|7||4||7 students - stage 4||7 students - stage 5||4x40mins
The data shows that the group are now working “at expectation”, but within this group, there are still differences in levels of confidence and security of concepts.
Children generally enjoyed coming to maths sessions. They were keen to take home games to improve their learning.
For some, an improvement in maths ‘self-image’ was very noticeable. This was most obvious when students were confidently sharing their thinking within the group.
Key pieces of advice for other teachers and principals who want to accelerate learning for students below the standards in their school
Making connections - don’t make assumptions
Children needed support to see the links between mathematical ideas. This seemed more evident with a group of under achieving students. It was important to always provide a range of equipment and model different ways to record their thinking. The ‘light went on’ for different students at different times, using different materials.
It was surprising to notice the lack of connections between ideas for some students. A student, who knows 7 + 7 = 14, doesn’t automatically know what half of 14 is, or just because they know 6 + 4 = 10, they may not know what 10 - 4 is. Student C instantly recalled the answer to 7 + 7, but when asked, “What’s half of 14?”, said “4…no, 10”.
Student T still is confused with the concept of ‘before’ and ‘after’.
Most of the group did not apply the commutative property. They knew addition facts to 10, but subtraction from 10 was like a whole new concept for some. It seemed to me that these children who needed accelerating had gaps in their learning which were crucial to making any further progress.
As teachers we assume that children have these links because we have taught them, but the connections are not necessarily there. They need repeated exposure to them in order for the links to be maintained. What has been taught isn’t necessarily what has been learnt.
Knowing the students
When working with a small group, withdrawn from the distractions of a whole classroom, and with specific time allocated to the small group, it is possible to learn more about exactly where individuals are at, and it becomes more possible to accelerate their learning. Things that were not obvious right away became obvious as I was able to listen closely in an uninterrupted environment and observe students playing games, discussing with partners, etc. For example, basic facts knowledge; students may have answered the questions correctly in the NumPA test, but did they really know them all? We listed Make Ten facts together and students answered ‘make ten’ facts correctly over several days, but when playing the Make Ten game, I was surprised to hear several students making incorrect statements when rolling the dice. For example “5 + 3, that makes 9” and the partner playing did not notice that it was incorrect. It was obvious that facts to 6, 7, 8, and 9 were not secure at all. I may not have noticed this in a whole class situation, especially if the game from a group box was played independently. I assumed if they knew facts to 10, then they would know the rest.
The children had lots of additional opportunities to share and explain maths thinking. Their confidence and clarity when explaining answers improved a lot. Students were so willing to share and they would argue about wanting a turn. In their own class maths groups, they may be the ones who sit back, processing slowly, and be hesitant to share.
The group had more group teaching time (four x 40 mins) than they would normally have in class group rotation (two x 15 mins per week).
Allow lots of practice time and time for maintenance.
What some children knew one day could be gone the next day. They needed lots of practice and revisiting of basic facts and place value activities to consolidate these, and couldn’t move forward with strategy learning until this was secure.
It struck me how much the group enjoyed playing ‘easy’ games. They said they liked coming to maths with me because it was ‘easy’. By easy I think what they were really feeling was that the games and learning was achievable for them.
Short profile of the school, teacher and students involved
Stanmore Bay School is a year 0-6 primary school in the Hibiscus Coast region with a roll of 420 students, and a decile rating of 8.
The target group consisted of three boys and four girls at year 4 with regular attendance, who were working within stage 4, advanced counting and below expectation. These children have five maths sessions per week and also have three days of number and two days of strategy with their own teachers in their classrooms. The teacher involved with the study is an experienced teacher who usually teaches at year 3 and is a member of the maths curriculum team in the school.
Outline of programme
The students worked with the teacher for seven weeks of four x 40 min sessions. Students were withdrawn to a quiet classroom environment. Children missed the first part of their own class maths, but were back in own classes for second part of maths and group teaching time, when possible.
Making (PV based)
---- All leading to knowledge
The programme was based on two main ideas:
- Improved MEMORY through memory activities and games (Deb Gibbs' ideas).
- TARGETED LEARNING GROUPS - using consistency and a very structured knowledge-based lesson framework. This was based on Marilyn Holmes' work, but adjusted to suit the needs of the target group, and included some strategy teaching (Julie Roberts' & Kaylene Wright’s ideas).
The lesson framework was adjusted slightly each week due to time constraints and according to students’ progress and needs.
The group enjoyed the structured lessons which helped them feel secure in their learning.
Children were given opportunities to work independently or with ‘talk partners’ when solving problems. Lots of the sessions involved sharing of solutions, and listening to others. Confidence when sharing was noticeably improved after seven weeks, as was the use of maths language (‘make ten’, ‘tidy number’, etc).
In addition to lessons, a letter to parents went home briefly explaining the programme, and children had the opportunity to take home maths games to practise. Most, but not all, chose to do this regularly. Student M made her own maths folder which she filled with facts, problems she had given herself, and examples of different strategies.
Individual numeracy knowledge profiles were adapted and kept in a clearfile, and next learning goals regularly discussed, dated once achieved, and stickers used. These have been given to classroom teachers to continue the learning and maintain the gains that have been made.