## Additional information

Dimensions | 8.5 × 11 in |
---|---|

Cover | Paperback |

Dimensions (W) | 8 1/2" |

Dimensions (H) | 11" |

Page Count | 111 |

Publisher | CRL |

Year Printed | 1991 |

Cecil D. Mercer

Problems like “3 + 6” and “0 + 9” may seem easy, but they probably cause a few anxious moments when students first learn them—especially at an automatic level.

To counter the confusion often encountered when moving from addition to subtraction, students need to understand what subtraction really is. To do this, *Subtraction Facts 0 to 9* takes students through the concrete-representational-abstract learning sequence. At the concrete level, students learn to solve problems like 7 – 3 by counting out seven objects, removing three objects, and then counting the remaining objects. At the representational level, students learn to draw pictures of objects next to a problem and use these pictures to determine the answer. Finally, at the abstract level, students use numbers alone to answer the problem, or, if they’re unable to recall the answer, draw out the problem using tallies.

Dimensions | 8.5 × 11 in |
---|---|

Cover | Paperback |

Dimensions (W) | 8 1/2" |

Dimensions (H) | 11" |

Page Count | 111 |

Publisher | CRL |

Year Printed | 1991 |

**Study 1**

**Overview**

A field test was conducted that involved 22 teachers and 109 elementary students who were experiencing difficulties learning math. This student group included 102 students with learning disabilities (LD), 5 students with emotional disabilities, and 2 students who were at-risk for school failure. The field test took place in seven school districts in both small-group (less than 7 students) and larger group (7 to 18 students) instructional arrangements. The teachers were trained to use programs in the Strategic Math Series. Different groups of students were taught addition facts, subtraction facts, multiplication facts, and division facts, depending on their needs. Three types of measures were gathered: student performance on a math-facts acquisition test (number of problems solved correctly with no time limit); student performance on a word-problem test; and student performance on a fluency test (number of digits correct per minute).

**Results**

The 14 students who received instruction in the Subtraction Facts 0 to 9 program earned a mean score of 17% on the subtraction acquisition pretest and a mean score of 95% on the posttest. The students earned a mean score of 28% on the subtraction word-problem pretest and a mean score of 84% on the posttest. With regard to fluency, the students produced an average of 11 digits correct per minute during the first abstract lesson and 24 digits correct at the completion of the program. On the follow-up generalization measure, in which students were asked to apply the DRAW Strategy to subtraction facts that had not been taught (i.e., subtraction 10 to 18 facts), students earned a mean score of 92%. The generalization measure was administered 3 to 5 days after instruction ended by examiners unknown to the students in school locations other than their typical classroom. On the follow-up fluency measure, also administered 3 to 5 days after instruction ended by unknown examiners in different locations, the students’ mean fluency rate was 18 correct digits per minute.

**Conclusions**

The results show that students with learning difficulties in math are able to learn basic subtraction facts and to solve associated word problems through use of the Subtraction 0 to 9 program. The students acquired subtraction knowledge and improved their ability to solve subtraction facts with fluency. They also generalized the DRAW Strategy to novel subtraction problems, to persons other than their math teacher, and to settings other than their typical classroom with high accuracy. Students also generalized their fluency with the subtraction facts to new individuals within new settings at levels that exceed initial baseline rates.

**Reference**

Mercer, C. D., & Miller, S. P. (1992). Teaching students with learning problems in math to acquire, understand, and apply basic math facts. *Remedial and Special Education*, 13(3), 19-35, 61.

**Study 2**

**Overview**

The purpose of this study was to test the effects of a graduated word-problem instructional sequence in teaching students to solve word problems. This sequence entails first teaching students to solve a problem that contains a few words, then a problem containing a phrase, a sentence, and next a paragraph. Finally, students are taught to solve word problems containing a paragraph that includes extraneous information and to write their own word problems. This sequence is used throughout the Strategic Math Series. It was specifically tested in this study with Subtraction Facts 0 to 9 instruction.

Student participants were 13 students with learning disabilities in math. Their ages ranged from 7 to 9 years. They were taught Subtraction Facts 0 to 9 by four special education teachers who were regularly assigned to teach them in either self-contained classes or resource rooms.

**Results**

On the pretest, the students’ mean score was 17% on the computation problems. They did not solve any of the word problems correctly. On the posttest, the students’ mean score on computation problems was 95%. Their mean score on paragraph word problems without extraneous information was 100%, on paragraph word problems with extraneous information was 86%, and on writing their own word problems was 91%. Thus, their overall mean score for these three types of word problems was 92%. All of the teachers indicated that they would use the program again.

**Conclusions**

This study indicated that the graduated word-problem sequence is successful in teaching students with learning disabilities in math to solve subtraction word problems at a high level of competence. Their performance improved with regard to computation problems and different kinds of word problems, including writing their own word problems.

