Every Child's Path is the result of a five-year research project that started by identifying common difficulties children were experiencing in mathematics and literacy in the early years.
Marie Clay, the founder of Reading Recovery discovered that children who make slow progress in reading, haven’t learned how to look carefully at print. They miss details, similarities and differences.
My testing revealed that children struggling with mathematics also missed details, similarities and differences. Since Reading Recovery teachers are trained to teach children to look carefully at print when reading and writing, I determined that there must be a way to teach them how to look carefully at print relating to mathematics.
My research led me to the work of Doug Clements, a math professor at the University of Buffalo, New York, who said that it is easier for children to learn concepts when they are introduced inside a box framework first, before a row and circle. The box leads to many concepts relating to spatial awareness and directionality.
Adapting Clements’ ideas on Subitizing, [instantly seeing how many] I wanted to see if kindergarten and grade one children could remember the positions of four spots inside a box when shown briefly. As the children tried to match the positions by placing four pennies in a box, I noted their speed and the direction of placement (left to right or right to left, top to bottom or bottom to top). I drew their incorrect placements for future analysis. Three of the nine boxes are shown below.
Those who had the most difficulty learning to read and write were generally the ones who were least accurate in remembering where they had seen the spots.
While the spots were clear in the box, many children didn’t notice that spots in a row across the box had spaces between them. They also didn’t notice that some were placed near edges. That is when I realized that the box needed features similar to those of a map with its identifiable grid, numbers across the top, letters down the side and a direction indicator.
To accomplish this, I used a large mat for the box shape, and assigned names to edges and corners. (See Structure of the Box below.) We discussed how knowing names for each edge and corner could become an anchor or reference point, for whatever was seen in box. When children learned the name and position of each corner and edge, further testing resulted in improvement in how almost all remembered seeing the spots in the boxes.
This knowledge then transferred to noticing how letters, numbers, words, sentences, sets and subsets fit into the box framework. Furthermore, they began to look critically and analytically at all print in both Mathematics and Literacy when placed within the boundaries of a box.
A large Noticing Mat can be compared to a page in a book. The children perform tasks on the “page.” When they know names for specific edges and corners, they use those names to help them understand where and how letters, numbers, words, sentences, sets and subsets fit.
Many questions guide them to look for details, similarities, differences and ways to solve problems. They respond using complete sentences.
Children see that when the mat is turned from portrait (vertical) to landscape (horizontal) positions, the top, bottom, starting and stopping positions remain constant.
Children are encouraged to complete tasks on the Noticing Mat quickly, to provide opportunities for many children to be actively involved.
Children who have difficulty concentrating can be involved early in the lessons. Giving them responsibility for holding objects for you and letting them participate many times also helps them to focus.
As children work with letters, words and sentences, they learn that there is a left to right, top to bottom progression. The names for each corner and edge (Starting, Stopping, Top, Bottom) provide a structure for the box giving the teacher and child a common way of communicating where to begin and end
Sentences from chart papers may be cut into individual words, and placed across the mat. Children walk from left to right saying the words of the sentence. These activities promote one to one correspondence and phrasing.
Large numbers and lower case letters are made with wool on the mat. Children pay close attention to where and how the teacher lays the wool. As the children walk on these numbers and letters, they begin to link parts of each to specific parts of the mat. They also remember direction of movement. Letters and numbers start at the top and go to the bottom, but may go from left to right (2) (m) or right to left. (c) (5)
They also learn that when counting, they may move from left to right or right to left, top to bottom or bottom to top.
Games like Chess, Checkers, Snakes and Ladders, Xs and Os, etc., all require moving across, down and on the diagonal.
By dividing the mat into two parts across the middle, concepts like: above, below, high, low, over, under, top, bottom, north, south, first, last can be explored. Other words like sub-zero or below zero, subway, submarine etc, can be introduced.
When printing on lines, letters have parts above and below those lines.
When reading the temperature we use the terms above and below zero.
Music notes also go above and below lines.
In science we study animals that live, above and below ground. We also found that the part of the vegetables we eat may be found above or below ground.
By dividing the mat into two parts down the middle, concepts like; first, last, first, second, left, right, east, west, beginning and ending can be developed.
Knowing the positions of first and last on the Noticing Mat, makes it easier for children to identify or listen for the first and last sounds in a word, parts of a story and digits in a number.
We find numbers that come before (first) and (last) after a given number or numbers.
Looking at the first and last parts of the mat is useful for teaching place value. When listening to a number like 43, they hear that the 4(0) belongs first and the 3 belongs last.
It can also be linked to the language used when telling time on a clock. [to, past, before, after]
By examining the diagonal, children are better prepared for seeing edges and corners. It helps them to see and subsets within that framework. Some games like Xs and Os, Snakes and Ladders and Chess require use of the diagonal.