- Title: Narrative characteristics of captivating secondary mathematics lessons
- Authors: Leslie Dietiker, Rashmi Singh, Meghan Riling, Hector I. Nieves & Erin Barno
- Access the original paper here
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Paper summary
This research explores why some high school mathematics lessons captivate students while others do not. The study compares lessons students found aesthetically pleasing (intriguing, surprising) with those deemed dull, using a “mathematical story” framework to analyze content. The researchers identified eight characteristics that distinguish captivating lessons, such as the number of questions considered and instances of misdirection. They found that lessons described as more interesting had more instances of misdirection, where students’ false assumptions led to surprising results. The study suggests that lesson designs incorporating these narrative characteristics could increase student curiosity and wonder in mathematics. The study analyzed observations and student surveys across multiple schools, with a focus on how mathematical ideas unfold across a lesson.
What are the key implications for teachers in the classroom?
The sources focus on a framework for teaching practice in professional education, with implications for clinical psychology and the clergy, as well as teBased on the study, there are several implications for teachers in the classroom.
Key points for teachers:
Consider the teaching context. When applying the findings, teachers should consider their teaching context, their students’ prior experiences, and their individual and collective personalities. Captivating lessons may not have the same aesthetic effects in other classrooms or with other teachers.
Design lessons with aesthetic qualities in mind. Lessons should provide opportunities for wonderment and surprise to prevent students from seeing mathematics as boring.
Incorporate narrative characteristics. The study showed that lessons with broad appeal had mathematical questions that remained open for multiple acts, spanned more of the story, and offered incremental progress throughout the lesson.
Use misdirection appropriately. While the study found misdirection was more common in captivating lessons, teachers should use it carefully. Misdirection, like equivocations, snares, and jammings, can increase tension and lead to surprise when the truth is revealed. However, inappropriate use could have detrimental effects.
Consider the sequencing of mathematical content. A student’s experience depends on how the story is told, specifically how the tension between the known and unknown shifts across the lesson.
Leverage open-ended questions. Teachers should consider when and how they ask open-ended questions. The timing of these questions in relation to the unfolding mathematical content is important. If students cannot answer the questions, it can open story arcs and create curiosity. However, questions that are too obvious may not create curiosity.
Design decontextualized or abstract topics to increase student curiosity. When teaching these topics, teachers may resort to direct instruction, which reveals information before students have an opportunity to become curious. The study suggests an alternative approach is possible.
Be aware of the importance of asking and pursuing questions. Captivating mathematical stories provide increased opportunities to ask and pursue questions that interest students. The questions in captivating lessons were more related to exploration and less related to known facts or procedures.
Quote
Secondary mathematics classrooms can be sites of delightful claims (‘Yo! N and I go together!’), surprise (‘Woah!’), and excitement (‘That’s crazy!’) for students
