The Resources section has rich pickings - plenty of hands-on, ready-to-use activities, ideas, posters and worksheets for teachers.
When do we know that a student has mastered a particular concept well? An ability to repeat a learnt process or a practised algorithm is not a necessary indication of mastery. One looks for the ability to apply the concept in situations or contexts, where the concept is embedded indirectly.
All mathematical topics that are taught in the primary school are born out of the need of children to understand their world. In the process of acquiring and growing in this understanding children encounter various types of numerical data.
Here are some questions which arise while teaching Multiplication: Should children memorise the multiplication tables? What is an easy and convenient way of modeling multiplication? Is it enough if one only teaches the procedure of multiplication? Perhaps answers to these questions can be found if we reflect on the importance we give to construction of knowledge. If we see that children must understand how facts are derived, how procedures are derived and how concepts can be visualized, then our approach will be dictated by that understanding.
It is well known that division and subtraction are generally found to be more difficult to learn by children, as compared with addition and multiplication. Particularly in the case of division, children have difficulty both in identifying the situations requiring division and the complex formal procedure involved in the long division process. There is also the role played by zero as a place value holder in the quotient. Given that these are the three main difficulties, teachers need to slow down and exercise care while teaching the division concept.
Most assessments conducted across the country indicate that the first stumbling block for many children is the subtraction operation, followed by division. On looking more closely we see that the difficulties often arise in subtraction contexts involving double digit or larger numbers. This difficulty is largely caused by three factors: (i) improper understanding of place values (ii) lack of understanding of the rationale behind the formal subtraction procedure, (iii) not seeing the connection between addition facts and subtraction facts.a
In the various workshops that I have held with primary school teachers I have often found that teachers do not spend sufficient time on scaffolding exercises and tend to plunge straight into formal operations. Often the pace at which they proceed and the text materials they use are not built up gradually enough to allow time for internalisation. Also the prerequisite knowledge and skills are not looked into adequately. I hope the suggestions made here help teachers to fill these gaps and lay a stronger foundation.
Teaching of the place value system happens in the context of teaching numbers and is very closely related to counting, grouping objects to aid counting, usage of number decomposition, learning the patterns in number names, learning the written representations of numbers, learning the patterns in the relationships between consecutive places, and developing a proper number sense.