HL Mathematics: pioneering problem-solving

Meet one of our Mathematics teachers, Guillermo Afonso!

IBDP HL Mathematics is a challenging option: research from the University of Leeds suggests that this subject choice requires students to develop university-level skills from Grade 11. Indeed, a glance at the IB course description will have students and parents alike amazed by a long list of expectations ranging from “refining powers of abstraction and generalisation” to “considering mathematics’s moral, social and ethical implications”.

But Mr Guillermo Afonso seems to have solved the equation for success. He is quick in his response when asked what his students have to master to succeed in HL Mathematics. “Tenacity,” he firmly responds. “To never give up, even when the challenge is unfamiliar.” 

After observing Mr Afonso’s class, we learned that one student’s Extended Essay scaled up Dijkstra's algorithm to plan global transport organisation. The pursuit of such a task provides some insight into the outstanding problem-solving nurtured at Halcyon.

Pioneering an environment for success

As he closely watches his students work through a set of problems, Mr Afonso explains to us that HL Mathematics has no set list of formulas and procedures - each question is unfamiliar by design, and requires a bespoke approach. Through problem solving-based teaching, Mr Afonso pushes students to master a flexible range of methods, approaches and tools - including high-level algebraic and statistical software such as Maxima and IBM SPSS Statistics. 

This allows Halcyon’s HL Mathematics students to develop a strong level of “resourcefulness”: a crucial factor in the formula for achievement. Mr Afonso smiles as he oversees his three HL students attempting a myriad of mathematical approaches. His determination that his students rely on their own bank of knowledge to solve problems shines through in his prompts: “What do you already know about this equation?” and “What rules apply to similar problems?” 

Mr Afonso is firm that his students must also be masterful risk-takers: speaking encouragingly to those that openly state their working-out “doesn’t make sense” and reassuring them they are closer to a solution as a result. The developing courage of these students is clear to us as we observe the lesson. They approach the large whiteboard without hesitation to quickly map out possible solutions; unafraid that their classmates may spot a mistake, and pleased that they have the chance to work collaboratively. 

Achievement beyond the IB 

Mr Afonso’s collaborative cultivation of students’ tenacity, resourcefulness and courage has an aim beyond success in the IB. He passionately emphasises the importance of quick problem-solving skills to careers even beyond mathematics: in politics, research and social roles, for example. The importance of determined critical thinking cannot be overstated in preparing our students for success in higher education and the world of work.

Here at Halcyon, our team recognises that the future that awaits our students is complex. For our students to be the leaders of tomorrow, our dynamic pedagogic practices must encourage them to thrive in decision-making, risk-taking and relationship-managing.