Among the questions that arose, the children especially grappled with the following:

• How do we define a question, and why is it necessary to do so?
• In this particular project, what might be the consequences of allowing everyone count whomever they wanted to?
• How can we represent the data in a way that can be understood by others?
• What values needed to be included in our representations?
• How do we begin to interpret and evaluate this data?
• What can we tell from the range, measures of typicality, gaps in data, and so forth?
• How does zero function as a placeholder in numbers vs. representations?
• How can we convey multiple levels of information in a coherent and concise representation?

The students were able easily use the data collected to answer the question posed.  This was never really questioned.  Rather, the interesting aspect of the investigation came about when the representations opened up the multitude of questions above.  Nothing was necessarily decided during the class time, but the higher-level questions demonstrated that students took the assignment as a jumping off point to grapple with some very advanced questions about data representation.  It demonstrates how authentic activities allow children opportunities for learning that simply cannot exist through rote activities. The ability to let go and give children space to legitimately explore their ideas is not always an easy one, but examples like this demonstrate its effectiveness.

Recently, in my own classroom, we had the students graph their birthdays on a chart.  Some of the ideas above came up for us as well.  For example, the students realized that if they wrote their birthdays on different kinds of paper depending on their sex, we could easily add another level of meaning to our graph.  The fourth-graders in Olivia’s class came to that conclusion as well.   Another thing that came up was the idea of defining our question.  We quickly realized that some of our children do not celebrate their birthday.  Not only that, a few don’t know when their birthday is!  While the question was designed to be one that was meaningful and relevant to all students, we quickly found that our assumption wasn’t necessarily correct.  Thus, we also addressed and tackled with the question, “How do we define a meaningful question and why is it necessary to do so?” much like the students in Olivia’s classroom.

When it came time to evaluate our representation however, our students were struggling.  It seems that they do work to get it done and don’t think much about it after the fact.  We are finding it difficult to get them to really think about their work once the “product” is completed.  For this reason, we never got to some of the other interesting questions shared above.  My hope is that we can begin to do so as the year progresses.