Although, Way (2008) pointed out that “Teachers’ instincts often tell them that they should use investigational mathematics more often in their teaching but are sometimes disappointed with the outcomes when they try it.” In my brief teaching experience, I have already faced a number of whole-group scenarios where I completed an activity or explanation and asked “Show of hands who understands this? Keep your hands up if you can convince the class how you would do this” Only to find a couple of children kept their hands up. Possibly, there are two reasons for this : one is that the children are inexperienced in this approach and find it difficult to accept responsibility for the decision-making required and need a lot of practise to develop organised or systematic approaches. The other reason is that the teachers have yet to develop a questioning style that guides, supports and stimulates the children without removing the responsibility for problem-solving process from the children .

On another occasion, a number of student teachers and I had the opportunity to conduct a mathematical problem to two classes of students (one class being in year 8 and on another session, class being in year 7), where each class was split into groups of 6-8 students. Working in pairs, we would spend about 20 minutes with one group and carrousel around to another group to work on the same problem.

During the first session, we introduced The Prime Numbers activity (UCL IOE, 2018, p. 2) – see below, to year 8 students and observed how they responded.

Students noticed the age gap between each child in the example was two years, I then observed some students writing down all the possible ages that the youngest to the oldest could be over the next 20 years. At the time I did not interfere to question whether even numbers are prime numbers. Observing others as they recollected what a prime number is and agreed that only even prime number was two and proceeded to write down only the odd integers whether or not they were prime. I was keen to scaffold the students’ mathematical thinking based on the four main categories