| Category | Details |
|---|---|
| Module | Light intensity graphs |
| Number of hours | 60-90 min |
| Grade/Age Range | Grades 7-9 (13-15 years old) |
| Brief Description | The aim of this module is to develop a qualitative understanding of functional relationships at the pre-definitional stage, particularly to develop covariational reasoning and shape the intuitive understanding of the notion of function and function graphs. Students create and explore graphs (of functions) using embodied experiments. Using their smartphones with PhyPhox software, they are involved in the experimentation – they change, through hand movement, the light intensity, they investigate it, mainly through the real-time graphical interpretation on the screen, they can also interpret the values of the measured light intensity. The students have the opportunity to create and observe many functions with different graph shapes, to try to move hands in order to ‘produce’ movement as described by the provided graphs in real time, as well as interpret and work with graphs. The module leads to an intuitive understanding of the formal definition of function. Due to the context of measuring the light intensity and the “impossible graphs” discussion, students, in a practical way, independently discover the conditions for the definition of a function and are able to distinguish between graphs of functional and non-functional relationships, all at the pre-definition stage. |
| Design Principles | |
| Functional Thinking | |
| Learning Goals |
- Meaningful: Building the students’ intuitive knowledge based on the experiment with representations of various continuous functions, from experiment to graph and vice-versa
- Embodiment: Building the understanding of graphs and the experience of producing graphs by moving hands, observing in real time, and analyzing the effect of hand movement on the shape of the graph, as well as reproducing some of the provided graphs through hand movement
- Inquiry based learning: Discovering:
- graphical interpretations of light intensity changes over time
- functional and non-functional relationships at the pre-definition stage
- Digital: PhyPhox (free software), the students’ smartphones.
- Didactical phenomenology: The covariation of distance in time during hand movement is mathematized.
- Building, drawing, analyzing, and interpreting graphs of various continuous functions
- Coupling hand movements to their representation as a curve in the graph (both directions: from hand movement to graph and from graph to hand movement)
- Discovering - at the pre-definition stage in practice - the conditions for defining the concept of a function
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