The workshop conducted on the 23rd & 24th June 2018, facilitated by Monika Kochar focused on the perspective and pedagogy in teaching and learning number sense. The participants were introduced to many activities that could make the learning fun-filled in Math classrooms.
Session 1: Number Gymnastics
The numbers are brain’s gymnastic. They can enable the development of ‘flexible thinking’ skill. A few ideas that can help students to do so are as follows:
A) Always… Never… Sometimes…
A statement is told to students; they have to respond by saying "always", "never" or "sometimes". They have to provide a reason for their response as well. This activity enhances students’ thinking, especially about numbers and their properties.
Examples:
- Any number multiplied by 1 is the same number. (Answer: “Always”)
- When two numbers are subtracted, the answer is always smaller than the subtrahend. (Answer: ‘Sometimes’; 18-(-2) = 20)
B) Fact Family
A mathematical fact is provided; students have to think and write as many related facts as possible. This task helps children to think beyond the box. Example: Fact given - 12÷3 = 4 (refer diagram)
C) Zooming In
Students are asked to think of a number between 1 and 20. Questions regarding the properties of numbers are asked to filter out and arrive at one of the numbers (student). This activity helps students to understand and think about the properties of numbers.
Sample questions to ask:
1) Those who have a number in mind which is divisible by 2 can sit down.
2) Those who have a prime number in mind can sit down.
D) ODD One Out
13, 16, 17, 19
From a given set of numbers children have to choose the odd one out and justify their choice.
Examples: 16 is odd since it is an even number. 19 is odd since it is bigger than others.
This task will stimulate students to think about numbers.
All the ideas described above represent ELPS - Experience Language Pictures Symbols.
ELPS method of teaching Mathematics:
In order to keep the students engaged in learning, teachers can use four different methods to solve a problem. They can be represented as E- L- P- S.
E- Experience: this implies using experimental, hands-on activities.
L- Language: this includes speaking about a problem and what we have to do to solve the problem.
P- Picture: implies using representational pictures for understanding.
S- Symbols: this includes introduction of arithmetic operator signs.
Session 2: Operations
Introducing Place Value
Understanding place value is a base for performing mathematical operations.
A hindrance that primary school students face in acquiring number sense is in understanding the value of the number depending on the place it holds. The solid idea of place value could be taught through numerous activities, wherein each child may pick-up the idea during different activities.
Some ideas that can be used to teach place value are as follows:
A) Using Fingers
Students are familiar with representing up to 10 using fingers. When higher numbers (more than 10) are to be represented, the idea of place value has to be introduced to students. In other words, it is to say that the students who understand the idea of place value, could represent any number using fingers.
Example: To represent 15 - the students can assume any quantification to each finger. One possibility is to quantify 1 finger on one hand as 10 and the five fingers on the other hand as 1 each. Since any finger can be quantified as any number, it is possible to represent all numbers. In case of 98, four fingers can be quantified as 20 each, and the remaining six fingers can be quantified as 3 each. So the total becomes 98 (4x20 + 6x3 = 80 + 18 = 98). Thus students can be allowed to think "out of the box", than the traditional methods of representing.
B) Using Poly Plug Grids
The poly plug grids sheet is a circled 5 x 5 grid paper. The students can be asked to represent a number on the sheet. Buttons could be used as a material for the representation and different colors could be used to show different ‘quantification’.
Example: To represent 52, the following pattern can be made, where yellow denotes 10’s and blue denotes 1’s.
C) Ten Frame Games
‘Ten frames’ support the development of early number sense and ‘place value ten frames’ are useful in teaching the concept of place value. A few games that can played in class using these frames are as follows:
Game 1: Ten-Frame Flash (4 - 6 years) For 4 players
Materials: A dozen ten frames with dot arrangements on them, blank ten frames, counters.
Game: A student flashes a ten-frame with counters for three seconds. The other students place counters in the same positions on their blank frames recalling the flashed frame. The 'flasher' shows the frame again and helps the other student check their displays.
Game 2: Twenty (4-6 years) For 3-4 players
Materials: Blank ten-frames (two per child), counters, dice.
Game: Each child takes a turn to roll a die, places that number of counters onto his/her ten-frames, then announces the total number of counters on the frames. The winner is the first player to fill all twenty spaces.
Variations/Extensions:
1. Each turn could include placing the correct numeral cards under the frames.
2. Each player can also announce the number of counters needed to reach twenty, during the last possible turn. The exact number must be rolled to win the game.
Game 3: Guess What? (5 – 7 years) For 2 players
Materials: Blank ten-frames, counters, a large board to act as a screen/barrier between pairs of players.
Game: One player secretly arranges some counters on a ten-frame. The other player asks questions that can be answered yes or no, trying to gain enough clues to work out the arrangement of counters. For example: Is the top row full? Are there 8 counters? Is there an empty box in the bottom row?
Variations/Extensions
As players become more skilled, the number of questions can be counted. The player who asks fewer questions wins.
D) Base - 10 blocks (Diene’s blocks)
Base ten block material is used to introduce place value as well as to introduce basic operations.
Introducing addition and subtraction: Base 10 block will help the student visualize the number representation and also help them in understanding carry forward addition and borrow subtraction.
Introducing multiplication: Diene’s block can also be used to demonstrate multiplication. The students first write down the given numbers in ‘place 10’ and ‘place 1’ representation in the grid as shown in the figure. Simple multiplication is to be performed for each number in a row with the corresponding column and the results are noted in the grid. Finally the numbers are added to get the answer.
Introducing division: The students represent the dividend using the block and the block is divided according to the divisor and the remainder is then converted into the next lower place value i.e. the remaining hundreds is converted using the tens block and the process is repeated.
Assessment
After every activity, the teacher needs to evaluate the understanding of the students. Simple tests with a minimum of one question can be given. Children can evaluate among themselves. TPS - Think – Pair – Share; i.e. children can form pairs and correct each other’s work. After the test, they can share their knowledge. When they share their knowledge, their reasoning skills improve.
Term:
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