It is a surprise when Ms Peggy Zee, an Early Education Mathematics Specialist with 32 years of experience, reveals that she had failed Maths “practically all my life”.
The educator later concluded that she had simply not been taught in a way that helped her to comprehend the subject. Thankfully, those early years of mathematical fumbles have not stopped Ms Zee from pursuing her understanding of the field.
These days, apart from training preschool teachers in Early Mathematics, Ms Zee runs a “homeschool” programme from her home, provides consultancy to early childhood centres (including ECDA for Sparks), and training to teachers and parents via private engagements. She wants to help preschool children “have a better chance of enjoying maths and excelling in the subject in their formal education years”.
In that vein, she shares with us the following tips on how we can help our children build a firm foundation in mathematics.
Ground Abstract Ideas in Real-life Experiences
The challenge of mathematics is two-fold. First, it lies in understanding and translating abstract concepts into concrete experiences. Second, it is the ability to apply these concepts to get tangible solutions in the real world.
Ms Zee believes that parents can engage children in mathematical thinking and reasoning without formalised teaching or worksheets. How? “By providing preschoolers with substantial amounts of foundational free play where they experience patterns and shapes and count objects,” she says.
Given enough materials, opportunities, and time to experience such informal experiences with numbers, preschoolers will develop their own understanding of the relationship between number and quantity, she adds.
Numbers and Quantity
To a preschooler encountering them for the first time, numbers are merely abstract symbols. How can you help your child understand how numbers represent the quantity of something? First, don’t rush to show them the numerals. Count objects with them before showing them the numerical symbol representing that number of objects.
Other activities that you can try with your child:
• Make number cards from cardboard and display them with dominoes. Encourage your child to use two dominoes to combine spots to make the total amount. For instance, your child can combine the domino piece with two dots and the domino piece with five dots to make a total of seven.
• Write out numbers in chalk on the floor or wall, call out a number, and have your child erase that number using a water gun.
Symbols like “+” (plus), “-” (minus) and “=” (equal) are abstract concepts that need to be tied to concrete experiences.
Before a preschooler can comprehend and compute addition or subtraction equations, she first needs to understand “more than”, “less than” and “equals”.
Help your child visualise these concepts through the following activities:
• Give yourself and your child some small pieces of paper. Ask your child to compare who has more pieces of paper or determine whether both of you have the same number of pieces. You can continue by asking “How many pieces of paper do we have altogether?” or “What can we do so that both of us have the same amount of paper?”
• Grab a handful of plastic counters (or other similar objects like buttons, plastic water bottle caps etc) and ask your child to grab a handful as well. Lay your counters in a row. Get your child to lay out her counters in a row below yours, corresponding the positions of her counters with yours. In this way, it is clear who has more counters. Ask your child “Who has more counters?” and get her to count out how many more counters you (or her) have. By laying out the counters in this manner, your child will be able to visualise the difference in the number of counters.
• Play “Go Fish” with a pack of playing cards. This is a great game to reinforce the number bonds which make up the number 10. Distribute 10 cards to each player and place the remaining cards in a stack in the middle of the table. Players are expected to make the total of 10 using two cards. This can be done using the cards that players are are holding in their hands, or cards that they fish out from the deck in the middle. This game reinforces your child’s addition ability.
Ms Zee explains, “Number sense can only be developed when children have opportunities in their daily life experiences to guess, compare, estimate and find ways to confirm their guesses about quantity or size.”
So let your children play, try, make mistakes, and learn through discovery. “It is vital not to expect perfection from the very beginning but to allow for guesses, trial, and error so that the child dares to learn,” advises Ms Zee.
Algebra and Patterns
The understanding of what a pattern is and recognising that repeating element is an important cognitive skill.
When preschoolers match, sort, group, classify and compare objects, or form patterns with them, they are actually making use of algebraic reasoning to do so. In sorting objects, a child is making a specific rule based on the attribute of the object (such as sorting by colour) and generalising this rule to apply to all the other objects.
“Once children are able to sort objects by specific rules they follow or develop, they can begin to use these attribute qualities to create patterns. The more children have the chance to play with patterns, the better they are at recognising, describing, extending, and creating patterns that repeat,” says Ms Zee.
Collect repeat-able objects such as bread tabs and bottle caps for your child to create patterns with. Show your child how to create patterns with these objects using the attributes of colour, size, and shape.
This involves introducing children to shapes and giving them an understanding of position and location. Ms Zee suggests the following activities for teaching geometrical concepts:
• Have your child describe the characteristics and relationships of geometric objects. For instance, “a triangle has three sides” or “two triangles can make a square”.
• Let your children manipulate shapes to explore symmetry.
• Play “scavenger hunt” at the playground, giving your child clues that include positional words such as, “You will find the bear behind the climbing frame”. The more often children have the chance to use positional words, the better they will be at understanding how objects relate to them in space.
A child first learns about measurement by comparing the sizes of objects. You can introduce words such as “big”, “little”, “taller”, “shorter”, “more”, and “less” as they go about their daily activities.
You can also teach your child to measure distances or height by:
• Using wooden blocks to measure the distance which a toy car has rolled.
• Using an object such as a book to measure the height of a taller object.
• Encouraging your child to find out for herself the height, size or distance of things.
Explain to your child:
• why it is necessary to use same sized objects as measuring tools
• that each repeated object must be exactly touching one another with no gaps in between
• that each object should be precisely placed so that the measurement is as accurate as possible.
Learn more about how you can teach your child though play. Ms Zee’s ideas on early childhood development can be found at her Facebook page Interested in Children Development.