A Note from the Author
Early in my special education teaching career I had a student who could do no math. She could not even count to ten, although she could read. Conventional math learning steps were incomprehensible to her, and she had not yet developed any math memory. To get through to her I developed lessons which broke the learning sequence into such small steps that she could master them one step at a time, and could make progress without having to memorize anything, not even the order of the numbers. Since it was difficult for her to differentiate or mix concepts I added many lessons which juxtaposed new and old steps to highlight differences. She made steady progress, developed math confidence and learned basic arithmetic.
The materials and methods I had developed for my special student proved to be useful for all of the students in my special education classes. The small steps anticipated and solved many common problems and highlighted special, individual problems. So, as new children came to my classroom, I refined and expanded the materials and methods to accommodate a variety of problems (learning disabilities, aphasia, retardation, hearing loss, etc.). Subsequently, I used the materials in regular math classes where they proved to be especially useful for children who needed something more diagnostic than the conventional approach to math. The Math Lifeboat series is based on those materials and and methods.
The lessons in The Math Lifeboat are fundamentally different from those in conventional texts or workbooks:
Small Steps. The conventional learning strides have been subdivided in these books into such minute steps that even the slowest students can master them, one step at a time.
Gradually Combined. Small steps are gradually combined until the conventional strides are mastered.
Differences Highlighted. Processes which can be confused with each other are juxtaposed in such a way as to highlight their differences.
Memory Not Required. The learning sequence allows the student to make progress and gain math confidence without having committed to memory those facts which are assumed to be (and treated as) prerequisites in standard learning sequences.
Common Problems Avoided. The more common problems encountered using conventional teaching methods are anticipated and avoided.
Less Common Problems Anticipated. A variety of the less common problems are anticipated and extra work or specialized review programs are proposed.
More Continuous Flow. The content and sequence of the lessons provide a more continuous flow from the concrete to abstract concepts. For example, when learning addition, the student does not shift abruptly from manipulative material directly to mental arithmetic. Instead he gradually moves through stages which utilize first a vertical numberline where adding goes up and subtracting goes down, next his fingers and a numberline, and finally a form of mental addition in which he counts up from the larger addend in his head. Interposed in this gradual progression are lessons to teach the student to count forward or backward starting from any number since that skill is a prerequisite for the simplest forms of mental addition or subtraction.
Develops Student's Confidence. The lessons are expressly designed to help the student anticipate and sidestep errors. They also contain work checking devices to help him discover his own errors.
Teaching Guide Treats a Spectrum of Problems and Abilities. Facing each student workpage in the Teaching Guides is a page for the teacher. That page provides instructions both for conducting the lesson and for modifying the lesson to deal with a multitude of problems and/or levels of math maturity. Problems which individual students might encounter are identified, ways for detecting them are described, and remedies are presented. Learning stations and supplementary worksheets are described. And procedures are offered to clarify difficult concepts, sidestep common errors, or increase the impact of a lesson.
Organized for Individual Monitoring. The Teaching Guides are organized to facilitate the teaching and monitoring of students moving through the program at different rates. With them the teacher can glance at the guide page provided opposite each lesson to jog her memory, and refer back to it if the student encounters difficulty.
Multiple Uses. The Math Lifeboat series can be used:
as the principal texts in special education classes;
as adjuncts in conventional K, 1, 2, or 3 classrooms to help children who are experiencing difficulties with any of the fundamental concepts;
as texts in college level courses which address methods of teaching children with special needs; and
as frustration-free workbooks and guides for tutoring by teacher or parent.
About the Author
Ernestine Sadotti Smith, M. Ed., Phi Beta Kappa, Sigma Xi, a former biologist at NIH and special education teacher, has been a special education math consultant in public and private schools in Maryland, Virginia and the District of Columbia . She is now the lower school consultant and tutor at Broadwater Academy in Exmore, Virginia.