# Susan Dwyer

## Monday, 7 August 2017

### "When Are We Doing Maths?"

In a recent discussion at our team meeting we looked at the idea of making Maths fun and meaningful using problem solving. My Inquiry topic is maths based and the Geometry and Measurement topics we are doing this term lend themselves well to developing children's natural problem solving abilities.

The children work in groups or with a buddy exploring a simple activity that can arise from a real life situation in the class or a structured activity to support the topic. They are able to use trial and error methods or a more structured mathematical way of solving the problem. All answers are accepted and evaluated to see which answers might be a better explanation.

I hoped that this approach might also have a positive outcome of getting children talking more by being able to describe what they are doing and how they came to a conclusion. There is a lot more talk during our problem solving sessions. By being with friends they are more comfortable at attempting to put their thoughts together and take more risks in exploring other avenues. Finding the right words is often a problem for our children.

The children are now learning to think about maths not just as "doing Maths" using the basic mathematical processes but as useful knowledge to use in a wide variety of different situations and to see the different areas of maths are all connected.

For me it has meant that I need to think about the questions I ask. Do the children do most of the taking? How do I answer children's comments? How do I encourage describing, reasoning and getting children to explore the context further? How can I create opportunities for problem solving as well as using opportunities as they arise?

The children appear to be engaged, they are willing to give the activities a go and they are involved.

## Monday, 24 July 2017

### Developing Number Properties

End of Term 2 Maths Inquiry

Most of the children have developed an understanding of, and can discriminate between, the properties of number - ordinality, nominal aspects as well as cardinality.

They can use this "information" about ordering things to find solutions. They have an understanding that the number line is a pictorial representation of ordering numbers. To do an addition it means increasing the number so they move to the right to increase the magnitude of the number. To answer the number sentence 3 + 2 = they can find the third number on the number line and make two jumps to the right to find the answer is 5.

Similarly to do subtraction or to make something less by taking away means to move to the left or make numbers smaller. Subtraction has been the more difficult concept to teach as the children didn't see straight off that it was the reverse of addition. It was something I needed to teach them. They also find it more difficult to find a number before or to "count down".

Some children are able to solve simple addition and subtraction without symbols. They can orally state what they are doing or they can use manipulatives. With practise they are beginning to rely less and less on manipulatives or fingers.

They also have an understanding that a number can also be a label to distinguish an item. The bus is number 625 or a phone number is 579 3654.

Counting a variety of objects into different sized sets has helped the children develop an understanding of cardinality. Counting the same sets several times starting from different objects has developed their understanding that the number in the set stays the same unless you add or take away some objects.

A small number of children are still struggling with these three aspects. The number line being a visual representation and the corresponding mental representation to work out the magnitude of number remain a mystery. Difficulties with sequencing or ordering is not only with Maths.

We continue to use a variety of examples with songs and chants to learn numbers, to use opportunities through out the day to count items and answer the question "How many?", use guided as well as independent opportunities to practise of counting, use dice and dominos to look at groups, get students to verbalise their strategies and use visual representations. Monitoring their learning is still an important part of helping those with weaker skills.

This does raise the question would some students benefit from intensive one on one help - a "Maths Recovery" series of lessons like the Reading Recovery programme?

Most of the children have developed an understanding of, and can discriminate between, the properties of number - ordinality, nominal aspects as well as cardinality.

They can use this "information" about ordering things to find solutions. They have an understanding that the number line is a pictorial representation of ordering numbers. To do an addition it means increasing the number so they move to the right to increase the magnitude of the number. To answer the number sentence 3 + 2 = they can find the third number on the number line and make two jumps to the right to find the answer is 5.

Similarly to do subtraction or to make something less by taking away means to move to the left or make numbers smaller. Subtraction has been the more difficult concept to teach as the children didn't see straight off that it was the reverse of addition. It was something I needed to teach them. They also find it more difficult to find a number before or to "count down".

Some children are able to solve simple addition and subtraction without symbols. They can orally state what they are doing or they can use manipulatives. With practise they are beginning to rely less and less on manipulatives or fingers.

