## Description

### Research on the Math Strategies Series Level II

**Addition With Regrouping**

**Study 1**

**Overview**

The *Addition With Regrouping* program was initially field tested in a study in which a total of 24 students participated. Ten students (i.e., four females and six males) took part in the *Addition With Regrouping* program. Of these 10 students, two had disabilities (i.e., one with a learning disability and one with an emotional/behavioral disability). All 10 students were identified as students with math difficulties. The students were attending a summer remedial math camp and had just completed the second grade. A comparison group consisted of 14 students (i.e., 5 females and 9 males). Of these 14 students, four had disabilities (three with learning disabilities and one with a traumatic brain injury). All 14 students were identified as having math difficulties and had just completed second grade. The comparison group received instructional lessons from their typical basal mathematics program.

**Results**

A two-way mixed ANOVA, with one repeated measure (pretest/posttest) and one between–subjects effect (treatment and comparison) revealed a significant difference between the computation pretest and posttest F(1,16) = 11.14, p = .004. There also was a significant interaction effect (i.e., Trial X Group) F(1,16) = 6.49, p = .021. Thus, both treatment and comparison groups improved significantly from pre- to posttest, but the treatment group improvement was significantly greater than the comparison group. Mean percentage computation scores increased from 49% (9.86/20) to 90% (18/20) for the treatment group and from 66% (13.27/20) to 72% (14.36/20) for the comparison group.

There also was a significant difference between the word problem pretests and posttests F(1,15) = 19.46, p = .001. The interaction effect approached significance F(1,15) = 18.70, p = .063 in favor of the treatment group. Mean percentage word-problem scores increased from 41% (3.22/10) to 89% (8.88/10) for the treatment group and from 51% (5.11/10) to 69% (68.9/10) for the comparison group.

Finally, there was a significant difference between the fluency (*Addition With Regrouping* Minute) pretest and posttest scores F(1,18) = 10.60, p = .004. The interaction effect was the same F(1,18) = 10.60, p = .004. Both the treatment and comparison groups improved significantly from pre- to posttest on the one-minute probe, but the treatment group gain was significantly greater than the comparison group’s gain. The number of problems completed per minute increased from 3.22 to 8.11 for the treatment group, whereas the number of problems completed remained the same (i.e., 6.00) for the comparison group.

**Conclusions**

These results suggest that students with learning difficulties in mathematics improve their computation, word problem, and fluency skills after participating in the instructional lessons included in the *Addition With Regrouping* program. The gains for students who received instruction using the *Addition With Regrouping* program were greater than the gains made by similar peers who received instruction using a traditional basal series.

**Reference**

Miller, S. P., & Kaffar, B. J. (2011). Developing addition with regrouping competence among second-grade students with mathematics difficulties. *Investigations in Mathematics Learning, 4*(1), 25-50.

**Study 2**

**Overview**

In a multiple-probe across-participants study, nine elementary students with learning disabilities (six males and three females) participated in the *Addition With Regrouping* lessons. There were two second graders, three third graders, two fourth graders, one fifth grader, and one sixth grader. The nine students were assigned to three triads for the purposes of the multiple-probe design with two replications. They took multiple and parallel forms of a test containing eight computation problems and two word problems across the duration of the study (i.e., baseline, treatment, maintenance [administered seven days after instruction]), and generalization (administered 14 days after instruction in a new setting with a new teacher).

**Results**

The mean baseline score for students in the first triad was 23.33%, with a range of 5.77% to 65.00%. The mean treatment score for these students was 92.74%, with a range of 89.52% to 95.50%. The mean maintenance score was 93.33% with a range of 90.00% to 100.00%. The mean generalization score was 90.00%. All three students earned a score of 90.00% on the generalization probe.

The mean baseline score for students in the second triad was 22.50%, with a range of 0% to 67.50%. The mean treatment score for these students was 94.43% with a range of 92.38% to 96.00%. The mean maintenance score was 96.67% with a range of 90.00% to 100.00%. The mean generalization score was 93.33% with a range of 90.00% to 100.00%.

