|8||4 students - year 6
4 students - year 7
|8 students - stage 5||3 students - stage 5
4 students - stage 6
1 students - stage 7
The classroom teacher took the accelerated learning group everyday for 15-20 minutes. In addition to this, the group also received addition block teaching during the teacher’s release day. The initial decision to do this related to manageability and also provided optimum learning time to be spent with these children. This increased the possible number of sessions that could be taken over the eight week period.
The attendance of most of the students was excellent. Those that missed the intensive sessions often took the initiative to team up with another child from the group to catch up. The children demonstrated increased motivation as the programme progressed. There was enthusiasm and keenness to attend all lessons, even if that meant staying within breaks or missing literacy. It is felt that the reason for this is that students had an equal say in every step of the process, thus the teacher had them on board from the word go! Another reason for the change of attitude can be attributed to the students experiencing success along the way. The students were keen to know how they were doing and were affirmed by consistent targeted feedback and feed forward.
Intervention starting point was
- Stage 5 basic facts
- Stage 5 place value – with planned focus on forward/backward connections
- Teaching knowledge whilst developing explicit links to strategy.
- Developing stage 4/5 fractions knowledge and strategy.
Trends in data
- Intervention focused on place value understanding to enhance forward/backward knowledge as well as basic facts. Children in both these domains have improved at least two or more stages.
- Students' basic fact knowledge helped them to move within strategy domains.
- Proportion domain shift can be credited to students increased understanding of multiplication basic facts as well as foundation fractions knowledge.
- Some children who tested on GloSS at stage 5 addition/subtraction early part-whole at the beginning of the intervention have since then managed to do double digit part-whole strategies but they could not get to stage 6 as they were unable to do subtraction strategies.
Advice for other teachers and principals
For an intervention like this to be successful, one needs to start from getting the students on board. I have been very open and honest about the programme, outlining where the children were at and where they needed to be. I also invited the students to opt into the programme so that they felt that they were in control of the situation. In an attempt to avoid any stigma, the group was portrayed as the ‘selected ones’ to be put through the trial. The students were informed of the purpose of the study and the possible benefits of the programme. At all times students knew what the next steps of their learning were going to be and were encouraged to share their learning with their parents.
The facilitator was also a crucial contributor to the success of the programme. It was quite obvious that any queries that I had were going to be received and responded to immediately. The facilitator also kept checking in to see where the children were at and helped to develop possible avenues for progression based on the reflections of the children and the teacher.
The support of parents and the principal has been noted and was immensely appreciated. Both parties took a vested interest in the progress of the students and often checked in with the students about their progress. I also had an open door policy and the parents were in touch with the teacher to discuss progress over the course of the intervention. The students were encouraged to share their learning with their parents and had follow up work that they could do at home.
The principal also checked in with the students who were very proud to talk about their learning. This level of care and genuine interest in student learning ensured that all students knew how important their learning was to us all.
Effective pedagogy in mathematics
- Mathematical communication and language
I have often found that children struggling with mathematics do not understand the language demands of the task and therefore are unable to access the maths in order to succeed in the subject. With this knowledge in mind I ensured that children were given exposure to appropriate language which I modelled consistently. It is important that teachers understand that the language necessary for learning and educational attainment, takes between five to seven years to develop thus needs to be explicitly taught through the use of scaffolding and clear instructions (Cummins, 1978, 2000b cited in Baker 2001). I ensured that I consciously planned for and taught language objectives and mathematical objectives concurrently, to allow the students an “opportunity to learn what is most relevant at the time for them to participate in class, so that they could be fully engaged in learning activities and challenged at an appropriate conceptual level” (Gibbons, 2002, p.13).(Theme 8)
- An ethic of care
For this intervention to be successful I needed to establish an inclusive classroom culture in which the students felt ‘safe’ to voice their opinions and to clarify or seek support when misunderstandings occurred. I felt that the students needed to feel as if they were in control of the situation and that they were on an equal footing with the teacher to develop the course of the intervention. Wink (2005) asserts that “we learn by reading, talking, writing, listening, experiencing, engaging, interacting… and we do it better if we are in a safe and secure environment” (p. 18). I have taken care of the way I share children’s learning needs and I model to the children how to ‘take risks’ in their thinking as well in their clarification so that they feel safe to have a go.(Theme 1)
I also ensured that all children respected each other and set an expectation of the way they communicated during teaching sessions. I have noticed a positive flow-on effect in other areas of the curriculum and this is especially evident in the way the intervention children seek clarification from others in other group teaching situations or when they were trying to catch up when they had missed a session.
- Arranging for learning
During all group-teaching sessions I ensured that children were provided the opportunity to think, pair and share before sharing back to me and the whole group. I also allowed time after pair sharing whilst other group members asked questions or paraphrased what they had heard. Firstly this ensured that everyone was listening but ultimately it helped to consolidate through listening to explanations and provided multiple opportunities to learn the new concepts being explored.
