concern was with the variability within the groups of MD pupils, especially in light of the general literature showing substantial heterogeneity in the performance characteristics of the mathematically less able children.
The sample included 32 MD pupils in grade 1, 33 MD pupils in grade 3, 36 MD pupils in grade 5 and a corresponding number of MN pupils in each of the grades.
The pupils were asked to solve 28 single-digit addition problems on two different occasions separated by an interval of two years. The task-specific strategies used by the pupils were recorded on a 'trial-by-trial basis' and were classified as defined single variants of backup strategies and retrieval strategies, respectively.
The pattern of development as it emerged in a longitudinal perspective in the present study showed the mathematically disabled pupils as being characterised by: (a) use of backup strategies only, (b) use of the most primary backup strategies, (c) small degree of variation in the use of strategy variants and, (d) limited degree of change in the use of strategies from year to year throughout the primary school.
Compared with the mathematically normal pupils, the mathematically disabled exhibited a divergent pattern of development, with unexpectedly little variability within the group itself.
另外几项关于特定任务策略的研究表明，与数学能力正常的同龄人（数学能力正常的学生）相比，数学能力有缺陷的学生（数学能力有缺陷的学生）在解决问题时经常使用低效策略。然而，这些研究或多或少都只关注单一年龄组，尤其是最年幼的年龄组。在小学阶段逐年发展过程中策略使用的特点尚未得到充分研究。
本研究的主要目的是调查数学能力有缺陷的学生和数学能力正常的学生在解决基本加法问题时使用特定任务策略方面的差异特征和程度，这些学生在小学阶段从一年级升至七年级。特别关注数学能力有缺陷的学生群体内部的变异性，尤其是鉴于一般文献表明数学能力较弱的儿童在表现特征上存在很大的异质性。
样本包括32名一年级数学能力有缺陷的学生、33名三年级数学能力有缺陷的学生、36名五年级数学能力有缺陷的学生，以及每个年级相应数量的数学能力正常的学生。
要求学生在相隔两年的两个不同时间解决28道一位数加法问题。学生使用的特定任务策略在“逐次试验的基础上”进行记录，并分别归类为备用策略和检索策略的特定定义变体。
本研究从纵向角度呈现的发展模式表明，数学能力有缺陷的学生具有以下特征：（a）仅使用备用策略，（b）使用最基本的备用策略，（c）策略变体使用的变化程度较小，以及（d）在整个小学阶段每年策略使用的变化程度有限。
与数学能力正常的学生相比，数学能力有缺陷的学生表现出不同的发展模式，其群体内部的变异性出人意料地小。
