Immersive Workshop on Foundational Numeracy: Understanding Student Perspectives

The main goal of maths education in schools is the mathematisation’ of a child’s thinking. Clarity of thought and pursuing assumptions to logical conclusions is central to the mathematical enterprise. There are many ways of thinking, and the kind of thinking one learns in mathematics is an ability to handle abstractions and an approach to problem-solving. (Position Paper, NCERT)

Stall3

Background

Since the resumption of classes in June 2022, following an 18-month interruption caused by the pandemic (from March 2020 to June 2022), it has become evident that a significant number of students have experienced learning setbacks. The return to school has been tough on most of them, who have not received adequate support in learning during this time and face several challenges, such as adapting to school routines, as well as a decline in their literacy and numeracy skills. To address this, adjustments were necessary in teaching to facilitate student learning and rekindle students’ enthusiasm for learning.

The reasons that led to the inception of this workshop on foundational numeracy were many but the primary reason was the immediate need for teachers to teach effectively in the classroom, equipping students with a better understanding and fostering a fear-free environment for learning maths. This urgent requirement was communicated by the Deputy Inspector of Schools. He suggested that the workshop should also immerse teachers in the perspective of their students. In response to this, a plan was devised for teachers to experience practical teaching methods. Each of these practices is recommended in the notes accompanying every NCERT book for teachers to implement, encouraging an experiential approach for students.

The main goal of maths education in schools is the mathematisation’ of a child’s thinking. Clarity of thought and pursuing assumptions to logical conclusions is central to the mathematical enterprise. There are many ways of thinking, and the kind of thinking one learns in mathematics is an ability to handle abstractions and an approach to problem-solving. (Position Paper, NCERT)

With this as the background, we designed a workshop. Since there were approximately 700 teachers, we grouped them batch-wise with 40 teachers per batch. Each batch had a one-day programme, so this workshop was conducted for 16 days. These were held at the Education Department and the Foundation’s Teacher Learning Centres (TLCs).

Objectives

The workshop aimed at building teacher capacities in the following areas:

  1. Learner-centric pedagogy
  2. Scope for exploration and mathematical thinking
  3. Exploration of manipulative/​toy pedagogy
  4. Medium of instruction – to not restrict the communication to English and to use the home language of the students where necessary
  5. Integrating mathematics with other subjects
  6. Ways of communicating mathematically
  7. Alternate strategies and supporting problem-solving
  8. Recreation with mathematics (joy in mathematics)
  9. Allowing students to make errors while learning/​practising
  10. Collaborative learning

Rationale

Most schools follow a standard form of teaching that can leave gaps in understanding. To support and change the existing practices in schools, some new ideas and practices providing a foundational understanding of the concepts were suggested for integration with the current methods. These practices are developed based on the NCERT learning outcomes. This approach can be considered more effective, especially when there is an opportunity to conduct assessments with the class after implementing these practices.

Teacher challenges

Motivating school teachers to attend workshops or to implement new learnings in their classrooms is not easy because of various other challenges they face in their work, such as:

  • Adapting to hectic schedules, including managing events and completing the curriculum
  • Disruption of practices due to sudden transfers
  • Classroom management issues in classes with more than 30 students
  • Adjusting to the expectations of the Inspecting Officer

Content of workshops

The workshop was set up as a series of stalls’ where participating teachers could spend time understanding various types of practices.

Stall 1. Genre: Games

Estimating quantity and distributing seeds

Addition and subtraction are essentially the concepts of combining and rearranging collections. The focus is on the number of objects within the collection. Before introducing these concepts, it’s important to give children ample exposure and experience in combining collections. Children should have opportunities to work with a wide variety of concrete materials.

Stall 2. Genre: Activity

Domino card activity & playing with a number chart 

  • Grouping
  • Re-grouping
  • Varieties of form the numbers.
  • Connecting dots to numbers
  • Addition
  • Play with properties of additions.

Stall 3. Genre: Project

Data handling

Projects provide valuable learning experiences as children observe their environment, engage in conversations with peers and elders, and create things that piqué their interest. This project involved handling data of opinions to a statement and students are expected to present their findings in the form of Tally Marks, graphs and concluding notes.

