Digging Deeper into … Early Mathematical Activities

Digging Deeper into … Early Mathematical Activities

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Early Mathematical Activities (EMA) is a strand in the Primary Mathematics Curriculum (1999) for children in junior infants only, although the activities might also be suitable for children in senior infants as revision, as well as being suitable for many children in their final preschool year.

It includes the strand units of:

  • Classifying
  • Matching
  • Comparing
  • Ordering

While comparing and ordering appears as a strand unit also in the strand of Number, for EMA the emphasis should not be on using number or counting to describe relationships, rather on the attributes themselves. However, once the children have been introduced to the numbers,  the early mathematical activities can be repeated, but now to include using the opportunities presented to incorporate numbers or counting to describe relationships.

Sets

EMA is fundamentally all about sets; a set is any collection that has been grouped together in some meaningful way. Sets are all around us, and much of a young child’s exploration of the world involves the child seeing things in terms of sets e.g. my toys, the set of toys that belong to me as opposed to all other toys. Sets are also fundamental to developing an understanding of number and operations: numbers are used to describe the quantity in a set;  a quantity will be removed from a set to model subtraction etc.

Matching

Although classifying is listed before matching in the Primary Mathematics Curriculum (1999), matching is actually less complex, as typically we understand matching as completing a pair, whereas classifying is typically interpreted as organising a collection into two or more subsets. For this reason, in Operation Maths for junior infants, the children first match pairs of identical objects (reinforcing one-to-one correspondence), using the language same for those that match and different for those that don’t match.

 

  • Start with a limited amount of objects e.g. eight, where each has a match that is the same (ie fully alike). This can be demonstrated using real objects and/or on the class IWB, using a representation of real objects, using the Operation Maths Sorting e-Manipulative (see image above).
  • Working with a small group of children, isolate one of the objects and ask a child to “find the match/find the one that is the same” i.e. identify the other that is fully alike, and most importantly, to verbalise why it is the same and therefore the correct match. In this way, you are asking them to justify their choice using the language of the attributes.
  • The children can also be asked to orally justify why certain objects are not the same/are different.
  • Initially, you can use objects where each pair is completely unlike the other pairs e.g. four different shapes, in four different colours. Then, progress towards collections where, while there are like objects, there is only one match that is fully alike/exactly the same (see example above).
  • To make this task more complex:
    • introduce more attributes (e.g. size) and a larger range of attributes (e.g. more shapes and colours).
    • increase the size of the collection
    • remove/conceal an object and ask the children to identify the object which now has no match and to use this to be able to describe the object that has been removed/concealed.
    • See also the Clothesline activity in the Junior Infants TRB (p 16). The materials could be expanded to include gloves as well as socks. Initially try to ensure that there is two of everything (in order to make complete pairs). When the children locate the matching items, they should explain why they are the same, before hanging them up using clothes pegs (clothes peg activities have the added advantage of developing pincer grip and fine motor skills necessary for correct pencil grip). A development of this activity if the teacher deems it suitable: include odd socks/gloves and observe how children react. Use questioning to elicit their own “rules” for dealing with these and how they might describe them. If appropriate, use the opportunity to discuss and introduce language such as even, odd etc., if the children do not suggest this terminology themselves.
    • For further experience using one-to-one correspondence, the children should also have opportunities to match pairs of related objects,  i.e. objects that are not the same, but that purposely go together,  e.g. putting out knives and forks, buttoning coats, putting lids on boxes/tubs. Again, many of these activities, using objects from the children’s daily lives, will also be useful for developing and strengthening fine motor skills.

HINT: Commercial products such as attribute bears, shapes and people are very useful for all EMA and may appear to even be the most suitable material because the attributes, and therefore the “rules” that govern a set can be deciphered clearly. However, they can also be limited, in that there is little negotiation required. Thus more arbitrary materials, such as items from nature (stones, rocks, leaves etc), children’s own clothing items (socks, shoes, gloves) and assorted toys (threading beads, toy cars, soft toys etc) and indeed any objects in the classroom for which there is at least one other that is fully alike, can provide greater opportunities for mathematical discussion and thinking, as the children have to come up with their own ways to group them. In particular, see the Aistear play suggestions in the Operation Maths TRB for Junior Infants.

