# CCE : Source Book On Assessment For Class I To V [Mathematics]

## Languages - Mathematics

School mathematics is often viewed by students and teachers as application of procedures and formulae. This perception receives support from the nature of assessment followed in most schools. Frequently, tests are designed only to assess a student’s knowledge of facts, formulae and procedure. As a result assessment of understanding of concepts and principles is given less importance. Almost every teacher, when asked, justifies formal assessment as a way of finding out what the students have learnt. In this section on assessment in primary school mathematics, the emphasis is on assisting the teacher on how to assess the understanding of the learners, provide feedback to them as well as guage the effectiveness of her pedagogical practices in mathematics. We have tried, in this part of the source book, to bring out the various dimensions that need to be assessed in order to give teachers a holistic view of the child’s learning of mathematics as well as her own pedagogy and the curriculum. We have also tried to suggest the varied possibilities in terms of design of items and techniques for assessment that could be used by the teacher in both formal and informal settings. For a thorough understanding of issues related to curriculum organisation, pedagogy and assessment in mathematics, teachers or need to refer to the NCF-2005, Position Paper of the Focus Group on Mathematics and the NCERT’s mathematics syllabus for elementary stage.

## Our approach to learning mathematics

The aim of school mathematics in the primary school years is to develop both ‘useful’ capabilities in the areas of numbers, number operations, measurement, spatial thinking and data handling. Further, it aims to develop the ability to reason mathematically, formulate and solve problems, make estimations, find approximate solutions and desirable attitude towards mathematics. As a result the child learns to communicate precisely through mathematical concepts and symbols. Visualisation and representation skills are also important and modelling situations using quantities, shapes and forms are part of mathematical development.

Children develop mathematical thinking through everyday interactions in the world. In fact the everyday world of most rural children is rich in oral mathematical traditions including techniques for computation, mathematics in riddles and recreation and even problem solving and optimisation. These are the cognitive resources that  children already have access to, and which can be drawn upon by the pedagogic processes at school. School experiences introduce children to more formal aspects of mathematics beginning with the written representation system, formal understanding of number and number operations and then proceeding to many new concepts,
operations and abstractions. It is well established that children’s initial understanding of mathematics is ‘concrete’ and ‘contextualised’, and that learning is aided by designing tasks that involve the manipulation of concrete materials and provided in a context that enhances their meaningfulness and invites children to engage with them in a problem solving mode. It is through such activity that children ‘construct’ mathematical knowledge. Such a mode of doing mathematics can also be enjoyable and satisfying to most children. Mathematics is hierarchical and logically structured and children’s learning is developmental. We can therefore expect gradual changes and deepening of children’s understanding.

## Our approach to assessment

The effort in this source book is to present tools for assessment that are consistent with the process of learning mathematics and to enable teachers to monitor the progress that children have made in learning mathematics.
The process of assessment in mathematics includes the following dimensions of mathematical learning:

• concepts and procedures

• mathematical reasoning

• dispositions towards mathematics

• using mathematical knowledge and techniques to solve problems

• communication