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There are many different ways teachers can go about creating open ended tasks that engage and enrich the mathematical lives of students. One such suggestion, as outlined by Open Assess,,, (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. Tell students that hair grows 10 cm each year. Have them create a question that involves multiplication around this fact and have them solve it. Making students interested in what they are doing is over half the battle with teaching math. Think about the difference in these two questions and student’s interest level– ‘What is 45 x 6? How do you know?’ and ‘Choose two numbers to multiply. Talk about how you went about finding the product. Then tell three things about the product’. Students would probably be more willing to complete the second question just because they can choose the two numbers. Even if students choose two very simple numbers to multiply, teachers can use appropriate questioning techniques to upgrade this answer. Teachers will get more assessment data from this type of question than any type that is similar to the format of question one.
Open Assess… continues by suggesting another way open ended questions can be created is by 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 the perimeter of the room, given the dimensions? This could be turned around and look something like this – Mary said that when she found the area of the room, it was 62. Bill said that when he measured the room it was 36. Who is correct? How do you know? It is really fun when you make the teacher wrong and the student’s solution is the one that is correct!
Small (2008) suggests yet another way to create open ended tasks. Ask students to think about how things are similar and different, or the alike and different strategy. 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.
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, 1 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 ass (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 are 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.
Another engaging way to assess student learning through open ended tasks is to give students an answer, such as 45, and ask them what the question could be. This could turn boring fact questions, or outcomes, into interesting and engaging learning opportunities. Look at and think about the level of engagement, for example, between the following questions:
• What is 35 divided by 5? * The answer is 5. What is the question?
Students can also be engaged in open ended tasks when asked to tell or explain what it is they know about a certain number after being given certain criteria. For example, you may want to ask a student to tell you what they know about a number that is a three digit number whose digits add to 10. Then ask students to list all the possible things that must be true about the number.