Mathematics – sharing the journey !
Primary Mathematics is deceptively simple. Yet it encompasses thousands of years of the journey of the human spirit-a journey of years of working on the earth, of measuring and building and transforming the world. The patterns discovered have evolved into mathematical objects that today confront the child in the classroom. New and powerful paths of reasoning have emerged that have made it possible for us to ‘go beyond the given’.
Children need to develop these new abstract skills. But how does one start?
Very often we make the mistake of starting from where we should be ending i.e. the abstract final notation and try to explain it. Instead, if we start from where children are, the level of context embedded specific meaningful activities, we would be more successful. To make the journey from concrete situations to the abstractions of mathematics, it is useful to have concrete mediators. These tools then further evolve with appropriate scaffolding by the teacher into ‘tools of the mind’.
Thus for example, a fraction cutout is a piece of cake for the child to begin with. But she is able to reason out using it that 2 pieces of 1/8 are equal to 1/4. Later slowly the meanings of denominators and numerators are developed. The patterns produced by a child with Rangometry provide the teacher the background to have a conversation with the children about the relationships between the different polygons. The color coding of the Ganitmala provides a powerful basis for the journey to the heights of place value.
What we have developed is a set of toolkits to support this process across the pre- primary and primary grades and these have been tried out in the classrooms over the years. These toolkits also include detailed manuals about the different activities and games that can be conducted.
These class specific toolkits are made according to NCERT syllabus. But the content is flexible enough to accommodate school-wise or board-wise syllabi. We have tried to keep the cost of the toolkit low enough so that it is affordable to all schools. We are very keen that the toolkit gets actually used in the classroom and does not face the well known problem of remaining in locked cupboards.
In order to sustain and improve the program, we will be conducting a series of six workshops and review along with one field visit to each school using the toolkits. Below we provide an indication of the concepts supported by these toolkits.
- Developing cardinality by counting, synchronizing with counting words, without skipping or double counting
- Early Number sense Seriating with meaning- concrete support in story contexts
- Hand-eye coordination and color recognition
- Numeral Recognition Addition and subtraction with object support
- Structuring of numbers up to 20
- Pattern recognition
- Number facts of 10
- Extending Number Sense beyond 20
- Doubling and halving of numbers up to 20
- Structured counting using patterns of tens
- Recognizing and manipulating triangles in their variety
- Understanding expanded notation of numbers and starting with place value
- 2-digit addition and subtraction mentally
- Skip counting and beginning of multiplication
- Extending number sense to 200
- Distinguishing between rectangles, squares and other quadrilaterals
- Developing Angle Sense
- Extending number sense to 1000
- Automatising multiplication tables
- Understanding 3-D shapes Measurement- meter and centimeter and gram
- Understanding Fractions
- Understanding Distributive property
- Extending numbers up to 10,000 and beyond
- Strengthening mental arithmetic
- Consolidating angles and 2-D and 3-D Geometry
- Consolidating Place Value 5 digit and beyond
- Addition and subtraction of fractions
- Understanding Decimal notation
- Angles transition from non formal units to degrees
- Understanding factors and multiples Polygons, polyhedrons and circles
- Understanding area and perimeter