Teaching for Mathematical Resilience Dr Clare Lee Clare.lee@open.ac.uk

Developing Mathematical Resilience The Project Background NCETM Enigma Hub supported project offered as CPD 23 teachers from 12 schools The teachers met 4 times over one academic year and each school developed their own small scale research into mathematical resilience 8 schools (16 teachers) completed the project by submitting a report The data is from the reports submitted but also from notes recorded during the meetings of the schools

Developing Mathematical Resilience Limiting Factors Of the schools that did not complete their study or did not attend all the sessions One school had staff turnover such that they could not support attendance. Two schools had trouble fitting the ideas in with the school’s demands for ways of working. They stopped coming after session 2. One school simply could not find the time to write a report despite attending three out of four sessions and continuing their project. They reported that this was to a large degree because the two attendees were the only teachers in their department who had higher qualifications in mathematics.

Developing Mathematical Resilience Enabling factors   Characteristic of an environment that fosters mathematical resilience Stress the growth mindset and work to counter the fixed mindset 2.  Show throughout learning tasks that mathematics has value within the real world 3.  Are overtly and consciously inclusive of all learners n a community of those learning mathematics 4.  Enable the students to learn the vocabulary of the mathematics community so that the students take part in mathematical discourse 5.  Show the students that learning mathematics involves “Struggle” but promote ways to ensure that anxiety is not established 6.  Ensure that their students know how and when to seek help and how to give help

Stress the growth mindset and work to counter the fixed mindset Enabling factors Stress the growth mindset and work to counter the fixed mindset Developing a growth theory of learning (Dweck, 2000). Displaying of posters encouraging use of growth language For example don’t say I can’t do it – say I can’t do it YET! Involving the whole school may be important here. All staff in the school needed to express the idea that there is no limit to the mathematics that students can understand and use given the right support and effort. The systems used in school may label students and emphasise that more was expected from some people than from others. Introducing the idea that all students were expected to understand and use each aspect of mathematics that was studied was important. Different ways to work on each aspect were offered and each child made the decision about how much support they needed and how they wanted to learn. Removing the labels gave everyone a chance to grow.

Show that mathematics has value within the real world Enabling Factors Show that mathematics has value within the real world One pair of teachers in particular used contexts that were of interest or familiar to their students to generate interest and engagement. For example they showed a video of an English astronaut who was in the space station at the time and asked the students to generate mathematical questions about the situation. The questions were slow to be asked at first but gradually and collaboratively the students posed questions about space and the space station. A list of questions was generated and the students used the mathematics they already knew to generate answers. They had to explore ideas and make connections challenging themselves in ways that the teacher may not have done to get a good answer. Working in this way meant that the students began to uncover the extent of mathematics that is present in the world but also to see that they can engage with mathematics and find solutions. This group of students found that bubble wrap offered a great deal of mathematics as well.

Enabling Factors Learning environments are overtly and consciously inclusive of all learners n a community of those learning mathematics This idea featured in most of the schools who wrote a report and usually took the form of enabling the students to make their own choices in how they supported their learning, rather than the actual content that was to be learned. The teachers acknowledged that some students were better than others in making these choices and saw part of their role to help them to be able to assess where to start and what their learning goal might be. For example in one school the teacher offered several choices of ways to approach the learning one of which was to work on a table were the teacher was working. However she stipulated that the students had to have a good reason to work on this table “not knowing your seven times table was not a good enough reason!”

Enabling Factors Enable the students to learn the vocabulary of the mathematics community so that the students take part in mathematical discourse Helping the students to use the vocabulary and ways of expression that are a necessary part of using and reasoning with mathematical concepts (Sfard, 2008) was regarded by the teachers across the age range as important. One teacher who worked with secondary age students (11-19years) discovered that one of his students who was aged 16 years, had never been helped to understand what may be considered very basic mathematical vocabulary and thus felt completely excluded from any discussions, causing him to exclude himself rather than appear ignorant. Understanding and using the vocabulary is a vital part of feeling included in the community of those who engage with and use mathematical ideas (Lee 2006). Making sure that the students use the language of mathematics, not just the teacher, is a vital part of developing mathematical resilience.

Enabling Factors Show the students that learning mathematics involves “Struggle” but promote ways to ensure that anxiety is not established Helping their students understand that learning to use and control mathematical ideas involves a certain amount of struggle. Many teachers in the USA see their job as “path-smoothing” (Wigley 1992). This attitude appears to have created students who consider that making mistakes or not being able to move smoothly through some mathematical problem as meaning that they “can’t do it” or that the teacher has not explained the idea well enough. Many of the teachers also reported that their pupils seemed to be ashamed if they made a mistake and that mistakes were to be hidden rather than acknowledged. Teachers helped their pupils understand that learning involved some struggle and perseverance, but that they were not struggling alone, support was readily available. One school did did this by celebrating “today’s big mistake” asking their students to explain where they made a mistake and what they did about it. Teachers also stressed that if the students were not making mistakes then the level of challenge they were experiencing was not high enough to enable them to learn as well as possible.

Enabling factors Show the students that learning mathematics involves “Struggle” but promote ways to ensure that anxiety is not established Teachers talked about moving from the comfort zone into the growth zone where they were learning something new. They challenged their students to move into their growth zone, often asking the students themselves to choose work which would enable their learning to grow. The students supported by encouraging peer collaboration or other help including IT as they needed it. The teachers also talked about an anxiety or “red” zone which students could move into if they took on too much or did not seek appropriate support. Students were told to acknowledge if they were entering the red zone and take steps to return to growth, by changing what they were doing, seeking more support or collaborating with another student. Learning mathematics involves struggle but not too much.

Enabling Factors Ensure that their students know how and when to seek help and how to give help Collaboration between peers was shown to be important in developing mathematical resilience as working together meant that the support to sustain a student in the growth zone was readily available. One school had already begun to expect their students to collaborate in mathematics as in all other subjects. However they noticed that “helping one another learn” in mathematics seemed less well develop than in other subjects. Many children sought help too soon, they were reluctant to “have a go” and wanted to work with someone they saw as more capable from the start. Rules had to be established as to what constituted “being stuck” and therefore needing help. The students also needed to explore how to give help when learning mathematics; many students saw help in mathematics as “giving the right answer”.

Developing Mathematical Resilience Can be a struggle in itself as you may have to … overcome the prevalent performativity agenda exempt yourself as a teacher from practices known to develop a fixed mindset help the whole school talk growth mindset But if you … Stress the growth mindset Show the value of mathematics Overtly and consciously include all learners Enable the students to learn the vocabulary of mathematics Show that learning mathematics involves “Struggle” but support is there Ensure students know how and when to seek help and how to give help Then learners of mathematics will be empowered to use and control mathematics in their lives and careers.

Developing Mathematical Resilience References Boaler, J. 2015. Mathematical Mindsets, Oxford: John Wiley and Sons Dweck, C. 2000. Self Theories: Their Role in Motivation, Personality and Development. Lillington NC: Psychology Press, Taylor & Francis. Lee, C. 2006. The Role of Language in the Learning of Mathematics, London; Open University Press Sfard, A. 2008. Thinking as communicating, Cambridge: Cambridge University Press Stigler, J. W. and Hiebert, J. 1999. The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York: Free Press. Wigley, A. 1992. Models for teaching mathematics. Mathematics Teaching 141: 4

Thank you