Place Value Knowledge and Equipment

At its core, place value concepts requires students' need to learn multiple representations of the same idea where: 

1. the same digits, 0 to 9 can be used in any of the places 
2. each digit has a different value depending on the place in which they're located on the place value chart
3. our number system have patterns with ten as its base. 

My students lack understanding in each of the aformentioned concepts. This was clearly expressed when  they didn't recognise place value equipment (boards and blocks) when put in front of them, didn't know how to use the equipment, and were unable to answer place value related questions when manipulating place value blocks. 

Clearly the students did not know where to place the digits on the place value chart.

I was surprised that the students knew so little about using the place value equipment, not least because believe in using place value manipulatives as a part of the teaching process - especially for students that fall behind in maths. Cathy Draper, 2006 (in her paper about high school students, It Is All About Connections) expressed the results of inadequate place value understanding among students: "many students.........at these upper levels have never recognized this pattern - and they are good students". In short, students who didn't know our number system has patterns with 10 as its base, couldn't explain why the same digit had different values according to where it sits in the pace value chart. 

If manipulatives do not get used in a classroom, it could be because "teachers need support making decisions regarding manipulative use, including when and how to use manipulatives, to help them and their students think about mathematical ideas more closely" (Puchner, L., Taylor A., O'Donnell, B., Fick, F., 2008, Teacher Learning and Mathematics Maniuplatives: A collective case study about teacher use of manipulatives in elementary and middle school mathematics lessons. School Science and Mathematics). 

As teachers, we must ensure students regularly use place value equipment throughout their years of mathematics learning, not just in one or two year levels but at every level during their years at primary school (for example: addition and subtraction in lower levels and decimal numbers in upper levels). Our students must engage in the patterns and representations involved in the process rather than just moving place value blocks around (Early Childhood and Mathematics, Smith, 2009). I like to see place value equipment used at all levels and in every classroom so that students get the benefit of this equipment which will support them to understanding number patterns better.