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Hands-on Maths with Thornewood Treasures

Hands-on or experiential learning occurs when a child is placed in direct contact with concrete objects which she can handle, manipulate, investigate and use to gain first-hand experience about its properties and the way it works.  Consider this insightful finding by a team of researchers:

“Early childhood learning experiences can have a powerful impact on children’s later life outcomes. Yet, adding more time for drill and testing has not proven an effective strategy as reflected by both paltry international testing scores for many countries as well as achievement gaps between different demographic groups within the United States. While there is no question that even preschool children profit from a strong curriculum in math, literacy, and science,better outcomes are likely if this curriculum is delivered with an age-appropriate playful pedagogy The playful learning approach offers the opportunity to deliver rich mathematics learning through child-directed, adult-supported play activities. Research from the science of learning indicates that when learners are active, engaged, meaningful, and socially interactive, learning can soar.” You can access the complete article here.

My experience in educating our own four children has taught me that playful, hands-on learning is most effective if also combined with a concrete to abstract approach.

Concrete → Symbolic → Abstract

This has been proven over and over to be the most beneficial way for a person to learn, yet we neglect this sequence in the teaching of our young children to their detriment. In a country where our matric Maths pass rate is among the lowest in the world, South African parents can give their children an enormous advantage by introducing hands-on, experiential and playful ways to master early numeracy skills.

At Thornewood Treasures we used this exact sequence in teaching our own four young children, and four products emerged from our family’s learning journey:

Counting Blocks for concrete learning from age 2/3 up to Grade 7 and beyond!)

Counting Mushrooms for moving to the symbolic stage

Number Houses for progressing to the abstract idea of written numbers

The Multiplication wheel for combining concrete, symbolic and abstract number concepts to teach skip counting, multiplication and telling the time.

Here are a few ways to use Thornewood Treasures’ range of handcrafted tools for giving your child a solid, hands-on foundation in Maths through playful learning:

Number Concept:

Remember, optimal learning happens when we move from

CONCRETE to SYMBOLIC to ABSTRACT.

In numeracy this will mean that you move from

COUNTABLE, TOUCAHBLE OBJECTS to DOTS OR PICTURES representing the number of objects to NUMERALS (written numbers)

A numeral (the written symbols of 1, 2, 3, 4, 5 etc) holds no meaning for a child if she does not first grasp the concepts of amount, more than, less than etc. Numerals are abstract and it is therefore crucial for parents to keep in mind the maxim:

Do not give a concept to the brain without first giving it to the hand.

Thornewood Treasures’ COUNTING BLOCKS is the best tool for introducing the idea of number (amount) in a tangible way.

  • Young children should be encouraged to always be counting things – it really strengthens their ‘number muscles’! Parents can help children understand amount/number if they themselves understand the cardinal principal, that is, the fact that the last number counted is also the name for the total number of items. So if your little one counts one, two, three, four, five, six seven Counting Blocks, immediately ask: how many blocks are there? It sometimes means they will start back at one and do it again. Then ask again: how many blocks? You may even have to go through this process a few times before they start to grasp the idea that the last number counted is also the total number of objects. Model this over and over every chance you get: count the apples you are unpacking one by one, placing emphasis on the last number and happily announcing that THAT is how many apples there are! Count the lorries, the eggs, the birds on the fence!
  • Use your Thornewood Treasures COUNTING BLOCKS for acting out counting rhymes and songs like ‘Five Little Monkeys’ or ’Ten Green Bottles.’ The pleasantness of rhyme and song greatly enhances a child’s understanding of number concepts when used in combination with tangible manipulatives like Counting Blocks!
  • Playful storytelling for number sense: Place three small bowls on the carpet. Tell a little story about a child going to pick strawberries with her mom and pretend that your bowls are the pails they use to put the berries in. Ask your child to put three ‘strawberries’ (blocks) in the first one, help her count out ten blocks for the second bowl, and ask her to place two big handfuls in the third. Which bowl has the MOST? Which bowl has the LEAST? Does the middle bowl have MORE or LESS that the first bowl? If those blocks really were strawberries, which bowl would you prefer to have for lunch? If it were full of very sour grapes (or worms!!) and you had to eat it, which bowl would you pick then?
  • Ask your child to count out five blocks and place them in a row on the carpet. Explore the many ways in which you can break the five blocks into two groups: 1 and 4, 2 and 3, 0 and 5 etc. Make this more fun by using a toy knife to ‘cut up’ five and move each set a little apart. This develops a critical early number skill called constancy of numbers or number permanence which is the ability for a child to realise that five remains five even if broken into different sets.
  • Another way to practice counting for developing number permanence: the parent makes two groups using Thornewood Treasures COUNTING BLOCKS. Each group is made up of 5 counting blocks, but arrange them differently: make a small, tight group of two, two and one blocks, leave a bit of space and then pack five blocks out in a line with a space of about two fingers between each block. Children may guess that one group is bigger than the other, because spread out it looks like more. Number permanence helps them understand that five is five, regardless of how it is arranged.
  • After playing the two games mentioned above a few times, you can move on to this one: ask your child to count out 5 COUNTING BLOCKS and place them on the carpet between you. Let him close his eyes. Make little scurrying noises as the blocks ‘run away’ to go hide behind your back. Ask him to tell you how many blocks there were altogether (5). Now ask him to open his eyes and count how many are left. (2) Can he guess how many little blocks are hiding behind your back? This sounds so simple, but what you are teaching here is maths facts, solving for the unknown and deconstructing numbers. Keep playing this game often. Do not go on to numbers over 5 until your little one can confidently make 5 by putting together

1 and 4

4 and 1

2 and 3

3 and 2

0 and 5

5 and 0

This is an excellent game for teaching the concept that zero means nothing.