The mean baseline score for students in the third triad was 5.00%, with a range of 0% to 12.00%. The mean treatment score for these students was 91.29%, with a range of 85.91% to 97.00%. The mean maintenance score was 90.00% with a range of 80.00% to 100.00%. The mean generalization score was 90.00% with a range of 80.00% to 100.00%

All nine participants increased their performance level only after the introduction of treatment, thus confirming that the treatment lessons were responsible for the performance improvement. To further assess the treatment effect, the percentage of nonoverlapping data (PND) was calculated to be 97.83% (i.e., a large effect size).

**Conclusions**

The results show that students with learning disabilities are able to acquire and maintain the ability to solve computation and word problems after participating in the lessons in the *Addition With Regrouping* program. They also are able to generalize these skills to their general education classrooms with their general education teachers.

**Reference**

Carmack, C. (2011). *Investigating the effects of addition with regrouping strategy instruction among elementary students with learning disabilities*. (Unpublished doctoral dissertation). University of Nevada Las Vegas, Nevada.

**Subtraction With Regrouping**

**Study 1**

**Overview**

The *Subtraction With Regrouping* lessons were field tested in a study involving a total of 23 students. Eleven students (i.e., five females and six males) participated in the Subtraction With Regrouping program. Of these 11 students, 3 had disabilities (i.e., one with autism, one with learning disabilities, and one with other health impairments). The remaining eight students were identified as students with math difficulties. The students were attending a summer remedial math camp and had just completed the third grade. A comparison group of 12 students (i.e., nine females and three males) received instruction from a basal mathematics program that involved regrouping instruction. These 12 students were identified as having math difficulties and had just completed third grade.

**Results**

The mean score for the treatment group on the regrouping computation pretest was 60%, and their mean score on the posttest was 86%. In contrast, the comparison group earned a mean score of 76% on the computation pretest and 78% on the posttest. A two-way mixed ANOVA with one repeated measure (pretest/posttest) and one between-subjects effect (treatment and comparison) revealed a significant difference between the pretest and posttest, F(1, 16) = 5.56, p = .031, and a difference between the groups that approached significance, F(1, 16) = 3.92, p = .065. Thus, both groups made computation gains, but the gain made by the treatment group was greater than that made by the comparison group, and the gain made by the treatment group was socially significant (i.e., students’ mean scores when translated to grades improved from D to B), whereas the mean score of the comparison group remained at the C grade level.

Additionally, with regard to solving word problems, there was a statistically significant difference between the groups’ scores, F(1, 17) = 7.96, p = .012, favoring the treatment group. The mean scores on the word-problem pretest and posttest earned by the treatment group were 45% and 77%, respectively. The mean scores on the word-problem pretest and posttest earned by the comparison group were 62% and 57%, respectively. The treatment group gain was socially significant when translated to grades (i.e., F to C), whereas the comparison group mean scores, when translated to grades, decreased from D to F.

**Conclusions**

The results suggest that the test scores of students with learning difficulties in mathematics improve with regard to solving both computation and word problems after participating in the *Subtraction With Regrouping* program. The gains for students who received instruction in the *Subtraction With Regrouping* program were greater than gains made by similar peers who received instruction using a traditional basal series.

**Reference**

Kaffar, B. J., & Miller, S. P. (2011). Investigating the effects of the RENAME Strategy for developing subtraction with regrouping competence among third-grade students with mathematics difficulties. Manuscript in preparation.

**Study 2**

**Overview**

In a multiple-probe across-participants study, five fifth graders with learning disabilities participated in the *Subtraction With Regrouping* lessons. There were four males and one female. The students took multiple and parallel forms of a test containing eight computation problems and two word problems across the duration of the study (i.e., baseline, treatment, maintenance [administered seven days after instruction]).

**Results**

The mean baseline score for the participants was 10.95% with a range from 0% to 70.00%. The mean treatment score for the participants was 87.20% with a range from 30.00% to 100.00%. The mean maintenance score (i.e., 7 days after instruction ceased) was 86.00% with a range of 80.00% to 90%. All five participants increased their performance level only after the introduction of treatment. The percentage of non-overlapping data (PND) was 90.2%, representing a large effect size.

**Conclusions**

The results show that students with learning disabilities are able to acquire computation and word problem regrouping skills after participating in the lessons in the*Subtraction With Regrouping* program. They also are able to maintain these skills seven days after instruction ends.

