Investigating creativity-directed tasks in middle school mathematics curricula

https://doi.org/10.1016/j.tsc.2021.100823Get rights and content

Highlights

  • The framework for analyzing creativity-directed tasks in math curricula has six main categories along with 17 subcategories.

  • The framework can be employed to determine what strengths and weaknesses mathematics curricula have in terms of their potentials to engage students in creative actions and behavior.

  • The framework informs teachers’ instructional practices for developing their students’ creativity.

  • Open-ended problems are more common in the 6th grade textbooks than 7th and 8th grade textbooks in the present study.

  • The emphases of creativity-directed tasks in the textbooks are parallel with each curriculum’s main goals.

Abstract

Developing students’ creative thinking abilities while learning mathematics has been recently emphasized by many scholars, with many nations including creative thinking in mathematics as one of their overarching curriculum goals. The first purpose of the present study is to develop a framework to identify what type of mathematical tasks promote the mathematical creativity of students. The second purpose is to analyze to what degree the most commonly used three middle school curricula (i.e., Eureka, The Go Math!, and CPM) in the U.S. include creativity-directed tasks in their textbooks using this framework. Analyzing 1,500 mathematical tasks in each curriculum revealed that different curricula emphasize different dimensions of the creativity-directed tasks categories (i.e., open-ended tasks, problem-posing, connections, extensions, visualizations, and communication) presented in the framework. The result also revealed that open-ended problems are more common in the 6th grade textbooks than 7th and 8th grade textbooks regardless of the three selected middle school mathematics curricula. The implication of this study is to guide teachers with the strength and weakness of textbooks in terms of their inclusiveness of creativity-directed tasks to inform their teaching. Additionally, it is critical for curriculum developers to pay particular attention in including tasks that supporting each category and subcategory proportionately across the three years of middle school rather than emphasizing a few of them in one grade and almost completely ignoring them in previous or later years.

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.

References (76)

  • A. Bicer et al.

    A meta-analysis of the relationship between mathematics achievement and creativity

    The Journal of Creative Behavior

    (2020)
  • A. Bicer et al.

    Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity

    Educational Studies in Mathematics

    (2020)
  • J. Boaler et al.

    Mathematical mindsets: Unleashing students potential through creative math, inspiring messages, and innovative teaching

    (2016)
  • H. Burkhardt

    Curriculum design and systemic change

  • J. Cai et al.

    Teaching mathematics using standards-based and traditional curricula: A case of variable ideas

  • Common Core State Standards Initiative (CCSSM)

    Common core state standards for mathematics

    (2010)
  • S.A. Chamberlin et al.

    Model-eliciting activities as tool to develop and identify creativity gifted mathematicians

    The Journal of Secondary Gifted Education

    (2005)
  • G.A. Davis

    Identifying creative students, teaching for creative growth

  • K. Devlin

    The math gene: How mathematical thinking evolved and why numbers are like gossip

    (2000)
  • S. DeZutter

    Professional improvisation and teacher education: Opening the conversation

  • S.J. Dollinger

    “Standardized minds” or individuality? Admissions tests and creativity revisited

    Psychology of Aesthetics, Creativity, and the Arts

    (2011)
  • L.D. English

    Problem posing in the elementary curriculum

  • J.L. Fleiss

    Measuring nominal scale agreement among many raters

    Psychological Bulletin

    (1971)
  • A. Gajda et al.

    Creativity and academic achievement: A meta-analysis

    Journal of Educational Psychology

    (2017)
  • D.A. Grouws et al.

    Curriculum and implementation effects on high school students’ mathematics learning from curricula representing subject-specific and integrated content organizations

    Journal for Research in Mathematics Education

    (2013)
  • J.P. Guilford

    Traits of creativity

  • J.P. Guilford

    The nature of human intelligence

    (1967)
  • L. Heitin

    Common-core math textbooks to get online rating

    Education Week

    (2014)
  • B.A. Hennessey et al.

    Creativity

    Annual Review of Psychology

    (2010)
  • S. Hershkovitz

    Mathematical creativity and giftedness in elementary school: Task and teacher promoting creativity for all

  • B. Jacob

    Implementing standards: The California mathematics textbook debacle

    The Phi Delta Kappan

    (2001)
  • E.S. Jay et al.

    Problem finding: The search for mechanism

  • M. Karwowski et al.

    Delving into creativity and learning

    Creativity Research Journal

    (2020)
  • M. Kattou et al.

    Connecting mathematical creativity to mathematical ability

    ZDM

    (2013)
  • J.C. Kaufman et al.

    Beyond big and little: The four C model of creativity

    Review of General Psychology

    (2009)
  • C.S. Lee et al.

    A measure of creativity or intelligence? Examining internal and external structure validity evidence of the Remote Associates Test

    Psychology of Aesthetics, Creativity, and the Arts

    (2014)
  • R. Leikin

    Openness and constraints associated with creativity-directed activities in mathematics for all students

    Broadening the scope of research on mathematical problem solving

    (2018)
  • R. Leikin

    Exploring mathematical creativity using multiple solution tasks

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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.

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