WEEK FIVE: Pre/Early Number

The BIG ideas covered and related concepts, skills and strategies:

Pre-number concepts: (Birth – 3/4 years of age)

(Week 5 Lecture)

Mathematical Concept: That objects are comprised of attributes, and can be sorted as such.

Mathematical Skill: What am I doing? Determining attributes, matching by attributes, sorting by attributes, comparing attributes, ordering attributes, patterning

Mathematical Strategy: How I am going to do this? Use a sorting chart, use cups to sort into etc.

Early number development:

(Week 5 Lecture)

Mathematical Concept: Concept of counting which is to assign a numeric number to a value and the concept of patterns as a repeating set of objects following a rule

Mathematical Skill: Using the five counting principals for counting and working out the rule to the repeated objects to continue the pattern

Mathematical Strategy: Strategies for counting as below and for patterning using blocks or drawings to help represent repeating sets

Counting:

(Week 5 Lecture)

Mathematical Concept: To assign a numeric number to a value

Mathematical Skill: One to one correspondence, stable order, cardinal principal, abstraction, order irrelevance

Mathematical Strategy: Count out loud, touch and count, move and count, line up and count, count on

Cardinal, ordinal & nominal numbers:

(Week 5 Lecture)

Reflection: It was never obvious to me why pre-number skills were so important to children. It is clear through this week, that children must comprehend the concept of attributes, sequencing and patterning within pre-number, to then apply this knowledge in higher order mathematics. For example, if we look at a rectangle, but can not classify it as such (by looking at its attributes), how will we know which formula to use when working out the area? Formation and exploration of number sense begins at birth, and is apparent in children’s daily lives, for example;

Toddlers learn about numeracy as we: - Count things, look for shapes - Use words about weight and measurement / talk about the volume a bucket will hold

- Estimate distances – “It’s a long way to the Mulberry tree, but the sandpit is much closer“

- Divide up and share out food.

(EYLFPLP, n.d.)

For this reason, I will endeavour to view maths as a life long process and make learning contextual to each child’s developmental stage, in acknowledgement of the rich learning environment it can foster.

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The Language Model:

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Teaching Strategies:

Activity: Order by Attributes (Concrete / Using substituted objects)

Explore Attribute Blocks as a class, asking questions to help students form concepts of attributes, such as;

- What colours can you see? What shapes can you see? How thick are they? What size are they? What do their edges and points look like?

As a class, decide on ways to classify the blocks based on attributes. Have the students separate the blocks by the decided attributes.

* In tutorials, we sorted the attribute blocks using two classifiers – Colour and thickness *

Concept: Objects all have differing attributes, of which they can be sorted by.

Skill: Classify and sort by; Shape, size, colour and thickness

Strategy: Firstly classifying by one attribute, then continue to classify by a second attribute

Activities for Matching: Looking at attributes to do matching activities

(Concrete / Using substituted objects and learning resources)

(Week 5 Lecture)

Concept: There are things that are the same, but are represented differently (eg; 4 is four and ////)

Skill: To recognise and sort by matching on sameness or likeness

Strategy: Use your senses – touch, sight, smell, taste and hearing

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Misconceptions and strategies to remediate:

Misconception: That when a child recites numbers in order, that they understand counting, however they could be drawing upon their memory. We know that for a child to fully understand the concept of counting, they must;

- Display one-to-one correspondence

- The number-name group must be used in a fixed order every time a group of objects is counted

- The order in which the objects are counted doesn’t matter

- The last number name used gives the number of objects

(Reys, Lindquist, Lambdin, Smith, Rogers, Falle, Frid & Bennett, 2012)

Strategies to avoid or remediate misconception: Do activities that help student explore; number in sequence, counting of objects (in varying orders) and counting on from a given number. The activity sheet below explores the above, whilst also representing counting visually and symbolically, to help children understand that 5 crosses (xxxxx) is the same as 5 and five.

(Miss Giraffes Class. (2015). Number sheets [Photograph]. Retrieved from http://missgiraffesclass.blogspot.com.au)

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Australian Curriculum and Scootle links:

ACARA Links to Foundation Year:

(http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1)

Scootle Resources:

What Comes next in line?

(http://splash.abc.net.au/home#!/media/29547/)

Monster Choir – Look and listen

(http://www.scootle.edu.au/ec/viewing/L494/index.html)

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EYLF:

(EYLFPLP, n.d.)

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Addition learning and teaching resources:

Teaching Resource:

(Hand 2 Mind. (n.d.). Learning about attributes blocks. Retrieved from http://www.hand2mind.com/pdf/manipulatives/AtrBlk_GrPK-K_Sampl_1.pdf)

This teaching resource can be used by educators alongside a set of Attribute Blocks to help guide student learning effectively

Learning Resources:

These learning resources can be introduced from kindergarten and into foundation years. These resources help children develop the concept and skill of patterns.

1. Amusant Blogspot. (n.d). Lego Chart [Photograph]. Retrieved from https://au.pinterest.com/source/apprendre-en- sam usant.blogspot.fr

2. Life Over Cs. (n.d.). Rainbow Pattern [Photograph]. Retrieved from http://lifeovercs.com/rainbow-patterns/

3. The Measured Mum. (2014). Free bear counter pattern strips [Photograph]. Retrieved from http://www.themeasuredmom.com/ free-bear-counter-pattern-strips-for-preschoolers/

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Chapter 7: Counting & number sense in early childhood and primary years

Pre-number concepts:

Pre-number experiences are everywhere (5 fingers, 5 cents, a star has 5 points etc). These experiences, if nutured lead to counting skills and number sense

Classification: Sorting and classifying, pre-requisit to any meaningful number work

Patterns: Creating, constructing and describing patterns require problem-solving. Patterns can be based on geometri attributes, physical attributes, relational attributes or affective attributes. Activities include; having children copy patters, finding the next in the patterns, extending a patters

Early number development – Counting:

Counting is a pattern, however is not repeated correctly until after 20.

Counting stages: Rote counting (knows some number names but not necessarily the correct sequence). They often can not maintain correct correspondence between the objects being counted and the number names. Rational counting (the child gives the correct name as objects counted, and can answer questions about the number of objects being counted.

Counting Strategies: Counting on (The child can count on from any number, can be represented on a number line. Children must know the starting number and the previous numbers). Counting back (counting backwards from a number ‘Bob had 8 flowers and 3 died, how many were left). Skip counting (Counts by values oher than 1s, correctly).

Cardinal, ordinal & nominal numbers:

Cardinal: Counting and finding a correct number name. Answers the question, How many?

Ordinal: Arranging things in an order. Answers the question, which one?

Nominal: A label or classifier. Examples; licence plate number, postcode, telephone number etc.

(Reys, Lindquist, Lambdin, Smith, Rogers, Falle, Frid & Bennett, 2012)