Pondering....

October 3rd, 2008

Open Vs. Closed. What’s the question?

I have been reading about open ended tasks and questions, and I am starting to understand why it is important to ask such questions, especially in math. When we ask students open questions, such as what can you tell me about 13X52, we are able to get an insight into how they think about this question and what they know about mathematics that surround this question. When we ask such a question, we are not looking for them to tell us the exact product, but to see how they go about thinking about what that product may be.

As we ask more open ended questions, we get a chance to see how students develop their own methods of doing. I did not think of this until now, but students get really good at making us believe they understand something, and we get really good at believing them. If we asked students what the product of 13 and 52 was, they may or may not get the answer correct. If they didn’t get it right, we are lead to believe they don’t know how to multiply two- two digit numbers, when in fact they really did. Or, similarly, they may have gotten the product right, which would lead us into thinking they understands multiplication and can demonstrate this understanding by getting the product right, which again, could be the furthest from the truth. That being said, we also need to ensure that our questions do not encourage this deception. Some very important things for me to ponder in the next few days.