**Reference**

Ferreira, D. (2009). *Effects of explicit instruction on fifth-grade students with learning disabilities*. Unpublished doctoral dissertation, University of Nevada Las Vegas, Nevada.

## About the Author

**Susan P. Miller, Ph.D.**

**Affliations**

Professor

Department of Special Education

University of Nevada Las Vegas

Las Vegas, NV

Certified SIM Professional Development Specialist

University of Kansas Center for Research on Learning

Lawrence, KS

**My Background and Interests**

One of my favorite childhood pastimes was playing school. My students, at that very young age, included stuffed animals, dolls, and sometimes neighborhood friends. My more formal teaching experience was acquired years later when I taught employability skills to adults who lived in poverty, social studies and compensatory math to junior- and senior-high students without disabilities, reading and language arts to middle-school students with disabilities, and math, reading, and language arts to elementary students with and without disabilities. I loved each of these teaching experiences, and I like to believe that I touched the lives of my students in positive ways.

Subsequent to this teaching experience I worked as Program Administrator for the Multidisciplinary Diagnostic and Training Program at the University of Florida and currently serve as a Professor of Special Education at the University of Nevada Las Vegas (UNLV). In this role, I teach courses in learning strategies, instructional methodology, and leadership. My research interests focus on learning strategies and mathematics interventions. I’ve had the opportunity to share much of what I’ve learned from colleagues within the SIM network, teachers, and students as author of *Validated Practices for Teaching Students with Diverse Needs and Abilities* and as co-author of *Designing and Implementing Mathematics Instruction for Students with Diverse Learning Needs* as well as the Strategic Math Series.

**The Story Behind the ***Strategic Math Series: Level 2*

Upon completion of the Strategic Math Series: Level 1, I knew that additional work should be done with skills that extended beyond basic math facts and initial place value. Through my work with teachers in the area of mathematics, skill deficits related to addition and subtraction with regrouping and related word problems consistently emerged as areas of particular concern. Bradley Kaffar, one of my previous doctoral mentees and one the coauthors of *Addition With Regrouping* and *Subtraction With Regrouping* programs, contacted me about conducting math-related research in a summer camp designed for students needing help in elementary math skills (e.g., addition and subtraction with regrouping). The rest is history. Lessons were developed, field tested and revised until we believed they were ready for publication. We were thrilled to learn that Jean Schumaker and Don Deshler supported the initiation of Level 2 of the *Strategic Math Series*.

**My Thoughts about the ***Strategic Math Series: Level 2*

It has been a joy to witness the positive effects of the *Addition With Regrouping* and *Subtraction With Regrouping* lessons with students who struggle with this type of computation and related word problems. Students who receive this instruction develop conceptual understanding, learn to use procedural strategies, and develop fluency related to regrouping problems. Students also learn to discriminate between problems that require regrouping and those that do not. They learn to attack word problems without fear, and they absolutely love the one-minute timings and the Pig Games! Engagement in these fluency-building activities provides the extensive practice needed for skill mastery and keeps student motivation high. Students who receive instruction in these two programs will be ready to advance to more complicated math skills with the necessary prerequisite knowledge for future success.

**Teacher and Student Feedback on the ***Strategic Math Series: Level 2*

Both teachers and students report high levels of satisfaction with the two programs. Teachers report that the lessons are easy to implement and they plan to continue using the program with future students. Students report the base-ten blocks, drawings, and the “RENAME” Strategy all help with solving regrouping problems. They also report that the Pig Games and Minute timings helped them learn. A doctoral student recently taught a group of elementary students the addition with regrouping lessons. In a follow-up session with these students, one of the students asked her to please teach his teacher how to teach this way. Another heart-tugging event occurred when the doctoral student met individually with students to discuss the progress they made during the program. When one student was shown her progress chart and told how much she improved since the pretest, she began to cry and said, “You mean I’m not stupid?” I can think of no greater reward than teaching students in ways that allow them to experience success, feel pride, and discover that they are NOT stupid.

**My Contact Information**

Susan P. Miller, Ph.D.

Professor

Department of Special Education-Box 453014

University of Nevada Las Vegas

Las Vegas, NV 89154

Email: millersp@unlv.nevada.edu

Work Phone: 702 895-1108