JOIN EVENT
Session chair: Margrét Björnsdóttir
Paper 1: Developing whole-class teaching practices for preventing mathematical difficulties: Arithmetic strategies in 1st to 3rd grade
Maria Grove Christensen Sofiendalskolen, Aalborg, maria@grovechristensen.dk
Abstract
Excessive use of counting strategies in single-digit addition has been linked to mathematical difficulties (Snorre Ostad). In my experience, as a math teacher and teacher-consultant, teaching with an aim for increasing the use of derived fact strategies is unknown to many Danish teachers.
An intern study at my school showed that the teachers’ knowledge of teaching strategies were limited. Furthermore, 25% of the students did not have sufficient repertoire and flexibility in their strategy use when solving single-digit addition in grade 3, to a degree where intervention would be recommended. Arithmetic strategy use and numeracy was already my focus in the early intervention program at the school, but it became apparent that the need for early intervention by far exceeded the resources available.
In a class I taught, throughout grade 1 – 3, with a continuous focus on students’ strategy development only 6 % of the students showed insufficient strategies after three years. This led me to believe that the particular way we teach influences the amount of students in need of early intervention. The assumption was reinforced when we, in a class without specific focus on increasing the use of derived fact strategies, again experienced 25% students in need of early intervention. In this class, we did a small group intervention in grade 3. A group of 6 students received an intervention on strategy development consisting of four lessons (each lesson 90 minutes, total 4 x 90 minutes) over a six-week period. This rapidly lowered the number of students in need of further intervention to only 10 %. In my opinion it raises a concern that way too many students are in risk of mathematical difficulties due to insufficient general teaching practice.
To increase teachers’ awareness of the importance of teaching strategies in the classroom we have introduced mandatory evaluation of students’ strategy use every year in grade 1 – 3. Furthermore, the teachers and I cooperate on strengthening the focus on strategy repertoire and flexibility in the classroom through implementing the use of newly developed teaching materials. At the conference I will present examples from our teaching practice with single-digit addition in the classroom.
Paper 2: Mathematical learning difficulties: How to understand, investigate and identify suitable instruction measures
Irina Jensø & Statped, Department of Complex Learning Difficulties, Irina.Jenso@statped.no. Co-author: Jeanette Lindhart Bauer
PRESENTATION (PDF)
Abstract
In 2019 and 2020, Statped (the Norwegian national service for special needs education) cooperated with educational psychology services and local schools in Vestfold County, Norway, in a project which aimed to increase local competence on addressing mathematical learning difficulties.
Three main goals were defined:
- Increased understanding of the diversity of mathematical learning challenges and how these may be expressed
- Increased knowledge on how to investigate mathematical learning difficulties, taking both environmental and individual factors into account
- A broader knowledge base of research-based facilitation measures for mathematical instruction for pupils with diverse learning difficulties
The project was organised as four whole-day gatherings combining theoretical instruction with group discussions. The participants were divided into case groups, each consisting of an educational psychologist, a mathematics teacher and a special-ed teacher who cooperated on working with a pre-selected pupil with mathematical learning difficulties. The groups were instructed to implement the new theory by carrying out defined tasks between gatherings and to send anonymised reports describing their work to Statped’s lecturers. Their results and experiences were actively used in planning the lectures and group sessions for the next gathering.
There were several reasons for choosing this design:
- to make the theory more tangible and relevant for the participants by enabling them to make mental connections to “their” pupils
- to ensure that the participants put what they have learnt into immediate practice, as experience shows that newfound knowledge stands in considerable risk of being forgotten if it is not soon actively used
- to demonstrate the importance of considering the pupils’ own understanding of their difficulties and their views on what might be helpful
After the project period, the participants expressed a sense a sense of increased competence and of confidence in understanding and meeting the needs of pupils with diverse learning difficulties in mathematics. Hence, the project goals were to a large extent achieved. However, this competence appears only to a limited extent to have been shared with colleagues and systematically developed. Sharing and maintaining competence is therefore a challenge that needs to be addressed more actively in future implementations, both at an early stage in planning and throughout the implementation period.
Paper 3: Pre-school mathematics: Pilot study on a course for mathematics leaders
Margrét S. Björnsdóttir, University of Iceland, School of Education margreb@hi.is. Co-author: Valdís Ingimarsdóttir
The purpose of the paper is to shed light on a developmental project with the goal of educating mathematics leaders in pre-schools. The aim with the project is to encourage the building of learning communities in pre-schools where the focus is on children’s mathematical activities and thinking. We report on a pilot study with three schools in Reykjavík from fall 2020 to spring 2021.
The project is based on the program Matematiklyftet from Skolverket, Sweden. The course Preschool mathematics builds on the six fundamental pillars that Bishop (1988) found to be universal and also necessary and sufficient for the development of mathematical knowledge. These pillars are: counting, locating, measuring, designing, playing and explaining. The course is divided into three parts and this year we ran the first part. It consists of four modules where the focus is on mathematical activities, playing, explaining and recording. From the outset of the course emphasis is on noticing (Mason, 2002) and recording the children’s mathematical activities.
The leaders meet with mathematics educators at six sessions (three hours each) throughout the school year. At the first meeting we focus on the role of the leader (Knight, 2011) and the remaining five on the four modules. The leaders have access to texts about children’s mathematical development and activities, and video-clips of pre-school children engaged with mathematics and in discussions about their explorations. We discuss and reflect on this material and then the leaders introduce it to their colleagues within their pre-schools. They encourage their colleagues to notice and record the children’s mathematical activities and do the same within their own groups. At the following session the leaders report from their experience and discuss with the other leaders and teacher educators.
Data is collected of teacher educators’ notes, program descriptions, recordings from workshops, learning stories from pre-schools and the leaders answers to open questions.
Throughout the project we, the teacher educators, write memos to help us focus on important features in the development of the program. We discuss our experience from previous sessions and how our observations help to progress our work with the leaders. Through this process we are developing our own way of supporting the leaders and adapting Matematiklyftet to our conditions. By collaboratively recalling experience from previous sessions, we try to prevent missing out relevant information that can support us in developing the program (Saldana, 2009). This cyclic way of working with data from a longitudinal project helps in improving the project.
Our preliminary findings reveal that pre-school teachers are not used to pay attention to children’s intuitive thinking about mathematics and their mathematical explorations. The participation in the course has helped them focus on important features of children’s mathematical development and how to support it. Their strength in writing learning stories from the children’s activities has helped them focus on the children’s mathematical learning. Learning communities were created in two of the schools but in one school lack of support resulted in inactivity. In our future planning of courses, we will focus on collegial learning and reporting from teachers noticing of children’s mathematical learning. Our vision is that if pre-school teachers notice, record and reflect on children’s mathematical activities and thinking they will pave the way to equal access for all learners to quality mathematics education.
References
Bishop, A. J. (1988b). Mathematics education in its cultural context. Educational Studies in Mathematics, 19, 179–191.
Knight, J. (2011). What good coaches do. Educational Leadership 69(2) p. 18–22.
Masson, J. (2002). Researching your own practice: The discipline of noticing. Routledge Falmer.
Saldana, J. (2009). The coding manual for qualitative researchers. Sage.