They also have an understanding that a number can also be a label to distinguish an item. The bus is number 625 or a phone number is 579 3654.

Counting a variety of objects into different sized sets has helped the children develop an understanding of cardinality. Counting the same sets several times starting from different objects has developed their understanding that the number in the set stays the same unless you add or take away some objects.

A small number of children are still struggling with these three aspects. The number line being a visual representation and the corresponding mental representation to work out the magnitude of number remain a mystery. Difficulties with sequencing or ordering is not only with Maths.

We continue to use a variety of examples with songs and chants to learn numbers, to use opportunities through out the day to count items and answer the question "How many?", use guided as well as independent opportunities to practise of counting, use dice and dominos to look at groups, get students to verbalise their strategies and use visual representations. Monitoring their learning is still an important part of helping those with weaker skills.

This does raise the question would some students benefit from intensive one on one help - a "Maths Recovery" series of lessons like the Reading Recovery programme?

## Tuesday, 16 May 2017

### Cardinality "Under Construction"

My inquiry topic to help move children from stage one to stage two is still "under construction". As with building real buildings gaining knowledge for some requires an ordered process of laying down one brick at a time and not just pouring a large slab of concrete and seeing a building suddenly appear.

I am building up the number knowledge and number sense of those who have not yet fully grasped the idea of cardinality and therefore can not move on to addition and subtraction. Some children have moved from rote counting "onetwothreefourfivesix..." to assigning a value to the words and connecting one word to one object. Others are working on counting the number in a set only once and I have found putting these sets into a regular pattern or order helps these children. Irregular or scattered patterns leads to double counting. Another block some children still need to overcome, is that a number is always the same no matter where it is or the size or colour of the objects.

I am building up the number knowledge and number sense of those who have not yet fully grasped the idea of cardinality and therefore can not move on to addition and subtraction. Some children have moved from rote counting "onetwothreefourfivesix..." to assigning a value to the words and connecting one word to one object. Others are working on counting the number in a set only once and I have found putting these sets into a regular pattern or order helps these children. Irregular or scattered patterns leads to double counting. Another block some children still need to overcome, is that a number is always the same no matter where it is or the size or colour of the objects.

We continue to practice and enjoy maths even though progress it is at a slower pace for some.

## Monday, 3 April 2017

## Sunday, 2 April 2017

### Growing Number Knowledge

Over the past six weeks, I have been using activities to strengthening and develop the children's number knowledge and strategies to provide a good foundation for the development at further stages. I have focussed on number identification so that they are able to read, sequence, rote count and record the numbers 1 to 10. And the second focus has been on forwards and backwards number sequences. Both areas are part of the number framework.

I am using a wide range of activities such as playing games, going on a number hunt and taking photos of groups of objects and putting them in order, iPad activities, puzzles, dot to dot, choral chanting or rote counting, poems and taking any opportunities during the day to count and record numbers.

The early number activities were done with concrete objects so the children could physically manipulate the objects as they counted. This reduced the task of learning to count to an enjoyable activity where the manipulative objects were used as "thinking tools". For example the Cliposaurus activity reduces the amount of recording for children but still required the reading of numbers.

The children enjoy choral chanting and clapping as a maths warm up so most are able to correctly say the number sequence to ten. Some children are still struggling with written recording so this is still a part of our daily practise.

Physical activities are enjoyed by the children where they pretend they are a given number and need to line up by finding the number that goes before them and checking who comes after them. This physical moving is helping them with the concepts of before and after which they are finding tricky.

I have found that games provide a fun way to practice their number knowledge that meet a specific mathematical purpose. The children learn to explain and justify simple concepts such as in the game "What is the Missing Number?" by justifying what comes before or after or by checking against a number line.

The children need to become proficient "doers and learners" to make sense of numbers and help them think for themselves.

I

I am using a wide range of activities such as playing games, going on a number hunt and taking photos of groups of objects and putting them in order, iPad activities, puzzles, dot to dot, choral chanting or rote counting, poems and taking any opportunities during the day to count and record numbers.

