The document discusses approaches to teaching mathematics at the foundational stage. It focuses on developing both higher-order skills like problem-solving and content-specific skills. Teachers should emphasize real-world connections, use concrete examples initially and move to more abstract concepts over time. A four-block approach is recommended: 1) oral math talk, 2) skills teaching, 3) skills practice, and 4) math games. The gradual release of responsibility model shifts responsibility from teacher to students. A variety of pedagogical tools can aid learning, including toys, games, stories and spending time in nature.

1. LEARNING-TEACHING MATHEMATICS
AT FOUNDATIONAL STAGE
PROF. ANUP KUMAR RAJPUT
HEAD, PUBLICATION DIVISION
ANUPNCERT@YAHOO.CO.IN

2. BASIC SKILLS THAT NEP 2020 AND NCF-FS 2022 FOCUS ON
• Creativity
• Flexibility
• Organization
al skills
• Patience
• Communication skills
• Problem-solving
skills

3. Teaching Mathematics/Numeracy
• Children bring various mathematical skills from their surroundings and culture
into the class-room, which must be the basis of learning mathematics.
• Mathematics learning goals can be categorised into
(i) Higher Goal
ability to handle abstract thinking
problem-solving
visualisation,
representation,
reasoning, and
making connections of mathematics concepts with
other domains
Shapes
Patterns
Understa
nding
numbers
(ii) Content Specific Goal

4. Achieving Goals of Learning Mathematics
• Teaching and learning in the early years must emphasise achieving both higher goals and
content-specific goals as both goals are interdependent and interconnected.
• 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 are related to life
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.
These skills gradually move to more complex and higher skills (e.g., quantity, shapes and space,
measurement) at later ages.

5.  problem-solving i.e., solving mathematical problems both
realistic and ‘pure;’
 reasoning i.e., justifying and reasoning about solutions and
processes;
 connection-making i.e., connections between one concept and
another;
 representation i.e., using concrete, visual diagrams to
represent mathematical concepts and ideas;
 communication i.e., explaining and communicating mathematical
ideas;
 and estimation i.e., using approximation to quantify and solve.
Processes which help children achieve goals.

6. 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.
• 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.
Approaches to Teach Numeracy

7. 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.
Approaches to Teach Numeracy contd.

8. B. Connecting learning with children’s real-life and prior knowledge
• Real life examples also help children to
• understand a concept,
• develop the ability to apply skills in real life and,
• more importantly, see concept as worth learning and doable. ( Attitude)
So, while teaching skills, Teachers should use real life examples to build
conceptual and problem-solving abilities.
C. 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.
Approaches to Teach contd.

9. D. Using Oral 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 live e.g., addition, multiplication, +, -, =.
• A child may be encountering these for the first time
• There is a need for rich conversation. This discussion must focus on the
topic that
• children encounter in their real life and provide an opportunity for children to
explain
• their mathematical thinking, reason,
• justify and listen to other ideas and
• also the opportunity to listen to the Teacher’s explanation, reasoning, and justification.
Approaches to Teach contd.

10. E. Developing a positive attitude towards learning
• There is vast research on the strong dislike and negative attitudes children
may develop towards learning even as early as Grade 3.
Early learning should not only focus on developing competencies but also on
supporting children to develop a positive relationship with all subjects as
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 learning can play in pruning the negative image the
subject has for many. Children should learn to enjoy learning.
Approaches to Teach contd.

11. 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.
Components/Areas of Mathematics/Numeracy Learning in the Early Years

12. Blocks of Teaching for Mathematics/ Numeracy
Children need to build conceptual understanding,
procedural understanding, strategies
competence/application, communication and
reasoning, and a positive attitude towards
mathematics.
Block 1: Oral math talk: At the beginning of class, for 5-10 minutes, children could sing a poem with
numbers or discuss their experiences with mathematics or problems they encounter in their life.
Discussion can also be on oral calculation, concept, strategies, and reasoning. It works as a warm-up
activity before going into the formal teaching process.
Four Block Approach
Block 2: Skills teaching (combining all strands): This is teaching mathematical concepts, problem-
solving, and communication through concrete experience, systematic activities, and instruction that
follow the Gradual Release of Responsibility approach, though not necessarily in the same sequence
for every activity or mathematical task. Every child must get an opportunity to learn, explain, and be
given feedback.
Four blocks for the daily classroom
process.

13. Block 3: Skills practice: Providing children with
various kinds of rich mathematical tasks based
on concepts, processes, problem solving,
reasoning, and communication for practicing
mathematical skills. This can be through a
workbook, textbook or a Teacher-created task
set.
Block 4: Math game for reinforcing learning/problem solving: Children enjoy playing
games. There could be various kinds of mathematical games which help children to
strengthen their learning in various ways. These games must be based on problem-
solving, concepts as well as reasoning.
Group-wise games can also be planned according to the learning levels of the children.
The total suggested time in the day for mathematics is 60 minutes.
Four Block Approach Contd.

15. FIVE STEP LEARNING PROCESS: PANCHAADI

16. Toy based Learning Indoor games Outdoor games
Story Telling
Spending time in
And with Nature Art and craft
Pedagogical Tools for young Learners

17. GRADUAL RELEASE OF RESPONSIBILITY : GRR
Teacher Explains Model and Strategy : I do {you watch}
Collaborative Use : We do it together
Guided Practice: You do {I watch/guide}
Independent Practice: You do it alone
Teacher Responsibility
Student Responsibility

18. Thanks
Its time to have free discussion
We can interact more through emails
anupncert@yahoo.co.in

19. Spending time in and with Nature
nature
Indoor games
Art and craft
Toy based Learning Outdoor games
Field Trips