So many ways to plant a garden!

October 16^th, 2008.

The planting a garden activity resumed as students picked up where they left off. I gave them about 20 minutes to finish up and then brought the whole class together to discuss their findings. I got each group to come forward and explain their methods and procedures and any conclusions they came to. This was the hard part for me, to give up taking the lead in the discussions and step back to encourage student lead discussion.

As students began explaining their methods and procedures, they began writing the numbers on the board that they investigated. It happened so naturally and so beautifully – without them realizing it, students began isolating the prime numbers from the composite numbers on opposite sides of the board. Once the presentations were over, we were left with a very detailed list of composite numbers and prime numbers. At the very end of this lesson I introduced the words factors, as being the length and the widths and prime as being the numbers or area that there was only one way of ‘doing’ it and composite as being the areas or numbers with multiple ways of getting it. I then used closed questioning to ensure they had understood this by asking them to tell me, if for example, 15 was prime or composite, or to list the factors of 30.

I really enjoyed seeing students work through this activity and for the first time this year, seen how an open ended task can lead to students entering it in different ways. Each of the five groups thought about and attacked this problem in a different way, but all came to the same intended understanding about factors, and prime and composite numbers. Some did have a more deeper understanding, but everyone demonstrated and communicated their understanding of these outcomes. One thing I am learning through this whole process is the importance of making the tasks open and equally accessible to all students. Boaler (2002) discuss Phoenix Park’s belief that in order to achieve equity for all, teachers must work with students to ensure they understand the problem, as they decided how to support student’s needs. Boaler (2002) notes that teachers never left students alone to understand what the text based problem and always made sure everyone in the class knew how to at least start the problem. By explaining the problem, as I did in this case with the potato garden, all students were able to take it and run with it without being caught up in trying to understand what they question was semantically asking.