Mathematics and Memory
An all too common scene in the home during the evening: a child sits at the kitchen table, staring at math pages with their head held in their hands. Time ticks by. Sometimes tears are involved in the scene, sometimes even anger or rage, but the scene does not change. As parents, we long to help our children, yet often feel inept or too far removed from mathematics or teaching.
Students who struggle often understand the math work while at school, or while sitting with a tutor, but given time alone with the subject, they can draw a blank. By taking a closer look at the relationship of memory and mathematics, we can begin to unravel the mystery of why the learning of mathematics does not always stick in the minds of those who study it.
The development of memory is of great importance to the advancement of thought. This maturity of thought in conjunction is of great significance to the ability to perform math. By first taking a look at memory, we begin during the first three years of life, where memory forms in three distinct ways: localized memory (movement memory), rhythmical memory and picture memory. (The First Three Years of the Child, Karl König, 2004)
Localized memory (movement memory) begins in the first year of life and is a memory that is created out of our limbs. Infants use their arms, hands, legs, feet and tongue to feel and to remember in this early stage of life. Out of the bodily experiences of moving themselves and the objects in their environment, up/down, left/right and backwards/forwards they develop a sense of movement, of balance and of the space around them. These bodily experiences lead to the ability to move inwardly, through thought, and to remember. During the first three years of life, if movement of the young child is overly restricted or confined in some way, this faculty of memory may need some additional strengthening work during the later school age years. Long periods of time strapped in car seats, baby carriers and strollers may hamper the natural development of this fundamental piece of memory formation.
When it comes to mathematics, this underdevelopment of movement memory may first show up in kindergarten or first grade. The student will show difficulties with place value and the meaning of a number, which is called number sense. This is because a child may not have had enough bodily experiences of moving around various numbers of objects, counting and sorting during earlier stages of development. It may also become apparent in second grade where borrowing and carrying begin. Around the third grade, weakness in localized memory is shown when long division is presented. Without a very comfortable ability to move their own bodies and the objects around them, students cannot then move around comfortably within the context of all the operations (multiplication, addition and subtraction) and locations (left/right, above/below, forward/backward) in a long division math problem.
When these challenges present themselves, it is suggested to then take the child back into movement in order to strengthen the memory before proceeding. Those may consist of the following: large bodily gross motor movement (zoo exercise movements, jump rope, skipping, bean bag tossing, etc.) and fine motor movements like the use of manipulative (blocks, counting sticks, beads, bean, proper pencil grip, etc.) This child with weak localized memory may benefit from learning math, by moving every mathematical problem in a concrete form first using their limbs and with objects that can represent the thoughts.
Secondly, this child needs permission to stay at that stage of learning in order to explore the objects that make the math true before moving to the next stage. Luckily, in Waldorf Schools, many teachers recognize the importance of movement in learning and memory formation and thus support additional movement classes such as the Zoo Exercises in the second grade, Extra Lesson sessions or exercises and Curative Eurythmy.
The second step of memory formation is rhythmical memory formation. This piece of memory is connected with the use of speech and song during our second year of life. We see this clearly in a child's first words, "Ma ma" for mother or "da da" for father or "ba ba" for bottle. Sometimes this rhythm is stretched out further making the pattern more apparent: "Ma ma ma ma..." Every new word is repeated and repeated. This is the small child forming rhythmical memory. The person or object, in this case mother, is remembered through this rhythm of the sounds in this small monotone song. Later in school, this faculty of memory is called upon when the child sings a song to support remembering the names for the days of the week, states in a country or when creating a rhythm for the multiplication tables to support memorization.
The hazard of moving to the rhythmical memory state too early in school learning environments is that if the child has not sufficiently touched and moved with their limbs what is being now taught in rhythm, there is little or nothing for the child to connect the rhythm to within himself or herself. Thus the rhythm, while possibly fun, may not lead to independent thought formation if presented to early. Although many children may be able to get caught up in the classroom songs and rhythms, when asked to later reproduce them independently, there is a struggle and perhaps failure. Teachers often see this in the children that are challenged with saying their multiplication tables forward and backward on their own. While with the class, they participate fully in the reciting and chanting of the tables, seemly grasping the math facts, but without the group carrying them externally, they struggle reproducing independently. This is a piece of information a parent or teacher can glean from this situation and then take the child back to the localized memory stage with work involving their limbs and object able to be touched and manipulated followed by work with verses, poetry, story and speech.
Picture memory is the third step of memory formation and can be seen being developed in the small child through their use of imagination and story telling or fantasy play in the third year of life. This is where the inner movie screen comes into being or the ability to see in our "mind's eye" develops. This faculty is of paramount importance in the study of higher mathematics where abstract ideas are worked with. Conditions that can bring about deficiencies in the creation of the picture memory are environments with screens such as television and computer. Both of these screens provide completely formed images to a child and therefore the need to inner picture is superseded. Reading and pretending with children consequently support the growth of picture memory. Beginning with pre-algebra in the middle school years, this faculty of inner picturing or lack there of becomes very apparent in the student. Once diagnosed, a teacher can work with this deficiency in the math lesson through the use of stories, images, and color-coding of the work to stimulate the picture formation in the inner mind of the student.
Children who struggle with the subject of mathematics are trying to tell us something. Often it is not so simple as a dislike of the subject matter itself. There is an underlying reason. When we use the students struggle as information in a critical judgment free way, we can therefore support and heal the child.... as is the purposeful path of education.
I am a willow of the wilderness,
Loving the wind that bent me. All my hurts
My garden spade can heal. A woodland walk,
A quest of river-grapes, a mocking thrush,
A wild-rose, or rock-loving columbine,
Salve my worst wounds.
-Emerson, Ralph Waldo
Email: Lori@yourfullpotential.net
Blessings on your journey!