Place Value in the Horizon
In the history, the development of representing numbers experience advancements over time. It began with the numerical mark using slashes or tallies carved onto cave walls or into bone, wood, or stone by Paleolithic era. Then, it is refined by the use of knots arranged along cords in Persia. The Incas and Sumerian had advancement by representing numbers with different units using some stuffs. Another growth of the number representation occurred by notating symbols of numbers such as in Babylonian times, Mayans, ancient Egyptians and Roman. All of these systems are considered as additive numeration system. The important change happened when Indian method was introduced by Muhammad ibn Musa al-Khwarismi in which we use it nowadays. This system relies on place value system in which most children feel difficulty to come up the idea thereof.
Many children think the numbers as additive numeration system e.g. they consider the symbol of one hundred and three as 1003. In order to help them solving this problem, teachers guide them to understand the core insight namely unitizing in which students recognize, for example, ten can be represented and thought of as one group of ten or ten individual units. Before dealing with unitizing, students are suggested in developing mathematical notation. Over time, students represented objects in pictures without attempting represent the amount. Then they began to represent objects in pictographic representations followed by use iconic representation. Finally, they understand the concept of cardinality from which the students use formal mathematical symbols representing amount of objects.
Some contexts can be presented as an activity for students in learning unitizing. Grouping objects as the exercise of students can help students to get unitizing. It is continued by counting objects by group. In next activity, teacher emphasizes an activity for students to group objects by tens. For instance, packing T-shirts in tens and counting how many packs students can make. Then, the teacher comes up with the exercise for students in making a group of many objects, counting and determining the group which can be made and count the looses. The concept of place value appears in this case since the students will explore, for instance, the loosing objects to be grouped as one unit and make them into a new full pack. In short, unitizing is the core insight to come up with place value.
In summary, the development of number system in the history is parallel to the students’ development in understanding number sense.