|4||1 student - year 5
3 students - year 6
|3 students - stage 4
1 student - stage 5
|3 students - stage 5
1 student - stage 5/6
How do we accelerate learning in maths for our under-achieving students? What works and why?
We chose one group of students from my year 5/6 class to work with (one year 5 and three year 6). The group consisted of two girls and two boys.
The areas I chose to focus on were:
- doubles to 20
- transfer of knowledge into strategy work
- subtraction more than addition
- compatible numbers to 10, 20, 100, 1,000
- tidy numbers
- repetition and consistency
- moving onto bigger numbers.
I decided that the best intervention to help me with my focus areas was the one advocated by Julie Roberts, developing simple additive strategies to solve addition and subtraction problems.
I took this maths group and I saw them daily for 30 minutes during the study, which ran for 8 weeks. These teaching sessions were held from 10:00am to 10:30am. The children then went away and practised their strategy work, did knowledge activities or played a game reinforcing new knowledge from 10:30am to 11:00am. These daily sessions were taken during the class’s timetabled maths session. On Fridays, I took them for an intensive one and a half hour session.
As well as under-achieving in maths, I also considered other factors when selecting the children for this group, such as attendance, behaviour and self-confidence, and parental support:
- Attendance - None of these children missed a session of their maths time during the project’s duration.
- Behaviour and Self-Confidence -
Before (Teacher Observation):
All of these children were well behaved and were very keen to attend the daily sessions. All of these children didn’t think they were very good at maths. They were all very quiet during group sessions and shy to volunteer their ideas, as they were worried about being wrong.
After (Student Voice):
SACR said, “Before I wasn’t confident at maths. Now I’m feeling good about my maths now. I like doing the different strategies.”
ANCR said, “Before I would say that I got it (the strategy work), even though I didn’t really. I like working in a small group. I like working with bigger numbers now.”
SAKE said, “Before I got frustrated because I always wanted to know stuff. Now I know new knowledge, which is making it easier for me to understand. I know my doubles really well now. It’s helping me with my times tables.”
DRRI said, “Before I wasn’t confident with maths. Now I think my maths has improved and I like working in a small group because I can think.”
- Parental Support - The parents of these children are very supportive and interested in their child’s learning. They were very keen to have their child involved in the study. I have kept them informed via telephone mid-way and at the end of the study.
Effective pedagogy in mathematics
An Ethic of Care
In order to make a difference I had to show my students that I believed maths was important and pull out all stops to do this. The sessions were held at the same time daily and no matter what was going on during the day, maths happened regardless. The children were highly excited to be part of the “Top Secret Government Project” and were eager to be ready for their lessons. The children’s confidence has increased significantly from this project. These children were able go back to their original maths groups and help their mates with activities now – ones that they originally couldn’t do! It was fantastic to see the relationship that these children built together – they were so supportive of each other and wanted to make sure that they all succeeded.
Arranging for Learning
I thought long and hard about the size of the group. I chose four students because I wanted to be able to see quickly whether a child was making connections or needed some individual help. I also chose to have one main focus group because I didn’t want to stretch myself in too many directions. Even within the group the children’s understandings were at different levels so the tasks had to be modified to suit the capability of each child.
I had been keen to have another focus group as well. These were the children who were 'stuck' at stage 4. However, I had concerns in this potential group about the attendance and behaviour of some of the students. I decided to work with one focus group, but I have been able to transfer what I have learnt into working with my stage 4 group, with pleasing results.
Building on Student’s Thinking
Each session started with a quick “warm-up” fun and competitive (but non-threatening) game with knowledge that the children already had. They were always racing against time, me and the other children in the group. I was surprised at the assumptions I had made about the knowledge I thought children already had. I was also surprised how long it took for the children to make this knowledge automatic. It simply does not happen without repetition, repetition and more repetition. The knowledge was also linked explicitly to the strategy teaching. It was really important to keep reminding the children of this – “What knowledge do we have that will help us with our strategy work?”
