## Additional information

Dimensions | 8.5 × 11 in |
---|---|

Cover | Paperback |

Dimensions (W) | 8 1/2" |

Dimensions (H) | 11" |

Page Count | 132 |

Publisher | Edge Enterprises, Inc. |

Year Printed | 1992 |

Susan P. Miller

Whether they are calculating their income taxes or the amount of paint needed for the back bedroom, chances are that students will eventually need some multiplication skills. Multiplication Facts 0 to 81 is just the ticket for this task.

In a graduated series of lessons, students progress through three different levels of instruction: concrete, representational, and abstract. At the concrete level, they use objects (like pennies) to understand that a problem, like 5 times 7, is the same as five groups of seven pennies. At the representational level, they use pre-printed pictures to expand this understanding. Finally, they graduate to the abstract level, where they use numbers alone to answer the problem, or, if they’re unable to recall the answer, draw out the problem using tallies. Timed practice activities, motivational “pig games,” and practical word problems round out the instruction at each level.

$14.50

Dimensions | 8.5 × 11 in |
---|---|

Cover | Paperback |

Dimensions (W) | 8 1/2" |

Dimensions (H) | 11" |

Page Count | 132 |

Publisher | Edge Enterprises, Inc. |

Year Printed | 1992 |

**Study 1**

**Overview**

The *Multiplication Facts 0 to 81* program is used to teach students the multiplication facts. In this study, 123 second graders participated. Thirteen of them had a disability (a learning disability or an emotional disability), 11 were low achievers, and the rest were normal achievers. Their six teachers were trained to teach the*Multiplication Facts 0 to 81* program, and they implemented the program in classes containing heterogeneous groupings of 25 to 27 students. The point of the study was to compare the effects of the program with regard to the performance of the three groups of students: students with disabilities, low achievers, and normal achievers. First, the performances of the students with disabilities and low achievers were compared. Then, the performance of the normal achievers was compared to the performance of the combined group of low achievers and students with disabilities. Two types of measures were gathered: student performance on an acquisition test (number of correct responses to problems; and student performance on a proficiency/fluency test (number of correct responses per minute).

**Results**

MANOVA results revealed no statistically significant differences between the performances of the students with disabilities and the low achievers on six dependent measures including untimed tests of multiplication acquisition and timed tests of multiplication proficiency. A statistically significant difference was found between the students’ pretest and posttest scores [acquisition, F(1, 22) = 187.42, p < .01; proficiency, F(1, 21) = 17.59, p < .01].

When the performances of the students with disabilities and the low achievers were combined and compared to the performances of the normal achievers, no statistically significant differences were found on four of the six dependent measures. Differences were found on the students’ performance after abstract lessons and their performance on the untimed test of acquisition. Again, a statistically significant difference was found between the students’ pretest and posttest scores [acquisition, F(1, 120) = 875.66, p < .01; proficiency, F(1, 119) = 59.23, p < .01].

Both teachers and students indicated that they were satisfied with the program. All six teachers indicated they would use the program again and rated the program as “excellent.” Student surveys indicated that 97% of the normal achievers, 100% of the students with disabilities, and 100% of the low achievers liked learning multiplication.

**Conclusions**

These results suggest that different groups of students can experience statistically significant gains with regard to learning multiplication facts when taught together in inclusive classes using this program.

**Reference**

Miller, S. P., Harris, C. A., Strawser, S., Jones, W. P., & Mercer, M. M. (1988). Teaching multiplication to second graders in inclusive settings. *Focus on Learning Problems in Mathematics, 20*(4), 50 – 70.

**Study 2**

**Overview**

Three seventh-grade students with mental retardation were taught multiplication facts and how to solve multiplication word problems using the *Multiplication Facts 0 to 81* program. One of the students was visually impaired, and another had a physical disability. A special education teacher taught the lessons after receiving training in one session. A multiple-baseline across-students design was used.

**Results**

All three students’ scores on multiplication tests improved from baseline to after instruction. Student 1 earned a mean score of 73.3% in baseline and 90.5% after instruction began. Student 2 earned a mean score of 67.5% in baseline and 93.5% after instruction began. Student 3 earned a mean score of 58% in baseline and 91.5% after instruction began. The multiple-baseline design showed that the improvement did not occur until after the intervention had begun. When the students began to learn to solve advanced problem-solving skills, their performance dropped slightly. The mean scores for the students during these lessons were 83%, 87%, and 90%.

When the performances of the students with disabilities and the low achievers were combined and compared to the performances of the normal achievers, no statistically significant differences were found on four of the six dependent measures. Differences were found on the students’ performance after abstract lessons and their performance on the untimed test of acquisition. Again, a statistically significant difference was found between the students’ pretest and posttest scores [acquisition, F(1, 120) = 875.66, p < .01; proficiency, F(1, 119) = 59.23, p < .01].

**Conclusions**

The results showed that students with mental retardation can learn multiplication facts through the use of the *Multiplication Facts 0 to 81* program, and they can learn to solve the more advanced multiplication problems at a socially significant level, with mean scores above the 80% level in all cases.

**Reference**

Morin, V. A., & Miller, S. P. (1998). Teaching multiplication to middle-school students with mental retardation. *Education and Treatment of Children*, 21(1), 22 – 36.

**Study 3**

**Overview**

The purpose of this study was to determine the effects of teaching multiplication skills to diverse groups of students in inclusive general education classes. The students were second graders and included 99 normal achievers, 12 students with learning disabilities (LD), and one student with an emotional disability. Six general education teachers were trained to teach the *Multiplication Facts 0 to 81* program to the diverse groups of students regularly enrolled in their classes. A multiple-baseline across-classes design was used.

