Best Seat in the Class

This week I would like to share a PBL article that provides an authentic, mathematical driving question, that I believe is generalizable. The 2023 article is entitled, “Where Is It Best to Sit in Class? Description of an Experience Based on Problem (PBL) Solving in a School Context” by Ferrando, Albarracín and Diago.

The authors describe an activity whose starting point is a driving question (DQ) based on an authentic problem: to identify the areas of the classroom where the intensity of sound is higher. By trying to give an answer to the DQ, students have the opportunity to develop progressively more complex mathematical models from already known concepts. They conclude that the design of the activity and the choice of data acquisition technology are key, but also the interaction between the students and the instructor.

“The project challenges students to describe mathematically the way in which the sound propagates in the classroom. The activity leads the students to make decisions, first about the process of data collection, then about data representation and, finally, about data analysis. The students’ work in the classroom is complex, as they have to deal with the physical characteristics of the physical phenomenon, the mathematical knowledge that allows them to describe it formally, and the use of the technological tools to collect and analyze real data. Throughout the process, the teacher acts as a facilitator and intervenes in the learning process.”

Often “the inductive (inquiry) part of math (and other subjects) is ignored and the deductive part is presented as a series of rote procedures rather than as a way of making sense of reasoning. One way to overcome this dichotomy and to promote complete reasoning is to provide students with appropriate experiences that allow them to bring into play the content related to formal mathematics to organize and systematize experiences (Li & Schoenfeld, 2019).

The authors consider that the development of PBL activities may include (Duijzer et al., 2019):

1. Promote improvement of critical thinking and problem solving skills;

2. Creativity should be encouraged, so it is necessary to design complex PBL activities that challenge students to develop creative solutions.

3. Collaboration should be encouraged. This is a key aspect of teaching students to learn to work effectively with and through others.

4. Provide practical learning opportunities. Identifying applications of academic content to real-world problems can contribute to increased motivation and sense of achievement.

Taking an inductive, PBL approach to authentic learning can be challenging for several reasons. First, it is not always easy to integrate content. Also, instructors often lack confidence or pedagogical background. Finally, instructors often have only one area of specialization. Zemelman, Daniels and Hyde (2005) list the following effective practices for integrating conceptual frameworks:

1. use of manipulatives and hands-on learning;

2. cooperative learning;

3. discussion and enquiry;

4. questioning and conjecture;

5. use of justification of thinking;

6. writing for reflection and problem solving;

7. use of a problem-solving approach;

8. integration of technology;

9. teacher as facilitator; and

10. use of assessment as part of instruction.

Also, Doerr (1997) develops a theoretical framework for an approach to PBL that involves the use of technological tools. Tech can play a crucial role in PBL in the following ways:

1. Enhancing the learning experience, where tech can make concepts more engaging and interactive. It can provide visual aids, simulations, and interactive tools that allow students to experiment and test their hypotheses. This helps to bring abstract concepts to life and makes learning more enjoyable and memorable.

2. Developing problem-solving skills by providing opportunities to work on real-world problems to apply skills to solve challenges they may face in the future.

3. By fostering collaboration among students, teachers, and experts students can work together on projects, share ideas and resources, and collaborate to find solutions to complex problems.

Ultimately the authors conclude it is not enough to design an effective PBL, it is imperative that the instructor knows how to foster classroom situations to promote learning opportunities. These learning opportunities are significant when the instructor invites students to participate. Our study shows that for teacher interventions to be effective, the concepts must emerge from the interaction between students (DeRuntz et al., 2022). There is also evidence of differences between intra-group and extra-group debates. During the intra-group debates, we found that the instructor’s interventions lead to the promotion of procedural and managerial learning opportunities, but always help to concretise the procedures necessary to materialize the concepts. Therefore, the richest learning opportunities have a complex catalyst, starting from the difficulty of obtaining a measurement or representing data, through a discussion among the students in a group in which the concepts that support the constructed model are generated. However, in whole group discussions, the instructor tends to act as a facilitator and promotes conceptual learning opportunities (Blomhoj & Kjeldsen, 2006).

References

Ferrando, I., Albarracín, L. & Diago, P.D. (2023). Where is it best to sit in class? Description of an experience based on problem solving in a school context. Educ. Sci, 13, 417.

Blomhøj, M. & Kjeldsen, T.H. (2006) Teaching mathematical modeling through project work. ZDM, 38, 163–177.

Li, Y. & Schoenfeld, A.H. (2019). Problematizing teaching and learning mathematics as “given” in STEM education. Int. J. Stem Educ., 6, 44.

Zemelman, S.; Daniels, H.; Hyde, A. (2005). Best Practice: New Standards for Teaching and Learning in America’s School; Heinemann: London, UK.