MATCHSTICK

MATHEMATICS: LIGHT

UP MATHEMATICS AS A

SCIENCE

LALIT KISHORE

Towards low cost math lab activities with

matchsticks

Mathematical dilemma: Just

joking

CBSE’s position on math as a

science

Mathematics laboratory is a tool to project math as a science can effective tool in the hands of a teacher to illustrate to the students that they can construct mathematical knowledge by making use of processes of science to make smooth transition to abstract thinking and vice versa.

Imparting procedural knowledge through math lab activities provides hands-on learning experiences to enable a student to learn a concept in mathematics with more clarity and understanding.

The syllabus prescribed by CBSE, students are made to perform experiments and activities in mathematics from class 4 to 10.

Attributes of science

~ Objective in nature

~Processes of science : Experimentation (lab work), verification, measurement, recording observation, seeing patterns or relationship, drawing inferences, reliability, validity, procedures

~Dynamism: Research and filling gaps, unifying knowledge, improvements, precisions, action into theory and vice-versa (application), creativity in communication with use of visual symbols and diagram, abstraction

Naming and defining concept labels: science

says, if you can precisely define, you can measure

Definition consists of:

attributes , properties or

characteristics

Functions and uses

composition

Matchsticks math-lab

Matchstick investigations can

provide hands-on experiences

in the processes of science as

low-cost activity in the normal

classroom at the middle

school level

What is common?

In most textbooks, a common approach of

developing rules from patterns is used to

introduce algebra with matchstick pictures as

teacher directed activity.

It could be better if in grade six matchstick

patterns could be converted into math-lab

activities to give a feel of math as a science

and art

What was thought?

It was thought to develop some available ideas

further in the form of investigatory math-lab

activities to get students in the hands-on way

‘inside the patterns formed by matchsticks’.

Purpose was develop math skills of

Algebraic thinking.

Visual-spatial thinking

Processes of science

FOCUS

It’s on:

Perceptual learning with open-endedness by playing with matchsticks

Linking learning through match-sticks to numeracy, geometry and algebra

constructing and manipulating representations (patterns/figures/shapes) that lead to the expression of a generalisation

visualisation as a way of seeing how patterns are constructed

identifying the recursive nature of some sequences

Codifying the activity and communicating generalisations to others and justifying your logic

Triangle path: Initial and additive

matchstick (s)

A to look at the sequence

Sequence

1+2

1+2+2

1+2+2+2 or 1 + (3 X 2)

:

:

:

1 + (n X 2) or 2n + 1

A second way to look at the

sequence

Sequence

3

3 + 2

3 + 2 + 2 or 3 + (2 X 2)

3 + 2 + 2 + 2 or 3 + ( 3 X 2)

:

:

:

3 + (n – 1) X 2 or 2n + 1

Viva questions

Questions to know the strategic thinking

What numbers could you use to describe the way

the pattern is made?

How did you work that out?

Can you think of any other numbers you could

use?

Linear square and house paths

Lab-activity observation recording

sheet

Odd square paths

Square tiles paths

Some other patterns

More…

More…

Fencing sequence

Layering to get next bigger

shape

Open-ended activity

Open-ended activity

Match-stick moving activities

Think over…

Move 1

matchstick

to turn the

donkey

What I did?

Reviewed literature

Collated puzzles

Classified them

Converted them into math lab activities

Carried out two lesson studies with a teachers

Handed over the resource material to

neighborhood girls school

Resource material

1. Laboratory activity sheets

Hand written

Meant for producing multiple copies

2. Teacher’s handbook…Single copy as reference

material