**Results**

The students with disabilities began instruction performing at about the same level on the pretests as the normal achievers. During instruction, the median scores of the students with disabilities on learning sheets were about the same as those of the normal achievers. During the phase of instruction where students had to demonstrate conceptual understanding of the multiplication process, the scores of the groups were also very similar. During the phase of instruction where students had to read or write and solve word problems, the students with disabilities earned lower scores than their peers. On the acquisition posttest, the median score for students with disabilities was 70%, which was 15 percentage points lower than the median score for the normal achievers. Nevertheless, the posttest scores of the students with disabilities represented a 65 percentage point mean gain over their pretest scores. On the fluency measures, the mean rate increase for the students with disabilities was 10 correct digits per minute, and the mean rate increase for the normal achievers was 9 correct digits per minute.

**Conclusions**

This study shows that students with disabilities can be successfully taught multiplication skills with the *Multiplication Facts 0 – 81* program while enrolled in inclusive general education classes. Their scores on learning sheets during instruction were comparable to the scores of normally achieving peers except when asked to read or write and solve word problems. Their rate of solving multiplication problems was higher than the rate of the normal achievers. Their posttest acquisition scores were somewhat lower than those of the normal achievers, which is probably due to their lower performance on the word problems on the test.

**Reference**

Harris, C A., Miller, S. P., Mercer, C. D. (1995). Teaching initial multiplication skills to students with disabilities in general education classrooms. *Learning Disabilities Research & Practice*, 10(3), 180-195.

**Study 4**

**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 correct responses to multiplication problems); student performance on a word-problem test (number of correct responses to word problems); and student performance on a fluency test (number of correct digits per minute).

**Results**

The 52 students who received instruction in the *Multiplication 0-81* program earned a mean score of 43% on the acquisition pretest and 91% on the posttest. They earned a mean score of 36% on the word-problem pretest and a mean score of 92% on the word-problem posttest. With regard to fluency, the students correctly produced an average of 5 digits per minute during the first abstract lesson and 14 digits per minute at the completion of the program. On the follow-up generalization measure, in which students were asked to apply the DRAW Strategy to multiplication problems that had not been taught in the program (e.g., 12 x 3), students earned a mean score of 96%. 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 in different locations, the students maintained their mean fluency rate of 14 correct digits per minute.

**Conclusions**

The results show that students with learning difficulties in math are able to learn basic multiplication facts and associated word problems through use of the*Multiplication Facts 0 to 81* program. The students acquire multiplication knowledge and improve their ability to solve multiplication facts with fluency. They also generalize their fluency skills with multiplication facts to new instructors within new settings at levels that exceed initial baseline rates and match mean instructional 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 5**

**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 *Math Strategies 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 correct answers to math problems

Figure 2: Number of digits correct per minute in timed fluency tests

The results for the Multiplication Facts 0 to 81 program are shown in the sixth pair of bar graphs on the right side in each figure. Students earned a mean score of 48% answers correct on the acquisition pretest and a mean score of 92% cottect on the posttest. They produced an average of 7 correct digits per minute in baseline and 16 digits correct per minute after instruction.

**Conclusions**

The programs in the Strategic Math Series produce significant 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 in all areas.

**Reference**

Miller, S. P., & Mercer, C.D. (1998). *Strategic Math Series professional developers’ guide*. Lawrence, KS: Edge Enterprises.

**Cecil D. Mercer, Ed.D.**

**Affliations**

- Distinguished Professor (Emeritus)

- Department of Special Education

- University of Florida

- Gainesville, FL

- Certified Learning Strategies Trainer

- University of Kansas Center for Research on Learning

- Lawrence, KS

**My Background and Interests**

I am retired as a Distinguished Professor of Special Education at the University of Florida. As a professor, I taught courses in learning disabilities, learning strategies, instructional methodology, and behavior management. My research interests focused on learning strategies and reading and mathematics interventions. I authored numerous books and curriculum materials, including *Students with Learning Disabilities*, *Teaching Students with Learning Problems*, *the Strategic Math Series*, and *Great Leaps Reading*. For 11 years, I was Co-Director of the University of Florida Multidisciplinary Diagnostic and Training Program. In addition, I served on the Board of Directors of the International Dyslexia Association and on the Professional Advisory Board of the Learning Disabilities Association of America. I was awarded the College of Education Teacher of the Year award three times at the University of Florida and also received the University of Florida Graduate School Advisor/Mentoring Award and the College of Education Lifetime Achievement Award. As an alumnus of the University of Virginia Curry School of Education, I was awarded the Outstanding Higher Education Faculty Award.

**The Story Behind the Strategic Math Series**

Many students with learning problems lack proficiency in basic number facts and are unable to acquire and maintain math facts at fluency levels. Given the problems that many students with learning problems exhibit with lower-level math skills and the importance of these skills to overall math achievement, the need existed for comprehensive programming to teach basic math facts. Susan Miller, one of my doctoral students at the University of Florida, also was interested in determining effective ways to teach mathematics. For her dissertation, 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. Because the CRA sequence is appropriate for teaching the understanding of math throughout the span of math concepts, skills, and word problems, we conducted 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 for enjoyable practice. Due to the research results, the success and excitement of students in the program, and the enthusiasm of teachers using the CRA teaching sequence, Don Deshler and Jean Schumaker encouraged and supported the creation of the

**My Thoughts about the Strategic Math Series**

The

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

Teachers report that the math strategies instruction is easy to implement and that the students really understand addition, subtraction, place value, multiplication, and division when they finish the instructional lessons. Teachers who use comprehensive math programs indicate that the

**My Contact Information**

Cecil D. Mercer

Email: cecilmercer@cox.net

Phone: 352-378-4849

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