 

Classifying

Classifying (or sorting) is different from matching as classifying involves reorganising a collection into two or more subsets. When presented with a large set of objects e.g. toys, children will often isolate a certain group of objects e.g. take out all the toy cars. In this way they have made a set of cars and (by default) a set that is not cars. This is referred to as a binary sort, where two subsets have been created: one which has the chosen attribute and one which does not. In mathematical terms this “opposite” set is the complement of the chosen set.

  • The children should have lots of opportunities to explore various collections of objects from which they will likely create their own sets. Through questioning, elicit from the children an explanation (ie rule) for their set.
  • The teacher can also isolate objects to create sets and then ask the children to identify the rule of the set: “What’s my rule?” (see image above). This is more complex than matching since, while the objects are all the same shape, they are not all the same size or colour. The children can also be encouraged to play the “What’s my rule?” game in groups.
  • Initially, the isolated objects should only have one attribute in common, e.g. in the image above, there is the set of all the shapes that are square and all the shapes that are not squares.
  • Ultimately, it is hoped that the children appreciate that while the collection above has been classified according to  a certain attribute (i.e. whether it is a square or not a square), that the same collection can be sorted in various other ways  e.g. triangles/not triangles; pink/not pink; big/not big. And then for these children, they can be asked to identify the rule of a set that have two attributes in common e.g. a set of yellow squares (which then also creates by default a set of shapes that are not yellow squares).
  • The children will likely begin themselves to sort objects into multiple sets. Instead of two sets of yellow shapes and non-yellow shapes (i.e. a binary sort) they will produce a set of yellow shapes, red shapes, blue shapes etc. The production of multiple sets will naturally lead on to comparing and ordering these sets (see next section).

HINT: The children themselves can also be used for classifying; use rope or yarn circles on the ground, and ask a small group of children up to stand at the top of the class. Point to each of the sets saying “This is for the children wearing glasses and this is for the children not wearing glasses”; “This is for the children with curley hair and this is for the children who don’t have curly hair”; “This is for the children with brown eyes and this is for the children who don’t have brown eyes” etc. 

 

Comparing and Ordering

Comparing is instinctive in humans, and children are no exception to this: “He got more than me! I have a smaller piece!”

Comparing is also intrinsically connected with matching and classifying: when a child explains that two shapes are different/not the same because one is yellow and one is red, they are already comparing according to colour. When a child classifies a set into big toys and small toys, they are already comparing the items in the sets according to size. Therefore, to compare is to measure or quantify in some way how two items or two sets are similar or different.

As well as colour and size, the children can also compare objects according to length, width, height, weight or thickness.

  • Use collections of pencils, crayons, ribbons, strings etc., to compare length. Note how the children do this; do they use a common baseline/starting point, and if not, highlight the need for the same.
  • Sort attribute shapes into sets that are thick and thin
  • Use the opportunities to introduce vocabulary that will reinforced later in the year as part of measures e.g. long/short, longer/shorter, heavy/light etc.
  • Compare sets without counting: when sorting, look for opportunities where the resulting sets are obviously different in quantity and ask the children to identify which has more and which has less. Some children may even demonstrate their ability to verify their comparison by counting; this is an added bonus, but not required from all the class at this stage.

Ordering is a development of comparing, in that the children are now comparing three or more objects and ordering them according to length, height etc. The children can compare and then order sets also; “there are more yellow shapes than red shapes, there are more blue shapes than yellow shapes, (then in desceneding order) so it’s blue shapes, then yellow shapes, then red shapes”. An important conceptual development is where the child realises that if A is more/bigger than B and B is more/bigger than C, then A has to be more/bigger than C, and thus A must be the largest and C must be the smallest.

HINT: In your materials for EMA include (real or play) coins and notes, with the  emphasis being on their attributes of material, colour, shape, size and design. Provide the children with opportunities to suggest ways to classify the coins themselves. Using money in this way is an excellent way to prepare them for the strand units of money, later in the year.  NB: While the emphasis should be on the attributes of the coins/notes, as opposed to their value and/or the numbers visible on them,  if children recognise their value and use as an attribute for matching, classifying, comparing and ordering the coins/notes, then this should be acknowledged as a valid response to the activity.

 

Further suggestions:


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