Additional information
| Dimensions | 8.5 × 11 in |
|---|---|
| Cover | Paperback |
| Dimensions (W) | 8 1/2" |
| Dimensions (H) | 11" |
| Page Count | 108 |
| Publisher | CRL |
| Year Printed | 1991 |
Addition Facts 0 to 9
Susan P. MillerCecil 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.
With Addition Facts 0 to 9, however, students reallyunderstand what such problems mean, using the concrete-representational-abstract method of learning. At the concrete level, students count out objects like checkers or sticks to understand that the problem 5 + 2 really means 5 objects being added to 2 objects (or vice versa). Once they have acquired this level of understanding, they move on to the representational level of learning. Here, they create pictures of boxes or circles next to each of the numbers. Finally, they graduate to the abstract level, where they use numbers alone to solve the problem, or, if they’re unable to recall the answer, draw out the problem using tallies.
Along the way, students also become proficient solvers of word problems involving addition facts 0 to 9. They also have fun practicing these facts with the colorful “pig dice” that come with the book, and they learn to increase the speed at which they are able to recall these foundational facts. Follow up with either Addition Facts 10 to 18 or Subtraction Facts 0 to 9.
Description
Research on Addition Facts 0 to 9
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. Students were taken through a series of lessons for each topic that included lessons where they manipulated concrete objects, lessons where they drew pictures, and lessons where they used numbers.
Results
The four students who received instruction in the Addition 0 to 9 program earned a mean score of 40% on the acquisition pretest and a mean score of 98% on the posttest. With regard to fluency, the students produced an average of 10 correct digits per minute during the first lesson, 18 correct digits per minute at the completion of the program, and 18 correct digits per minute three to five days after instruction ended. The latter fluency measure was administered by examiners unknown to the students in school locations outside of the classroom where instruction took place.
Conclusions
The results show that students with learning difficulties in math are able to learn basic addition facts through use of the Addition 0 to 9 program. The students in this study acquired addition knowledge and improved their ability to solve addition facts with fluency. They also generalized their fluency with addition facts to new situations where new examiners administered the test at levels that exceeded initial baseline rates and matched mean instructional rates.
Reference
Mercer, C. D., & Miller, S. P. (1992). Helping 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
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: Students’ percentage scores on untimed math tests.
Figure 2: Number of digits correct per minute on timed fluency tests.
The results for the Addition Facts 0 to 9 program are shown in the first pair of bar graphs in each figure. Students earned a mean score of 34% correct answers on the acquisition pretest and 93% on the posttest. They produced an average of 11 correct digits per minute in baseline and 21 digits 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 on acquisition tests in all areas.
Reference
Miller, S. P., & Mercer, C.D. (1998). Strategic Math Series professional developer’s guide. Lawrence, KS: Edge Enterprises.
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
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 Strategic Math Series was born!
My Thoughts about the Strategic Math Series
I have enjoyed witnessing the positive effects of Strategic Math Series instruction on students who struggle with their basic math facts and place-value skills. Students who receive this instruction develop conceptual understanding, learn to use procedural strategies, and develop fluency related to the basic math facts. Students also learn to attack word problems without fear, and they absolutely love the Pig Games! Engagement in these games provides the extensive practice needed for skill mastery and keeps student motivation high. Mathematics is hierarchical with one skill building on the next. Mastery of basic math facts and place value understanding is needed for students to progress through the mathematics curriculum. Without this understanding, higher level mathematics skills are a tremendous challenge for teachers to teach and students to learn. Fortunately, this program sets students up for future success in their mathematics endeavors.
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
