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Port Ahuriri School: ALiM report

Number of
Year Initial stage
Final stage
Time in programme Predominant
6 4 1 student - stage 2
3 students - stage 4
2 students - stage 5
2 students - stage 4
4 students - stage 5
4x50mins weekly +
1x20mins weekly
Place Value

Key pieces of advice for other teachers and principals who want to accelerate learning for students

The following principles were selected as the major focus for the project at our school.

Arranging for learning – Effective teachers provide students with opportunities to work both independently and collaboratively to make sense of ideas.

Making connections – Effective teachers support students in creating connections between different ways of solving problems, between mathematical representations and topics, and between mathematics and everyday experiences.

Mathematical language – Effective teachers shape mathematical language by modelling appropriate terms and communicating their meaning in ways that students understand.

Allow for a lot repetition when students are learning new concepts.

Lower achieving students need longer to work out problems. They need to use materials when learning a new concept. Once they can successfully solve problems, using materials and without teacher assistance, then move on to imaging and using number properties. It was encouraging when students had an “aha” moment. While using equipment they realised what was being learned.

This is outlined below:-

As the project evolved it was evident that the children had difficulty understanding place value. We spent considerable amounts of time partitioning numbers. We used place value arrow cards, place value blocks, place value houses, flip charts and a place value card game to help learn how numbers are made up. We used mathematical language to describe digits, thousands, hundreds, tens and ones.

We focused on the importance of keeping numbers in columns. Students five and six struggled with the concept, unless completely directed by the teacher. They still require materials to help them partition a number. All other children could image the numbers in their head. All children can now read and say numbers up to 1,000 with confidence. We will continue to focus on larger numbers. Student six made considerable progress with his understanding. This student was so excited about his learning that he was asked to share what he had learned with the principal. He spoke confidently, explaining the digits within the number and showed understanding of how the number was made up.

Arranging for learning

I was fortunate to be able to work in a quiet space away from the regular classroom. The decision to move out of the class was made when it became very apparent that the children in the target group were very distracted by other children. It was highly important to be organised for the learning and have all necessary equipment ready. The children could then discuss their learning with each other without fear of being wrong, or someone beating them to the answer.

At least two sessions a week were held within the regular classroom, so that the rest of the class could see this group having success with their mathematics learning. The target group also helped teach others some of the games they had learned.

At the end of the project the students commented how much fun they had in maths now. They also said that they enjoyed having the teacher for all of their maths lessons, not just for part of it. Within the small group there were ample opportunities for the children to have one on one time with the teacher. It was easy to get around the whole group without having to worry about what the rest of the class was doing.

Allowing for this type of instruction has been most beneficial for the students. Despite some of the children not making big gains, they have all had a real positive shift in their attitudes towards the learning of mathematics.

Key learning points - Use of materials, responding to questions, recording.

  1. It is important that students are taught how to use materials correctly as soon as possible. One of the most interesting factors for me was seeing the children join groups of counters together. They would find the prettiest colours, or make a pattern, rather than focus on joining the groups in a logical sequence.
    All children were provided with a bag of clear counters – two groups of 10 different colours. We used these on number lines, decomposition sheets, hundreds boards and also to make 10s. Children were taught to organise counters into 10s frames when joining sets. Only student one could do this at the beginning of the project.
  2. One of the key issues that needed to be addressed was that the children were often reliant on the teacher providing answers, or were used to other students answering questions quickly so they did not have to think about the question. There was an element of learned helplessness from students one, three, five and six. Students were also very quick to answer questions without actually thinking about what the problem was. There was also a lot of calling out at the start of the project. Children now know to put their finger on their nose when they know an answer. All of the students in the group now understand the importance of letting all members of the group have ample thinking time. They are not distracted by children calling out answers.
  3. Recording of mathematical learning was difficult for most of the students. They need explicit instruction and it needs to be repeated often. I found that I could never assume that the children had learned how to set out an equation. As this wasn’t a particular focus for my group I did not spend too much time on this, however it is something that is important to keep working on with these children.

Profile of the school, teacher and students involved

Port Ahuriri School is a decile 6 school, with 232 students. We identified eleven year 4 students as our targeted numeracy group this year. Of these students, four have been involved in the accelerating learning in mathematics project. The two other students were considered too low to be included in the target group. The target group students were taught as part of the normal maths programme in term 1. Another teacher was employed in term 2 to help the classroom teacher specifically responsible for these students. In July we identified the neediest students from this group for the ALiM project. Three students were excluded from the project because of known absences. We selected six students who were all working at stage 4. These students were still not able to use part-whole strategies to solve mathematical equations. All of the children had difficulty with memory problems.

Students had four sessions a week – a total of 50 minutes each of these days. Each Monday the children also had an extra 15-20 minute session, either by themselves or in pairs.

The teacher involved has had two year's experience teaching at this level, and previously had been working with year 8 students working at stage 7/8 in numeracy.

A short summary of the programme

The main focus of the programme was improving memory and understanding place value. The students were given a diagnostic memory test in the first lesson to ascertain where their gaps were. Students three, five and six could not answer any questions. The other three students could not answer the multiplication questions. Recalling numbers was also a highlighted weakness for most of the students. Students two and four could recall all numbers that were said. At the end of the intervention all children showed significant improvement, apart from student six. He needs to see and hear questions in order for him to have an understanding of what has been asked.

Developing memory was paramount to the success of the students’ learning. Each lesson comprised of at least one memory task. The students played matching games, and recalled basic facts often. A highlight for all of the children was a speed test (see below to download). This was a short test of 25 questions, focusing on basic addition facts. Once this was mastered we moved onto subtraction. We are still working on these facts. The children enjoyed seeing their times and accuracy all improve. They were very competitive, with each other and also within themselves. All students would get very excited when told they were doing the test.

Games also played a major role in the programme. All new learning tasks were followed up with games to reinforce learning. This ensured that students were learning to work with others and also independently.

The use of materials was hugely important. Children were exposed to a wide range of materials. They could choose the materials they wanted to use to help solve problems. If the materials were not appropriate then they were encouraged to try something else. We always tried to use at least two different types of material to solve each problem – so that the children could decide which was easier for them to use.

Active working memory is the ability to remember what you're doing while you are doing it, so that once you've completed a step, you can use this information to move on to the next step. In a way, active working memory allows children to hold together the parts of math problems in their heads. (http://www.pbs.org/wgbh/misunderstoodminds/mathbasics.html) I used this quote as a basis for my understanding of how to approach the accelerating learning intervention with my students. I kept referring back to known facts and problems with the children so that they became more confident by experiencing success.

Click here to download the 'Speed Test' (37kb)