(2004)
Fuchs and colleagues (2004) conducted a study that investigated the effects of teaching students how to transfer known solution methods to problems that are only superficially different from those they already know how to solve.245 The
authors randomly assigned 24 teachers to three groups: 1) transfer instruction, 2) ex- panded transfer instruction, and 3) regular basal instruction (comparison group).246
The 351 students in these 24 classes that were present for each of the pretests and posttests were participants in the study. The intervention included 25- to 40-minute lessons, approximately twice per week for 17 weeks.247 Students in the expanded trans-
fer condition learned basic math problem- solving strategies in the first unit of instruc- tion (six sessions over three weeks). They were taught to verify that their answers make sense; line up numbers from text to perform math operations; check operations; and label their work with words, monetary signs, and mathematical symbols.
The remaining units each focused on one of four problem types: 1) shopping list prob- lems (buying multiple quantities of items, each at a different price); 2) buying bag prob- lems (determining how many bags contain- ing a specified number of objects are needed to come up with a desired total number of
245. Fuchs, Fuchs, Finelli et al. (2004).
246. Since the comparison between the expanded transfer condition and the control condition (reg- ular basal instruction) is most relevant to this practice guide, we do not discuss the transfer instruction condition here.
247. Although this intervention was taught in a whole-class format, the authors reported sepa- rate effects for students classified as low achiev- ing and for students classified as learning dis- abled; therefore, the results are relevant to this practice guide.
APPENDIx D. TECHNICAL INFORMATION ON THE STUDIES
objects); 3) half problems (determining what half of some total amount is); and 4) picto- graph problems (summing two addends, one derived from a pictograph). There were seven sessions within each unit.
In sessions one through four, with the help of a poster listing the steps, students learned problem-solution rules for solving the type of problem being taught in that particular unit. In the first session, teachers discussed the underlying concepts related to the problem type, presented a worked example, and explained how each step of the solution method was applied in the example. After presenting several worked examples, the teachers presented partially worked examples while the students ap- plied the steps of the solution method. Stu- dents then completed one to four problems in pairs. Sessions two through four were similar, but more time was spent on par- tially worked examples and practice, and at the end of each session, students com- pleted a problem independently.
In sessions five and six, teachers taught students how to transfer the solution meth- ods using problems that varied cover sto- ries, quantities, and one transfer feature per problem. In session five, the teachers began by explaining that transfer means to move and presented examples of how students transfer skills. Then, teachers taught three transfer features that change a problem without changing its type or solution, including formatting, unfamiliar vocabulary, and posing a different ques- tion. These lessons were facilitated by a poster displayed in the classroom about the three ways problems change. Again, teachers presented the information and worked examples, and moved gradually to partially worked examples and prac- tice in pairs. Session six was similar to session five, but the students spent more time working in pairs, and they completed a transfer problem independently.
In the seventh session, teachers instructed students on three additional superficial problem features including irrelevant infor- mation, combining problem types, and mix- ing superficial problem features. Teachers taught this lesson by discussing how prob- lems encountered in “real life” incorporate more information than most problems that the students know how to solve. They used a poster called Real-Life Situations to illus- trate each of these superficial problem fea- tures with a worked example. Next, students worked in pairs to solve problems that var- ied real-life superficial problem features and then completed a problem independently. The authors used four measures to deter- mine the results of their intervention on word problem-solving proficiencies. The first measure used novel problems struc- tured the same way as problems used in the intervention. The second incorporated novel problems that varied from those used in instruction in terms of the look or the vocabulary or question asked. The third incorporated novel problems that varied by the three additional transfer features taught in session seven. The fourth was a measure designed to approximate real-life problem solving. Although this intervention was taught in a whole-class format, the au- thors separated results for students classi- fied as low performing248 and for students
classified as learning disabled. The average impacts on these four outcome measures were positive and significant for both the sample designated as low performing and the sample designated as learning disabled. It is notable that the intervention had a posi- tive and significant impact on the far trans- fer measure (the measure that approximated real-life problem solving). This study dem- onstrates a successful approach for instruct- ing students with mathematics difficulties on solving word problems and transferring solution methods to novel problems.
248. Using pretest scores on the first transfer problem-solving measure, the authors desig- nated each student as low performing, average performing, or high performing.
A PP EN D Ix D . T EC H N IC A L I N FO R M A T IO N O N T H E S T U D IE S ( 73 )