Wednesday, 28 February 2018

Our Journey Begins

My 2018 Inquiry about the role of language in mathematics began with using a maths wall and associated discussions to encourage children to acquire language and participate in such sessions.

My hunch is that by using words frequently in a familiar setting the children will begin to view it as "normalised" and transfer this language to their everyday conversations.  For example in maths we are precise in describing shapes.  A shape is not just "that one" with a vague wave of the hand but "the large yellow rectangle".  This language needs to be taught so that they can understand, read and interpret mathematical terms.

I am hoping to make the children "word smart" as well as "number smart" and confident to explore a simple problem that may arise from a real life situation or a structured activity.  They are expected to work in small groups or pairs with everyone contributing in some way.  They can use trial and error or a mathematical method of solving the problem.  They need to encourage others by listening and responding positively even if they feel the answer may not be correct.  In reporting back to the larger group all answers are accepted and discussed to see what might be the best explanation.

I purposely grouped 6 children into 3 pairs for our first try of DMic maths as I thought it would be easier to have a smaller group to see how these groups worked in pairs and to be able to hear all discussions. 

We have used the maths wall since day 2 of this term so the children are already familiar with different forms of numerals (numerals, dot patterns, finger patterns, groups of objects) and how to justify some shapes.  I used the subitized patterns to introduce a simple problem of how many dots do you see and how do you know.

To begin with the children simply counted one to one with each one confirming that there were 8 dots when sharing, although they counted the dots in a different order.  This is the lowest strategy of simple counting.  I referred back to our maths wall discussion when we had 5 dots and someone recognised it was 4 dots on the outside and one in the middle and asked them to look again at the dots.

One child quickly saw a group of three dots and I watched him put a pencil down the line to show his buddy where it was.  At this point, interest by two members of a group waned and they drifted off but the remaining members were keen to try and find groups.  Trying to describe the groups to their partner, visualise what numbers they were using and hold this information proved difficult so I provided different coloured counters to help them map out their numbers as they were talking about.  This made it easier to describe the groups.

Notation was difficult because they didn't understand how to write it down or that they needed to add the groups together.  We came together to discuss what did they think they needed to do to move from the single groups they had found, to finding the answer of how many dots there were altogether on the page.  The word "altogether" suddenly became important and they remembered a problem we had done about adding up our swimmers and non swimmers earlier in the day when "altogether" meant we added the two groups to find out if we had counted everyone.

One group then went away and found that

4 + 3 = 7

and 7 + 1 = 8

The other group found

2 + 2 = 4

take this 4 and add another group  4 + 3 = 7

then take 7 and do 7 + 1 = 8

The two groups looked and said it was the "same end number"
but group one had a "little" way of doing it (ie it had fewer steps in it.)  They had difficulty trying to explain what they meant but they were able to point to their workings and said how many sums they each had.

I plan to give the groups the same pattern next week to see if they can come up with any further ways of recording this pattern.

Points to ponder: difficulty of notation, making sure children are aware of "maths terminology" so that they know what is required of the problem, keeping interest up and making sure children are paired correctly, discussions - too teacher directed?

Sunday, 25 February 2018

Manaiakalani COL Achievement Challenge 2018.

The Manaiakalani  COL Achievement Challenge that I am basing my 2018 Inquiry around is to lift achievement in maths of my Year 1 students.

My inquiry will focus on the role of language in mathematics and how this language can be "normalised" and transferred into other areas of the curriculum and relates to their everyday conversations and usage.

Year 1 students often lack the verbal tools to begin to look at a maths problem or to justify concepts of how they solved a problem so they are less likely to participate in a maths lesson, remaining silent or shrugging their shoulders and therefore do not make as much progress in maths as they are capable of. 

They switch off saying they "can't do maths"  but what they really mean is "I can't find the right words to explain what I am suppose to do and how I did it."

I propose to look at the role of language in mathematics and how I can support my students to acquire this language and thinking that they need to raise their achievement.

Friday, 26 January 2018

Raising Maths Achievement.

2018 Professional Development: Developing Mathematical Inquiry In a Learning Community.

Pt England staff were privileged to begin 2018 with professional development taken by Dr Roberta Hunter.

