Following Children's Ideas in Mathematic
How children develop mathematically? This question was the main purpose observed in video I.
The activity which the children paticipated in was absolutely different from direct addition, subtraction, multiplication, or division operations. It pulled them toward unusual experience where their thinking as well as their hands were both involved in finding the solution. This combination let them use two different strategies to solve the given activity: "Drawing a
Picture" or "Making an Organized List." The two startegies are found in mathematic text books in different levels and grades.
During the activity, the students were engaged in an open discussion, revision, comparison, and presentation of their work. Also, they were able to control and extend their solution. Thus, the algebraic thinking was present. It does exist.
How the algebraic thinking exists in students' mind who were never exposed to it in a direct way? The answer is simple. Let's go back in time and try to look at this students at the age of one and half to four years old. During this stage, children devolop their algebraic thinking -observ, analyze, and conclude when they are: playing -either with toy(s) or in the playground, eating, taking baths... on their own or with partner(s), guided or unguided. They are always looking for answers to their why and how questions. How is it my plate, full with food, is now empty? How is it the bucket was filled many times with sand, and then emptied, and yet the castle is getting larger? Brain development not only allows advancement of supporting yourself, but also how to solve problems in different fields, logically.
Back to our video. The question discussed within was, how children develop mathematically? I would ask: How can teachers guide students to applying algebraic thinking (which is already developed in a child, but simply unused) on their own?