This week in lectures and tutorials, we covered a large array of content. We firstly looked at number sense, numeration and mental computation. Numeration and mental computation was linked back to our content from weeks 2-5, and we were reminded of the big 7 thinking strategies across addition, subtraction, multiplication and division.
We then moved on to place value, which I found to be a much larger concept than I expected. This week I learnt that there is not just the ‘ones, tens, hundreds, thousands’ or the base 10 system. I found it really interesting to learn about other bases such as base 5 and base 3, and to see them modelled for me, as I was only ever taught the base 10 system at school.
As a teacher, I will need to ensure I emphasise the importance of place value to my students and incorporate it into every area of mathematics. This is because place value is “one of the cornerstones of our number system” and is part of all work with whole numbers, the metric system, the four operations, money and decimals (Reys et al., 2020, p.222).
Concept, Skill or Strategy
According to Reys et al. (2020), place value rests on two key ideas:
1.“Explicit grouping or trading rules are defined and consistently followed”
2.“The position of a digit determines the number being represented” (p.224)
Place value can be described as “the mother of all mathematical concepts,” as there are actually 8 concepts of place value (Jamieson-Proctor, 2021).
The Language Model
Misconception
Children may only recognise zero as a label for an empty set, or nothing, and do not understand its use of being a place holder for numbers in our base-10 structure e.g. numbers such as 30 or 306 could be considered 3 and 36 by a child who does not understand zero as a place holder. As a teacher, I will need to remediate this misconception early as it is a vital concept to understand, and use PV mats and other concrete materials to model this.
(Maths & Learning Videos 4 Kids, 2015)
ACARA
Place value concepts are first seen in the Australian curriculum in foundation year (ACMNA002)
Strand: number and algebra/ patterns and algebra
Sub-strand: number and place value
Scootle
This is a short, but engaging clip for young children that teachers could use as an introduction or support when they are teaching the place value concept of zero as a placeholder.
(ABC Education, 1999)
Teaching resource
This website includes a range of teaching tools that have been created to help students conceptually understand place value with a hands-on approach. These would be suitable for children in the mathematics stage of the language model. These would need to be adjusted depending on the year level you were teaching, as some of the numbers featured in these examples include thousands and above.
(TeacherThrive, 2021)
References
ABC Education. (1999). Importance of zero. https://education.abc.net.au/web/splash#!/media/2006751/
Jamieson-Proctor, R. (2021). Week 7 learning activities: Part 2a lecture. Australian Catholic University. https://vimeo.com/user36828324/review/200614369/0a699008ad
Maths & Learning Videos 4 Kids (2015). Place value first grade - tens and ones [Video]. https://www.youtube.com/watch?v=1F3AycEDksY&ab_channel=Math%26LearningVideos4Kids
Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Cooke, A., Ewing, B., & West. J. (2020). Helping children learn Mathematics (3rd Australian ed.). Milton: John Wiley & Sons.
Teacher Thrive. (2021). Hands-on activities for teaching place value. https://teacherthrive.com/hands-activities-teaching-place-value/
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