Dr Hunter gave us the startling fact that "62% of Maori and Pacifica students are failing Maths."

But she also gave us hope that if we radically rethink the teacher's role, and tap into the richness that each child brings to school, these children can raise their achievement levels and be successful at maths.

"Every child is good at maths - it is how they are taught that makes a difference."  (Dr Hunter)

To develop this "culturally tailored approach" of getting to know the children's cultures and how culture impacts on their learning will be a first step.  The need to see the children's culture as a strength and a part of maths which can allow children to connect with each other and see inside each others worlds is an important beginning.  Providing a problem that centres on a particular culture allows a quiet student to open up, show the other children how the problem would be looked at in his culture and be the centre of an explanation.

The children work through culturally based "group worthy" problems.   If the problem can be solved by an individual it is not "group worthy".  These groups are carefully selected and are not based on ability - something we often overlook as we test and group children according to ability in the belief that they learn and work better with similar peers.

After launching and making sure the children understand the problem, they talk, ("friendly argue") discuss, question and reason their way through the culturally based real world problem to come up with a logical answer.  Children are given the tools they need to help solve the problem.  If the problem requires multiplication and they do not know their times tables a sheet may be given.  The teacher does not give a solution but gives the tools needed for the children to discover a solution.

They are all "drivers" not "passengers" with all students expected to participate, contribute and learn.  Inclusion is a key factor.  Getting all children to actively participate and be able to offer explanations, even to think back to how they solved a previous problem and use this knowledge makes maths sound exciting.

This raising of maths achievement takes time - it is a journey that has its ups and downs but if it can engage our children and help the children see that they can reach and achieve higher levels I am excited to be able to take part in such a journey.

Monday, 4 December 2017

Reflections on 2017 Maths Inquiry

I began my maths Inquiry this year wanting to find ways to strengthen and develop children's number knowledge and strategies to provide a good foundation for the development of future stages.

Number identification was the main focus to begin with so that children could read, sequence, rote count, and record the numbers 1 to ten.  For some students, language was a difficulty in developing "number sense" and I looked at ways to help these students with games, physical movement, concrete manipulatives, subitising and iPad activities.  Once the students started to gain number identification we moved on to solving number problems using various strategies.

Solving number problems provided lots of opportunities to talk.  Group work with friends was important for some children to gain confidence at explaining their findings without the pressure of performing in a whole class situation.  They talked about the strategies they used, compared answers and worked out who was more likely to be correct by sharing their findings all the while building up their essential skills and language needed for a good foundation.

I hope to able to use the information I have gathered this year to give my next years learners a head start.  I plan to use a maths wall from the beginning of the year to provide the children with the "verbal tools".  By purposely exposing the children to mathematical language repeatedly and posing everyday maths problems I hope that the children will see how they too can use the strategies such as skip counting to solve problems. And they will see that numbers are not just used in maths time but are an important part of our lives.

Being more aware of aspects that children found difficulties with such as sequencing, ordering and making sure objects to be counted are in an ordered pattern has made me more aware of thinking of and providing lots of different types of opportunities for learning.

Data has been gathered by the formal JAM testing and has provided further information.  There has been mixed acceleration in the priority group (as can be seen from the data) with some being significant by moving through the stages while for others even a minor change in a stage has still been significant for them.  But the overall growth in confidence, the willingness to explain and give things a go, to use mathematical language and make connections show the children have made a good start in laying solid foundations for their maths learning.

Friday, 24 November 2017

Accelerated Shift

A quote from John Hattie about "the collective self perception that teachers in a given school make an educational difference to their student..." led into a discussion about what visible strategies did we leverage Learn, Create, Share to enable shift in our students.

Team one began their discussion thinking we did not have as much accelerated shift as other areas in the school.  We then started to think about where our students are at when they start school.  Typically,  they begin school with less language and knowledge than other 5 year olds and they have "to run to catch up".  To achieve what they do in the first year means there is shift.  To move from Stage 0 through to Stage 2/3 or even Stage 4 means they do achieve accelerated shift.

