Investigating creativity-directed tasks in middle school mathematics curricula
Introduction
Creativity separates human beings from artificial intelligence. Many job categories that formerly required human involvement (e.g., automation, economy), but do not involve active and daily creation can now be performed by robots (Sawyer, 2015). While the skills (e.g., fast computation) that were previously highly respected became less valued due to the development of advanced computers, creative thinking as a distinct feature of human beings became one of the most important skills needed in the 21st century (Partnership for 21st Century Skills, 2008). Potential employers seek individuals who can generate diverse ideas to solve multifaced problems, particularly in Science, Technology, Engineering, and Mathematics (STEM) fields (Bicer, Lee, & Perihan, 2020a; Pink, 2006). In order for young students to keep up with the increasing demand for creativity in STEM fields, today’s educators should prepare students to go beyond what facts and procedural knowledge they have learned to build new knowledge and to creatively apply newly acquired knowledge (Sawyer, 2015). Although the idea of teaching to foster creative thinking is not new, as it has been suggested since 1950s (Sawyer, 2015), most teacher education programs do not include creativity in their education plans at all (Mack, 1987), most education textbooks do not mention how to promote creativity (DeZutter, 2011), and most teachers do not integrate creativity into their instruction (Schacter, Thum, & Zifkin, 2006), particularly mathematics instruction (Bicer, 2021).
Among STEM majors, developing creative thinking of students in mathematics is exceptionally important because much of the foundation for being able to generate innovative ideas in science, technology, and engineering depends on developing early mathematics skills and understanding (Gajda, Karwowski, & Beghetto, 2017; NCSM & NCTM, 2018). Accordingly, several countries (e.g., South Korean, Singapore, Israel) incorporated creativity as a learning goal in their mathematics curriculum (Gallagher, Hipkins, & Zohar, 2012). This incorporation is not always directly specified as mathematical creativity; for example, the Common Core State Standards for Mathematics (CCSSM, 2010) in the United States. Teaching for both mathematical creativity and the CCSS-M mathematical practices (e.g., making sense, reasoning, modeling) can be done simultaneously and support one another, but the synergies between them are not always obvious for teachers (Beghetto, Kaufman, & Baer, 2014) because many mathematics textbooks include mathematical tasks, problems, and, activities that only require memorization of facts and procedures with very little or no emphasis on creative thinking (Hadar & Tirosh, 2019).
It is important for textbooks to consist of problems that promote creativity, reasoning, and present real-life learning situations that are challenging and interesting. The textbook is used as one of the main teaching tools and is a key determinant of classroom practice especially “in mathematics, where elementary teachers rarely have specialized backgrounds in the subject and where, even at the secondary level, a shortage of certified math teachers is already apparent in some districts” (Jacob, 2001, para. 2).
Despite the textbooks’ importance for shaping instruction, very little is known in regards to developing mathematical creativity of students through curriculum materials. To shift the mindset of an education system with one correct answer to an educational framework that encourages solving non-linear, open-ended, and mathematical modeling problems, it is essential to support teachers and students with curriculum materials that promote mathematical creativity. This necessitates knowing what kind of mathematical tasks have potential to support mathematical creativity of students and whether commonly used textbooks include these tasks. Therefore, the present study has two main purposes: 1) developing a framework to identify what type of mathematical tasks offer opportunities to promote mathematical creativity of students and, 2) applying this framework to analyze to what degree the creativity-directed tasks are currently used in the most commonly used three middle school mathematics textbooks (i.e., Eureka, The Go Math!, and CPM) in the U.S (Heitin, 2014).
Section snippets
Domain general creativity and education
Domain general creativity refers to the ability to generate various solutions to open-ended problems (Guilford, 1967). This definition emphasizes the importance of divergent thinking ability in domain general (Volle, 2017). Sawyer (2015) provided an example to state the relationship between domain general creativity and learning as “a school could add a class to their curriculum that would provide students with creativity exercises and techniques, which they would then be encouraged to use in
Establishing the framework
Establishing a framework requires an initial systematic literature review to manifest specific categories of investigated topic (Wolgemuth, Hicks, & Agosto, 2017). The first author of the present study currently conducted a systematic literature review to identify what discipline-specific and general instructional tasks or practices (see Fig. 1) were suggested to integrate into mathematics instruction for promoting mathematical creativity (Bicer, 2021). The focus of Bicer (2021)’s study was not
Findings
After coding 1,500 tasks in each curriculum, we computed the percentages of creativity-directed tasks based on the subcategories (e.g., semi-structured problem-posing) available in the textbooks. Then, we computed the percentages of tasks to present what percentages of these tasks were designed according with the main categories (e.g., open-ended tasks/problems). The results including the percentages for each subcategory and main category were listed in Table 2 as well as the results by
Discussion
The present study developed a framework for the analysis of mathematical tasks in terms of their potential to promote creativity in middle school mathematics curriculum materials. This framework can also be used for upper elementary or high school mathematics curriculum materials. Hadar and Tirosh (2019) recently introduced a framework for elementary school mathematics curriculum materials and tested the validity of their framework by applying it to an elementary school textbook in Israel. We
Limitations
One limitation of the present study is considering only middle school mathematics textbooks; however, analyzing curricula that include a series of upper elementary, middle school, and high school mathematics textbooks using the framework for creativity-directed tasks can give a complete picture of curricula in terms of their potential to give students opportunity to develop their creativity across K-12 years. Another limitation of the present study is analyzing the first 500 tasks in each
For future research
Future research can be conducted to test if the potential of high school mathematics textbooks for supporting mathematical creativity of students can be measured through the framework produced in the present study (see Table 1). A cross-cultural comparison of mathematics textbooks’ potential for promoting mathematical creativity of students is suggested for future investigations to identify if there are different or similar patterns in K-12 mathematics textbooks’ creative potential across
Author statement
Ali Bicer: Conceptualization, Methodology, Writing, Supervision, Editing.
Aylin Marquez: Data Analysis, Writing, Editing.
Karla Valesca Matute Colindres: Data Analysis, Writing.
Angela Ann Schanke: Data Analysis, Writing, Editing.
Libni Berenice Castellon: Data Analysis, Writing.
Luke M. Audette: Data Analysis.
Celal Perihan: Writing- Reviewing and Editing.
Yujin Lee: Writing- Reviewing and Editing.
Dr. Ali BICER is an assistant professor in the field of mathematics education at University of Wyoming. His research interests include mathematical creativity, problem solving & posing, STEM education, and writing in mathematics.
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Dr. Ali BICER is an assistant professor in the field of mathematics education at University of Wyoming. His research interests include mathematical creativity, problem solving & posing, STEM education, and writing in mathematics.
Aylin Marquez is a doctoral student in the field of mathematics education at University of Wyoming.
Karla Valesca Matute Colindres is a doctoral student in the field of mathematics education at University of Wyoming.
Angela Ann Schanke is a doctoral student in the field of mathematics education at University of Wyoming.
Libni Berenice Castellon is a doctoral student in the field of mathematics education at University of Wyoming.
Luke M. Audette is a doctoral student in the field of mathematics education at University of Wyoming.
Dr. Celal Perihan is an assistant professor in the field of Special Education at Idaho State University. His research interests include emotional behavior disorders and positive behavioral support.
Dr. Yujin Lee is an assistant professor at University of North Dakota research. Her research interests include STEM education and affective engagement in mathematics.