Problem Solving (Scenario)

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You're a VET teacher supervising a group of students during a teaching session aimed at developing problem-solving skills. As a case, you decide to propose a challenge: calculate the area A of a triangle with no information on the height (the height is used in the standard formula: area of the triangle = ½ base x height). You know you can use the information on the length of the sides, which is directly measurable as an alternative to the standard formula.

Normally, the way of calculating the area of a triangle without knowing the height is not taught. On the other hand, it is more straightforward to measure the length of the sides of a triangle than to calculate its height.

 

What are the alternative strategies for mentoring the students in addressing the challenge, so that they can improve their problem-solving skills?

Exercise 1: Multiple choice

Explain to the students that, besides the classical formula: A = ½ × base × height,  there is an alternative formula found by Heron of Alexandria: 

  •  A = √[s(s - a)(s - b)(s - c)] , 

Where a, b, and c: are the lengths of the triangle's sides, and s: is the semi-perimeter of the triangle, calculated as (a + b + c) / 2.

How would you handle this situation?
Choose one of the following options.

Exercise 2: Sorting

Arrange the actions in the right column from most effective (1) to least effective (4). Order them based on their effectiveness in supporting student understanding and learning.

Action 1
Action 2
Action 3
Action 4
Let all students explore and support them. Make sure they understand the two formulas and their alternative use according to the context.
Provide both formulas and ask the students to comment, with the possibility of accessing the source.
Provide alternative formulas only once students have at least tried to discover them on their own.
Provide both formulas, explain them, and ask students to memorize them.
Hint
Exercise 3: Reflection question

How confident are you in your ability to help students understand that problem-solving requires openness to different possible approaches?
Choose one of the following options.

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