Using the Model Method in Math Problem-solving

by Kevin Sonico

Mr. Cheng and I are conducting a research project in our classrooms on how using the model method or strategy in math improve students' problem-solving skills. Effectiveness of the method will be measured in the increased ability of students to solve word problems and enhanced confidence to communicate their thinking and process.

Students in Singapore are first taught the model method in the 3^rd grade. Hoven and Garelick (2007) stated that “[i]n Singapore, where 4^th and 8^th grade students consistently come in first on international math exams, students learn how to solve problems using the bar model technique.” They go on to write that “the bar modeling tool has taught [students] not only to solve math problems but also to represent them symbolically – the mainstay of algebraic reasoning.”

In choosing to teach this particular method or strategy, that is the model method, we are making problem-solving an integral part of the concept, rather than an add-on. Problem-solving scenarios bring context to the abstract nature of numbers, hopefully adding meaning to the curriculum. Content areas where the model method will be used are fraction, ratio, proportion, percents, and algebra.

For our study, we will document our use of the model method through the exploration of word and numerical problems (around the theme of proportional reasoning). Student progress throughout will be monitored with video journals, quizzes, surveys, interviews, and assignments.

In our years of teaching, we have not seen much evidence from student artifacts that show visual models for solving problems. Making it a focus will expose students to a new way of thinking and problem-solving. In addition, the visual method of teaching has been exclusive to the fractions unit in our practice. Expanding it to other curriculum/content areas encourages us to adapt new teaching strategies and techniques that we may not have previously employed.

We acknowledge that students learn in different ways. The model method argues that “through the construction of a pictorial model to represent the known and unknown quantities and their relationships in a problem, students gain better understanding of the problem and develop their abilities in mathematical thinking and problem-solving.” (Hong, K.T., et al., 2009). By explicitly teaching the model method, we are equipping students with another strategy to use in solving problems aside from the procedural and/or symbolic perspective.

Ultimately, the measure of success is improved confidence among students in solving word problems. As this study focuses on teaching the model method to solve problems, our goal is for students to be utilizing this strategy as a method for problem-solving or as an alternate way of verifying their solutions. Therefore, the number of students using the model method and the frequency with which they utilize the model will also serve as indicators of success. Rubrics will be in place to gauge students’ ability to solve problems.

Another expected outcome is the impact that teaching the model method will have on our teaching practice. If used extensively in the classroom, we will be able to observe the model method’s benefits as well as its limitations. We also hope that other teachers will begin to adapt or implement the model method in some capacity in their practice.

Feel free to contact me via email should you have some feedback or comments on our study. You may also choose to follow me on Twitter (@ksonico). We look forward to connecting with other teachers who use the model method or who are interested in using it in their practice.

Click here to read about other math ideas from the Calgary Science School.

References

Hoven, J. & Garelick, B. (2007) Singapore math: simple or complex?. Educational Leadership (vol. 65 no 3).

Hong, K.T., Mei, Y.S., & Lim, J. (2009). The Singapore Model Method for Learning Mathematics. Singapore: Panpac Education.