Numeracy, maths and learning difficulties
Postgraduate Education students at Flinders University are helping to support young people who struggle with mathematics. A unit of their course called Numeracy, Mathematics and Learning Difficulties connects each student with a primary school learner in need of special assistance.
The students initially participate in two on-campus lectures/workshops, where they reflect on their past and current numeracy/mathematics understandings and practices. They discuss key issues such as the links between numeracy and mathematics, effective approaches to teaching, and the impact of government policy on the work of teachers.
The students also consider and make use of both formal and informal assessment processes to gather information for, as, and of learning. They learn to administer the Booker Profiles (Booker 1995), a diagnostic tool that helps to identify what a young learner knows and needs to know next in relation to maths. The use of this common assessment tool will also help the students support each others' analyses and planning in a school setting.
The next part of the course is held at Bellevue Heights Primary School. While the students continue to reflect on matters of mathematics teaching and learning, some of their session time is now spent with school students. Over the semester each student is assigned to an individual child, identified by classroom teachers as having numeration/computation difficulties. In the first school session students visit the classroom of their assigned young learner and observe how they work, in groups and independently. The students also arrange times to speak with classroom teachers and to source previous documentation about the young person's mathematics progress to date.
During the next session, the students establish a starting point for their intervention program using the Booker Profiles, and in the process develop a stronger practical understanding of this resource. They then write a report for the teacher and parents summarising their assessment information and setting a learning objective for the child, to be achieved by the end of the intervention.
In the intervention sessions, the students work to deepen the children's conceptual understandings. They are also mindful of helping the children to make conceptual connections within mathematics, to other Learning Areas, and to contexts outside of school. The students make wide use of materials and ensure that their young learners are brought to a point where they can explain and monitor their own thinking.
At the end of each intervention session the Flinders students have an opportunity to discuss their reflections about the teaching session, and share strategies and resources. A specific time is set aside on the final visit for students to talk with each other about what each young person has achieved, and what they have learned as teachers through involvement in the intervention. Having the lecturer and peers all in the same teaching space has supported a collegial approach where breakthroughs can be celebrated, frustrations shared, and practices reviewed.
The students draw on this discussion to prepare a summative report for the classroom teacher and the parents, indicating the child's learning achievements to date and providing recommendations for further mathematics learning.
The Bellevue Heights classroom teachers have reported significant improvement in the mathematics and numeracy skills of each of the children who have participated in one of the interventions. All showed an improved understanding of mathematics concepts, and are now confident enough to answer mathematics questions in class. One student, for example, excited and proud of her new knowledge, asked her teacher if she could show her how she could now subtract.
Impact on the university students
The postgraduate students have become more aware that a learner's knowledge of mathematics language or concepts cannot be assumed, and does not necessarily correspond to age level. They have also become more aware that symbolic recording is taught in many different ways; that learners often fail to generalise learning across different contexts; that learners cannot always recall basic number facts automatically and fluently; and that young learners' ability to work symbolically does not necessarily entail a real understanding of what these symbols mean.
The students have come to realise that it is essential to be aware of young learners' beliefs about themselves as mathematicians, as their negative self-perceptions can seriously impede their willingness to engage with the subject. By working to develop learners' sense of mathematics self-efficacy and ability, the students have seen how they can make a significant difference to learners' engagement and self-concept.
Professional development of Bellevue Heights teachers
Staff at Bellevue Heights Primary School are currently participating in a series of after-school sessions to further their knowledge of strategies for mathematics teaching. These sessions, led by the Flinders University lecturer, involve reading research papers about mathematics, engaging in practical workshops, and completing classroom-based tasks. These set tasks provide teachers with an opportunity to engage with and implement new strategies and learning. The sessions offer a forum for subsequent discussion of how particular strategies have contributed to their students' knowledge, skills and understandings. The focus of these sessions has been on areas identified as key issues during the Flinders students' interventions: numeration and computation, problem solving, and assessing mathematical understanding and competence.
As of this year, these professional development sessions, along with additional tasks, can be counted toward the completion of a Masters degree.
The interventions and professional development sessions have benefited the teachers' approaches to mathematics, according to feedback from the school leadership team and the classroom teachers themselves.
One key benefit has been to highlight the importance of appropriate and consistent mathematics terminology across all year levels. This is particularly relevant when teaching students from non-English speaking backgrounds. The school leadership intends to release staff to work on a 'common terminology and process' chart for mathematics, which will be displayed and used in every R–7 (K–7) classroom and the school's New Arrival Program classes. An electronic version for use with the interactive whiteboard is also in development.
Teachers have also become more specific in their lesson planning, have monitored students' understandings more closely, and have made use of a broader range of assessment tools, such as the maths journal. They have also increased their use of targeted questioning within the classroom.
The professional development sessions are part of a wider ongoing professional learning program at Bellevue Heights. Over the past five years, the school has offered whole-staff professional development in school priority areas including ESL in the Mainstream; the Primary Years Program (PYP) associated with the International Baccalaureate; the STARS program; Stop Think Do; and Inquiry Based Learning.
Bellevue Heights Primary School has participated in Flinders University's Numeracy, Mathematics and Learning Difficulties program since 2005. The classroom teachers have been supportive, accommodating, and appreciative of the work undertaken by the university students, and the postgraduate students have similarly been positive about the benefits of hands-on learning, and the chance to apply their knowledge and skills in a school setting.
Booker, G. (1995). Booker Profiles in Mathematics: Numeration and Computation. Camberwell, Vic: ACER.
Key Learning AreasMathematics
Subject HeadingsMathematics teaching