Week 5

Chance and Data

Looking at the title for this session, made me wonder; How young kids learn about data and chance? Why do they need to learn data and chance? How can a teacher teach little ones data and chance? The learning experience gained from this session was quite liberating. Three-hours worth of our workshop was really not enough to stop me from thinking about the doubts above. I really felt that I must figure it out myself.

First, I was provided with a box of skittles. The possibility came into play when I need to state ‘which colour has the greatest chance of being selected?’, ‘Is it possible to select 10 orange skittles?’ and so on. Then, in order to answer several questions, I needed to count the skittles in my box. While completing the activity, I realized that I used many of the beginning processes mentioned by Irons (1999). The processes include, ‘sorting’ them into coloured group, ‘comparing’ the amount of individual colour and with peers, and ‘ordering’ the individual colour in ascending and descending order. Personally, I believe that young children will have a better understanding of the beginning processes when they learn using skittles. Also, I really liked the idea of using a children’ favourite (skittles), in learning the concepts and also indirectly teaching data and chance.

Smith (2001) mentioned that very young children spend time comparing, sorting and classifying everyday objects and they need those concrete experiences with the real world. After finishing counting and ordering, I needed to compare my result with my peers. We were required to gather data from other friends and represented the data. We found that the number of skittles in our boxes were not similar; however the average was 38. We also tried to find the mode, median and so on. Curcio and Folkson (1996) suggested that preschool and kindergarten age children experience many exploratory data collecting activities, using their own way of organizing information. It reminded me how an interesting environment can enhance our learning. Also, we were lucky to have some friends videoed our learning experiences using skittles.

In addition, all the data was gathered to include a class chart; using online graphing. NCTM (2000) also claimed that through their data investigations, young children should develop the idea that data, charts, and graphs give information. Personally, I thought graphing was quite hard for young kids. This is supported by Smith (2001) that there are several challenges for young kids; first is one to one correspondence as a key relationship. Young kids need to use suitable graphs to enable them in building their one-to-one corresponding. Watson and Mortiz (1999) proposed that it can be in representation such as on pictograph. I also agreed with Watson and Mortiz (1999) that elements of pictographs involving one-to-one correspondence may be counted to tally quantities compared to bar graphs that use scale. Thus, pictographs are obviously better than bar graph and other graphs. While graphing in this session, I also realized that by using line graph, young kids cannot make effective connections with the data and they do not see differences.

There are three levels of reading data mentioned by Watson and Mortiz (1999); which are reading data from graph, reading between data and reading beyond data. Smith (2001) also mentioned that reading a graph uses two kind of questions in the early years; comparing questions and counting questions. Here are some examples of questions:

Which group has more? Which group has fewer?

Or which group is biggest? Smallest? Any there any groups that are the same?

The third level of reading data from Watson and Mortiz (1999), was evidenced when a debate aroused; why was the number of skittles in the box not the same? It is because, when graphing our data on a bar graph on the amount of skittles in individual box, there number varied. We came out with some possibilities and predictions and there was no correct answer as supported by Watson and Mortiz (1999).

Furthermore, NCTM (2000) suggests that young children explore concepts of chance and classroom discussion may focus on events that are certain, are likely to happen, or that are unlikely or impossible. Two games in this workshop gave me a deeper understanding of teaching and learning about chance in EC. First, I played spinner. This is aligned with Wall and Posamentier (2007), that teacher should address the beginning of probability through informal activities with spinners or number cubes that reinforce conceptions of other standards, primary number and operations. Children also may talk about the likelihood of an event using a spinner of various colour and may using a spinner of two colours, where there are blue and red (Smith, 2001). I realized that three different spinners provided various numbers of results. It depended on the number of areas or bows. For me, it was quite tricky since I did not know much about the areas. However, it was a challenging activity because we needed to find out ways to make the spinner ‘fair’. Therefore, it may help us while teaching children to note that an imbalance can occur.

My second game was ‘Feeding a Greedy Cat”. Here, the dice have different number of faces between red and blue. Thus, the result depended on the faces of dice and there was huge possibility for blue side to win. Personally, I thought the use of the word ‘greedy’ was used symbolically to indicate an ‘unequal’ distribution of faces on dice and the possibility that the blue side will win is very high. Interestingly, Smith (2001) indicated that it is natural for children to want to be on the winning side and our society emphasis is that ‘more is better’. Thus, the teacher needs to overcome the misconceptions that might arise later on. Lastly, it needs to be highlighted for the students’ self esteem and self-confidence that if you are on the red side (fewer face on dice) you can feel frustrated and disappointed. This is what happened when I throwing the dice.

Referring back on the question which made me wonder; How young kids learn about data and chance? Why do they need to learn data and chance? How can a teacher teach little ones data and chance?, Taylor (1997) gave me the answer!

“Our primary goal as teachers is to equip children with tools they will need to become thinking, responsible citizens on a democratic society, we believe that surrounding them with opportunities to gather, organize and discuss information- and defend it when necessary- involves them in higher levels of thinking, nurtures an investigative spirit and develops competent problem solvers” (Taylor, 1997, p. 149)

References

Curcio, F. R. & Folkson, S. (1996). Exploring data; Kindergarten children do it their way. Teaching Children Mathematics, 2, 382-385

Irons, R. R. (1999). Numeracy in early childhood. Educating Young Children: Learning and Teaching in the Early Childhood Years, 5 (3), 26-32.

National Council of Teachers of Mathematics. (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

Smith, S. S (2001). Early childhood mathematics. Boston: Allyn and Bacon.

Taylor, J. (1997). Young children deal with data. Teaching Children Mathematics, 4 (3), 146-149.

Watson, J.M. & Mortiz, J.B. (1999). Interpreting and predicting from bar graphs. Australian Journal of Early Childhood, 24 (2), 22-27.