PROBLEM-BASED LEARNING

In PBL, students analyse and propose solutions to a real-world problem that is usually presented to them in an unstructured and often open-ended manner. PBL originated in medical education where it is still extensively used today, but it has also found application in many other fields. The main advantages of PBL are that it has been found to lead to improvements in information processing, skill proficiency (Prince 2004) and the development of a variety of skills, including problem-solving, reasoning, teamwork and metacognition.

As Prince and Felder (2007) identify, in PBL, the students usually operate in teams or collaborative groups and work through a problem-solving process to:

• define the problem precisely

• find out what they know and what they need to know

• decide how to proceed to find out what they need

• gather all the information—this can be provided by the teacher, or not

• analyse all the information gathered

• create possible solutions

• work through the feasibility of each one

• narrow the possibilities down to their best, justifiable solution (which may then be presented to the rest of the class, and a whole-class analysis of the possible solutions undertaken).

(Prince and Felder 2007) PBL can be a hugely powerful teaching strategy that promotes active learning and a student-centred pedagogy. It is important, though, to take care that students are exposed to a balance of both positive and negative scenarios in order to avoid an overly pessimistic focus on problems.

Teaching based on inquiry does demand a shift in teaching style from teachers whose primary role is to supply answers to teachers whose primary role is to promote questions. It also involves a shift in some of the responsibility for learning from teachers to students (Oliver-Hoyo, Allen and Anderson 2004). While this can seem a major challenge for some teachers, there are two key underlying principles that can help teachers to understand the change to inquiry-based methods.

1. Learning is constructed by a process that moves from real-world examples to concepts, ideas, theories and facts.

2. Students are responsible for finding much of the information themselves, and processing it to draw the important conclusions,

At a more practical level, simple things that teachers can do to introduce a more inquiry-based approach include:

• posing questions, outlining problems, setting challenges, giving clear measurable objectives

• putting students into small groups (3–4 students), assigning clear roles and allowing for role rotation within each group

• enabling and helping students to connect to the best subject-based resources

• focusing the students on both the answers they are finding and the research skills they are using

• viewing their own role as facilitators of students’ journeys, rather than simply providers of answers.

The potential benefits of an inquiry-based approach can be seen in the example of DP science lessons, where adopting such an approach can help students to learn the process of scientific inquiry through being involved in an inquiry themselves: “students are presented with a challenge (such as a question to be answered, an observation or data set to be interpreted, or a hypothesis to be tested) and accomplish the desired learning in the process of responding to that challenge” (Prince and Felder 2007).

Alignment with Ontario Catholic School Graduate Expectations and the Global Competencies

In the IB Mathematics programme, students make use of technology to engage in inquiry-based learning as they compare, examine and analyse various characteristics and features of functions. Not only do students become familiar with utilising graphing calculators, but they also learn how to leverage other computer software programs like Desmos. 

Through this inquiry-based learning model, students utilize Google Sheets to calculate measures of central tendency of data sets while studying statistics. They work collaboratively to construct linear regression models, analyse trends in the data, and to identify correlations between variables. 

Through cooperative learning, students become inquirers and reflective thinkers, as they work through challenges and collaborate with their peers to problem solve. Students develop the skills necessary to reflect on their findings and communicate their thought processes with others. Students engage in “Math Talk” sessions both in-person and remotely, where they have opportunities to engage in higher-order questioning and mathematical reasoning. Students develop the skills necessary to articulate their thinking, pose questions of their own and analyse the justifications and methodologies of others. 

When engaging in exploration tasks, students are asked to find connections between mathematics and real world applications. Through their own curiosity and investigation, students discover the relevance of mathematics across other disciplines including economics, science and physics. 

Integrating the IB Approaches to Teaching and Learning in Mathematics

Carter’s IB math students investigated The Cantor Set in virtual breakout rooms, where they used Jamboard to collaborate and engage in “Math Talk”. Students used the interactive whiteboard to examine the set of real numbers between 0 and 1 and discussed the elements and properties of The Cantor Set. In addition, students were able to apply their acquired knowledge from the Sequences and Series unit to determine the infinite sum of the series. This guided inquiry challenge provided students with a starting point to begin the exploration activity, and subsequently encouraged students to use their critical thinking skills to work through the task collectively as a group.The Cantor Set gives the students a chance to look at some of the work of famous mathematicians and start to think about big ideas in pure mathematics:  countable and uncountable infinities.