You are a VET teacher leading a collaborative classroom project in which you must develop problem-solving skills in the context of classroom learning
You choose to challenge the students to face unexpected problems for which traditional formulas are not applicable. You decide to take an example from geometry, specifically, alternative ways of calculating the area of triangles. Heron of Alexandria was a researcher, innovator, and academic from Egypt. Historians are still uncertain whether he lived during the late Hellenistic Egypt or in the first centuries of the Roman Empire. Heron solved the practical problem of calculating the area of a triangle without knowing its height, a situation often encountered, for example, when needing to measure the area of patches of land.
How do you broaden understanding of the logics of geometry and its practical uses? Have students face the problem and mentor them towards understanding the solution.
Exercise 1: Multiple choice
Scenario
You illustrate Heron’s challenge. Measure the area of a triangle knowing only the length of the sides.
What do you say?
Choose one of the following options.
Exercise 2: Sorting
Arrange the actions in the right column in order, from the most urgent to the least urgent. List them so that 1 represents the action that should be taken first, and 4 represents the final.
Action 1
Action 2
Action 3
Action 4
Ensure all students are involved, if necessary, have a moment of mutual sharing.
Ask the group if they knew the traditional textbook formula or not, and if they were aware of an alternative formula in case one doesn’t know the height existed.
Use the example of measuring the area of a piece of land as a short reflective discussion with the whole class.
Record the reactions in your notes.
Hint
Exercise 3: Reflection question
How confident are you in your ability to help students approach problems from an open perspective, as far as approaches are concerned?
Choose one of the following options.
