Problem-Based Tasks in Mathematics Learning: Opportunities and Challenges for Teachers

Authors

  • Sri Suryanti Mathematics Education Department, Universitas Muhammadiyah Gresik
  • Toto Nusantara Mathematics Department, Universitas Negeri Malang
  • I Nengah Parta Mathematics Department, Universitas Negeri Malang
  • Santi Irawati Mathematics Department, Universitas Negeri Malang

DOI:

https://doi.org/10.31764/jtam.v7i2.12864

Keywords:

Problem-based tasks, Mathematics problem, Challenge, Hands on.

Abstract

Mathematics education and teaching should not only include routine tasks; but tasks that need practice and memorization are mathematically more prosperous and more difficult because they promote problem-solving, investigation, and the discovery of the actual value of mathematical assertions. Therefore, the teacher must be able to select, create, and modify assignments under the established goals. This study attempts to examine opportunities and challenges that teachers encounter while adopting problem-based tasks. The subjects involved in this study were three secondary school mathematics teachers that are acceptable, in East Java, Indonesia. The teachers involved have more than five years of teaching experience and have good academic qualifications. The data collection consisted of observing three classes of secondary school during the implementation of a problem-based task related to the topic of rectangles and algebra. The study begins with the introduction and giving of several examples of problem-based tasks in secondary school mathematics designed to foster advanced learners' critical thinking and creativity. The findings show that teachers gain new knowledge about problem-based assignments and pedagogical insights on how they explain them to students. The results also provide an overview of the challenges for teachers to design and implement problem-based tasks.

 

References

Boesen, J., Helenius, O., Bergqvist, E., Bergqvist, T., Lithner, J., Palm, T., & Palmberg, B. (2014). Developing mathematical competence: From the intended to the enacted curriculum. The Journal of Mathematical Behavior , 33 , 72–87.

Bosica, J., Pyper, JS, & MacGregor, S. (2021). Incorporating problem-based learning in a secondary school mathematics pre-service teacher education course. Teaching and Teacher Education , 102 (103335), 1–10. https://doi.org/https://doi.org/https://doi.org/10.1016/j.tate.2021.103335

Casa, TM, MacSwan, JR, LaMonica, KE, Colonnese, MW, & Firmender, JM (2019). An analysis of the amount and characteristics of writing prompts in Grade 3 mathematics student books. School Science and Mathematics , 119 (4), 176–189.

Clarke, B., Grevholm, B., & Millman, R. (2009). Tasks in primary mathematics teacher education . Springer. https://doi.org/https://doi.org/https://doi.org/10.1007/978-0-387-09669-8

Clarke, D., & Roche, A. (2018). Using contextualized tasks to engage students in meaningful and worthwhile mathematics learning. The Journal of Mathematical Behavior , 51 , 95–108. https://doi.org/https://doi.org/https://doi.org/10.1016/j.jmathb.2017.11.006

Delisle, R. (1997). How to use problem-based learning in the classroom . Ascd.

Doyle, W. (1988). Work in mathematics classes: The context of students' thinking during instruction. Educational Psychologist , 23 (2), 167–180.

Drake, KN, & Long, D. (2009). Rebecca's in the dark: A comparative study of problem-based learning and direct instruction/experiential learning in two 4th-grade classrooms. Journal of Elementary Science Education , 21 (1), 1–16.

Freudenthal, H. (1977). What is algebra and what has it been in history?. Archive for history of exact sciences .

Glasnovic Gracin, D. (2018). Requirements in mathematics textbooks: a five-dimensional analysis of textbook exercises and examples. International Journal of Mathematical Education in Science and Technology , 49 (7), 1003–1024.

Grevholm, B., Millman, R., & Clarke, B. (2005). Function, form and focus: The role of tasks in elementary mathematics teacher education. In Tasks in primary mathematics teacher education (pp. 1–5). Springer, Boston, MA. https://doi.org/https://doi.org/10.1007/978-0-387-09669-8

Henningsen, M., & Stein, MK (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education , 28 , 524–549.

Hmelo-Silver, CE (2004). Problem-based learning: What and how do students learn? Educational Psychology Review , 16 (3), 235–266. https://doi.org/https://doi.org/1040-726X/04/0900-0235/0

Jaffe, E. (2020). Mindset in the classroom: Changing the way students see themselves in mathematics and beyond. The Clearing House: A Journal of Educational Strategies, Issues and Ideas , 93 (5), 255–263.

Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers' pedagogical content knowledge and content knowledge: Validation of the COACTIV constructs. ZDM: The International Journal of Mathematics Education , 40 (5), 873–892.

Liljedahl, P., Chernoff, E., & Zaskis, R. (2007). Interweaving mathematics and pedagogy in task design: a tale of one task. Mathematics Teacher Education , 10 , 239–249.

Livy, S., Muir, T., & Sullivan, P. (2018). Challenging tasks lead to productive struggle!. Australian Primary Mathematics Classroom , 23 (1), 19–64.

