|Year|| Initial stage
| Final stage
| Time in
|8||3||4 students - stage 2/3
4 students - stage 4
|2 students - stage 4
6 students - stage 5
|Part of 1day/week||Mult/Div. Strategies
Mult/Div. Basic Facts
|8||5||6 students - stage 4
2 students - stage 6
|4 students - stage 5
4 students - stage 6
Profile of school
Waterloo School is a large decile 9 contributing school catering for students in years 1-6 in Lower Hutt.
In 2008 we undertook numeracy development for the first time. Being in our third year of the numeracy programme we have begun to monitor students closely and are considering ways to help children who are working below the expected level. The opportunity to participate in the ALiM pilot has provided us with a chance to address the needs of the identified students as a whole school.
Because of the size of our school it was decided to have two lead teachers involved with the pilot. One teacher from the middle school and one teacher from the senior school provided the coverage we needed to address the needs across two syndicates.
Identification of students for the pilot was based on several pieces of information:
- NumPA results.
- Identified target students for specific year levels.
- Conversations with classroom teachers on individual students (refining selection of children from the identified target group).
- Syndicate meetings (shifts in development, looking at students who would benefit from focused teaching over a short period of time).
There were 2 groups selected for the ALIM pilot
- Year 3 (eight children)
- Year 5 (eight children)
Summary of programme
Structure of the day
Because two teachers were running the groups we shared one day per week. Each lead teacher would alternate each week so that they would get a three hour morning block or a one and a half hour afternoon session.
Structure of the session
Each teacher developed their own lesson structure based on the needs of the children. A repetitive format was integral in ensuring that children knew what was expected of their learning but flexibility within the lesson structure became important. We discovered that it was essential to address student responses at the time to capture the teaching moment.
Focus of the programme
Using multiple sources of evidence (NumPA, classroom information, target data) it was identified that both groups would focus on multiplication and division strategies and supporting knowledge of basic facts (multiplication and division facts).
Strategies that reinforce the weekly teaching
Because the students were working with the lead teachers only one day a week, we set up the following strategies to support their learning:
- Effective home-school partnership: home packs were sent home weekly which reinforced the learning in each session and communication was encouraged.
- Using support staff to facilitate learning from each session within a small group setting on a weekly basis.
- Math buddies: year 5 students worked with another student in their classroom. The focus of this was to share their learning and play the games.
- Regular communication with classroom teachers on a weekly basis to inform and make connections with current teaching and to discuss the shift in students' learning and attitude.
Three points of difference
1. Tools and representations
The selection of appropriate tools and representations to provide support for students’ thinking was essential in assisting them to make connections between mathematical ideas.
‘With the help of an appropriate tool, students can think through a problem or test an idea that their teacher has modelled’ (Anthony, G. & Walshaw, M., 2009, p.23)
Students needed the opportunity to explore a range of materials to make sense of the mathematical ideas. We found that we could not rely on one piece of equipment to model the idea but had to use several different pieces to ensure that learning had been met. For year 3 students we used a range of representations of arrays linked to a story context. Year 5 children physically represented arrays using a range of materials such as sports equipment. This allowed children the opportunity to make connections between the representations and the mathematical concepts and ideas. To support this idea it was essential also for the children to see the connection between the symbols and the representation. It was important to provide children with adequate scaffolding of mathematical concepts in order for them to succeed.
|Doubles/halves grid using flyswats.||Children explaining how to use a number line to derive.||Place value charts were used to support FNWS/BNWS.|
2. Environment for learning
The year 5 children thrived in an environment that fostered on the opportunity to be challenged and compete against each other during mathematical tasks. This environment provided these children, particularly the boys, with the motivation they needed. A lot of these children had a negative view of mathematics so it was important through the teaching and learning programme to give them an opportunity to succeed during each lesson.
The year 3 children benefited from an environment that allowed them the opportunity to work independently but also collaboratively in pairs. Discussions with partners engaged the children in their thinking and helped to reinforce the learning tasks.
‘Pairs and small groups are not only useful for enhancing engagement; they also facilitate the exchange and testing of ideas and encourage higher order thinking’. (Anthony, G. & Walshaw, M., 2009, p.9)
A responsive environment where communication between students and teachers within a group’s session was vital to students clarifying their thinking and making connections to the key mathematical ideas. Questioning throughout a task allowed the teacher to elicit, support and extend students’ thinking. Allowing the opportunity for think-pair-share during lessons gave the children the chance to bounce ideas, clarify their thinking and consider other ways of problem solving.
Here are a couple of reflections from students who participated in the ALiM pilot.
"It was fun when we did the fly swats with the number grid outside. It was also cool when we did the number lines outside with chalk. Normally we do things on paper so it was cool to do it outside." (Child A)
"I thought it was good working with R because he wouldn't complain if I said an answer and he didn't agree with me... I really enjoyed using the Dodgeballs. It was a good way to work out the answer." (Child B)
These three key points of difference have made a positive impact on our students’ thinking and attitude towards mathematics within our school. As lead teachers this has highlighted that, for students who are underachieving, we need to consider the alternative approaches to support their mathematical needs. It is essential for teachers to deconstruct the learning progression in order to provide a learning environment that addresses the needs of these children.
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