THE BIG IDEAS
One of the important points this week was the five principles that are involved with counting. These include:
- One to one correspondence (one number for each object)
- Stable order (the correct order of numbers e.g. one, two, three)
- Cardinal principle (the last number counted tell us how many there are altogether)
- Abstraction (There are things that can be counted such as the number of blocks in the toy box, and other things that can't like the number of sand grains on the beach)
- Order irrelevance (no matter the order the objects are counted the number will always be the same unless more is added or removed)
Helping children learn mathematics (2012) discusses the intricate natures of counting on page 150 where it states:
"What is counting? It is a surprisingly intricate process by which children call number values by name. A close look at the counting process shows that finding how many objects are present involves two distinct actions. A child must say the number-name series starting with one, and point to a different object as each number name is spoken."
These principles are important to note as all principles must be demonstrated by a child before they can be considered as knowing how to count. This means for me as a teacher, interviewing children in my foundation class at the beginning of the year is necessary to fully understand the stages of development the children are currently situated and gain insight into how to further assist this development.
This may be an assessment piece in a school setting, however in a prior to school setting, this could be a checklist to be revisited over an extended period of time to demonstrate the child's progress.
VIDEO: Counting interview This video is a recording of a child that demonstrates the cardinal principle, stable order and is in the beginning stages of one to one correspondence. This interview does not address abstraction or order irrelevance, however additional questions may be added to include these aspects.
THE CONCEPT, SKILL, STRATEGIES AND SUPPORTING RESOURCES
Focusing on pre-number, there is a group of six concepts and related skills that fall under this group. These concepts include:
Concept
For sorting by attributes, the concept is that we are taking a large group of objects and splitting them up into smaller groups based on one or more attributes. The concept of sorting can be taught using discussions starting with the questions "Can can we make smaller groups?". Children begin to recognise that objects can be catagorised, this can begin simply by showing the child objects that can be catagorised by strong and obvious differences and slowly move into other groups of objects that require more thinking.
- Determining attributes
- Matching by attributes
- Sorting by attributes
- Comparing attributes
- Ordering attributes
- Patterning
For this section, only 'sorting by attributes' will be dissected and explored further.
Concept
For sorting by attributes, the concept is that we are taking a large group of objects and splitting them up into smaller groups based on one or more attributes. The concept of sorting can be taught using discussions starting with the questions "Can can we make smaller groups?". Children begin to recognise that objects can be catagorised, this can begin simply by showing the child objects that can be catagorised by strong and obvious differences and slowly move into other groups of objects that require more thinking.
VIDEO: Class recognising different attributes they can sort by In this video the children are demonstrating the concept of sorting by explaining what attribute the shapes have been sorted by.
Skill
The ability to move objects into groups based on an attribute. This skill can be practiced using any objects that share one or more attribute.
VIDEO: Child sorting rocks by what it reminds him of
VIDEO: Child sorting keys in various groups
During these videos, the children are seen grouping various objects differently. This is practicing the skill of sorting.
Strategies
In sorting, the thinking strategy used is planning how to complete the task. Strategies used may be a sorting chart, separating into groups (as shown in the videos in the 'skill' section) or placing each group in a different cup or container.
VIDEO: Child sorting keys in various groups
During these videos, the children are seen grouping various objects differently. This is practicing the skill of sorting.
Strategies
In sorting, the thinking strategy used is planning how to complete the task. Strategies used may be a sorting chart, separating into groups (as shown in the videos in the 'skill' section) or placing each group in a different cup or container.
THE LANGUAGE MODEL
The language model is used to display the relationship between the visual, verbal and symbolic elements of mathematics and forms 'stages' of learning.
Student language - During student language, all language used should be familiar to the child and accompanied with familiar objects. This may vary depending on the 'story'. For example, 'Three bird families were sitting in a tree and they decided to go home to their nests. Can you help them go to the right nest?'. In this situation, an image of a tree, three separate nests and groups of three different birds would be used.
Materials language - At this stage, there is still no introduction of mathematical terms. The language is very similar to student language however the visuals used have become more abstract. For example, 'Can we separate these counters into groups? What makes each counter in this group the same?'
Mathematics language - Moving away from 'stories', this stage introduces mathematical terms. For example, 'How can we sort these objects? What attributes can we sort by?'
Symbolic language - Pre-number and early number does not use symbolic language or symbols.
THE LANGUAGE MODEL FOR SORTING
THE MISCONCEPTION
A misconception children may have with sorting is misinterpreting the attribute being sorted. This is particularly prominent when sorting more than one attribute (an example of this is in the link below). This can be remedied by using a table for a more visual representation of what attribute is being sorted.
THE ACARA LINK
Sorting is first introduced in the foundation year.
Strand: Number and Algebra
Substrand: Patterns and algebra
Content descriptions: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Elaborations:
- Observing natural patterns in the world around us
- Creating and describing patterns using materials, sounds, movements or drawings
Scootle resource ideas:
1. Kitchen Stacker: Sort and Label is an online game that allows students to sort a large number of different objects by a variety of attributes.
2. Clean up time is a video that sorts toys by a number of attributes (colour, type and shape). This could be used as an introduction to a lesson as it ends with the open-ended question 'Can you think of anything we can sort?'
3. Letter Detective: Letter Case allows students to sort upper case an lower case letters
3. Letter Detective: Letter Case allows students to sort upper case an lower case letters
THE RESOURCES AND IDEAS
- 'Sorting Game' by My First App is an app designed for the ipad used to introduce sorting using one attribute during pre-number.
- ABCYa Educational Games: Rainbow fuzzbugs counting, sorting and comparing is an online game that introduces sorting as well as names of different attributes (such as largest and smallest)
- Sesame Street has a video that can be used to teach sorting by multiple attributes - in this video, two characters are sorting blue squares and stripped circles when they come across a stripped square. This shape doesn't fit in either group so they make a new group for it.
- Sort it out! by Barbara Mariconda and illustrated by Sherry Rogers is a children's story that uses rhyme to explore attributes such as colour, size, texture, shape and material.
THE TEXTBOOK SUMMARY
- Number development is not a finite entity that a students either has or has not, it's development is a life long process.
- The stages include pre-number and informal number; early number development; number development and counting
- These stages form the basis of whole-number development and provide the underpinnings for basic facts as well as mental and written computation involving addition, subtraction, multiplication and division of whole numbers
- Early number content descriptors can be found in the Australian curriculum in the foundation year
- Young children have vast amounts of early number experience, many experiences of which do not rely on numbers but provide the basis of early number concepts and foundation for later skills. Such experiences are called pre-number experiences. (Reys, Lindquist, Lambdin, Smith, Rogers, & Falle, et al., 2012)
THE REFERENCES
ACU,. (2016). Learning Environment Online. Leo.acu.edu.au. Retrieved 3 March 2016, from http://leo.acu.edu.au/course/view.php?id=18458
Australia, E. (2016). Home - Scootle. Scootle.edu.au. Retrieved 3 April 2016, from https://www.scootle.edu.au/ec/p/home
Australian government,. (2016). Home - The Australian Curriculum v8.1.Australiancurriculum.edu.au. Retrieved 3 April 2016, from http://www.australiancurriculum.edu.au/
Reys, Lindquist, Lambdin, Smith, Rogers, & Falle, et al. (2012). Helping children learn mathematics. Milton, QLD: John Wiley & Sons.
YouTube. (2016). Youtube.com. Retrieved 3 April 2016, from https://www.youtube.com/
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