How to do it?
So, the verdict is in. Open questioning is the way to go. So how do I do it? How do I go about creating questions that are open enough to allow multiple entry points so all my students can experience success?
There is no shortage of resources out there discussing how to go about creating open ended tasks and questions. There are free web sites available that offer already made open ended questions, such as www.heinemann.com/math. No matter how many open ended questions sites like this offer, there will come a time when it is necessary to create unique, authentic open ended tasks that suit the students in your class.
Open Assessment in Math (2008) suggest different ways to go about creating open ended questions, which is also consistent with Marian Small’s ideas about creating these types of tasks.
One suggestion, as outlined by Open Assessment in Math (2008) is to get students to come up with or create a situation or an example that meets certain criteria. For example, if you want to assess student’s understanding on multiplication, as them to pose a problem that involves multiplying as a way to solve it.
Open Assessment in Math (2008) continues by stating another type of open ended questions involve asking students to explain why, or how they know something or someone is correct or incorrect. This could easily transform a traditional, procedural based question into an open one. Let look at the question – what is 7 X 6? This could be turned around and look something like this – Mary said that when she multiplied 6 by 7 she got 42. Bill said that when he multiplied 7 by 6, he got 36. Who is correct? How do you know?
Small (2008) suggest to ask students to think about how things are similar and different, or the alike and different strategy, is another way to create open ended questions and tasks. An example of this could be to ask students to tell you how a triangle is alike or different from a square, or how the number 35 is alike or different from 45.
Yet another effective strategy to creating open ended tasks, as Small (2008) suggests is to use the ‘use these digits’ strategy. Here you would ask students to create some type of situation of choice, addition, multiplication, where students would have to use specific numbers somewhere in their sentence to make it correct. For example, create a multiplication sentence where you would use the digits 2, 7, and 15 somewhere in the question.
Asking students to solve the problem in more than one way is another way to create open ended tasks as suggested by Open Assessment in Math (2008). By doing this, you are requiring students to think of other ways to solve the problem. One thing to remember here, though, is to ensure there is more than one way to solve the problem and that students are able to come up with more than one possible way. Representing numbers, and asking student to show situations such a how to get a product and sum could be examples of how to use this particular strategy.
Small (2008) also suggests that by increasing or decreasing the value of the numbers in the various problems that are created can really open the problem up for a broad range of abilities. Making the value of the number greater than the initial problem would challenge students, whereas decreasing the value of a number may be just what someone else would need to access the situation.