Mental Computation

More than quick recall

Understanding and fluency are two of the four proficiency strands identified in the Australian Maths Curriculum. Understanding means more than simply recalling rote-learned facts, it means being able to construct answers efficiently and reliably to addition, subtraction, multiplication and division questions selecting from a wide range of available strategies. Fluency means knowing what operation to select and which strategy to apply.

Mental arithmetic traditionally called for little more than rote-learning and recall of basic facts with little understanding. Mental computation calls for much more. It calls for strategies that can be used to construct rapidly answers to addition, subtraction, multiplication and division questions. It requires thinking skills as well as simple recall.

For 27 + 26 for instance there are many ways to mentally compute the answer. Mentally adding the ones, remembering to trade and then adding the tens is not a very efficient or reliable strategy for students when they do not have access to pencil and paper. Knowing that double 25 is 50 and adding 3 can be carried out very easily in the head and requires less memory space than the traditional method.

We have been working with teachers, students and parent to develop strategic approaches to mental calculation, also called as mental computation. This has resulted in the following list of strategies that are important. We have also developed a secret weapon for learning and applying efficient strategies; we call it the Secret Code.

Mental Computation Strategy subitize count on (addition) count back (subtraction) turn around doubles (addition and multiplication) halves (subtraction and division) rainbow facts skip counting near doubles

Secret Code co cb ta d h rf sc nd

Mental Computation Strategy friendly numbers tallies bridge through 10 number splitting landmark number round and adjust balance and compensate

Secret Code fn btt ns ln ra bc

Click below to see Java applets that demonstrate the mental computation strategies in a way that can be used in the classroom or at home.

Subitizing and count on

Doubles and Rainbow Facts
(more to follow soon)

Helping Parents

Parents often comment that they do not understand the way maths is taught today and words such as subitizing, rainbow facts and number splitting were not part of their maths programs when they were at school. But they want to help their children and do not know the best way to go about it. We had many requests from schools and from parents for help with this issue of mental computation and so Natural Maths Strategies for Parents books were born.

Interestingly schools often buy a set for their teachers so that they are all on the same wave-length as they teach mental computation strategies.