Scenario: Amy teaching a lesson about counting
Country: UK
Grade (student age): Reception/Kindergarten (age 4-5)
Contributed by: Fay Turner, University of Cambridge, UK
Context – national, curricular, professional, other
This lesson took place during the second half of Amy’s first term teaching in a large city primary school. It was a lesson with Amy’s Reception class about counting. The national curriculum for England at this time (2006) put great emphasis in the early years on counting. Two key objectives for pupils in their first formal year of school were that they should be able to:
- Say and use the number names in order in familiar contexts
- Count reliably up to ten everyday objects
By the end of Year 1, pupils were expected to count up to 20 objects and to count in tens. Amy had completed a one year graduate teacher programme the previous year.
Scenario
In the warm-up part of the lesson the children practiced counting forwards and backwards to 20. They were supported by a number line on the wall constructed from pupils’ pictorial representations of the numbers. For the introductory part of the lesson Amy produced a number of brightly coloured boxes of different sizes. Inside each box were a number of different objects e.g. glass beads and plastic snakes. The children were invited to guess how many objects were inside the boxes. The objects were then revealed and counted by the children. When the children were counting the objects, Amy praised them for, and drew attention to, the strategies they used, i.e. putting the objects in line, pointing to each in turn with their fingers, saying the numbers in order, and saying that the last number was the answer to ‘how many’. At the end of the introductory part of the lesson, Amy reinforced what had been good about their counting, saying “We said the numbers in the right order, we touched each thing once, and the last number we said was how many there are.”
The class topic was ‘pirates’ and in the activity part of the lesson, Amy worked with a group of children counting gold coins in a treasure chest. Amy encouraged the children to count the coins in groups of ten and then to count in tens to find the total.
In the plenary part of the lesson Amy asked the children to count the number of times she hit a chime bar. The children matched a ‘counting number’ to each hit and a few children continued counting after the last strike. Amy told the children that they should not continue counting unless she hit the chime. She asked “What number tells us how many times I hit the chime bar?” A child responded “six” and Amy said, “Yes, the last number we say is the number of times I hit the chime bar”.
Knowledge Quartet Coding Commentary
Contributed by: Fay Turner, University of Cambridge, UK
Knowledge Quartet Dimension: Foundation
Knowledge Quartet Code: Theoretical Underpinning (TUP)
Scenario: Amy teaching a lesson about counting
Gelman and Gellistel (1978) proposed that in order to count meaningfully children need to know the number names in order, understand one to one correspondence, and recognise the cardinal principle i.e. that the last number said in a count is the answer to the question ‘how many?’ They also suggested that in order to teach children to count effectively it is important to know the order in which children attain these pre-requisites. Observation of this lesson suggested that Amy had good pedagogical knowledge about what was involved in learning how to count. She was quite explicit in referring to the pre-requisites of counting when the children were counting the objects from the boxes. In saying “We said the numbers in the right order, we touched each thing once, and the last number we said was how many there are”, Amy referred to the stable order principle, the one-one principle and the cardinal principle (Maclellen, 2003) in turn.
In the final part of the lesson Amy asked children to count the number of times she hit a chime bar. This suggested that she recognised that counting different sorts of objects, i.e. those that can be heard as well as those that can be seen or touched would help to consolidate children’s understanding of counting.
In a reflective account of this lesson, Amy showed that she was aware of drawing on her pedagogical content knowledge in relation to counting when planning and teaching the lesson:
When I was planning this lesson I drew on my knowledge of the pre-requisites for counting: knowing the number names in order, one to one correspondence, the cardinal principle, being able to count objects that cannot be moved/touched and counting objects that cannot be seen e.g. sounds or beats. These developmental stages formed the progression and structure to the lesson. (Amy, 2a, RA-OL)
The principles of counting that Amy referred to, and made explicit in her teaching, were part of the knowledge she had gained during her postgraduate initial teacher education year. The theory that she learned during this year informed and underpinned the teaching in this lesson.
In summary, this is an example of TUP because Amy demonstrated during the lesson, and explicitly stated during a post-lesson interview, that her teaching was underpinned by her knowledge of the pre-requisites for counting learned during her teacher education course.
References
Gelman, R. and Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.
Maclellen, E. (2003) ‘The Importance of Counting’, in I Thompson (ed.) Teaching and Learning Early Number, pp. 33 – 40. Philadelphia: OUP