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How to Build a Solid Understanding of Numbers
Learning to count from one to ten, and later to a hundred, is an important milestone in early math development.
However, it’s equally important to learn to understand the “how manyness” or the value that every number represents.
Teachers and therapists refer to this important school readiness skill as number concept.
Grade R’s typically count to a hundred, but few truly understand the quantities that different numbers describe. Many freeze when you ask: “If he has six balls and she has eight balls, who has more?”
Children who don’t understand the value of numbers will naturally not be able to conjure up a mental image of two sets of objects (in this case, a set of six balls and a set of eight balls) and then compare the sets against each other to determine which one of the two is bigger or smaller. And, as a result, they won’t be able to add and subtract with understanding.
It’s important to engage with your child on three levels if you want him to develop a crystal clear understanding of the value of different numbers.
Firstly, use body movements to demonstrate numbers; also provide many opportunities for him too use his hands to handle and count off certain numbers of objects, and lastly – make sure to include games that encourage your child to visualize different numbers of objects in his mind’s eye.
You can, for instance, teach a three-year old to do the following:
– To include body movements, ask him to move (e.g. clap, jump or twirl) one, two or three times;
– To incorporate the handling of objects using his hands, you can ask him to hand you one, two or three of something whenever the opportunity pops up, and
– To involve the mind’s eye, you can place a heap of single Lego blocks, 2 block towers and 3 block towers in a bag and then take turns with your child to use your sense of touch to find one of each number without looking. Then arrange your towers from one to three.
Games should naturally become more challenging as a child grows older, but the basic prerequisite for success remains unchanged throughout the first seven years: The more concrete (hands-on and tangible) the experience, the easier it is to learn.
As children develop into the primary school stage, they slowly but surely progress from functioning on a concrete level (where they need to touch and handle tangible objects to discover and understand ideas about those objects) to being able to fully grasp unseen ideas on an abstract level. In other words, they need time and playful practice in order for them to grow into being comfortable in the world of representations and symbols.
Ultimately, it’s crucial for every Grade R learner to reach the point where he or she is able to picture an image in the mind’s eye of a number line with each of the numbers in its place, based on the value that it represents.
Sadly, the majority of our South African children across all income groups don’t reach this milestone in time. That is a big deal because learners need to feel as comfortable with the number line as they are with their own name for them to confidently experiment and play around with numbers.
A child who isn’t confident enough to experiment with the number line simply does not have what it takes to develop a solid footing in math.
Q: What can I expect from my child at every age along the way?
A: Toddlers discover the meaning of “one and many” during the second year of life. Two-year olds usually learn to rote count to three and you can teach them to hand you either one or two toys. Three-year olds can be expected to count to five and they understand the concepts of one, two and three well enough to be able to hand you that many of an object. Well-developing four-year olds can be expected to rote count to 10 and count off any number of objects from 1 to 5. Most five-year olds can count to 20 and have a real understanding of numbers up to 10. And finally, a six-year old should be able to count to 100 (also in tens), count off any number of objects between 1 and 20 and arrange the numbers from 1 to 10 in order to build a number line.
Q: “My child is advanced for his age with regards to his understanding of the value of numbers. Should we now skip the activities that are listed for his year group in the Parents Guide?”
A: No. Don’t skip. If need be, adapt the games slightly to include bigger numbers.
Bear in mind that Practica’s math games are not only aimed at developing number concept in your child. They also provide hands-on opportunities at every step along the way for discovering many other valuable mathematical concepts.
Learning to work with numbers is much like learning to speak a special kind of language.
Learning the language of mathematics is largely about getting better at understanding the properties of numbers and recognizing relationships and patterns ever more quickly.
Naturally, acquiring these skills takes time simply because learning a new language always involves building new brain wiring.
Repeated activation is necessary for brain cells to change structurally so that they can reactivate one another more easily in the future. And that’s why brain building can be understood better through the analogy of muscle building: practice is key and you need to train all the muscles without skipping levels of progress.
Ultimately, you want your child to reach a point where navigating around in the world of numbers will become automatic for him – like a golfer’s swing.
Any kind of math play is better than none, but if you want your child to optimally benefit from the Practica Programme, you need to play as many of the listed games as possible and repeat them a number of times.
Q: What does this mean in terms of time invested?
A: There are between 20 and 25 math games listed for each age group from two to six years of age. So, roughly speaking, you can introduce a new game every two weeks and set aside about 10 to 15 minutes once or twice a week for repeating it a few times.
Q: Will playing math games once or twice a week get the job done?
A: Yes, as long as you play one-on-one, or with two children at the most. When the group is bigger, the majority of the children transfer the responsibility of coming up with possible solutions onto a few bright and confident individuals.
Children are so receptive and interested in learning through fun and games during the preschool years that it’s absolutely breathtaking to witness the cumulative effect of a number of one-on-one focused play sessions per week on their overall development, specifically their aptitude for numbers.