Stall 4. Genre: Puzzle

Making letters H, F, T & tangram puzzle

Stall 5. Genre: Games

Arithmetic (Clearly involving basic arithmetic operations)

1. Addition Draw
2. Subtraction Draw
3. Multiplication Draw
4. Division Draw
5. Fraction Draw

Stall 6. Genre: Activity

Geoboard activity

  • Forming shapes
  • Exploring orientations of shapes
  • Manipulating area and perimeter of standard and non-standard shapes
  • Concepts of circle
  • Solving puzzles using area and perimeter
  • Connecting online geoboard for more activities

Stall 7. Genre: Project

Finding the area & making a scale

This stall had two different projects on the theme of measurement.

  1. Using the grid sheet, students are expected to draw an object and find its area using the squares present in it.
  2. Using strips of paper, students are expected to make a scale of their own and use it to measure 3 objects in their surroundings.

Stall 8. Genre: Puzzle

Peg Board Puzzle

4×4 Square Puzzle

Magic Hexagon

Octanumeric Puzzle

Stall 9. Genre: Games

Tricky Track

  • Logical thinking
  • Think about the possibility of chance

Board Games

  • Addition tile
  • Subtraction tile
  • Multiplication tile

Stall 10. Genre: Activity

Play with Dienes Cubes

  • Place value
  • Counting
  • Addition (2 digit, 3 digit)
  • Subtraction (2 digit, 3 digit)
  • Multiplication (2 digit-standard algorithm)
  • Division (connection to standard algorithm)

Stall 11. Genre: Story

Tamil/​English Mathematical stories

  • Stories that illustrate various mathematical concepts, enabling students to connect them to real-life situations and apply them to problem-solving
  • Songs that capture students’ interest with rhyming words and incorporate concepts related to numbers and measurement

Stall 12. Genre: Puzzle

4’s Puzzle

Soma Cube

Tower of Hanoi

Key takeaways

  • The format of the workshop turned out to be highly engaging.
  • The practical experiences led teachers to consider incorporating more low/no-cost TLMs in their classrooms to create an engaging math learning environment
  • It was surprising to see the number of new songs and stories created to support various mathematical concepts (these would also help enhance students’ language skills).

Workshop to school

A handbook containing all the practices demonstrated at the workshop was distributed to the teachers to help them experiment with these methods in their classrooms to support both teaching and learning. Some of the practices teachers have used in schools and the benefits they have observed are:

Classroom activities

At first, teachers attempted to introduce the ideas they had explored during the workshop into their classrooms to gauge their students’ reactions. To do this, they created modules centred around specific games and activities designed to teach particular concepts. For instance, a teacher used the Domino Cards game to illustrate comparisons between two numbers involving all four operations.

Feeback

  • Students enjoyed the games.
  • The teacher observed that students were able to grasp the concept much faster in this mode.
  • The teacher found it useful to organise such games and puzzles once a day or during the bagless day, which makes students pay more attention and enjoy learning.

Teaching-Learning Materials (TLMs)

To sustain this practice on a daily, weekly, or monthly basis, classrooms need to have the necessary teaching-learning materials (TLMs) to facilitate the type of learning discussed in the workshop. The handbook shares the methods for creating these TLMs, allowing teachers to make these for their classrooms. Additionally, it is recommended that teachers involve students in the process of making TLMs, as it can provide valuable insights and enhance their learning. Here are some examples of materials created in the classroom and used in teaching various concepts

School Event

As a continuation of the workshop, a Math Day’ was celebrated in schools, incorporating elements from the workshop. On this day, parents and members of the community were invited to observe the practices and learning experiences their children are engaged in in the classroom.

Feedback

  • The method is highly practical and engaging for primary students.
  • These age-appropriate methods aid students in grasping concepts more easily.
  • They enable students to understand the practical applications of mathematics in real life.
  • This approach addresses the why’ of learning mathematics and encourages different perspectives.

Concluding note

It is remarkable how even small changes can have a powerful impact on classroom implementation. I believe that by making use of the suggested practices, it would be effective to track the impact on both teachers and students.

  • In all, more than 10 different ideas (including games, activities, and puzzles) have been implemented and continue to be used in the classrooms.
  • Our school visits and observations demonstrate that our efforts are contributing to bringing about a significant transformation in the teaching-learning process in the classrooms.

Some glimpses of the workshop

AUTHOR

Narendran V, Resource Person, District Institute, Azim Premji Foundation, Puducherry