|Year|| Initial stage
| Final stage
| Time in
|6||6||4 students - stage 4
2 students - stage 5
|2 students - stage 5
4 students - stage 6
|Targeted Learning Group (TLG)|
The students became very positive about their maths and how they viewed their ability and success. This was especially noticeable in the regular classroom where the ALiM students were able to offer a lot more to discussions, and to answer oral and written questions with a noticeable assurance. They were also more positive in how they approached all learning.
At no time have any of these students exhibited behaviour problems.
Attendance was interesting as, for at least a third of the sessions, one member of the group was away. Two students had had a pattern of moving schools or absenteeism over the preceding five years. Both students made significant progress, highlighting that perhaps they had missed key teaching over the years. The four other students exhibited indicators of specific learning difficulties and had already all had extra support over the last two years in spelling, reading and writing.
Key pieces of advice
Teacher knowledge. Teachers need deep knowledge of mathematical ideas and how to implement them successfully. Professional development needs to be ongoing and linked to effective practice. Many teachers recognise gaps in students' learning but are unsure of how to meet the need.
The Numeracy Project and its accompanying resources have enabled Makauri to continue to build effective practice. The ALiM focus has lead us to reflect on all current practices, deliberate acts of teaching and teacher knowledge. All teachers have made a commitment to providing good learning opportunities for all students from school entry onwards. To this end we have put additional resources in place to meet learning.
Deliberate acts of teaching to teach number knowledge and strategy. Using assessment information to effectively add to a pool of knowledge about students' individual and collective learning, is integral to successful acceleration in students learning. This then enables targeted teaching to follow. Teaching and practice in using knowledge and strategies must be regular and accompanied by feedback and feed forward. Well modelled learning enables learners to support each other and at times to be the teachers with others.
Mathematical connections. Our experiences reinforced the importance of connecting maths to other areas of students' learning and to life in general. I include maths language and knowledge transfer under this umbrella as well. One issue that I think is relevant to stage 4 students and above in particular, is that some class teachers start teaching with abstract modelling only. While this is appropriate for some students, all students would benefit from a concrete model to link the learning concept to. The use of interwrite boards in particular lends itself to this.
Using a programme such as Target Group Maths can make a significant and positive impact on the learning of number knowledge. Makauri School is using this programme (TGM) to provide for year 4, 5, and 6 students who are below expected levels of achievement. A teacher aide has been trained to take the programme, supervised by a teacher. Results are very positive.
School, teacher and student profile
Makauri School, a decile 8 contributing rural school of 180 students, is on the outskirts of Gisborne. Strong links to the community are evident through community support of internal and external events, such as fundraising ventures, education outside the classroom and parent evenings. Students participate in a range of learning and recreational opportunities of which cultural experiences are a feature. Students are confident, articulate and sociable young learners. They demonstrate high levels of engagement and enjoyment in meaningful learning tasks. Teaching is characterised by well-planned programmes that cater for the range of children's learning abilities and interests.
Current achievement information indicates that students achieve well in literacy and numeracy. The wide range of assessment practices provides a rich source of achievement data for appropriate decision-making by both board and senior managers. (ERO 2007)
I was very keen to use the Targeted Learning Group programme working on number knowledge and place value. The programme is very structured and requires the teacher to closely follow a consistent format. Each day the students' session would involve counting forwards and backwards, ordering numbers, saying (reading) numbers out loud, dictation, basic facts practice or place value teaching, strategy revision, number games, self evaluating progress and a homework check. The predictability of the session was a key ingredient for my six students. I added a number of clapping/counting games to our format and this was quite an eye opener. All the students struggled to put an action and a number together and we were only working from 1-6 initially. This lead me to reflect on the changing nature of children’s play and how the common games of hopscotch, skipping and clapping to rhymes (games where actions, words and movement are all interlinked) were fast disappearing from our schools. Another implication is, if some students find it difficult to link action with information, how disadvantaged they might be in our busy, moving learning spaces.
Careful use of equipment
One day we were using magnetic counters to model subtraction using compatible numbers (Numeracy Project Book 5: Teaching Addition, Subtraction and Place Value, page 26). The required number of counters to be removed, was physically moved to the side of the board by the children. BUT as we discussed our answers the students began moving the put-aside counters back into the remaining pile. They found it difficult to mentally set aside the removed amount. In subsequent teaching I therefore took off the removed amount of an equation and ensured that it was out of sight of the students. I routinely discussed this with the students encouraging them to mentally remove a number from their mental pictures as we explored subtraction. Discussion with other teachers led us to reflect that newer equipment might be creating differing mental images for some of our students.
As part of the programme I included some memory activities. Students were also encouraged to play memory card games and other memory games such as “I went to the shop and bought a banana, I went to the shop and bought a banana and an orange etc..” and looking a an assortment of items on a tray then recalling them when the tray is removed. The students also used computer programmes to recall and imitate patterns. I can’t say how effective these activities were, but the students certainly improved their short term memory.
Students enjoyed repeating activities covered and would ask to revisit learning. What was exciting was the way that they began to challenge themselves by making some games more difficult. Of course the conversations that took place helped to consolidate the learning.
Learning strategies was a huge challenge. One of my initial goals was to teach the strategy of subtraction using compatible numbers. However in order to do this the students had to have number knowledge and be able to use and transfer this knowledge confidently. It took over half of our four 40 mins sessions weekly to reach this point (five weeks). However, in learning how to use derived knowledge, the students became a lot quicker at applying the concept to two, three and even four digit numbers. In fact they managed both squared area and addition and subtraction of decimals (tenths and hundredths) very confidently within the regular classroom programme using the strategies that we had used in our ALiM sessions. My suggestion to our younger classes has been to take time consolidating new learning by creating as many ways as they can for student to use their knowledge across a wide range of equipment. Ask students to model their ideas more and encourage conversations.
Teachers need to be aware of when and how to teach key ideas. I felt that my six ALiM year 6 students had bits and pieces of learning and could not select appropriately from their knowledge. During our time we moved from compatible numbers to rounding up or down to the nearest 10 on a number line then using the number line to solve problems. Although the improved strength of the students' number knowledge helped them, the students still needed prompting in order to change from one strategy to another.
Were we successful?
Definitely the students have improved in the depth and understanding of number knowledge. They have some effective strategies to use and are confident enough to try out their ideas and to discuss their mathematical ideas.