Using open-ended questions in mathematics
I first became interested in open-ended questioning back in 2012 when I read the book: The Open-Ended Approach: A New Proposal for Teaching Mathematics by Jerry P. Becker and Shigeru Shimada, 1997. The book focused on presenting open-ended tasks in mathematics classrooms in Japan and stated this approach had been used since the 1970s. At that time, I was a curriculum director and I began working with a mathematics instructor on this approach. It was interesting, but at that time, I did not have the means to pursue it further and did not completely understand how to move forward.
Generally, I was asking the teacher to start problems backwards by giving students a solution and asking them to come up with a problem. They obviously struggled. We hit a roadblock, and I did not pursue it further until I read Jo Boaler's Mathematical Mindsets book in 2017. At this time, I decided to pursue my doctorate in curriculum and instruction, with a focus on using open-ended questioning in secondary mathematics. So, in 2018, I enrolled and was accepted to pursue my doctorate.
I found that research has shown that utilizing open-ended questioning or an open approach to mathematics has benefited students in a variety of ways. It has been shown to build students’ abilities to think creatively, divergently, and critically while promoting differentiation, communication, and collaboration (Becker & Shimada, 1997; Fatah, Suryadi, Sabandar, & Turmudi, 2016; Kwon, Park, & Park, 2006; Munroe, 2015; Nohda, 2000; Viseu & Oliveria, 2012).
Over the years, I have become much more knowledgeable about open-ended questions, strategies to use when presenting open-ended questions, and how to develop open-ended questions. I have made it my goal to pass on what I have learned and pass on the benefits of this approach in supporting the learning and thinking of students as well as building their conceptual understanding of mathematics.
Open It Up!
Dr. Kimberly Hansel
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Resources
How to use open-ended questions in math, downloads, and more! (See the website tabs above)
Strategies to use with Open-Ended Questioning
In my research, I found that there are definitely a few strategies that play a huge role with incorporating open-ended questioning.
You, Y'all, We Strategy - This strategy was presented during my research and came from a New York Times article titled: Why Americans Stink at Math.
This strategy is opposite of the typical I do, we do, you do gradual release model that many American mathematics classes currently use. You, Y'all, We asks students to complete a problem individually (I would like to argue that an open-ended problem would be best here), then they would converse with a partner about their answers and students would post their answers on the board or in another location for review, lastly the class would have a discussion about the answers in groups or as a whole class.
Student Discourse - Students talking about math means students are learning about math and discussing math topics. If students are just listening to the teacher talk about mathematics, then they are not learning about mathematics. They are seeking to mimic as opposed to thinking critically about mathematics.
Collaboration and Correction - Students should be working together to review problems, find potential answers, and try to understand any misconceptions.
Beliefs about mathematics instruction
Open-ended questions and the strategies utilized with open-ended questions, takes on the viewpoints of the principles of the Constructivist Learning Theory. The Constructivist Learning Theory is a theory that emphasizes the importance of building upon a student’s prior knowledge by understanding that learning occurs using active student participation as opposed to passive absorption. This learning theory values the teaching practices that promote the construction of new knowledge, which includes using collaborative work, discussions, engaging activities, open-ended questions, critical thinking, and utilizing a student-centered approach. The goal is to allow students to construct their own knowledge about a topic based on how the student critically engages with the curriculum, materials, their prior knowledge, and their peers.
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