Ways in which this is achieved is through knowing your learner and how they learn, creating EE's with the learner in mind- using sound bites to make it easier for those that find reading a barrier, supporting the learner and repeating activities if necessary, using personal refections and planning accordingly.

Visible evidence of how the learners are supported include sharing on airplay, peer to peer sharing, sharing with a group and sharing with the teacher.  As language is gained, the confidence to share instead of a shrug become greater.

The main data that shows evidence other than a child's EE that they have done is through JAM testing.  A child at the beginning of the year would not participate in any of the discussions.  He scored Stage 1 for number identification.  By June he had accelerated to Stage 3 and by November he is at Stage 4.  He has gained so much confidence that he readily joins in discussions being one of the first to put his hand up.  This shift is huge when one thinks where they have come from over a period of 10 months.

Sunday, 29 October 2017

Maths PD with Jo Knox.

After our previous Maths PD with Jo, Team One had asked to see a modelling session of rich addition and subtraction tasks to develop strong foundations to build on and to use to extend more able students.

Jo often uses books to introduce the theme.  This time she used a book with the intriguing title of "One is a snail, Ten is a Crab" By April Pulley Sayre and Jeff Sayre illustrated by Randy Cecil.  It is a humorous and colourful way of looking at part-whole thinking.

The book is a "foot counting" book so it uses the number of feet on various animals or people to denotes the numeral - a snail is 1, a person is 2, a dog is 4, an insect is 6, a spider is 8 and a crab is 10 (including its pincers).  So 40 can be 10 dogs (10 x 4) but also 6 insects and a dog (6 x 6 + 4)

She talked us through the book and then introduced the book to a group of children who had not previously read the book.  She also had pictures of these animals and people prepared to use after the reading.  The children were able to see that the snail was the number 1 because it only had one foot.  Two was a person, then they were asked what numeral a number 3 was.  The children counted 3 feet so they quickly saw that a snail (1) plus a person (2) made 3.

After introducing all the numbers up to 10, the book jumps up to the number 20.  By the time Jo reached the page about 90 an immediate reply was given.

Jo posed a question about 4 feet - what pictures could we use?  A child responded with "A dog" and was given the task of writing the numeral 4 underneath it.  Jo then draws out their thinking by asking could 4 feet look any different?  She shows a person.  The children discussed, counted, checked and gave reasons, and wrote the numerals with Jo adding the addition and equals symbols.

By the end of the lesson the children have learnt how to make 6 in different ways.

A group of older children also worked with Jo using the same book.

We discussed ways in which we could extend the lesson for more able students to include skip counting and multiplication.  We also looked at the NZ Maths site to become familiar with their resources, and Jo suggested using other books to introduce and reinforce number concepts and strategies.

Monday, 25 September 2017

Sharing is Fun

I have continued to use the problem solving approach for maths with our new topic of fractions.  We have used both everyday problems that have arisen opportunistically or more planned situations to get the children talking and involved in maths.  It is an important way of learning because the children are motivated to use their previous knowledge to solve a new problem and to try out different ways of solving problems successfully.

They respond to both real and imaginary problems using book characters or toys they can relate to.  Feeding the toy animals a quarter of the food, or sharing out the class fruit equally are problems that they feel they can help solve.  Discussing how we can solve the problem when sharing is not equal leads to some imaginative thinking such as two children might not like milk so that would give enough to share equally, or the fruit might need to be cut up and then the discussion centres on how to cut it up so that there is enough to go around.  Would halves be enough or would we need to cut the fruit into quarters?  Would they get more than one quarter?

The children are enjoying the "Maths warmup" whereby we go over many of the mathematical topics we have covered this year.  It is like a quick review and helps to remind them of strategies they can use when they are looking for a solution such as counting in two's, distributing and redistributing, measuring, doubles and so on.

Some children still prefer to let others do the talking so it is important to monitor this.  Sometimes a quick discussion with these children on a one to one basis is helpful or just saying we need to give these children more "thinking time" during the discussions gives them more confidence to offer solutions.  One child coming up with an inventive solution which is accepted helps others find new ways.