To teach multiplication to students with learning disabilities
Four males ranging from nine years six months to thirteen years ten months, all of whom have learning disabilities
Two groups of two students work during fifteen minute periods of their daily scheduled math classes five days a week. Each session consisted of presenting ten multiplication facts with three trials per fact. Three material prompts - chips, a number line, and fingers - were allowed to be used when teaching the students the multiples of 6s, 7s, and 8s. There were three phases in which the students were taught multiplication. One was baseline, where the teacher presented the flash cards with the facts on them. Students then had five seconds to answer. If they responded correctly, they received verbal praise. If the answer was wrong, they received supportive statements. The second phase was called teacher-directed prompting. This was when the teacher presented the controlling prompts using a most-to-least hierarchy (which prompt provided the most or least intrusiveness) over time. On the other hand, in the student-selected prompting, which is the third phase, the student picked the prompt which would be more helpful to them on a trial-to-trial basis. In either the teacher or student-selected prompting, the teacher first presented the multiplication facts by using a constant time delay procedure, which ensures the accuracy of the student's response by requiring the identification of the prompt. The educator showed the flash card to the student and then stated the problem. The student then restated the problem and answered.
Only the results of the first trial of the three trials per fact were recorded daily. The two prompting procedures--teacher-directed prompting and student-selected prompting--were compared based on total direct instructional time, number of sessions, and average time per session. By comparing the two, one can see that the student-selected prompting proved to be more efficient.
Williams, D. M., & Collins, B. C. (1994). Teaching multiplication facts to students with learning disabilities: Teacher-selected versus student-selected material prompts within the delay process. Journal of Learning Disabilities, 27, 589-597.
Improving multiplication skills
Below average early elementary students
The instructor worked with individual students in a daily ten minute session. The instructor pretaught three component skills of multiplication before drilling students with 16 flashcards. The first skill taught was the counting by various number sets skill, i.e., 2, 4, 6, 8, or 9, 18, 27. The instructor modelled the proper methods of "counting-by" various numbers in a turn taking session, until the child could respond without a correction in three consecutive trials. The instructor spent four minutes practicing this exercise.
The second skill taught was decoding, where the instructor wrote a multiplication fact on the chalkboard and explained in words how the problem asked them to count. For example, the instructor would say, "This problem says count by two, three times." With each modelled problem, the instructor would ask the student to repeat the task. This activity was continued until the child decoded three consecutive problems successfully.
The third skill taught was the "count-by" strategy, where the student was taught to incorporate the two previous skills. During this task, the instructor wrote a problem on the board and said, "We count by two, three times. Two, four, six," demonstating on three fingers. Once again, turn taking occured, and the session of decoding and applying the "count-by" strategy lasted for two minutes. A second four minute session was used to reinforce the "count-by" various numbers skill.
Once the concepts of the three skills were grasped by the student, the instructor led the students through the entire procedure for working multiplication problems by presenting a series of questions and instructions.
Calculate the percentage of correct responses to flash card drills. These cards should include those previously used, in addition to those never used during training sessions.
Carnine, D. W. (1980). Preteaching versus concurrent teaching on the component skills of a multiplication problem-solving strategy. Journal for Research in Mathematics Education, 11, 375-379.
Tamara Josaitis, and Kelley Smith, UVA