Merritt, J., Lee, MY, Rillero, P., & Kinach, BM (2017). Problem-based learning in K–8 mathematics and science education: A literature review. Interdisciplinary Journal of Problem-Based Learning , 11 (2), 3. https://doi.org/https://doi.org/https://doi.org/10.7771/1541-5015.1674

NCTM. (2000). National Council of principles and standards for school mathematics . NCTM. https://www.nctm.org/uploadedFiles/Standards_and_Positions/PSSM_ExecutiveSummary.pdf

Nicol, C., & Krykorka, F. (2016). The Place of Problems in Problem Based Learning: A Case of Mathematics and Teacher Education. In Problem-Based Learning in Teacher Education (pp. 173–186). Springer, Cham. https://doi.org/https://doi.org/https://doi.org/10.1007/978-3-319-02003-7

Prendergast, M., & Treacy, P. (2018). Curriculum reform in Irish secondary schools–a focus on algebra. Journal of Curriculum Studies , 50 (1), 126–143.

Regier, & Savic. (2020). How to teach to foster mathematical creativity may impact student self-efficacy for proving. The Journal of Mathematical Behavior , 57 , 100720.

Shimizu, Y., Kaur, B., Huang, R., & Clarke, D. (2010). The role of mathematical tasks in different cultures. In Mathematical tasks in classrooms around the world (pp. 1–14). Brill Sense.

Sierpinska, A. (2003). Research in mathematics education – through a keyhole. Plenary Address CMESG 2003 Conference .

Smith, M., Hughes, E., Engle, R., & Stein, MK (2009). Orchestrating discussions. Mathematics Teaching in the Middle School , 14 (9), 548–556.

Stein, MK, & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation , 2 (1), 50–8 0.

Stein, MK, & Smith, MS (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School , 3 (4), 268–275.

Sullivan, P., Clarke, D., & Clarke, B. (2012). Teaching with tasks for effective mathematics learning . Springer. https://doi.org/10.1007/978-1-4614-4681-1

Suryanti, S., Nusantara, T., Parta, IN, & Irawati, S. (2022). Problem-based task in teacher training program: Mathematics teachers' beliefs and practices. Journal on Mathematics Education , 13 (2), 257–274. https://doi.org/https://doi.org/10.22342/jme.v13i2.pp257-274

Swan, M. (2011). Designing tasks that challenge values, beliefs and practices: A model for the professional development of practicing teachers. In Constructing knowledge for teaching secondary mathematics (pp. 57–71). Springer, Boston, MA. https://doi.org/https://doi.org/https://doi.org/10.1007/978-0-387-09812-8

Szczygieł, M., & Pieronkiewicz, B. (2020). Exploring the nature of math anxiety in young children: intensity, prevalence, reasons. Mathematical Thinking and Learning , 1–19.

Takahashi, Y. (2008). Problem-based learning and task-based learning: a practical synthesis. The Kaohsiung Journal of Medical Sciences , 24 (3), S31–S33. https://doi.org/https://doi.org/https://onlinelibrary.wiley.com/doi/pdf/10.1016/S1607-551X%2808%2970091-3

Tarhan, L., & Acar, B. (2007). Problem-based learning in an eleventh grade chemistry class: “Factors affecting cell potential.†Research in Science & Technological Education , 25 (3), 351–369.

Tseng, KH, Chiang, FK, & Hsu, WH (2008). Interactive processes and learning attitudes in a web-based problem-based learning (PBL) platform. Computers in Human Behavior , 24 (3), 940–955.

Uden, L. (2003). Problem-Based Task Knowledge Structures in Projects. 4th Annual Conference of the LTNS Center for Information and Computer Science . http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.500.5522&rep=rep1&type=pdf

van Barneveld, A., & Strobel, J. (2009). Problem-based learning: effectiveness, drivers, and implementation challenges. In Research on PBL practice in engineering education (pp. 35–44). Brill Sense.

Van Zanten, M., & van den Heuvel-Panhuizen, M. (2018). Opportunity to learn problem solving in Dutch primary school mathematics textbooks. ZDM: The International Journal of Mathematics Education , 50 (5), 827–838.

Warshauer, HK (2015). Productive struggles in middle school mathematics classrooms. Journal of Mathematics Teacher Education , 18(4) (4), 375-400.

Wijnen, M., Loyens, S., Smeets, G., Kroeze, M., & van der Molen, H. (2017). Students' and teachers' experiences with the implementation of problem-based learning at a university law school. Interdisciplinary Journal of Problem-Based Learning , 11 , 2. https://doi.org/https://doi.org/https://doi.org/10.7771/1541-5015.1681

Yeo, JB (2017). Development of a framework to characterize the openness of mathematical tasks. International Journal of Science and Mathematics Education , 15 (1), 175–191. https://doi.org/https://doi.org/https://doi.org/10.1007/s10763-015-9675-9

Yunianto, W., Prahmana, RC., & Crisan, C. (2021). Indonesian Mathematics Teachers' Knowledge of Content and Students of Area and Perimeter of Rectangle. Journal on Mathematics Education , 12 (2), 223–238. https://doi.org/http://doi.org/10.22342/jme.12.2.13537.223-238.

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Published

2023-04-08

Issue

Vol. 7 No. 2 (2023): April

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Articles

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