Number Tricks without reasoning - a waste of time?

Mathematical tricks are too frequently taught to students, with the expectation that students will remember them.  Over time this approach requires students to build a bank of facts that are not bound by any adhesive.  There are similarities in playing the 'Jenga' game where when you keep putting more blocks onto the pile, eventually the pile falls over - students can't remember the tricks and then fail to achieve their potential in their GCSE exams.

If tricks are to be of value then they need to be learning opportunities where the key is to develop reasoning and understanding.   MEI Newsletter Jan/Feb 2017 - a very useful publication, included this number trick which can be used as a starting point.

If students just show that the trick works then this has little or no benefit for the development of their mathematical learning.  Current GCSEs require students to reason and problem solve, therefore the key thing for students is to understand the reason why this trick works and develop their thinking by posing their own questions. 

As keen believers in supporting all learners and the key role visual methods play in this being achieved, we created this short video (use Chrome browser and click on full screen to see more clearly)

One possible next step is to ask students does this always work?  The structural manipulatives (resources) to support answering this question could be to provide students with counters to create arrays.

Mathematical Content met in this activity:

• arrays
• multiplication
• factors
• multiples

Mathematical Processes: 

• reasoning
• making conjectures

This is just one example of how our Mathematics Team of consultants support and develop conceptual understanding for all learners. Effective use of technology has an important role in providing students with dynamic images that support the development of their understanding - if you need help then Pip can provide both ideas and training for teachers to use in the classroom.