Brenton Lagarda – Mathematics Curriculum Leader
Below is a fragment of a conversation that took place between myself and my Year 10 Maths class in the run up to their End Of Year Examinations:
Me: Year 10, I’m so proud of your progress so far today. All the working on your whiteboards shows me you really understand this topic. Let’s challenge ourselves now; here is a tough problem I want you to think, pair and share your ideas.
Year 10 Student: I don’t get it!
Me: Which aspects don’t you understand?
Year 10 Student: All of it.
Me: But you just demonstrated that you understood how to apply Pythagoras’ theorem on your mini- white board!
Year 10 Students: But I can’t tell what I am supposed to do with the question.
Such an experience can be frustrating and disappointing for both teachers and students. No matter how well I feel I have taught a particular topic, students seem to fall down at the last hurdle, that is, the reasoning and problem-solving questions. But this should not be surprising, when reasoning and problem-solving is an intellectually demanding procedure. The process of extracting meaning, identifying and selecting relevant information, and sequencing ideas into a logical argument is complex.
One strategy I have been experimenting with to improve students’ confidence with problem solving is the use of Goal Free Problems. A Goal Free problem, as the name suggests, is a question which has no specified objective. Students are presented with information and then asked “What can you work out?”. The purpose of presenting students with such a task is that it encourages them to think creatively, making connections between topics and ideas while giving them the space and time to generate chains of reasoning in a non-threatening environment.
Goal free problems are easy to generate, by taking an examination question, and removing the actual question. For example:
I find it helpful when giving goal-free problems for the first time to include prompts for the problem-solving process. These prompts can be seen in a presentation slide I shared with my Year 10’s in the lesson following the “I don’t know” incident.
To my absolute delight, my students came up with some great ideas.
I then shared with them the actual question.
At this point some students were elated that they had solved the problem already. Others were happy the question was easier to complete than the questions that they had invented (like using trigonometry to work out missing angles). Although it is only an observation, the students seemed far more confident to take on the later problems that followed. I hope that with time, students will become even more creative and flexible with their ideas, tackling more complex problems.
You can find further examples of Mathematics Goal Free Problems from this website:
http://goalfreeproblems.blogspot.com/2018/07/other-writing-about-goal-free- problems.html
I hope this has inspired you to use some goal-free problems in your next lesson. I would
love to hear about your, and your students’ experiences.
SB Pedagogy 