Worthwhile Mathematical Tasks
I spent considerable time making sure that the activities for the children aligned with the knowledge or strategy being taught. A lot of time was then spent making the resources and equipment to enable me to teach the sessions. Children also took games home to reinforce the learning and this meant more resources. A positive I took away from this is that I now have a wider range of worthwhile mathematical tasks to use with children. If this programme were introduced into schools it would be helpful for teachers to have a selection of tasks to accompany each intervention.
This was an important and relevant part of each session. Just as we are always talking about making connections in our reading, it is vital that children can also do the same in numeracy. We always started with knowledge that the children felt comfortable with before tackling new learning. I spent a lot of time making connections between number patterns and the power of ten!
Assessment for Learning
Overall this was done verbally and was very much “on the spot” assessment of the children’s learning. The programme that I was following enabled me to see progressions quite clearly and allowed me to adapt the sessions as they were happening. In saying that, the Julie Roberts' intervention had a step-by-step structure that I followed for all of my teaching sessions.
Mathematical Communication and Language
Mathematical communication and language evolved as the children started to think of themselves as successful mathematicians. They talked about the purpose of the knowledge they were learning and the strategy they are using. Their confidence also meant they were more eager to share their new learning and to help each other out if they got stuck.
Something that was a major factor in accelerating learning was the variety of material that was available for children to use. We used a range of materials such as number lines, bundles, tens frames, hundreds boards etc. If a student didn’t click using one type of material I tried another. I think an important factor is that the children tend to think that the equipment is for “babies” or that it’s only the teacher who manipulates it. Once they found the material that worked for them I saw them selecting material to use of their own accord while doing independent work. Another spin-off was seeing other students using materials when working independently, after seeing their peers using it.
This programme and the interventions I used have enabled me to have a deeper understanding of the Number Framework, see connections between knowledge and strategy more clearly, and to make my teaching of numeracy more explicit.
So, what worked for Fernworth and what didn't?
- I felt confident in implementing the interventions at my school after the initial two days PD in Auckland. I thought the conference was well thought out and allowed ample opportunity to spend time with colleagues and facilitators. It was great to have the time with your facilitator to plan the initial stages of the study. It was also fantastic to attend the mini-workshops that each facilitator did and to hear first-hand about the intervention, rather than just reading a handout. It would be important that some PD was given to schools if these interventions were to continue to be successful.
- Children achieving success! It was fantastic to see some children move stages (4 to 5) or make measurable gains within a stage (for example to see SAKE go from the beginning of stage 5 to starting to transition into stage 6).
- A huge success was seeing the students gain confidence in their maths and seeing this confidence overflow into other learning areas. These children have also come back to their original maths groups with this confidence and are active participants during group sessions. In some cases they have been “experts” and are now helping out other students who are struggling during independent work.
- Something that was really pleasing to see was the way the children supported each other with their learning within the group. They were eager to see each other achieving success and willing to help each other out with this.
- I had the same teacher doing my release on the Friday, which ensured my class had consistency while I was out.
- My curriculum knowledge and teaching of maths has improved greatly. I feel I have become more explicit in making links between knowledge and strategy. My maths programme is running more smoothly and tighter as a result of this.(Theme 10)
- My facilitator was fantastic. She was always available via email and telephone to discuss next steps with me. She also saw me working with the group at least three times to check how our progress was going.
- I am a second-year teacher so I was out on PRT release every second week. I found it difficult at times to be out of my classroom for two days a week.
- As well as classroom teaching and implementing the exploratory study, I also had other school responsibilities (ICT). At times this was a real juggle and hard to prioritise what was urgent as everything was urgent!
- Term three was an extremely busy one for our school. We had 'book week' in week six, ERO in week seven and other programme disruptions. I had to suspend the programme for a couple of weeks as the release was starting to impact my classroom environment. I found that some of my students' behaviour was starting to deteriorate as some weeks they had three different teachers.
- I felt the ERO visit over-shadowed the study significantly as staff weren’t as interested as they might have been, at another time.