Origins: Semple Math evolved gradually as a basic skills mathematics program from my work with many different types of students. Over a period of several years I have had the privilege of working with a variety of pupils, from the severely retarded to the extremely gifted, all with a common learning problem – trouble with math.

As I met and worked with individual students, I discovered that many shared certain characteristics, such as an inability to master the basic facts or understand abstract concepts. Each, however, presented a unique combination of strengths and weaknesses. These abilities and disabilities could be clearly seen in the way students processed, or failed to process, specific kinds of information.

For example, a student with delayed language development may have great difficulty comprehending the terminology of mathematics but have no trouble with the alignment of figures required in setting up a math problem. Another pupil with strong language ability, but weak directional and spatial skills, may be able to understand the vocabulary being used but will have difficulty aligning numerals, and thus may not assign them their correct place value. Both of these students will have difficulty working with the concept of place value, but for different reasons.

As I created clues (mnemonics) to help each type of student overcome his or her particular difficulty, I began to realize that one well designed clue could accommodate several different learning problems. An example of how one mnemonic can serve many purposes can be observed in the use of the chant, “Numbers all together go PLUS PLUS PLUS” (see Lesson 18). This oral chant, coupled with the finger activity described in the lesson, gives the child (or adult) with directional and spatial problems a way to remember the shape and placement of the plus sign. The rhythm of the chant provides the language delayed child with a mechanism for retrieving the abstract word “plus”. And the association made between the words “all together” and “plus” will later provide both students with a vital key for successful interpretation of certain kinds of word problems. This clue, along with the other mnemonics and activities suggested in the lesson, provide a solid base for understanding the concept of addition.

Method: The teaching strategies in this program are multi-purpose. They are specifically designed to accommodate a number of problems simultaneously. For this reason I urge you to expose your students to every clue. Leave nothing out. Learning the clues is just as essential to success as learning the skills. The clues form associations in memory that will be used again and again to teach students more complex information.

Also vital to success in Semple Math is the sequence of exposure. Start every student, regardless of age or skill, at the beginning with Lesson One. The older student may move more quickly than his younger counterpart but, nevertheless, should follow the same path. As your student progresses through the program he or she will build on mnemonic clues learned earlier in the sequence to accomplish more complex tasks and internalize more sophisticated concepts. Every clue he or she learns will open up several new areas of mathematical awareness.

The Student: Beginning and young remedial math students adjust quickly to learning by association. They enjoy the use of clues and respond positively to the success they have using them. You will find no resistance among your young learners to the way skills are sequenced and taught. Most take to the approach like ducks to water.

The older remedial student, on the other hand, may at the start of the program protest, “This is too easy!” or “I already know this stuff!” He is probably right and I tell him so. He has no doubt, hundreds of pieces of information in his brain that he has learned over the yeas. The problem is that the information is not organized and stored efficiently in memory. Because of this he has great difficulty remembering the facts or working with place value or interpreting word problems. He cannot pull out of his brain the information he wants when he wants it. This prevents him from building new, more advanced skills with old elementary skills. The old skills are not reliable because they cannot be retrieved quickly. I assure the student that this problem with memory can be resolved by building a new storage system.

To show the student what I mean I tell him to close his eyes and form a picture in his mind of his own house. I ask him to pretend to take every single thing out of the house and dump it into a pile in the middle of the road. I then ask him to imagine trying to find a spoon or a bowl in the pile. He may be lucky and locate the two items immediately or he could spend a week searching through the rubble. Wasn't it much easier to find the spoon and bowl when they were organized and stored in the kitchen in a specific cupboard or drawer?

I then point out that our brains work the same way. I tell my student that he has lots of information dumped into his brain the same way the contents of his house were dumped into the street. I explain that what we are going to do is pick up all of the pieces of information and organize them and store them in places where they can be easily found. We will do this by learning a system of clues called “mnemonics.” Mnemonics are simply tricks or images that help us remember.

Your older pupils are not really re-learning skills they already know. Instead they are learning how to remember the skills they have learned, and will learn, by using mnemonic clues. The clues provide a filing system in memory for storing information. When your students need to know the answer to nine times six, they will not have to go searching through their brains for it the way they had to search through the rubble for a cup and spoon out in the street. They will know exactly where to find the answer. This ability to retrieve answers to basic facts quickly will leave the student free to concentrate on the concepts involved. Searching memory or counting on fingers will no longer interfere with the processing of more complex mathematical information.

The System: Your pupils will begin build their storage systems in the very first lesson by learning a new skill called “spotting”. Spotting is a term I use to describe the ability to focus attention on the whole of something as opposed to its parts. Learning disabled and young children tend to view the world in sections. They look at one item at a time. In my experience I have noticed that this inability to form a visual gestalt – or to spot – is frequently found in students who have difficulty internalizing number concept, i.e., understanding one-ness, two-ness, etc.

In Lesson One your students will be learning how to spot one, two and three dots on a card or die. I cannot stress enough how important it is for your pupils to learn to see the pattern the dots form as opposed to seeing just individual dots. Looking at one dot at a time encourages the student to count. When a student counts dots instead of focusing on the gestalt of the pattern, he is dealing with a series of ones and not absorbing the wholeness of the number involved. His awareness of number is reduced to one item at a time. He will continue this approach as he tries to learn addition and subtraction facts by counting on his fingers (or any other available objects). Once a student has established the habit of substituting one skill for another, in this case counting dots instead of adding and internalizing whole numbers, he becomes so caught up in the counting process that he cannot pay attention to remembering the concept he is learning. Young and disabled students often fall into this piece-by-piece pattern of learning because of the emphasis placed on counting by traditional and modern mathematics programs. Many students who are taught to add by counting objects only learn to add by counting objects. They may never commit the basic facts to memory.

This is not to say that counting as a skill should be ignored. Counting is an extremely important skill that needs to be taught and practiced. Students must be able to see the parts (counting) of a number as well as its whole (spotting). This analysis/synthesis process, so vital to internalizing mathematical concepts, is not an easy concept for many students to grasp. For that reason I have separated the teaching of spotting and counting. Equal emphasis is placed on each.

The abstract language of modern mathematics presents another stumbling block for many children. The terminology used is often confusing or meaningless. Words such as “minus”, “set”, etc. are avoided in the beginning of the Semple Math Program and concrete terms are substituted. For example, instead of using the word “minus”, or even “take away”, I substitute “punch away.” This vivid vocabulary is within the child's realm of experience. Therefore, its meaning can be pictured and, as a result, more readily comprehended. In place of the word “set” I use the concrete word “card”. Later, when the students are totally familiar with the concepts and operations involved, the abstract words “minus” and “set” will be introduced.

These and many other techniques provide the student with an experiential base for learning and internalizing the mathematical operations and concepts to which he is being introduced. At no time in the program is the student expected to memorize by rote repetition. All new information is associated and stored in memory in the student's own filing system of experiences. Associations between the known and unknown provide students with a mechanism for retrieving specific information and understanding its meaning.