Opportunity was also provided for children to work independently on their goals and next learning steps, as well as in pairs or small group sessions to practice, clarify or debate thinking. In providing a learning environment inclusive of small group debates I felt that children were able to collaboratively make sense of ideas and engage in mathematical arguments in order to make meaning of new learning. It is important to note that any pair or small group debates occurred more successfully when the children were familiar with the task at hand and each member understood their roles, such as taking turns, no put downs when sharing back and allowing time for people to think before they were to respond.(Theme 7)
- Assessment for learning
At the beginning the needs of each child as well of the group were established. Children individually were given their results and the teacher spoke to them about where they were at and where they needed to get to. Children were also told of how they may get there. All programme planning was tailored to the needs of the child and their preferred learning styles. The follow up sessions filtered and became part of the daily classroom programme. Essential to success was the approach of using formative assessment information throughout and therefore the teacher was flexible during the lesson to respond to the needs of the children. This ensured that the teaching and learning was targeted and helped students to consolidate their understanding and clarify any misunderstanding in the process.(Theme 6)
Sharing of goals
Children were given small achievable goals that were monitored and discussed on a daily basis. The students also knew of each other's goals and attempted to support each other in the process. This collegial approach ensured that a climate of risk-taking could be developed and it fostered a climate of joint ownership of the success of all by all. The teacher also shared formative assessment information when any progress was made. No matter how big or small, this was shared and celebrated as a group.
So why was this successful at our school?
The initial training in Auckland left the teacher with a strong sense of purpose. The support from our facilitator is another contributing factor to the success of this pilot programme. She is a knowledgeable and encouraging facilitator who was always there to lend a hand when required. She ensured that the programme was well planned for and executed. Time also played a huge part. The group of students were able to touch base with the teacher every day, discuss confusions and misunderstandings and the withdrawal time provided that extra bit of time for the children to consolidate their thinking.
From the eyes of our students
We all worked as a team and this included our teacher. We all knew we wanted to succeed. We practised and believed that we could do it. We began to feel like we could because every time we tried something new we could do it. It was like our teacher was tricking us because everything looked easy but now we know that all she was doing was giving it to us bit by bit so that we could be successful. We developed new skills and used more strategies - the more we learnt the better we became. We also learnt to combine strategies and looked at a variety of ways to get the answer. We had a say in what we did, for example, we could practice our strategies through games, and we were allowed to work in groups and individually if we wanted to.
About the teacher: Our teacher was very good at showing us how to use the strategies that we knew in a variety of ways. She helped us discover how different strategies worked and showed us relationships between addition and subtraction, multiplication and division. She always told us where we were at and what our next learning steps would be. She made us reflect on our work to help us understand what we had improved on and what we had to work on next. We always were encouraged to compete and beat each other in the way we talked and did maths but we also knew that we had to help each other out so that we all could be successful and nobody would be left behind. My teacher helped make maths fun!
About the facilitator: Ms S helped us by showing us how to do activities and explaining different ways to make learning easy. She always asked us how we were doing and that made us feel very important. We wanted to do better so that we could show her our progress when she came to see us each time (so we could show off our learning).
About our parents: Our teacher told our parents of what we were doing and they kept on asking us how we were doing. Each time our teacher saw our parents she would update them on how well we were doing and showed them what we could work on at home. My teacher talking to my parents made us feel very smart and proud because they got to see us doing so well. It was important for us to have our parents see the progress we were making because we didn’t think they thought we were good at maths, but they were wrong! We loved sharing our final results as we were very proud of our success and we wanted them to be just as proud.
About the Principal: Talking to Whaea B was great too because we got to tell her in person how much fun it was and how we had improved. We liked it when she asked us challenging questions and even better when we could answer them! We wanted for her to be proud of us and we wanted her to talk to our parents about how much progress we had made in a short time.
In a nutshell, our teacher made the strategies make sense by giving us clear explanations and examples. She helped us set new goals and reflect on them because she kept telling us that the sky was the limit. We all worked as a team. This means that we worked in a partnership with each other and our teacher.
Our teacher developed activities that helped to fill the gaps that we had in our knowledge and made sure we practised them. She helped us believe that we could do it!
The teacher had strong content and pedagogical knowledge, which gave her an added advantage because she could steer the lessons based on student responses, based on what was noticed during their discussions. The teacher was confident to deviate from the scripted lessons based on the ideas generated as she had a clear understanding of the different pathways that would lead to success.
The teacher had a strong belief in the Numeracy Project and that it has a positive impact on students’ learning. The teacher also knew that she had the responsibility to make the Project work for her students.
The teacher also adopted ‘teaching as inquiry’ approach to undertake this exploratory study as she felt that any intervention programme that is founded on data (from where the child is at) and genuine inquiry would be beneficial in developing a suitable programme for the students. Whilst using the ‘teaching as inquiry’ approach, the teacher decided to prioritise by using data to determine ‘what is important therefore worth teaching’. She consistently reflected and adjusted the programme and often sought advice from the facilitator as to what strategies may work.
The teacher also worked in partnership with the parents who were informed of the progress and were shown work that the students could do at home. The students were also encouraged to share their learning at home and relate back to the teacher how the parents felt or what they were thinking. The teacher had an open door policy and the teacher encouraged the parents to take an active role in their child’s learning.
I knew that my son was a talented writer but I had no hope that he would make such big progress so soon. I’m so excited that he had the potential. He just needed the right learning environment and support. He was my major concern because he was at the bottom for so long - down below trying to find his way up. He just needed to know that his teacher believed he could. He enjoys the teacher and learning! The positive is the partnership that we had between us and you (teacher) and we all encouraged him to improve. My son had competition from his older brothers but I never thought he would progress so much so quickly. I just hope he keeps the momentum going - keep at it both at school and at home. I now just tell him he is on a roll.
This has been captured from just one parent but others have expressed similar joy at their child’s success!