Function machines and hands on learning

In my readings I found this brilliant teaching idea for teaching functions to kindergartens by Willoughby (1997). I feel that this may even be a valuable learning experience for children in the older grades too. I would love to try this idea with children in an actual lesson. Please note that the function machine my graphic refers to is a large box big enough for a child to fit inside comfortably, decorated so that it looks like a machine, used for teaching functions. It must also contain a slot for the input and a slot for the output.




(Please click to enlarge this graphic)

As I reflected on this lesson plan by Willoughby (1997), I contrasted the potential learning described with Warren and Cooper's (2005) research findings, which stated that "the use of child volunteers to act as IN and OUT with respect to the function machine was a strong distractor in classroom 3." According to Willoughby (1997) the above-mentioned learning experience was one which he has carried out many times. Furthermore a photograph of a child remaining engaged while participating in this activity was included in the article. This led me to wonder, how could this be? Perhaps it was because of the fact that in the lesson conducted by Willoughby (1997), the child inside the box remained hidden to the rest of the class and therefore was less of a distraction. Or perhaps it could have been the fact that the child inside the box was in control of the transformation from recieving the input to the providing of the output. This was unlike the learning experience described by Warren and Cooper (2005) where several volunteers were responsible for only one aspect of the transformation, i.e. "Frank gives the green stick to Ned; Ned puts green stick in box; Researcher changes the green stick to red stick and gives this to Bonnie; Bonnie gives the red to Frank and the teacher records the change on the IN/OUT table." (p.157)

This reflection has reminded me that in designing learning experiences and assessments for children, simply having concrete examples, hands-on experiences and well-designed resources is not enough - aspects such as what the children are paying attention to must also be taken into consideration. As teachers we must ask ourselves, "What are the children learning?" and "How do I know he or she is learning it?"

References:

Willoughby, S. (1997). Functions from kindergarten through sixth grade. Teaching Children Mathematics, 3(6), 314-318.

Warren, E. & Cooper, T. (2005). Introducting functional thinking in year 2: a case study of early algebra teaching. Contemporary Issues in Early Childhood, 6(2), 150-160.