Modelling helps to bring abstract concepts alive to students. In lower grades, students are introduced to the concept of modelling in Mathematics for the first time when learning to use the scale. Later, students understand some problems better if they are able to make a model of it, for example by drawing mathematical diagrams. Some problems can be more easily solved if the students make a table, form an equation or develop a function which describes the problem.
My experience and research, have shown, that hands-on experiences – with a challenge that doesn’t have only one right answer, really gets students excited and engaged. The question is, which model do students need to build to answer specific questions or solve problems?
The following example is one that I have used with my 5th-grade students as well as with teachers during their in-service training courses. I use a rope that is tied into a loop. I ask four students to come to the front of the class, each one has to hold the rope so that they are forming a rectangle. At the same time, we talk about what the qualities of a rectangle are. Then I ask them to form another rectangle and then a third one! What is the perimeter of these rectangles? Students easily say – they have the same length.
When asked to form new rectangle students begin to wonder if there can be more. Someone from the class may shout out that they need to form a square! At this point, they may begin to discuss whether or not a square is a rectangle. This discussion is usually very beneficial in helping the students to concretise their knowledge. Asking them to form a new rectangle gets them excited – and in the end, they always say regardless of their this is a good time to teach them how it is used in mathematics.
The second example is, modelling our solar system. There is no book or tablet where you can build a model of the solar system so that the sizes of the planets and their distances are on the same scale! By Modeling, students get a deeper understanding of big numbers, how to calculate and understand different types of scales. Give student pairs their own planet, the Sun, Mercury, Venus, the Earth, Mars etc. while other students work as measuring men. The pairs will get the readymade models of the planets. Depending on the grade, you can share with them information on how to scale or ask them to count it or not to scale at all, this depends on their readiness. Students from 9th grade can calculate the size of the Sun using a given scale. One pair will cut the Sun from yellow cardboard, because it is a star, unlike the others! Secondly, they count the distance of their planet from the Sun using this scale.
When the model is moved outdoors; students get a feeling of the scale they have used in their calculations. Measuring men will help groups to find their place in the model. They are normally really excited when going to their place in the model of the solar system. The model can be improved so that all the planets will move. To extend the learning the following questions can be asked, how much time will it take, to travel from the Earth to Saturn at the speed of the light? The pupils’ responses will give the teacher an insight into the level of their understanding. This work can be integrated with physics, in which case the student’s task is to clarify the conditions on their own planet. Modelling the solar system can be an adventure for the whole class showing them the power of Mathematics.
By: Maarit Rossi