Caring classroom communities that are focused on mathematical goals help develop students’ mathematical identities.

The creation of non threatening mathematics learning environments and the cultivation of positive self concepts in mathematics are fundamental to the success and progress of all students, but particularly for those most at risk. Students operate at their best in an environment of trust. They feel it is safe to ask questions, to take risks, and to share ideas when the responses from their peers and the teacher are honest, constructive and without judgement. Students must also sense a growth not only in their own mathematics capability but also in their ability to achieve realistic expectations with increasing independence.

Descriptions of the co-construction with the students of inclusive, respectful and focused mathematics learning communities can be found in the following stories which describe the development of both mathematics competencies and identities.

     

Exemplars:

If we believe that teachers make the difference I knew that it was important that both sessions were held in my classroom where I have a maths corner. This would allow them to realise that maths is important and that I care for their well-being in the sessions. The sessions were held at regular times and the children in both the groups’ eagerness to come and get ready for each lesson was quite impressive. The older group in general was children behind the level expected but it was great to know that they felt included and valued throughout the lesson. Confidence increased. This was very evident when we, teacher and the group, returned to their own class and taught a group of their mates some of the activities. And boy did they shine!!! Perseverance for problem solving became evident and their support for each other when things got a bit challenging was pleasing to note.
There was a very noticeable change in their attitude straight away. I believe they felt ‘safe’ with these peers and the teacher.
There were many ‘lightbulb’ moments. One student threw his hands up in the air and said “I get it!” and the change in his whole attitude to our lessons was amazing. He tackled all maths problems with confidence and wanted more challenges.
Eight out of ten children were markedly more positive and capable by the end of our sessions.
The first two weeks focused on improving the students’ attitudes and their enjoyment of maths. Card games were taught as were achievable ‘hands-on’ activities to learn addition and subtraction facts, first to 10 and then to 20. Consolidation of place value knowledge to 100, using ideas from P. Hughes, also took place during the first few weeks.
Straight away, a noticeable shift to a more positive attitude was seen as students learnt and remembered basic facts. The games created a little positive competition in the groups as students wanted to win the games both at school and at home.
When interviewed at the end of the study, a big shift in attitude to maths was seen.
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 occur. 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.
Building confidence and building a community of learners: as soon as the children viewed themselves as being good at maths, and as being ’mathematicians’ they seemed to want to learn and were more willing to have a go at an answer even if they weren’t sure if it was right. Building the environment and ‘climate’ in which the children felt safe to take these risks was also very important from the beginning.

 

Aside from this quantifiable data an area of significant shift that I noted was in the students’ confidence in maths. While initially many would have said to you that they ‘sucked’ in maths, and clearly felt that most of it was beyond their ability, by the end of the project I was hearing comments like this each time we worked together; “I can do that”, “that’s easy”, “pick me, I know how to do that”. I feel that this shift in itself was worth the whole time and effort. To see these children take such huge strides in their confidence in this subject means that they now approach new learning with an “I can do it” attitude, rather than a “this is too hard for me” type attitude. This of course makes a huge difference to how well they learn and how much of that learning is sustained.
Many struggling senior primary students have very low confidence in their own mental maths and have developed strategies to avoid volunteering ideas or taking part in discussions. This confidence can be gained by working in small “safe” groups to develop specific areas of understanding.
Students were not motivated by maths and did not overly enjoy maths at the beginning of this study. At the end, students became proud of their learning and enjoyed coming to the sessions and learning new maths. In discussion with students they expressed how they enjoyed the sessions. The students particularly enjoyed arranging numbers to read aloud and wanted harder questions. They also liked to be out of the class in a small group situation as they didn’t feel pressured or embarrassed and it was quiet.
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.
The group enjoyed the structured lessons which helped them feel secure in their learning.
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, answering oral and written question with a noticeable assurance. They were also more positive in how they approached all learning.
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.
 

All the children initially had a poor image of themselves in maths. As the sessions progressed, most students developed a belief in themselves as mathematical learners.

The teacher needs to create a high expectation, caring and supportive learning environment and to also have in-depth pedagogical knowledge.
I think that the overall most important factor in the teaching of children who are not succeeding as well as they should, is the teacher/child relationship. The bond forged by the teacher to make the children feel secure and happy to take risks is all important. This often can not happen during group teaching, especially when a child is struggling. This can only happen when the teacher is passionate and dedicated in making the programme work.  (Intervention teacher October 2010)
The students need to feel that it is safe to take risks but that the teacher also expects hard work and focussed effort from them, as many of these students are adept at withdrawing from learning in the whole class environment. The experience at this school confirms the research in the Best Evidence Synthesis.
One of my personal beliefs in teaching is that we must, as teachers, show the students that we care about their learning in order to foster a valuing and respect of themselves. At all times, the language that we used in the group was positive. It took a lot of energy in the beginning to stop the habits they had formed of criticising and pointing at someone else’s work if it was different from theirs. We discussed acceptance of others everyday.
These students had come to the sessions with a lack of confidence, thinking they were no good at mathematics. It was important to engage them through activities that were hands on, fun and motivating. Often we would use little teddies as an incentive for work and the students loved them. We would make up little stories about the teddies and use them as rewards for attempts at answers, answering a question and proving how they got that answer. There was a noticeable shift in the learning climate within the group to a safe, caring place where it was okay to make mistakes, because everybody was a learner, including the teacher. This positive attitude towards mathematics transferred into the classroom and these students became more focused and engaged within the class.
“A positive attitude raises comfort levels and gives students greater confidence in their capacity to learn and to make sense of mathematics.”
(Anthony, G. & Walshaw, M. 2009, p.8)