Abstract:

Modeling activities have been considered as useful teaching methods in STEM education. The US Common Core Standards for Mathematics emphasize modeling as a K–12 standard for mathematical practice, in particular, at the high school level. However, researchers indicate that teachers struggle to use modeling activities in their math teaching. Consequently, students often have fewer opportunities to use mathematics in interpreting and explaining real-world phenomena, and thus, fewer opportunities to realize the importance and value of mathematics in their daily lives. To appreciate the benefits of modeling activities as teaching methods, it is necessary for teachers to have positive experiences regarding their own engagement in modeling activities. This study reports on a pilot study of 15 preservice teachers’ development in working on a modeling activity, which took place in a middle and secondary mathematics course. This study describes the preservice secondary teachers’ work on a modeling activity and their reflections on the activity.

The activity was designed for preservice secondary teachers to engage in a mathematical modeling activity and to develop their knowledge in teaching mathematics. A specific type of researched modeling activity, called Modeling Eliciting Activities (MEAs), was provided to support preservice teachers in having successful experiences with modeling actives. For this study, we created a modeling activity, entitled the Putting Green MEA, in which students are asked to develop a method to find an area of a curvilinear region/shape, that is, a putting green in a golf course (combining two curves of quadratic functions). Students’ methods should be reusable for various curvilinear regions/shapes and sharable with others in similar contexts. Fifteen preservice teachers worked in five groups on the Putting Green MEA. After sharing their solutions through a group presentation, the preservice teachers also discussed how they could use this modeling activity in mathematics classes.

The study shows that all five groups developed different models involving various mathematical ideas at different levels. The first level involved a definition of the area of a two-dimensional shape: one group used the strategy of making an estimation by counting the possible unit squares to cover the shape without overlaps or gaps. The second level involved common area formulas for geometric figures: two groups divided the curvilinear figure, minimizing marginal errors, into several smaller triangles, squares, rectangles, parallelograms, and parabolas. The third level involved interpretations of the Riemann integral: two groups used the second fundamental theorem of calculus to obtain the area of the putting green by finding two possible quadratic functions fitting the curvilinear figure. The preservice teachers’ reflections on this modeling activity revealed their positive experiences in appreciating the benefits of using real-world problems, and their potential ability to apply their experiences to their own teaching, involving a range of teaching basic geometry–such as finding the area of complex figures–to teaching calculus–such as interpretations of the Riemann integral. This study supports research indicating the need for positive experiences involving preservice teachers to have modeling activities as teaching methods in their repertoire for their future classes.

Keywords:

Teacher Education, Modeling Activities.