Solving subtraction with regrouping

Junior High School Students with mental retardation

To compare problem solving with a pencil and paper to using calculators, several phases were followed. In the first phase, the teacher gave the study group subtraction problems which were in columns on the paper. They were given two minutes to answer, using pencil and paper, then the teacher took up the papers and corrected them.The corrected papers were then given back to the students to look over for two minutes. Next, the teachers demonstrated and the students practiced subtraction problems. A hand out was given to the students with five subtraction problems on it. The teacher wrote similar problems on a chalkboard and spent five minutes explaining them. During the teacher's explanation of the problems on the chalkboard, the students attempted to solve the problems on their handouts. The papers were collected, corrected, and returned to the students. Each student had five minutes of interaction with the teacher, going over the subtraction problems they had worked on. The second phase involved the use of calculators to solve subtraction problems. The teacher handed out calculators to the students and showed them how to turn them on ,but did not teach them how to do problems. Phase three involved the use of calculators, pencil, and paper to solve subtraction problems. The teacher passed out a problem sheet and demonstrated how to solve the problems using specific key strokes required and the students modeled the teacher's behavior. The papers were collected, corrected, and returned to the students. The teacher then spent five minutes giving feedback to the students. The final phase involved the use of cue cards as well as calculators. the students were given cue cards with a subtraction problem on it. The teacher explained how to solve the problem using verbal demonstrations. Each student was given a packet of seven drill cards The students had five minutes to solve as many problems as they could. The results were collected and scored.

Students ability to solve subtraction problems with pencil and paper, with a calculator, and with a calculator and visual cues were measured by calculating the percentage of problems done correctly in each phase.

Horton, S., Lovitt, T., & White, O., (1992). Teaching mathematics to adolescents classified as educable mentally handicapped: Using calculators to remove the computational onus. Journal of Remedial and Special Education, 13, 36-60.

Mike Wilson , E.T.S.U.

**Target**

Teaching subtraction with regrouping

**Participants**

One male fifth grade student, one male sixth grade student and one female sixth grade student with learning disabilities

**Technique**

Self-monitoring may increase consistent problem solving strategies. The students in this study had mastered the basic operations of addition, subtraction, and multiplication but were not consistent with subtraction problems involving regrouping. The students were given fifteen minutes to complete worksheets from ten to twenty problems. This study included two baselines. The first baseline included verbal instructions on how to complete the worksheet then verbal praise and specific verbal feedback on errors. The second baseline included verbal instructions on how to complete the worksheets, verbal praise for right answers, specific verbal feedback on errors and two points for each correct response. The points were used in the classroom to be exchanged for prizes such as notebooks and pencils. The self-monitoring package was introduced as a third phase the study. The teacher analyzed the regrouping errors of each student then formulated a checklist for each student. The individual checklists were written in first person and gave specific reminders for students to check their work. The students were given the same type of worksheets used in the collecting of baseline data and were instructed to complete the worksheets as before with points, verbal praise and feedback given. Then the students were instructed to go to their checklists and make sure that they had completed the regrouping procedures correctly according to the errors they make the most. Using the checklist, the children put a plus sign beside the problem they did correctly and a minus sign next to the problems they did incorrectly. The children then redid the problems with a minus sign next to them, leaving the original problem that was done incorrectly. When the students achieved a consist high level of success, the checklists were removed.

**Evaluation **

The students were checked by their teacher for correct responses on the worksheets. The first and second baselines showed low levels of consistent correct responding. When the self-monitoring package was introduced, the children showed a significant and immediate improvement in correct responses. Each student responded correctly to more than one-half of the problems during the self-monitoring phase. Even after the checklists were removed, the students performed more successfully than when the baselines were collected.

**Source**

Dunlap, L. K., & Dunlap, G. (1989). A self-monitoring package for teaching subtraction with regrouping to students with learning disabilities. Journal of Applied Behavior Analysis, 22(3), 309-314.

**Developer**

Kristi Shell, ETSU

**Target**

Improving students' self-efficacy and subtraction problem solving

**Participants**

Middle school students classified as learning disabled in mathematics

**Technique**

Students were divided into one of three groups, one which verbalized while working on subtraction problems, one which was encouraged to verbalize only for the first half of the experiment, and then asked to work quietly, and the third which was never instructed to verbalize. All groups were monitored from time to time, and then asked at the end of each session either what they said aloud while working, or what thoughts they had while problem solving. Students also received performance feedback (such as, "That's fine.", or "Okay."), as well as varied amouts of effort feedback (such as, "You have been working hard."). Some students were given effort feedback during the first half, others during the last half, and others only received performance feedback. Students were also asked to think about their own work and evaluate how much each factor helped them solve problems. Both student and teacher verbalization facilitated task performance, and improved self-efficacy and skills.

**Evaluation**

Compare the total number of problems the student completed and the scores of self-efficacy (based on the written evaluation of attributional factors) from the post-test with those from the pre-test.

**Source**

Schunk, D. H., & Cox, P. D. (1986). Strategy training and attributional feedback with learning disabled students. Journal of Exceptional Psychology, 78, 201-209.

**Developers**

Robin Albertson-Wren, Nicole Frye, UVA