Techno-pedagogy in action: applets for classroom practice and self-directed learning (SDL)
MathIT’s curated open-source GeoGebra applets are designed to make CAPS mathematics visual, dynamic and accessible. Together with applet-aligned worksheets that support interactive self-directed learning (SDL), these resources have strong potential to assist self-discovery and reinforced learning in schools and colleges. This post uses a Grade 11 FET mathematics applet focused on Sketching the Hyperbolic Function to model techno-pedagogy and SDL in action.
Using the applet, teachers and learners can visually and dynamically explore the family of curves defined by a hyperbolic function of the form \( y = \frac{a}{x + p} + q \). By adjusting the parameters \( a \), \( p \) and \( q \), and toggling asymptotes, intercepts and lines of symmetry, learners immediately see how algebraic features control the shape and position of the graph. The applet also serves as a dynamic tool to explore a range of problems linked to graphing and applying hyperbolic functions.
The accompanying curated topic-applet worksheet turns this interactive experience into a structured learning loop that begins in the classroom, continues as self-directed learning (SDL), and returns to the classroom for reflection and reinforcement.
What will work
- Users can manipulate and instantly link the values of parameters \( a \), \( p \) and \( q \) to the orientation, stretch, vertical and horizontal asymptotes, and intercepts of the hyperbola.
- Toggling the “Show Asymptotes”, “\( x \)-Intercepts”, “\( y \)-Intercepts” and “Symmetry Axis” menu buttons in the applet helps learners check their own algebraic work and sketches in real time.
- The same open-source tool supports both whole-class demonstration and individual or small-group SDL at no extra cost.
- Because the applet can also be packaged to run offline as HTML, independent of any software, the techno-blended model and activities have great potential to continue even when classroom or home connectivity is limited. Contact MathIT for more information on this.
During the topic lesson in classrooms
The teacher projects the applet via data projector while introducing the general form of the hyperbolic function. If available, learners can also open the same applet on their own devices using a link or QR code (phones, tablets or computers). Together the class explores:
- the effect of changing each parameter;
- the location of the asymptotes;
- how intercepts appear and disappear as parameters change;
- the lines of symmetry that pass through the centre of the hyperbola.
- ... and more
As part of a dialogical teaching approach, short whole-class discussions based on key questions linked to concepts and procedures help learners develop understanding of how to sketch hyperbolic functions.
After the topic lesson in classrooms (SDL engagement by learners)
The teacher shares the companion MathIT worksheet (without solutions) as an SDL assignment together with a link to the applet via the class WhatsApp group, Google Classroom, or any other social/learning platform. QR codes linking to the online applet platform can also be used to share access. Learners work at their own pace—individually or in small groups—using the applet to:
- explore the questions visually and dynamically;
- verify algebraic calculations of asymptotes and intercepts;
- sketch graphs and immediately check them against the interactive model.
This cost-effective, anywhere-anytime engagement reinforces conceptual understanding through mathematical visualisation and applet interaction. Learners can return to the applet as often as they need before the next reflection session or follow-up lesson. Completing the worksheet’s Likert-scale self-evaluation also encourages them to reflect on how the applet supported their understanding.
Classroom reflection and Reinforcement (facilitated by teacher)
In the follow-up session, the teacher invites learners to share assignment solutions and common challenges. Using the projected applet, the teacher (or selected learners) demonstrates the key conceptual and skills points that arose in the SDL assignment. Solutions are then distributed so that learners can complete any unfinished items and consolidate their understanding. This closing of the loop turns the worksheet into a living assessment-for-learning tool rather than a static homework sheet.
