The Good, The Bad, and the Questions

              Before I started this class, and my journey towards being an effective math teacher, I would have told you that all math questions are inherently bad, mainly because they are math questions! Like I have stated throughout my last blog posts, I am learning so much about math, and how to teach math that the subject is slowly morphing into something that I no longer fear, rather something that I want to embrace. At first thought, I could say what makes a math question good, is whether or not it is an open question, because that is the kind of questions we have been focusing over the past few weeks. This is somewhat true, as open questions embrace collaboration and the use of students’ imagination to work through the questions. But through further instruction, we have learned about other key points as to what makes a math question good, and what makes a math question bad.

                Obviously clarity in how you are asking and presenting a question is the first step towards creating good math questions, or what is known as the use of “Soft language”. Educators like myself should focus on creating questions with what we can call a “High Ceiling”, which means structuring questions in a way that students that are learning at a higher level are able to continue their learning past what the question is initially asking, questions that allow all learners to get the most out it. Good math questions also have what can be dubbed as a “Wide Base”, another term that embraces the learning of all students, focusing on asking questions that enable all students to get started.  Good math questions should also be relevant to the students, like sticking to themes or interests the students have which promotes engagement. Good math questions normally involve an activity and or manipulatives as well as embrace student collaboration.

                One key aspect that good math questions have is being structured in a way that embraces different ideas and methods in order to solve the problem. An activity and problem that we worked through in class is an unbelievable example of a math question that embraces different methods to solve the problem. The problem, titled “Joel’s Kitten Problem” asked us to determine out of 2 stores what had the better deal for kitten food, one store selling 12 cans for $15 or the other selling 20 cans for $23. We were asked to find the better deal without using division to simply find the unit price. Even within our group, we had differing ideas on how to do it. What made this question great was that everyone could start it (Wide Base) and that each group basically came up with a different method to determine the better deal. The picture below, Method #1,  displays how a group determined that the way both stores sold their kitten food enabled them to buy 60 cans of food. By doing that, they could compare the two stores prices for 60 cans and determine the better deal.

Method #1

 Another method that a group used was to solve the problem by visualizing each can from either store being a standard and easy to work with value. After each can had the same value, they started to divide the remaining money into each can, essentially discovering a unit price and revealing what is the better deal.

Method #2

             Both groups shown in this post discovered that the better deal was at the store selling 20 cans foe $23.  Joel’s Kitten problem exemplifies how an educator can create good math questions. Answering these questions with the use of manipulatives would also be a good idea, also illustrating how this is a good question. Educators have a lot to consider when developing lesson plans, but it is important o remember the key aspects for what make questions good or not, because the quality of the question has a direct relationship to how much every students takes away from the exercise.