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Gracefield School: ALiM report

Number of
Year Initial stage
Final stage
Time in
9 2 5 students - stage 2
4 students - stage 3
9 students - stage 4 3x30mins weekly
6 weeks

How do we accelerate learning in maths for our underachieving students?

Gracefield School was asked to take part in a trial study with the aim of accelerating underachieving students in mathematics. Gracefield School is a small city school, decile 4, with a roll of approximately 230 students. The school was in its second year of in-depth refreshment in numeracy. As the lead teacher of numeracy, I was given the opportunity to participate in the project. Upon reflection, this has had a powerful impact on my classroom teaching and my professional ability to support staff in raising student achievement levels of numeracy throughout the whole school.

After looking at all the data available, it was decided to focus on the year 2 group as:

  • there was a substantial group in the at-risk (stage 2) and cause for concern (stage 3) group after two terms as year 2 students
  • it was thought that early intervention (like Reading Recovery) would put them back on track to achieve at the expected level during the rest of their time at school.

Children who were on the Reading Recovery programme, or who were working with the RTLB were not included in the study, as they were already having withdrawal times during the day. This meant a group of nine year 2 children were chosen, five girls and four boys. The group was made up of seven Maori, one NZ European and one Asian.

Programme structure

The programme was run three afternoons a week for 1½ hours on a Tuesday, Wednesday and Thursday for six weeks. This was to allow the children to still receive their mathematical programme in the classroom in the morning, while supplementing their mathematical learning, based on their needs identified from the NumPA.

The students were divided into two groups taught each session for ½ an hour, with ½ hour at the end for reflection and planning. This final half hour was crucial, as it allowed me to evaluate and reflect on each child’s progress during the session and prepare for the next lesson. Each session was structured in 10 minute blocks – counting, memory and strategy.

The aim was for all students to be at stage 4, advanced counting, by the end of the six week block. The emphasis was on meaningful tasks, with a focus on fun alongside learning. Most of these students had come with a lack of confidence in their mathematical learning and the focus was to increase their confidence and self belief that they could solve problems by themselves.

It was important to have a space set aside for the programme, with resources organized to be available as needed. One session was spent setting up the resources and room, making it a welcoming area where the students’ work was on display. The students enjoyed coming in and seeing displayed what they had worked on during the previous sessions and would often ask to have their current work copied for the wall.

There was a need to be flexible within the programme. At times, instructional decisions within a lesson were made, based on student responses, which meant what had been planned sometimes did not occur. Following a conversation with an advisor part-way through the programme over concerns regarding two students, it was decided to work with these students for a couple of sessions on their own. This decision was based on a need for a more in-depth and individualised focus on specific pieces of knowledge.

Whilst there was good progress for most students in both strategy and knowledge, barriers to learning were encountered. Student H was absent, due to sickness, for many sessions, and this is reflected in her knowledge results. Student A didn’t always want to leave the classroom to attend and often came with a negative attitude and would not actively participate. A reward system was introduced, which helped a little with this attitude problem. The other students loved coming and were upset if the sessions were not on that day. When the principal came to observe a session, he noted…

“I have never seen Student F so motivated…”

Both classroom teachers of students involved in the programme observed a change in the behaviour of all the children during class mathematical sessions. No longer would these children sit back and pretend not to be in the classroom. Now, when questions were asked, they often were up on their knees in their eagerness to contribute. They are now at the front of the class and amongst the first to answer problems.

Parents have noticed a change in their children as well. Some parents wrote:

“I thought this programme was really good for Student B and am really proud of B for participating in this programme. B likes the maths programme and wants to do it again to learn more.”
“C has a greater understanding of maths now, so maths has become more enjoyable. The improvement I have seen is C is quicker at answering questions which has boosted confidence.”

Key points of advice

Engaging Learners

These students had come to the sessions with a lack of confidence, thinking they were no good at mathematics. It was important to engage them through activities that were hands on, fun and motivating. Often we would use little teddies as an incentive for work and the students loved them. We would make up little stories about the teddies and use them as rewards for attempts at answers, answering a question and proving how they got that answer. There was a noticeable shift in the learning climate within the group to a safe, caring place where it was okay to make mistakes, because everybody was a learner, including the teacher. This positive attitude towards mathematics transferred into the classroom and these students became more focused and engaged within the class.

“A positive attitude raises comfort levels and gives students greater confidence in their capacity to learn and to make sense of mathematics.”
(Anthony, G. & Walshaw, M. 2009, p.8)

Meaningful tasks

To keep the children engaged and focused, it was important to keep the tasks short and meaningful. Activities were very hands-on (high use of equipment, games and student recording) and placed in contexts relevant to the students. Often students were coming up with the problems themselves.

Tasks were designed for working in pairs, with students discussing the answers with each other before sharing with the group. Their confidence in this grew during the sessions, and by the end of the programme, it had become automatic to turn to their partner to share their understanding.

Student conversations started to focus more on making sense of the mathematics they were learning and this fostered their understanding.

Tasks and learning experiences that allow for original thinking about important concepts and relationships encourage students to become proficient doers and learners of mathematics.”
(Anthony, G. & Walshaw, M. 2009, p.13

Embedding new learning

A key aspect, I noticed, was the importance of revisiting key new learning on a regular basis. Don’t expect it always to be secure. For example, having focused on place value of tens and ones for several weeks, later on, when working on this concept again, it was evident several students did not have secure understanding. It is important to revise prior learning on a regular basis. Some ways to achieve this are: through home tasks, informing the classroom teacher to include it in their group learning, the use of games and a weekly revisit within the accelerated learning programme.


The aim of the study was for all students to be at stage 4, Advanced Counting, by the end of the six week block. The intensive work with the students meant this goal was achieved, although it remains to be seen if these results can be maintained over time. Without the opportunity to work intensively with these children who were not succeeding in the class, the question remains, what stage would they have reached by the end of the year without intervention?


Anthony, G. & Walshaw, M. (2009). Effective Pedagogy in Mathematics. International Academy of Education: Educational Practices Series, 19. Geneva: International Academy of Education. Available at http://www.iaoed.org