Place Value - Summary and Reflection

Content area: Place Value (whole number).

Mathematical content knowledge

Base-Ten Concepts: a numeration system that groups numbers into ten (0-9)

(Van De Walle et al., 2019, Bartolini Bussi, 2011).

Base-ten models:

- Proportional models: students meaningfully develop number sense and the size of multidigit whole numbers. The ‘“10” is ten times larger than the “one”’. Examples include; unifix cubes and Multibase Arithmetic Blocks (MAB) (Van De Walle et al., 2019).

- Non-proportional models: the ‘“10” is not ten times larger than the “one’”. Used when students have developed conceptual knowledge of place value eg, money (Van De Walle et al., 2019).

Partitioning numbers: breaking down and representing numbers based on physical or mathematical qualities. Also called “number busting”, because students create “equivalent representation” of numbers (Van De Walle et al., 2019).

Mathematical pedagogical content knowledge

Strategies

Students need the ability to differentiate between digits and know that numbers are grouped into “ones, tens and hundreds” (Siemon et al., 2015). They can learn this through “equivalent representation” by representing numbers in different forms using different strategies (eg visual, oral and written concepts) (Van De Walle et al., 2019).

Materials

Teachers use “concrete materials” for learning because students can physically represent numbers (Van De Walle et al., 2019, Bartolini Bussi, 2011). There are two types of concrete learning tools:

1, Groupable base-ten models: blocks can be broken apart into different groups

2, Pre-grouped base-ten models: models cannot be taken apart or put together (Van De Walle et al., 2019, Burris, 2013).

Students learning should follow a sequential pattern. The Place value framework are incremental levels of difficulty that occurs during place value learning (Young-Loveridge, 1999). The four levels are “1. Unitary Concept, 2. Ten-structured Concept, 3. Multi-unit Concept and 4. Extended multi-unit Concept” (Young-Loveridge, 1999).

Implications for future practice and actions about this content area

Future mathematical teaching strategies:

-Use a variety place value resources specific to the needs and abilities of the students, including concrete models. Alternative strategies could be online maths tools such as virtual base-ten models which may support the learning outcomes for students with disabilities (Burris, 2013).

-Teacher questioning: “What are different ways of representing place value whole numbers? Can you represent that visually? How about numerically?” (Kari, A., & Anderson, C., 2003).

References

Bartolini Bussi, M. (2011). Artefacts and Utilization Schemes in Mathematics Teacher Education: Place Value in Early Childhood Education. Journal of Mathematics Teacher Education, 14(2), 93-112. Retrieved from https://link-springer-com.ezproxy1.acu.edu.au/article/10.1007/s10857-011-9171-2

Burris, J. (2013). Teaching Children Mathematics. National Council of Teachers of Mathematics Stable. 20(4), 228-236. Retrieved from https://www-jstor-org.ezproxy1.acu.edu.au/stable/pdf/10.5951/teacchilmath.20.4.0228.pdf?refreqid=excelsior%3A0e2429cdf16e65e222c5679f34f94a2e

Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2015). Place Value F-4. In L. Filleul (Eds.), Teaching mathematics : Foundations to middle years (pp.314-343). Retrieved from https://ebookcentral-proquest-com.ezproxy1.acu.edu.au/lib/acu/reader.action?docID=5306470&ppg=1

Victorian Curriculum and Assessment Authority. (n.d.). Mathematics. Retrieved from https://victoriancurriculum.vcaa.vic.edu.au/mathematics/curriculum/f-10#level=6

Van De Walle, A., Karp, J., Bay-Williams K., Brass, A., (2019). Developing whole-number place-value concepts. In M. Dankel (Eds.), Primary and middle years mathematics : Teaching developmentally (1 ed., pp. 227-252). Melbourne, VIC: Pearson Australia.

Young-Loveridge, J. (1999, December). Developing an Understanding of the Number System. Paper presented at the Australian Association for Research in Education – New Zealand Association for Research in Education, Melbourne, Australia. Retrieved from https://www.aare.edu.au/data/publications/1999/you99550.pdf