The early number activities were done with concrete objects so the children could physically manipulate the objects as they counted. This reduced the task of learning to count to an enjoyable activity where the manipulative objects were used as "thinking tools". For example the Cliposaurus activity reduces the amount of recording for children but still required the reading of numbers.

Children manipulating cut up numbered pictures |

The children enjoy choral chanting and clapping as a maths warm up so most are able to correctly say the number sequence to ten. Some children are still struggling with written recording so this is still a part of our daily practise.

Physical activities are enjoyed by the children where they pretend they are a given number and need to line up by finding the number that goes before them and checking who comes after them. This physical moving is helping them with the concepts of before and after which they are finding tricky.

I have found that games provide a fun way to practice their number knowledge that meet a specific mathematical purpose. The children learn to explain and justify simple concepts such as in the game "What is the Missing Number?" by justifying what comes before or after or by checking against a number line.

The children need to become proficient "doers and learners" to make sense of numbers and help them think for themselves.

I

## Tuesday, 21 February 2017

### Moving On - Maths Inquiry 2017

Our school wide Inquiry this year is focused on mathematics. Research results have shown we are achieving acceleration in reading and writing but it is time to turn our attention to maths to see if we can also achieve more acceleration in this area.

As I am a teacher of Year one children just beginning their mathematical journey it is important for the children to develop a sound number knowledge and strategies.

My inquiry will centre on a group of children who find difficulty in moving from stage 1 (counting one to one) to stage 2 (combining sets - adding and subtracting). They can count and form sets of objects up to ten but they are unable to solve simple problems that involve joining and separating sets like 3 + 2. They can count the 3 counters in one hand and the two counters in the other but when asked how many they have all together they say "three two".

This raises questions such as what strategies can I use to help these children? How can I strengthen these children's understanding? What key items of knowledge do the children need to developed? What learning activities can I select and implement that will aid these children? Would using manipulative equipment be more useful than iPad activities?

The beginning of this journey will involve an in depth look at reviewing their present knowledge to see what number knowledge they have and then working on activities to strengthen their understanding within the stage. This information, along with current literature and colleague's advice, will help me formulate an action plan for my teaching inquiry.

As I am a teacher of Year one children just beginning their mathematical journey it is important for the children to develop a sound number knowledge and strategies.

My inquiry will centre on a group of children who find difficulty in moving from stage 1 (counting one to one) to stage 2 (combining sets - adding and subtracting). They can count and form sets of objects up to ten but they are unable to solve simple problems that involve joining and separating sets like 3 + 2. They can count the 3 counters in one hand and the two counters in the other but when asked how many they have all together they say "three two".

This raises questions such as what strategies can I use to help these children? How can I strengthen these children's understanding? What key items of knowledge do the children need to developed? What learning activities can I select and implement that will aid these children? Would using manipulative equipment be more useful than iPad activities?

The beginning of this journey will involve an in depth look at reviewing their present knowledge to see what number knowledge they have and then working on activities to strengthen their understanding within the stage. This information, along with current literature and colleague's advice, will help me formulate an action plan for my teaching inquiry.

## Monday, 13 February 2017

### New Beginnings in a New Year - 2017.

It is the beginning of a new year with a group of 17 year one students. I am delighted to be teaching year one students again and to be taking the first steps in their learning voyage with them.

The focus this year is that "we are voyagers." It is fitting to think about navigating through our learning journey. We need to know who we are, where we come from and where we are going to.

Most of the children in Room 16 this year have previously spent a few weeks at school at the end of last year so they have a sense of belonging to Point England already. They are enthusiastic to get on with their learning voyage again. We have been getting into new routines and getting to know each other.

We look forward to sharing some of our adventures through our class blog.

The focus this year is that "we are voyagers." It is fitting to think about navigating through our learning journey. We need to know who we are, where we come from and where we are going to.

We look forward to sharing some of our adventures through our class blog.

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