Pedagogical Approach (GRR, ICT, LIT)

We apply the Gradual Release of Responsibility (GRR) as the guiding principle for every lesson unit. Known as the “I do, we do, you do” model (Archer & Hughes, 2010; Hollingsworth & Ybarra, 2009), each class begins with teacher modeling, followed by whole-class guided practice, and concludes with independent student work (Webb et al., 2019).

For example, in a lesson on Finding unknown angles using trigonometry, the class is structured as follows: 15 minutes of concept teaching on inverse trigonometric functions, 15 minutes of guided practice solving examples together, and 20 minutes of independent practice using Worksheet 5. Through ongoing scaffolding, students gradually gain independence as explicit teacher instruction decreases, making comprehension more accessible (Webb et al., 2019).

Students live in a rapidly changing technological world. The integration of Information and Communication Technology (ICT) in the classroom can enhance student outcomes (NSW Education Standards Authority [NESA], n.d.). In our teaching of Trigonometry A, we embed two appropriate technologies: GeoGebra and spreadsheets. GeoGebra provides a dynamic learning environment that makes abstract concepts more accessible by offering multiple, dynamically linked representations and visualisations (Zengin et al., 2012). The use of spreadsheets in secondary education supports the development of computational thinking skills by enabling students to apply formulas and parameters in problem solving (van Borkulo et al., 2023).

The topic Trigonometry A covers:

• Identification and labelling of the hypotenuse, adjacent and opposite sides in a right-angled triangle. Definition of the sine, cosine and tangent ratios for angles in right-angled triangles.
• Applying knowledge of similar right-angled triangles: Verify the constancy of the sine, cosine and tangent ratios for a given angle. Find approximations of the trigonometric ratios for a given angle. Find the size of an angle given one of the trigonometric ratios for the angle using digital tools
• Applying trigonometry to find the lengths of unknown sides in right-angled triangles with a given angle including angles in degrees and minutes
• Applying trigonometry to find the size of unknown angles in right-angled triangles including in degrees and minutes
• Solving a variety of practical problems involving trigonometric ratios in right-angled triangles

Why is Trigonometry A important to teach:

In mathematics, trigonometry is essential for accurate calculations of lengths and angles (Palmer et al., 2024). It helps students develop an understanding of important mathematical concepts such as periodicity and symmetry.

From an interdisciplinary perspective, it serves as a bridge between mathematical theory and practical applications. Trigonometric functions are not only aesthetically elegant in theory but also highly practical for solving real-world problems. These are some of the most common mathematical methods used, across a wide variety of practical occupations, including construction, manufacturing, farming, surveying, navigation and engineering (Palmer et al., 2024).

As a cornerstone of modern technology, trigonometry plays a crucial role in areas such as signal processing, wireless communication, and computer graphics. Without trigonometry, technologies like GPS navigation systems and 3D rendering in video games would not be possible.

From a cultural and historical standpoint, the development of trigonometry reflects the exchange and dissemination of knowledge among different civilisations. From ancient Greece to India, then to the Arab world, and later Europe, the evolution of trigonometry is a testament to the global and cross-cultural progress of science.

References

Archer, A. L., & Hughes, C. A. (2010). Explicit instruction: Effective and efficient teaching. Guilford Publications.

Hollingsworth, J. R., & Ybarra, S. E. (2009). Explicit direct instruction (EDI): The power of the well-crafted, well-taught lesson. Corwin Press.

NSW Education Standards Authority (NESA). (n.d.). Integrating ICT Capability. NSW Government website. Retrieved from https://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/understanding-the-curriculum/programming/integrating-ict-capability

Palmer, S., McDaid, K., Greenwood, D., Woolley, S., Goodman, J., & Vaughan, J. (2024). CambridgeMATHS NSW Stage 5 – Core and Standard Paths Year 10 (3rd ed.). Cambridge University Press.

van Borkulo, S. P., Chytas, C., Drijvers, P., Barendsen, E., & Tolboom, J. (2023). Spreadsheets in secondary school statistics education: Using authentic data for computational thinking. Digital Experiences in Mathematics Education, 9(2), 420–443. https://doi.org/10.1007/s40751-023-00126-5

Webb, S., Massey, D., Goggans, M., & Flajole, K. (2019). Thirty-five years of the gradual release of responsibility: Scaffolding toward complex and responsive teaching. The Reading Teacher, 73(1), 75–83. https://doi.org/10.1002/trtr.1799

Zengin, Y., Furkan, H., & Kutluca, T. (2012). The effect of dynamic mathematics software geogebra on student achievement in teaching of trigonometry. Procedia-social and behavioral sciences, 31, 183-187.