Week Five - Pre/Early Number

Synthesise the big ideas

• Pre-number is the early concept and beginning processes which include:
  - determining attributes
  - matching by attributes
  - sorting by attributes
  - comparing attributes
  - ordering attributes, and;
  - patterning (Jamieson-Proctor, 2016)
• There are four different ways that patterns might be used in developing mathematical ideas:
  - copying a pattern
  - finding the next one
  - extending a pattern
  - making their own patterns (Reys et al., 2012).
•  There are three different ways early number is development:
  - conservation
  - group recognition
  - comparisons and one-to-one correspondence (Reys et al., 2012). 
• There are four different counting principles:
  1. when counting objects each object is assigned only one number name
  2. stable order rule
  3. order irrelevance rule
  4. the number name which was assigned to the last object is how many objects there was (Reys
      et al., 2012)
• There are three different counting strategies:
  - counting on
  - counting back
  - skip counting (Reys et al., 2012) 
• Calculators are a helpful tool in demonstrating counting practice and getting over children's hesitation when reaching certain numbers, such as the next decade or century (Reys et al., 2012) 
• There are five counting principles:
  - one-to-one correspondence
  - stable order
  - cardinal principle
  - abstraction
  - order irrelevance (Jamieson-Proctor, 2016) 
• There are three different types of numbers:
  - cardinal
  - ordinal
  - nominal (Jamieson-Proctor, 2016) 
• Attribute blocks, which were used in the tutorial, are helpful in teaching pre-number 

How have the big ideas changed your understanding of the topic?

• Prior to this week I was unaware that pre-number understanding involves attributes 
• I was also unaware that there was three different types of numbers; cardinal, ordinal and nominal 

Demonstrate your understanding of the mathematical concept and related skill and strategies children need to assimilate and be able to use, that are related to the topic of pre/early number 

• There were many concepts this week including, pre-number, patterning, ordering, sorting, comparing, matching, early number, counting and subitizing. 
• Pre-number is a concept that "...leads eventually to meaningful counting skills and number sense" (Reys et al., 2012, p. 143).  
• The concept of pre-number is done using the following skills:
  - determining attributes
  - matching by attributes
  - sorting by attributes
  - comparing attributes
  - ordering attributes and;
  - patterning 
• The strategies for pre-number are:
  - matching by having all objects on a sorting mat
  - sorting by placing objects in different cups, circles or lines for the different attributes

Language model for pre number

Figure 1.16: Language model for the concept of pre-number

Describe/demonstrate a specific teaching strategy and appropriate resource/s that could be used to assist children to understand a key mathematical concept related to pre/early number 
When teaching children the concept of pre-number, attached are some resources that could be used to assist:

• Concept of pre-number: Taller and Shorter 
• Concept of pre-number: Bigger and Smaller
• Concept of pre-number: Heavy and Light
• Pre-number Concepts

Describe/demonstrate a specific misconception children might have in relation to pre/early number 

• A common misconception, in relation to the concept of pre-number, is that pre-number work is usually done before children do anything with numbers in school (Reys et al., 2012). This is a misconception for children and adults. 
• A way to re-mediate this is to make it known what the topic being taught is and the concept that it relates from 

Provide appropriate URL links to the ACARA year, strand, substrand, content description, elaborations and Scootle resources for the earliest mention of pre/early number 

• Pre-number can first be seen in the Foundation Year, ACMNA289, Number and Algebra strand, Number and Place Value sub-strand. 
• The content description for ACMNA289 is "compare, order and make correspondences between collections, initially to 20, and explain reasoning" (ACARA, 2016). 
• The elaborations for ACMNA289 are:
  - "comparing and ordering items of like and unlike characteristics using the words 'more', 'less',
     'same', 'not the same as' and giving reasons for these answers;
  -  understanding and using terms such as 'first' and 'second' to indicate ordinal position in a
     sequence;
  - using objects which are personally and culturally relevant to students" (ACARA, 2016)
• Attached are images of two Scootle resources which aid the teaching of ACMNA289

Figure 1.17: Scootle Resource One
Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA289&userlevel=(0) 

Figure 1.18: Scootle Resource Two
Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA289&userlevel=(0) 

Provide appropriate links to resources and ideas you have sourced personally to assist students to develop concepts, skills and/or strategies related to pre/early number 

Resources for students to understand the concept of pre-number:

• Concept of pre-number: Taller and Shorter 
• Concept of pre-number: Bigger and Smaller
• Concept of pre-number: Heavy and Light
• Pre-number Concepts

Resources for students to understand the skills related to the concept of pre-number: 

• Pre-number skills - this is a game that students could play using attribute blocks to development their pre-number skills 
• Attribute blocks - these are a resource that allow children to classify based on different attributes, such as shape, colour, thickness and size. 