**Reference**

Miller, S. P., & Mercer, C. M. (1993). Using a graduated word-problem sequence to promote problem-solving skills. *Learning Disabilities Research & Practice*, 8(3), 169 – 174.

**Study 3**

**Overview**

Multiple field tests were conducted that involved 56 teachers and 248 elementary students who were experiencing difficulties learning math. These field tests took place in seven school districts in self-contained, resource, and general education classes. The teachers were trained to use programs in the Strategic Math Series. Different groups of students were taught addition facts, subtraction facts, multiplication facts, division facts, and place value concepts and skills, depending on their needs.

**Results**

Substantial gains were made by the students in all areas. See the figures below for the results in each math area. Figure 1 shows the results on untimed acquisition tests, and Figure 2 shows the results on timed proficiency tests (i.e., fluency tests). The number of students participating in each field test is shown beneath each pair of bars on the graph.

**Figure 1: Percentage of answers correct on untimed acquisition tests**

**Figure 2: Percentage of digits correct per minute on fluency tests**

The results for the Subtraction Facts 0 to 9 program are shown in the second pair of bar graphs in each figure. For the Subtraction Facts 0 to 9 program, students earned a mean score of 32% on the acquisition pretest and 96% on the posttest. On the fluency test, they produced an average of 10 correct digits per minute in baseline and 22 correct digits per minute after instruction.

**Conclusions**

The programs in the *Strategic Math Series* produce substantial gains in student performance on math acquisition and fluency tests across several areas of mathematics. In addition, these programs all produce socially significant final performances with students earning scores around or above the 90% level on acquisition tests in all areas.

**Reference**

Miller, S. P., & Mercer, C.D. (1998). *Strategic math series trainer’s guide*. Lawrence, KS: Edge Enterprises.

**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**

I am 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 know 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*, and the *Strategic Math Series*. Prior to joining the faculty at UNLV, I worked as Program Administrator for the Multidisciplinary Diagnostic and Training Program at the University of Florida. Additionally, I’ve taught students with and without disabilities at the elementary and secondary levels. As a high-school general education teacher, I taught social science courses and compensatory mathematics. As a junior-high general education teacher, I taught geography and American history. As a middle-school special education teacher, I taught reading, and as an elementary diagnostic classroom teacher, I taught math, reading, and language arts to students with medical, learning, and behavioral challenges.

**The Story Behind the Strategic Math Series**

Arithmetic and mathematics were my least preferred subjects in the school curricula as a child and teenager. I spent a good bit of time memorizing procedures to get correct answers without truly understanding the meaning behind those procedures. From an early age, becoming a teacher was high on my list of goals, but I never imagined that mathematics would be the subject I’d teach. As fate would have it, my teaching assignments at both the elementary and high school levels included mathematics. It wasn’t until I began teaching math that I realized it was not math that I had disliked all those years, but it was the way I had been taught math. That realization launched my dedication to finding better ways to teach this complex area of the curriculum. Cecil Mercer, my doctoral mentor at the University of Florida (Go Gators!), also was interested in determining effective ways to teach mathematics. Thus, when dissertation time arrived, we designed a study that involved the use of the Concrete-Representational-Abstract (CRA) teaching sequence to help students acquire an understanding of place value. The positive results obtained in this dissertation study caused us to launch a series of studies and field tests related to teaching basic math facts using the CRA sequence with integrated strategy instruction, a graduated word problem sequence, math timings, and numerous PIG dice games to make math practice fun. The positive outcomes for students and positive feedback from their teachers motivated us to share our results with Jean Schumaker and Don Deshler, and shortly thereafter the

**My Thoughts about the Strategic Math Series**

I have enjoyed witnessing the positive effects of

**Teacher and Student Feedback on the Strategic Math Series**

Teachers routinely tell me that the math strategies instruction is easy to implement and that their students love it. They report that the students really understand addition, subtraction, place value, multiplication, and division when they finish the instructional lessons. Teachers who use a variety of comprehensive mathematics programs say that the Strategic Math Series is a wonderful supplement to these programs. They note that students need this supplemental instruction and practice to be successful in math. When Cecil Mercer and I conducted the field tests for the series, we had opportunities to talk with many teachers and to read their written feedback about the lessons. The 56 teachers involved in these field tests were overwhelmingly positive and indicated they would continue to use the program even though the field tests were complete. Written feedback from the students was very positive as well. I recently received a letter from a parent-volunteer who was using the program with her son and another child in an elementary resource room setting. She noted that the students were engaged and enthusiastic and wrote, “I’m so excited about how rapidly both children are progressing and what good feelings the children are experiencing due to their success.”

**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

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