Situation

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In a high achieving pre-primary classroom, I was required to teach place value, beginning in the teens and then extending upwards. Most of the children were confident with numbers in the high tens but there was a group of about 5 children who struggle with numbers beyond the teens. I knew I needed to ensure I had lots of concrete experiences for children and opportunities to see and represent numbers in different ways.

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Action

 

I began with teen number bingo as a form of diagnostic assessment for recognising numbers. I also gave each child a card and they had to put themselves into groups of 3 where they all had the same teen number shown in different forms (numeral, written and number of dots). I also had children come up to the front and use their fingers to show how we can count on from the tens which is an important skill to develop. The children did very well with these activities so I felt confident moving them to the activities. I began with very concrete experiences which Reys et al (2012) emphasise is essential in supporting children to make sense of mathematics. They also state that communicating our thoughts to others can clarify them for ourselves as well and consequently stress the importance providing opportunities for children to communicate their thinking and reflect on what they have done, thought and experienced during the mathematics session. Consequently, I provided activities that would stimulate discussion about what the children were doing and had them work in pairs. I began with having children bundle sticks into tens and then counted the ones left over. This also enabled me to differentiate easily as some children were still consolidating the teen numbers whereas others were into the high tens and even the hundreds, so I differentiated with number cards. I also created ‘think boards’ for children to represent their thinking and learning in different ways. Reys et al (2012) describe the importance of oral language and exploring pictorial representations alongside concrete objects in supporting children to develop conceptual knowledge (Reys et al, 2012, p.29). I utilised these experiences as an opportunity to provoke children’s thinking and challenge underlying misconceptions by asking questions that promote problem solving (Reys et al, 2012, p.25), such as “How did you work that out” “How did you know…” what did you think in your brain…”, ”What did you do to get those scales to balance?” “How did you know what to do?” “What does it mean if they balance/that side is lower/higher?”

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After 2 days of experiences with similar activities, I moved onto MAB blocks to expose children to this form and again, provide a different way or representing place value. I had tens and ones mats for both of these experiences, providing a hundreds mat to children who required the additional challenge. I also introduced ‘Think Boards’ to the students which provided opportunities for children to represent their thinking and understanding of numbers in various ways including concrete objects, drawing, breaking down tens and ones and then writing the complete sentence of ____ tens and ___ ones makes ____.  Think Boards are valuable as they provide children with opportunities to use pictures and symbols to represent concrete actions (Reys et al, 2012). Children require many experiences with concrete objects and concepts before they can comprehend abstract ideas such as symbols and consequently, oral language and written communication to convey thinking enables children to progress to mathematical notation with deeper understandings of the mathematical concepts (Reys et al, 2012).

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The children were highly successful with these concepts. I had 19 out of 24 children able to partition numbers successfully into tens and ones at least into the 30’s. I worked with those 5 children on the mat during a mini-lesson while I had the other children engaged in tens and ones games and activities such as memory games and I have Who Has. I had the children on the mat with MAB blocks and think boards where we practiced making the numbers and counting by tens.

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It was evident that most of the problem for the children who couldn’t move beyond the teen numbers were not confident with counting by tens so had to count the 10 blocks by ones which confused them in regard to tens and ones. Consequently, I integrated counting by 10’s to 200 into the morning routine and backwards from 100 by 10’s (the children loved this!). I also planned to spend a week on measurement to break up the amount of focus on number which provided something different for the children to experience something a bit more hands on and exploratory. I then followed onto sequencing numbers and learning greater than, less than and equal to provide further opportunity for children to apply their knowledge of tens and ones and transfer it to a different context which is an essential skill for problem solving (Reys et al, 2012). I introduced children to the idea of the crocodile eating the bigger number through a fun song and then using a PowerPoint for children to come up to the screen and snap the bigger number with their big crocodile arms.

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Outcome

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This was a very successful sequence as it enabled children to apply their new understanding of place value to explain and reason why a particular number was greater or less than another. This was particularly useful when exploring why a number with more ones is still smaller if it has less tens. Additionally, the children were highly engaged in these lessons. They loved the think boards, when I had children on the mat in a mini-lesson with the boards I had other children coming up to ask if they too could use think boards. The lessons were sequenced very effectively as they built schema and provided opportunities for children to connect new learning with their prior learning (Duchesne et al, 2013). By the end of the unit, each of the 5 children who experienced difficulty were able to partition into the teens, with 2 of those being able to partition into the twenties.

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