Learning mathematical skills must follow the simple to the complex path. It means that in the initial years, children learn mathematical vocabulary (e.g., matching, sorting, pairing, ordering, pattern, classification, one-to-one correspondence) and mathematical concepts related to numbers, shapes, space, and measures. These skills gradually move to more complex and higher skills (e.g., quantity, shapes and space, measurement) at later ages. In the mathematics teaching-learning process, those mathematical skills which are more focused on applying mathematical skills in a real-life situation to understand, solve, reason, communicate, and make decisions need emphasis.
National Curriculum Framework for Foundational Stage-2022
Mathematics Teaching Approaches at Foundational Stage
The following approaches can be integrated into mathematical teaching-learning processes to give children comprehensive mathematics experiences considering the nature and cognitive demand
of the tasks and skills.
a. Developing mathematical abstract ideas (concepts) through concrete experience (ELPS)
Mathematical concepts are abstract e.g., learning to understand numbers, doing operations, and drawing 2D shapes. So, it is important that children learn these abstract concepts through concrete experience and gradually move from the concrete to the pictorial to abstract notions.
When children engage with a concrete experience, they can understand the meaning of mathematical concepts easily. The following sequence can be followed to teach the abstract mathematical concept. (NCFFS-118)
An example of learning numbers through ELPS:
• E – Experience: Learning the mathematical concept of concrete objects, e.g., counting concrete objects for learning numbers.
• L – Spoken Language: Describing the experience in language, e.g., what is being counted, how many have been counted.
• P – Pictures: Representing mathematical concepts in a pictorial form e.g., if 3 balls have been counted, these can be represented through 3 pictures of the ball.
• S – Written Symbols: Mathematical concept that has been learned through concrete experience and pictorial can be generalized in written symbol form such as writing the number 3 for three balls.
Connecting mathematics learning with children’s real-life and prior knowledge
Learning mathematics must relate to children’s real life and their prior knowledge. Real life examples also help children to understand a mathematical concept, develop the ability to apply mathematical skills in real life and, more importantly, see mathematics as worth learning and doable. So, while teaching mathematical skills, Teachers should use real life examples to build conceptual and problem-solving abilities. (NCFFS-119)
Mathematics as a problem-solving tool
- Problem-solving is an important higher goal of mathematics learning and children must quickly understand that mathematics can be used as a problem-solving tool to solve a real-life mathematical problem. So, learning should not only focus on developing concepts but also on problem-solving skills. Problem-solving abilities provide children an opportunity of making meaning of skills and knowledge as well as an understanding of where they can apply their knowledge or skills. Setting up rich mathematical tasks, understanding the problem, devising strategies, solving, and checking the solution and justification are important steps to help children build problem-solving abilities. (NCFFS-119)
- The following steps could help develop problem-solving abilities among children:
- i. Understand the problem – What is known? what is unknown?
- ii. Devise a strategy/plan- Do I know a related problem? What strategies could be useful to solve it?
- iii. Solving the problem – What steps I am taking to solve it? Am I taking the correct steps? Can I argue about why and how I solved this problem?
- iv. Looking back/Checking the solution – Did I do the right thing? Did I answer the question?
- v. Encouraging flexible thinking and use of multiple strategies for problem-solving.
Children should learn more than one way of problem-solving. For example, what would be different strategies to solve 8+7? Children can count on 7 more from 8 or some children can
split 7 into 5+2 and add 2 in 8 to make it 10 and then add both 10 and 5 to arrive at 15. Hence, teaching-learning must be focused on helping children to invent multiple strategies to solve
the problem and not only a single way of problem-solving. Children must be encouraged to invent their own strategies but for these strategies, children need a strong understanding of
mathematical concepts and processes.
Using Mathematical talk, communication, and reasoning.
Mathematics has its own language, different from everyday language in many ways. It has its own unique vocabulary, symbols, and sign systems which are often not used in daily lives e.g., addition, multiplication, +, -, =.
A child may be encountering these for the first time in a mathematics classroom. There is a need for rich conversation between Teachers and children around mathematical concepts, processes, applications, and reasoning. This discussion must also focus on mathematics that children encounter in their real life and provide an opportunity for children to explain their mathematical thinking, reason, justify and listen to other mathematical ideas and also the opportunity to listen to the Teacher’s explanation, reasoning, and justification. So, an oral math talk must be encouraged in the classroom rather than engaging in written tasks silently.
Developing a positive attitude towards learning mathematics
There is vast research on the strong dislike and negative attitudes children may develop towards mathematics even as early as Grade 3. Early learning should not only focus on developing
mathematical competencies but also on supporting children to develop a positive relationship with mathematics as a domain. The system needs to generate awareness of the strong affective responses mathematics as a subject can generate, and the pivotal role a strong foundation in early mathematics can play in pruning the negative image the subject has for many. Children should learn to enjoy mathematics.
Components/Areas of Mathematics Learning in the Early Years
- a. Number and its Relations refers to understanding number concepts (Sound, Symbol, and Quantity) in various contexts, counting, representation, and its relation.
- b. Basic Mathematical Operation refers to understanding concepts of calculation and developing strategies to solve problems using them.
- c. Shapes and Spatial Understanding refers to developing an understanding of shapes and making and classifying shapes as well develop spatial sense understanding.
- d. Patterns refers to the understanding of the repeated arrangement of numbers, shapes, and designs and making a generalisation based on some rules and structure.
- e. Measurement refers to understanding units of measuring something and using it to quantify.
- f. Data Handling refers to understanding the collection of data, collecting and analysing it.
Excerpts from –
National Curriculum Framework for Foundational Stage-2022
https://ncert.nic.in/pdf/NCF_for_Foundational_Stage_20_October_2022.pdf
https://ncf.ncert.gov.in/#/web/home