Also, if a child can concretely learn that 4 and 1 makes 5 AND 1 and 4 makes 5, you can pat yourself on the back and impress your friends by telling them your child grasps the commutative property of addition!!

  • Ask your child to count the number of people in your home by placing one block down for each person. If each person in your home has a toothbrush, how many toothbrushes are there? If it is dinner time and each person needs a knife and fork, how many pieces of cutlery are needed? Let her build it with the blocks and count out the answer.
  • Move on up! Play a fun little counting game by seeing how tall a tower you can build with your Counting Blocks before it tumbles! Write down your scores and compare numbers to see who won. Moms who have a morning learning time with their little ones can start each morning’s numeracy lesson with asking the child to build Counting Blocks towers in the correct order from 1 to 10. Ask: how many is this? (5) What is one block less? (4) The next tower has one more block – how many blocks are in this tower? (6) Which tower is the tallest? (10) Which one is the shortest? (1)

SUBITIZING: (pronounced as soo-bitizing)

Subitizing is the ability to instantly, rapidly recognize a number without counting it. This is a critical early maths skill that can help children exercise their ‘number muscles’ so that they can easily decompose numbers (breaking a whole into its smaller parts), recognise patterns and count on. One of the first places children encounter subitizing is on the face of a die when they start playing simple board games.There are two ‘levels’ of subitizing: perceptual and conceptual. The fist one happens when you roll a die and immediately know that it landed on a six, because you instantly recognise the pattern. Conceptual subitising requires a little more effort and is used when we need to quickly count items that number more than 5. An older child or adult will look at the number of biscuits on a plate and quickly subitise by grouping the ‘sets’ together: 4 near the rim, 5 in the centre…there are 9 biscuits. You were able to do that because you can easily subitize 4 and 5.

You can help your child build strong subitizing skills using Thornewood Treasures COUNTING BLOCKS and COUNTING MUSHROOMS.

The COUNTING BLOCKS provide the first, concrete step, while the COUNTING MUSHROOMS now move the child’s number sense to the symbolic stage where each dot on the mushroom represents a concrete item.

The dots on Thornewood Treasures COUNTING MUSHROOMS follow a very specific pattern to aid young minds in learning to subitize rapidly. The design was born out of years of struggle in teaching my daughter with dyslexia to understand number concepts. We finally stumbled upon an approach by an American teacher named Chris Woodin and that was the turning point for our maths woes. I am in the process of writing a booklet to accompany our COUNTING MUSHROOMS that will be released toward the end of 2020 to explain more in depth how the patterning works and to give you practical ideas for whole body learning.

Here are a few quick ways to play with Thornewood Treasures COUNTING MUSHROOMS:

  • Start by building an ascending number line with Thornewood Treasures COUNTING BLOCKS. (1 block, then next to it two blocks etc all the way up to 12.) Now match the COUNTING MUSHROOMS to the counting blocks.
  • When your child can confidently do the above task, she can then start using only the mushrooms for practicing numerical order.
  • Make 12 piles of counting blocks all over the carpet, with each set containing a number of blocks from 1 – 12. Place the COUNTING MUSHROOMS in a little basket and ask you child to ‘plant’ the correct Counting Mushroom at each pile. This can be even more fun if you turn it into a story and give your little one some dress-up clothes! They can pretend to be a woodland gnome / fairy / squirrel whose job it is to help all the little woodland creatures learn to count by making Counting Mushrooms sprout all over the forest!
  • When your child is confident in recognising the patterns on the COUNTING MUSHROOMS and can easily match the concrete COUNTING BLOCKS to the mushrooms, you can now add Thornewood Treasures CHUNKY NUMBER HOUSES!
  • SEQUENCING AND ORDINAL NUMBERSYoung children need plenty of exposure and hands-on practice to develop and strengthen their sequencing skills, since sequencing forms the basis of reading, writing, mathematics and science. Sequencing helps us recognise patterns and make comparisons so that we can make informed decisions. It helps us to use a calendar, consider consequences, make hypotheses. In mathematics children need solid sequencing skills for understanding numerical order and for recognising and comparing sets.

All of Thornewood Treasures’ Rainbow toys (rainbow stacker, rainbow peg dolls, rainbow birds, number houses, counting mushrooms) can be used for matching and sequencing games. It is especially our charming, chunky NUMBER HOUSES that helps with the mathematical skill of using ordinal numbers. An ordinal number tells us the position of an object in a list and we use the words first, second, third, last etc. to express this.

  • Give plenty of practice in matching COUNTING BLOCKS (concrete), COUNTING MUSHROOMS (symbolic) and NUMBER HOUSES (abstract)
  • Ask the child to arrange the number houses in numerical order. As they become more confident, you can dump all the houses on the floor and use a timer to see how fast they can get it into the correct order. Keep track of their time over the course of a week and celebrate by the end of it!
  • Ask questions like “Which number comes before 5?” What comes after 9?”
  • Ask you child to close her eyes and then you remove two houses. At first, leave the gaps open and ask her to guess which numbers were taken away. As she becomes more adept at this, push all the houses together leaving no gaps and ask her which ones you removed.
  • Now move to ordinal numbers. This will work best if you use your number houses with either our Large Rainbow Stacker, Rainbow Peg Dolls or Rainbow Birds. Arrange the rainbow, dolls or birds to match the colours of the roofs of the houses. Now you can introduce the idea of first, second, third, last, middle etc! What is the colour of the fifth rainbow arch? Can you knock over the eighth and ninth peg dolls? Ride your toy car over the last rainbow arch!

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