Theory |
Common Student Misconceptions |
The fundamental counting principles will guide teaching. The principles include:
One-to-one correspondence – counting corresponds with each object Stable order rule - is knowing that numbers are in a repeatable order Order-irrelevance rule - knowing that the order in which objects are counted does not matter Cardinality rule – learner understands that the last number when counting objects is the quantity (how many?) (Thompson, n.d.) In order to teach early number concepts I require knowledge of:
Counting typically follows a developmental path known as the "learning trajectory" (Van De Walle et al., 2014, p. 139). The learning trajectory can assist with understanding where the child's development is currently and the path to develop their skills. |
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Mathematics Language for Early Number Concepts
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Early years
Uno’s Garden Read Uno's Garden to children and take time to count the animals on each page as well as predict the number of animals on the next page. Early Years Learning Framework (EYLF) - Outcome 5 page 6 key numeracy concept of number understandings. Student will display their ability to count and order numbers. Objective: Children engage in one-to-one correspondence as well as counting back and counting on. (Adapted from Buster the balloon video, n.d.)
Foundation Doing the dishes Use dot plates and a rope to develop a number line. ACMNA001 Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point Objective: students to understand the sequence of numbers between 1 and 20. Use subitising, counting on and counting back from any number between 1 and 20, and more or less. (Adapted from McAlpine, n.d.)
Year 2 Missing element Use a hundreds chart and transparent counters to explore number relationships. ACMNA026 Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences Objective: students use mental addition strategies such as counting on and 'how many more' questions to identify the missing number in an additive problem. It then connects to subtraction through counting back and 'how many less' questions. |
There are 9 cupcakes on the plate. If we add 1 more how many do we have?
I have 21 pencils in my hand but there are 27 people in our class. How many more pencils do I need for everyone to have a pencil? |
Resources
Curriculum Map
The key numeracy processes for early number are found in Outcome 5, page 5 of Early Years Learning Framework (EYLF). They include observing and describing similarities and differences between objects; and sorting, matching, ordering and classifying objects according to attributes such as size and shape. The key numeracy concepts (Outcome 5, p. 6) detail that students will have the ability to count and order numbers, recognise and write numerals, and compare quantities such as ‘more than’ and ‘less than’.
(Charles Sturt Universtity Early Years Learning Framework Consortium, 2009)
Early number is found in the Australian Curriculum under Foundation through to Year 3.
FOUNDATION
YEAR 1
YEAR 2
YEAR 3
(Charles Sturt Universtity Early Years Learning Framework Consortium, 2009)
Early number is found in the Australian Curriculum under Foundation through to Year 3.
FOUNDATION
- Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point. (ACMNA001)
- Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002)
- Subitise small collections of objects (ACMNA003)
- Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289)
YEAR 1
- Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero (ACMNA012)
- Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013)
YEAR 2
- Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences. (ACMNA026)
- Recognise, model, represent and order numbers to at least 1000 (ACMNA027)
YEAR 3
- Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051)
- Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)
References
Base, G. (2010). Uno’s garden. New York, NY: Abrams Books.
Buster the balloon [Video file]. (n.d.). Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=921025
Charles Sturt Universtity Early Years Learning Framework Consortium. (2009). Document 16 outcome 5: Children are effective
communicators. Retrieved from http://www.earlyyears.sa.edu.au/files/links/16_Outcome_5.pdf
Education Services Australia. (n.d.) Curriculum. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?
layout=3#page=3
Lawton, F. & Hansen, A. (2011). Numbers and the number system. In S. Hansen (Ed.), Children’s errors in mathematics (2nd ed.) (pp. 20-
46). Exeter, England: Learning
Matters.McAlpine, J. (n.d.). Mathematics: Counting on, counting back. Retrieved from
https://www.scootle.edu.au/ec/viewing/R11450/support_files/uw_003_counting_on_counting_back.pdf
Super Teacher Worksheets. (n.d.). Hundreds Chart [Image]. Retrieved from
http://www.superteacherworksheets.com/hundredschart/hundreds-chart-filled_WNRTB.pdf
Thompson, I. (2008). Teaching and learning early number. Retrieved from
http://site.ebrary.com.ezproxy2.acu.edu.au/lib/australiancathu/detail.action?docID=10274024
Thompson, I. (n.d.). The principle of counting principles. Retrieved from
https://www.ncetm.org.uk/public/files/712850/The+principal+counting+principles.pdf
Van De Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex,
England: Pearson Education.
Buster the balloon [Video file]. (n.d.). Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=921025
Charles Sturt Universtity Early Years Learning Framework Consortium. (2009). Document 16 outcome 5: Children are effective
communicators. Retrieved from http://www.earlyyears.sa.edu.au/files/links/16_Outcome_5.pdf
Education Services Australia. (n.d.) Curriculum. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?
layout=3#page=3
Lawton, F. & Hansen, A. (2011). Numbers and the number system. In S. Hansen (Ed.), Children’s errors in mathematics (2nd ed.) (pp. 20-
46). Exeter, England: Learning
Matters.McAlpine, J. (n.d.). Mathematics: Counting on, counting back. Retrieved from
https://www.scootle.edu.au/ec/viewing/R11450/support_files/uw_003_counting_on_counting_back.pdf
Super Teacher Worksheets. (n.d.). Hundreds Chart [Image]. Retrieved from
http://www.superteacherworksheets.com/hundredschart/hundreds-chart-filled_WNRTB.pdf
Thompson, I. (2008). Teaching and learning early number. Retrieved from
http://site.ebrary.com.ezproxy2.acu.edu.au/lib/australiancathu/detail.action?docID=10274024
Thompson, I. (n.d.). The principle of counting principles. Retrieved from
https://www.ncetm.org.uk/public/files/712850/The+principal+counting+principles.pdf
Van De Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex,
England: Pearson Education.