Divergent Thinking and Convergent Thinking: Are They Promoted in Mathematics Textbooks?

Bingölbali, Erhan; Bingölbali, Ferhan

doi:10.33200/ijcer.689555

Cited by 8 publications

(9 citation statements)

References 30 publications

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“…The aim here was to determine whether the questions presented by the teachers for the open-ended question were really open-ended. For this aim, the analysis framework presented in Table 3 was taken from the relevant literature, as it was appropriate for the analysis of the collected data (Bingölbali & Bingölbali, 2020). The data analysis was carried out with a deductive approach (Azungah, 2018) using a ready-made analysis framework.…”

Section: Discussionmentioning

confidence: 99%

“…were the codes containing the teachers' answers. However, as can be seen in the findings section, the definitions made were not based on the number of answers, as Bingölbali & Bingölbali (2020) stated. The teachers' definitions were quite inclusive and general.…”

Section: Discussionmentioning

confidence: 99%

“…His description suggests that he defines open-ended problems through problem situations that require active participation from students. Bingölbali & Bingölbali (2020) defined open-ended and closed-ended questions based on the number of correct answers and the variability of these answers. Questions that have only one answer (e.g., what is the smallest prime number?)…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…Questions that allow for finite variable correct answers (e.g., an example of an integer pair with a product of 50) or an infinite number of correct answers (e.g., giving an example of a rectangle with a perimeter of 20 cm) are described as open-ended. According to Bingölbali & Bingölbali (2020), if different solution methods are requested as output in a question, the question can be evaluated as closed or open-ended as above based on the number of outputs.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…c) The frequencies and forms of open-ended questions in mathematics textbooks (Bingolbali, 2020b;Bingölbali & Bingölbali, 2020;Gracin, 2018;Han et al, 2011;Yang et al, 2017;Zhu & Fan, 2006). d) The relationship between open-ended questions and higher-order thinking skills (e.g., creativity, divergent-convergent thinking) (Bennevall, 2016;Bingölbali & Bingölbali, 2020;Klavir & Hershkovitz, 2008;Kwon et al, 2006).…”

Section: B)mentioning

confidence: 99%

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How Do Middle School Mathematics Teachers Conceptualize Open-Ended Questions?

Bingölbali¹,

Cevik²

2022

msd

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The study aims at examining middle school mathematics teachers' conceptions of open-ended questions. A questionnaire consisting of open-ended items was applied to 40 mathematics teachers. The teachers were asked to define the open-ended question in general and the mathematical open-ended question in particular and provide examples to exemplify their definitions. This study employs phenomenographic study aiming at revealing middle school mathematics teachers' conceptions and experience regarding open-ended questions in an exploratory manner. The findings show that the teachers explained the open-ended question through its form (appearance), the number of outputs, the process/method required, and its functionality. In addition, teachers defined the open-ended question mostly using non-mathematical terms, and they had particular difficulties defining the mathematical open-ended question. The teachers regarded questions with variable correct answers as open-ended, could not give examples of open-ended questions with infinitely correct answers, and some deemed closed-ended questions as open-ended. Although the participants were mathematics teachers, the examples they presented for the open-ended question were mostly from outside the field of mathematics. This study points out the fact that teachers need a guiding conceptualization of open-ended questions.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Theoretical Frameworkmentioning

confidence: 99%

Section: Theoretical Frameworkmentioning

confidence: 99%