Number of students 
Year  Initial stage Add/Sub 
Final stage Add/Sub 
Time in programme  Predominant Focus 
8  7/8  2 students  stage 4 6 students  stage 5 
7 students  stage 6 1 student  stage 7 
2x1hr + 2x30mins/week  Add/Sub strategies Fraction knowledge 
Selection of students for the pilot was determined by mid year GloSS results for the whole school. These results were analysed and the area with the greatest number of students falling below national expectation was identified. We identified year 7/8 students still working at stage 4 and 5 in addition and subtraction, meaning they were at least two stages below expectation for their age. As we had 25 students in this category we then consulted with classroom teachers regarding behaviour and attendance issues and finally selected a target group of 8 students. We set up one hour sessions on Monday and Tuesday and half hour sessions on Thursday and Friday as we wanted to work with them regularly over the week. These lessons were also arranged to be in addition to students’ regular classroom maths programme and not in place of it.
In addition to working directly with students, I also set up fortnightly meetings with the senior syndicate where I could work with the students’ classroom teachers. In this way I could demonstrate activities and materials that could be used in their regular mathematics programme. This enabled me to build a link between our group work and students’ classroom maths progamme. It also encouraged the use of materials in these senior classes as there was still some resistance to, and lack of familiarity with, this from our intermediate teachers. Classroom teachers also took the opportunity to sit in on our sessions. This was both a behaviour management strategy, and a means of demonstrating to students the value their teachers placed on this programme. There was, as a result, a marked improvement in student engagement and attitude from what had been a rather difficult group of students. It also helped to reinforce the link between our work and their regular classroom. (Theme 2)

After looking at the data the biggest gaps for students appeared to be in addition and subtraction strategies and number knowledge around fractions and decimals. So I decided to structure our sessions with strategy, knowledge and then a game. Focus was given to making connections, tools and representations and to mathematical language.
Making connections
In strategy we looked initially at reversibility as it pertained to subtraction, for example 64 – 29 = __, and how it could be reworked as 29 + __ = 64. This was demonstrated using number lines. Once students became confident with this we then looked at applying the same concept to fractions. ¼ of 28 = 28 divided by 4. Then when we looked at fractions we made links to decimals, percentages and multiplication.
Tools and representations
We also focused on using materials and students “proving” their answers to others with equipment and clear explanations. Also because of the age group, I felt it was especially important to “keep it real” to both engage and extend students. Therefore, wherever possible, we used real life examples and materials such as shopping coupons and tape measures.
Mathematical language
Another focus was developing mathematical language. Initially, when I worked with the students, they were unfamiliar with mathematical terms, which made it difficult for them to explain their thinking as they lacked specific terminology. As students became more familiar with maths vocab their explanations of their thinking became much more succinct. I found the two factors that appeared to most aid the students' learning was their increased familiarity with materials and vocab, as they could then both demonstrate and explain their thinking. This gave the students great confidence in what they were doing and they became increasingly able to identify where things may have gone wrong and were then able to selfcorrect. (Theme 8)

The biggest change for students was a change in attitude. These were all students who had experienced difficulty with maths and as year 7/8 students these difficulties had persisted for many years. Most of them therefore had a very strong opinion that they were “useless” at maths and that they just “didn’t get it”. In one of the earlier sessions students were asked to rate their effort and attitude to the lesson. One student gave a very honest response of 1 out of 10. In the last few weeks of the programme this student was able to honestly give herself a rating of 10! As she experienced success she became increasingly enthusiastic and went from being reluctant to participate to being focused and excited about her learning.
Strategy domains
Addition and Subtraction
Rationale: many students showed in NumPA that when solving 53 – 26 they partitioned tens and ones but reversed 3 and 6 to 6 and 3 which showed a lack of number sense. They also tended to rely on counting back from 37 to solve 37 – 9, rather than partitioning.
Initially the key focus was around building understanding of reversibility, and the use of the number line to solve authentic subtraction problems. It took about four weeks to really embed this strategy as most of the students still relied on breaking into tens and ones and they needed to be reminded to use the numberline. To avoid this reliance on place value, we used increasingly large numbers so they had to draw their number line. As this strategy was mastered we then explored using rounding and compensating as it could be applied to both addition and subtraction and later looked at the same strategy as it applied to multiplication.
Another element we looked at was estimation, firstly with whole numbers and then with decimal numbers. It was apparent that students would sometimes fire off answers that were wildly inaccurate and needed to check if it was even in the realms of possibility.
All students moved 1 or 2 strategy stages. Achievement overall was pretty uniform.
Next steps for this group would be to develop their place value understanding so they could apply these strategies to decimal numbers with understanding.
Proportions and Ratios
Rationale: to help students solve problems that involve fractions or decimals.
Test results showed that this was for many students their weakest area. When talking with them, they identified understanding of decimals as what separated them from their more capable peers. Initially I tried to introduce decimals but it became evident that they first needed to do a lot more work on fractions.
Initially we looked at improper and mixed fractions, using materials to demonstrate how 5 halves was equivalent to 2 ½. After this learning was consolidated we moved on to equivalent fractions and later to decimals.
Although students became confident reading fractions and decimals confidently, their next step would be to apply this knowledge to problem solving and record their thinking as equations.
Results showed students now at least at stage 5 and one as high as stage 7, which was again significant progress for all but one student.
Multiplication and Division
Rationale: To help students to solve problems where the factors had more than one digit.
A minor focus for this group (four teaching sessions) was on multiplication. This was to help reinforce work we had been doing on rounding and partitioning, and was also because students had identified the need to be able to solve multiplication problems to be “good at maths”. All these sessions were around developing an understanding of the distributive property.
Although three students did not show any strategy stage movement, the other 5 students moved up between 1 and 3 strategy stages.
Katrina Day
Rangikura School