小组数学干预：优化覆盖、复制与比较法提升集体运算能力

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本文档《A GROUP MATH INTERVENTION: THE MODIFICATION OF COVER, COPY, AND COMPARE FOR GROUP APPLICATION》发表于1994年4月的《心理学与学校》(Psychology in the Schools)第31卷，作者是玛莎·J·李(Martha J. Lee)和丹尼尔·H·廷斯特罗姆(Daniel H. Tingstrom)，他们来自美国南方大学。文章关注的是在一个小型课堂环境中对基本数学事实（如加减乘除）提高学生运算流畅度（准确性和速度）的干预策略。研究者采用了一种名为“覆盖、复制和比较”（Cover, Copy, and Compare, 简称CCC）的训练方法进行实验，这是由斯金纳等人在1989年提出的。原始的CCC方法旨在提升学生的数学技能，但本文对其进行修改并针对小组教学环境进行了应用。通过多基线设计，研究者展示了在一组学生中，通过这套干预措施，他们在处理除法事实时每分钟正确完成的数字数量（DCPM，Digits Correct Per Minute）的变化。文章深入探讨了DCPM的组成部分，即速度和准确性，并分析了这些数据对于教育实践者实施基于基础数据的小组数学干预策略的意义。研究发现，随着近年来群体成就测试结果显示，越来越多的教育者无法满足学生日益增长的数学需求（Whitney, 1985），实施有效的小组数学干预变得尤为重要。文章的重点在于，通过实例展示了如何根据基线数据调整和优化小组数学训练方法，以便更好地满足学生的个体差异，提高他们的数学能力。这为教育工作者提供了宝贵的实践指导，尤其是在面临大规模学生数学挑战的当下，如何有效地运用训练手段以促进全体学生的数学学习进步。

Group Math Invervention

135

Dependent Variables

The number of digits correct per minute (DCPM) was used as the main dependent

variable. On each assessment sheet there were

possible correct digits: Each quotient

consisted of

digit, and there were

division problems to a sheet. After scoring an

assessment sheet for the number

correct digits, the total was then multiplied by

and divided by the number of seconds it took to complete the worksheet, resulting in

DCPM (Skinner et al.,

1989).

In addition, the components of DCPM (speed and ac-

curacy) were examined independently, resulting in two additional dependent measures.

Design

The DCPM score obtained by each student on assessment sheets was tracked using

a multiple baseline design across the three sets of division facts, replicated across subjects.

“The baselines (from untreated sets) served as within subject comparisons for evaluating

treatment effects” (Skinner et al.,

1989,

414).

In other words, if rate and accuracy

of responding increase for division facts within the set to which the intervention is ap-

plied and remain stable with untreated sets, a functional relationship is demonstrated

between the intervention and the dependent variable@).

Procedure

The students remained in their regularly assigned classroom, and the normal seating

arrangement was maintained. The intervention was conducted at the same time each

day, two to three times a week. A packet containing three assessment sheets (A,

and

C), three training sheets for the appropriate set, an index card, and a stopwatch was

distributed to each student at the beginning of the period. Students timed themselves

and recorded the number of seconds it took to complete assessment sheets A,

and C.

During assessments the classroom teacher and the experimenter spot-checked the

accuracy of students’ self-timing and recording by periodically following individual

students’ times with other stopwatches. If errors were found while spot-checking the

accuracy of students’ self-timing, the timing procedure was reviewed and the recorded

time was corrected. In the case

observed errors in recording the obtained time, the

student was corrected with the statement “the time you recorded does not match the

time on your stopwatch” and was required to correct the recorded time. Although a

couple

students’ times had to be corrected occasionally according to the above pro-

cedures, spot checks of accuracy did not reveal major problems with students’ self-timing.

During all sessions, each student completed three assessment sheets (A,

C) and

three training sheets (either Set A,

C) where the student had not yet achieved

mastery. Students completed assessment sheets prior to the training sheets. Students

began with training sheets for Set A until they met the criterion of

DCPM and

90%

accuracy on three consecutive assessment sheets for Set A; at this point, the training

process was applied to Set

until mastery, and then finally to Set C. The continuous

administration of assessment sheets for each of the three sets provided follow-up data

for mastered sets.

During the training phase, students worked their way down each training sheet by

(a) silently reading the first problem and its solution on the left side of the paper, (b)

covering that problem and solution with an index card, (c) writing the problem and solu-

tion from memory in the blank to the right side of the covered problem, (d) uncovering

the problem and solution on the left side to check their written response, and (e) repeating

the procedure with each

the

facts on three training sheets.

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