Academic journal article Australian Primary Mathematics Classroom

Good Concrete Activity Is Good Mental Activity

Academic journal article Australian Primary Mathematics Classroom

Good Concrete Activity Is Good Mental Activity

Article excerpt

Are you an early years teacher who uses or has children use concrete materials in maths lessons? Do you, like some teachers, wonder about the effectiveness of using concrete materials? If so, perhaps you ask questions like the following:

* For what purposes are concrete materials used in my mathematics classroom?

* Who decides if a student is to use concrete materials and who decides which materials?

* Does the use of concrete materials really stimulate my students' mathematical thinking?

These questions, which might be relevant to any early years mathematics classroom, underpin the telling of classroom stories in this article. The first two stories come directly from my visits to classrooms and then, to extend the discussion, I draw on classroom stories from papers I have read.

Early years mathematics classrooms can be colourful, exciting, and challenging places of learning. Fellow teachers and I have noticed that some students make good decisions about using materials to assist their problem solving, but this is not always the case. These experiences lead me to also ask the following:

* Are concrete materials necessarily helpful for all students in their learning of mathematics?

* Are concrete materials always used as effectively as they might be?

The focus of this article is the use of concrete materials in the early years mathematics classroom, but the issues and questions might apply equally to virtual manipulatives and to use of manipulatives in higher year levels. With the underlying belief that "good concrete activity is good mental activity" (Clements & McMillen, 1996, p. 272), three key messages are discussed. These are that:

* concrete materials can help students focus on key mathematical ideas;

* lessons that incorporate concrete materials can stimulate children's higher order thinking; and

* teachers may need to intervene when students use concrete materials.

Message 1: Concrete materials can help students focus on key mathematical ideas

Recently, as part of my involvement in the Contemporary Teaching and Learning of Mathematics (CTLM) project, I had the opportunity to teach a Prep (Foundation level) class. I wanted to engage the children and challenge them to think about key ideas of mass measurement. In the first activity of the lesson, six 'mystery bags' (paper bags each holding one object and sealed with a peg) were placed in the centre of the circle, resulting in much speculation as to what they might hold. The bags were then passed around, giving each child a chance to hold them (Figure 1). A very special moment occurred when a child who spoke very little English held two bags. Her eyes lit up and she excitedly said "heavy" and "light" to her friend who translated into English for us. I suspect that prior to holding the bags, this child had little sense of the mathematics of the lesson; the holding of the bags was essential for this child (and indeed most probably for all the children).

The key mathematical terms she had identified were recorded on the whiteboard.

The children suggested that to check which bag was heaviest we could use balance scales (Figure 2). While the bags were weighed, compared, and ordered, once again there was much discussion.

The statement from a child that "the heavy goes down" was recorded on the whiteboard.

Following the weighing and ordering of the bags by mass, we took the objects from the bags. The children discovered that although some were heavier and some lighter they all looked about the same size (volume). I had purposely chosen the objects as seen in Figure 3--a glass paper weight, a foam ball, a tennis ball, a cricket ball, a small apple and a small orange--to expose the children to the key mathematical idea that size (volume) does not necessarily determine mass.

The use of materials in the introduction to this lesson had performed some key purposes:

* Children were engaged in the lesson;

* Key mathematical terms 'heavy' and 'light' were articulated and highlighted;

* Attention was brought to the important measurement idea of comparison;

* Children had the experience of hefting and using balance scales to compare and order masses; and

* The idea that mass is not necessarily related to size (volume) arose in the discussion. …

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