Learning to model

Author: Prof. Katja Maaß

This example is part of a learning trajectory for guiding low achieving students (age 12) as they develop competencies in modeling. The aim of the activity is to introduce low achieving students into modeling. Here, they are particularly supported in making assumptions. The mathematical content is: Basic calculations, proportionality, sizes, (data collection).

The students are given a newspaper article were they say that a family can save 26.000 litres of water per year when closing the tap during brushing their teeth. The students then have to answer the question whether this is possible or not and to reason about this.
The activity can be performed in the classroom within about 90 minutes. A detailed lesson plan is given.

Pedagogical issues

The teacher’s role is to guide the students’ exploration process and discussion. The students are encouraged to explore the situation and to link it to their individual knowledge. This involves making assumptions. The teacher has to ensure that he actually supports the students in developing competencies in those activities named above by not helping them too much on the one hand without letting them completely alone and the other hand.
The activity allows students time to engage in and explore the situation. The activity is designed to offer students strategic hints and to encourage them to share their opinion about assumptions. They are encouraged to reason about a mathematical result. The discussion held at the end of the activity can offer the teacher the opportunity to see students conceptual understanding of basic mathematical calculations and in how far they are able to apply their mathematical knowledge to a given realistic problem. Students are required to simplify and structure a problem, to measure, to quantify, to make assumptions to discover relationships and to communicate about mathematics.

Characteristics

Open activity based on mathematical modelling.

Potential for PD

This activity could be used as PD-activity because it covers the entire spectrum of what is required for doing modeling in class. Further, it has potential to be used as a starting unit, as the starting is facilitated by the assumptions given at the beginning. The challenge for the teacher is to find the right way of supporting students.
In addition, it can be linked to the module "Tackling unstructured problems" for opening some of the structured tasks.

Commentary

The activity is designed for the project “Stratum”, financed by the research community for low achieving students (Forschungsverbund Hauptschule). The idea behind this project is to support low achieving in developing modeling competencies. As to make the teaching units be used in day-to-day teaching and by teachers who often do not think low achieving students capable of solving modeling tasks, a structured approach has been chosen which gives students gradually more freedom to work autonomously. The activity has proven its efficacy as it has been used in the project by many teachers and as it also has been evaluated.
It relates to IBL as students are encouraged to explore a problem, to simplify and structure it, to predict, to make assumptions, to quantify and to communicate about mathematics. It can be classified as an interdisciplinary activity as it involves measuring, thinking about water consumption and reasoning within a realistic context.

Links

Literature: Maaß, K., Schroers-Karrer, D. & Mischo, C. (2010): Modellieren mit leistungsschwachen Schülern. Berlin: Cornelsen
Teacher material

Last change: 13 maart 2012

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