Concept of Length - More About
The Early Numeracy Research Project (ENRP) described the development of the concept of length as including:
- Awareness of the Attribute
- Comparing
- Quantifying and
- Measuring.
In the literature, it is common to describe the key stages as:
- Conservation (things don't change their length just by being moved),
- Transitivity (if A is longer than B, and B is longer than C, then A is longer than C), and the
- Idea of a Unit and Iteration (using a unit - ie something of fixed size - over and over again to make a measurement).
Key stages of language development
There are several developmental sequences affecting language related to measurement attributes. Teachers can map individual students as they progress along these paths.
1. The move from multi-dimensional words to uni-dimensional words. Initially students will only express observations about size with the multi-dimensional word 'big'. An important part of teaching in the measurement dimension, is to give them a wide variety of uni-dimensional words that describe 'bigness' more precisely - 'tall', 'long', 'high', 'wide', 'old', 'heavy', etc. The move from multi-dimensional to uni-dimensional words is not only relevant to mathematics. For example, teachers encourage students to move from the multi-dimensional word 'nice' to uni-dimensional words such as 'tasty', 'friendly', 'good', 'beautiful', 'handsome'.
2. The development of comparative language. An understanding of the attribute of length is often revealed by tasks which compare lengths. Students need to develop appropriate language to describe their observations. Specific teaching attention needs to be given so that students can use 'long', 'longer' and 'longest' correctly.
3. Unmarked and marked words. In English, unmarked words such as 'more', 'long', 'tall', 'heavy', 'old' are generally mastered by students well before their marked counterparts such as 'less', 'short', 'light', 'young'. For example, 'more' is often a child's first word (at least in the sense of "give me more") whereas 'less' is not understood by a reasonable percentage of five and six year olds. Many of these students think that 'less' means the same as 'more'. Research shows that marked words are processed in the brain with reference to the unmarked word, even by adults. For example, if you ask me to select the shortest person from a group, it will take me longer than selecting the tallest person from the group, because I will mentally process the task in terms of tallness. Teachers should ensure that when the unmarked words are well established, attention is paid to the marked terms. For example, do not always ask students to read the greatest value from a pictograph; sometimes ask for the least.