Reaching Every Student

As a future educator, I had always worried about how I would be able to reach every student in my class. We have learned that every student learns in different ways and that it is crucial to differentiate learning in a classroom. It would be incorrect to assume that all students learn in the way that we, as teachers, have learned best in the past. Therefore, it is crucial to provide students with opportunities to demonstrate their understanding in different ways. Open-ended questions and parallel tasks are two ways in which students can demonstrate their knowledge of the mathematical content. 

Open-ended Questions

Mathematics is usually known as a subject that has questions with right or wrong answers. However, through the use of open-ended questions, we are able to eliminate the idea of right or wrong answers because the students have some freedom within the question. You may be asking yourself how a student could have any freedom in a subject that is usually very black and white. This question can be answered with open-ended questions because the students are able to create the question, as well as, the answer themselves. Since there is not one specific answer, these types of questions are excellent ways to guide conversations about the mathematical content. 

The following picture is an open-ended question that can be used for students in secondary school. 

More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction, p. 40.

This example shows how every student is able to find an answer to this question since there are many possible answers. For example, there are an infinite amount of lines with a slope of 2/3, therefore, students have the freedom to choose whichever one they would like to work with. Rather than solving for a specific point, this question allows students to become familiar with the different properties of a parallel line. This would also be an excellent opportunity to engage the class in a discussion about parallel lines.

Parallel Tasks 

Parallel Tasks usually involve two problems that are very similar in nature in order to address different developmental levels within a classroom. Since the questions are only slightly different, the same big idea can still be discussed as a class. Similarly to open-ended questions, these problems involve some freedom for the students because it allows them to choose which option they would like to complete. Using parallel tasks in a classroom creates an inclusive environment because students are able to engage in the discussions about the topic. An example of a parallel task is demonstrated below.  

More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction, p. 147.

In this example, the students are able to choose whether to calculate the area of a right-angled triangle or a triangle without a right angle. Since the two questions differ slightly in difficulty, this question demonstrates what content the student is comfortable to work with. However, both questions will be able to demonstrate the students ability to solve for the side lengths and area of a triangle. 

Using both open-ended questions and parallel tasks in a classroom allow students to have some choice in mathematics. It creates an inclusive environment that provides students with the opportunity to engage in discussions about the mathematical content. Both open-ended questions and parallel tasks are a great way to differentiate learning in a classroom. 

If you would like to see more examples of open-ended questions and parallel tasks, I would suggest that you read “More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction” by Amy Lin and Marian Small. The open-ended questions and parallel tasks are organized by grade level, as well as, mathematical topic. I hope that you find this resource as useful as I do!

Resources

Lin, A. & Small, M. (2010). More good questions: Great ways to differentiate secondary mathematics instruction. New York and London: Teachers College Press.