Maths, Motivation, Brain Maps, the Mind and Merit (Part 3)

The teaching strategies and classroom set up when teaching maths through a Responsibility Theory lens are explained here by Dr Ragnar Purje. Students were given a sense of agency over their maths instruction through reciting the mantras “I’ve got the power” and “I love maths”.

Circles, Ownership and Powerhouse Mantras
In terms of classroom teaching strategies, the children were placed in equal groups. Depending on the class size each group generally consisted of three to six students.
The class was organised into individual groups. Once this was achieved, the collective of these groups was organised into a single circle large sitting on the carpet on the floor. Before the maths teaching process began, the instructions were as follows: “Everyone say: I am using my powerhouse.”

I’ve Got the Power
With this instruction, I placed both of my hands on my head. The students followed this action and they repeated the mantra. “I am using my powerhouse.” The importance of this mantra is in the use of the word and letter “I”. The statement “I am using my powerhouse,” designates ownership, control and personal responsibility of thinking and action. With their hands on their head – their powerhouse – the next instruction was: “Everyone say: I am looking, listening and learning.” The students repeated the phrase enthusiastically. “Everyone say: “I am working hard!” The students again responded joyfully, emphasising the words, I am working hard!” “Everyone say: “I’ve got the power!” The students again responded enthusiastically with: “I’ve got the power!”

Ownership, Power and Responsibilities Confirmed
With all of this being achieved, and while the students still had their hands on their powerhouse, I was now able to publicly confirm to the class about the ownership of their power and their responsibilities. “You’ve just told me that you’ve got the power and that you will be working hard. You’ve also just told me that you are looking, looking, listening and learning. I can see that you are looking and listening and wanting to learn. Okay, let’s get on with our powerhouse learning. Everyone say: “I’ve got the power!” The enthusiastic and loud collective response followed: “I’ve got the power!”

From Addition, Subtraction and Onto Multiplication
As time progressed the students progressed through the operations of addition and subtraction, up to the number 50. This process had now progressed to the operation of multiplication. During this one particular multiplication lesson (the multiplication lessons had progressed through the operations of 2 times, 3 times and 4 times). During the multiplication process, the concept of addition (along with the ongoing application of sequential counting) and the use of physical counters, which in this could be described as Lego blocks. The class was now in the process of engaging in the ‘five times’ multiplication table. The class had completed 1 x 5; 2 x 5, and now the class was about to work on 3 x 5.

Instruction
The instruction to the class (as always, before attempting to find the answer to an algorithm), was for the students was to sit and watch as the algorithm (with its numbers and symbols) being announced and written on the board. On this occasion, as noted, the class had progressed to watching as 3 x 5 was announced and written on the board. When this algorithm had been completed and announced, the students then progressed (as had always been the case), in knowing how to create (with their counters), the algorithm as written on the board. With this, the students were then instructed to discover the answer with the use of their counters. All students began the process.

I Know the Answer
As this was taking place, one student called out: “Sir, I know the answer.” I asked the student where his counters were so that he could describe how arrived at his answer. He said: “I haven’t used my counters, but I know the answer.” “That’s good,” was my reply. “What is the answer?” “Fifteen,” the student immediately replied. “That’s good, that is the right answer!” I then asked him how he knew the answer to three times five was fifteen. He answered with the best brain-based “powerhouse” answer possible. His answer was “I don’t know, but I know the answer is fifteen.”

Unseen Neurological Changes
This answer confirmed to me that unseen neurological changes had taken place. These unseen neurological changes had now combined to form new neurons (the process of neurogenesis); new synapses (the process of synaptogenesis); new and additional neurological assemblies, and new brain maps (along with axonal myelination, along with additional dendrites, glia and much, much more).

Phenomenological Consciousness
All these unseen brain-based changes had ‘obviously’ changed this student’s brain. These neurobiological changes had now also advanced this student’s brain and mind to such an extent (that this student’s brain and mind) presented to the student’s ethereal phenomenological consciousness, the insight, the knowledge and the sentient consciousness answer (without having to engage in any calculations).

Further Testing
To further test this hypothesis, I then asked the student what the answer to four times five was. He immediately replied “20.” I then asked what the answer to “five times five” was. “Sir it’s 25.” “How do you know?” I again asked. “I don’t know,” was the smiling reply, with a supportive shrug of his shoulders. My hypothesis was that the student knew the answer (without having to engage in any sequential procedural counting), because his sentient thinking had advanced as a result of the ongoing sequential counting, and then ongoing work he had been undertaking.

Sentient and Ethereal Human Consciousness
All this thinking and action had obviously changed his brain and his mind. It was apparent because this student would not have been able to provide the answers if this had not taken place. The brain fires, rewires, serves and brings into existence the mind. As such, this student was now clearly operating at this most unique sentient and ethereal human consciousness level. Because of this taking place, this student was able (without any practical procedural counting taking place), to declare: “I know the answer.”

Declarative and Procedural Knowledge
In terms of application and result, this student’s declarative knowledge was built upon the ongoing sequence learning, the procedural counting and pointing to the blocks, along with explicit teaching worked examples that were constantly taking place. Declarative knowledge, according to Anita Woolfolk is, knowing that something is the case, while procedural knowledge is, knowing how to do something, such as, in this case, to count sequentially and to also add and multiply numbers.

Maths Self-management
It was clear to see, from the presenting behaviours by the students, that self-directed learning along with maths self-management was taking place. In terms of self-management, Anita Woolfolk points out that “[t]he most recent application of behavioural views of learning emphasizes self-management.” Added to this Woolfolk declares: “If one goal of education is to produce people who are capable of educating themselves, then students must learn to manage their own lives, set their own goals, and provide their own reinforcement…Life is filled with tasks that call for…self-management.”

I Love Maths
As time progressed, the students soon began to independently announce, at the start and end of each lesson, “I love maths,” and “I’ve got the power.” This mantra even advanced to even during playtime there were students regularly running around, laughing and shouting “I LOVE MATHS” and ‘I’VE GOT THE POWER!”

Dr Ragnar Purje (PhD; M.Ed.; M.Ed.(Guid.&Couns.); M.Ed.(Lead.&Man.); B.A.(Psych.); B.App.Sc.(P.E.); Grad.Dip.Ed.; Grad.Dip.Sp.Sc.; Grad.Dip.Ex.Sp.Sc.; Grad.Cert.(Comm.); Grad.Dip.(Health Couns.); Cert.IV in Assess.&Workplace Training) is an Adjunct Senior Lecturer at CQUniversity in the School of Education and the Arts. Dr Purje works with Professor Ken Purnell specialising in classroom behaviour management strategies. Dr Purje is the author of Responsibility Theory.® For presentations, Dr Purje is represented by Saxton Speakers Bureau.