Figure 1.19: Discount School Supplies. (2016). Attribute blocks: Set of 60. Retrieved from http://www6.discountschoolsupply.com/Product/ProductDetail.aspx?product=31378&Category=6353

Resources for students to understand the strategy of pre-number: 

• Sorting mat 

Figure 1.20: Teachers Pay Teachers. (2013). Free printable colour sorting mat. Retrieved from https://au.pinterest.com/edumom01/sorting-by-shape-color-size/

• Cups for sorting different attributes 

Figure 1.21: Osborn, S. (2016). Button sorting cups. Retrieved from http://aboutfamilycrafts.com/button-sorting-cups/

Provide a concise synthesis of the textbook chapter/s related to pre/early number

Chapter Seven:

• There are two pre-number concepts:
  1. classification
  2. patterns (Reys et al., 2012)
• There are three different ways to develop early number:
  1. conservation
  2. group recognition
  3. comparisons and one-to-one correspondence (Reys et al., 2012)
• Patterns facilitate the counting process (Reys et al., 2012)
• There are four different counting principles
  1. when counting objects each object is assigned only one number name
  2. stable order rule
  3. order irrelevance rule
  4. the number name which was assigned to the last object is how many objects there was (Reys
      et al., 2012)
• There are two different counting stages:
  1. Rote counting where you know some number names but not necessarily the proper sequence
  2. Rational counting where the child gives a correct number name when objects are counted in
      succession (Reys et al., 2012)
• There are three different counting strategies:
  1. counting on
  2. counting back
  3. skip counting 
• "Cardinal numbers...answers the question 'how many?'" (Reys et al., 2012, p. 158)
• "Ordinal number...answers the question 'which one?'" (Reys et al., 2012, p. 158)
• "Nominal numbers provide essential information for identification but do not necessarily use the ordinal or cardinal aspects of the number" (Reys et al., 2012, p. 159)

References 

Ashlar Kidz. (2015). Maths::concept of heavy and light – i. Retrieved from https://www.youtube.com/watch?v=nqU0yQzwxOo

Ashlar Kidz. (2015). Pre-number concept of bigger & smaller – ii. Retrieved from https://www.youtube.com/watch?v=5dv30Akzybs

Ashlar Kidz. (2015). Pre-number concept of taller & shorter – ii. Retrieved from https://www.youtube.com/watch?v=NAYNiyNnxc0

Australian Curriculum Assessment and Reporting Authority. (2016). Mathematics. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1#cdcode=ACMNA289&level=F

Cusack, B. (2013). EDX1280 foundation pre number skills. Retrieved from https://www.youtube.com/watch?v=DiVjbuarRsg

Discount School Supplies. (2016). Attribute blocks: Set of 60. Retrieved from http://www6.discountschoolsupply.com/Product/ProductDetail.aspx?product=31378&Category=6353

Education Services Australia. (2016). Scootle: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1

Jamieson-Proctor, R. (2016). EDMA202/262 mathematics learning and teaching 1: Week 5 Part 1. Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1180683&chapterid=28372

Osborn, S. (2016). Button sorting cups. Retrieved from http://aboutfamilycrafts.com/button-sorting-cups/

Pioneers Education. (2013). Learn maths – Class 1 – Pre-number concepts. Retrieved from https://www.youtube.com/watch?v=5HlIC90m-Hc

Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn mathematics. Queensland, Australia: John Wiley & Sons Australia, Ltd.

Teachers Pay Teachers. (2013). Free printable colour sorting mat. Retrieved from https://au.pinterest.com/edumom01/sorting-by-shape-color-size/