Opening Up Mathematical Questions

Some closed questions in math are true and false questions, multiple-choice questions, or some that just require simple input of numbers in a calculator. For example, one question from my unit plan is what is the mean from this list of data. One way to open up this would be to include additional conditions. This method will open up the questions and provoke a deeper understanding of the problem. This can be done by having students then think about what may occur to the mean if another data point was added to the set. For example, if the data point was larger or smaller than the mean how would that change the original mean. Another way to open up this problem would be the comparing/contrasting of three. For example with the question on mean, one way to open it up would be to compare the mean of 3 sets of data. Perhaps, here would be a great opportunity to have students think about outliers and how they can affect the answer. A third way to open up a closed question would be to use the always, sometimes, never true method. I like how this method really has students think about the way the question is posed and how the conditions of the question really have an influence on what the answer would be. For example with the mean question, one open-ended question that uses the always, sometimes, never true method would be the odd number mean always has an odd number of data points. This statement also students to explore several different possibilities and to really take their time to understand the question and the content. Another way to open up this type of closed question would be to pose the question where there can be several different possibilities. For example, what are 3 numbers that give a mean of 24? This question allows students to think about the infinite answers that are possible and how general this question is. The method that I like the best is the use of having additional conditions to open up the question. I like this because it allows shows the progression in having a question become more open-ended. I also like how the question can be changed slightly requiring the students to think about possibilities that they may have not considered on their own. The most appropriate method would also be the use of having additional conditions and posing questions where there can be multiple answers. I think both of these methods allow students to explore math ideas and to think about different perspectives and how there are multiple approaches they can take to answer a question. I like how both of these types of questions allow for scaffolding so there is an opportunity for the progression of closed to open-ended questions.