As a final year Bachelor of Education student at the University of Tasmania, II recently participated in an innovative program for improving mathematics learning outcomes for primary school students and the mathematics teaching development of pre-service teachers. As a participant in the program, I was required to plan, teach and assess a sequence of six mathematics lessons for a group of seven students at a local primary school. The planning was undertaken in collaboration with a fellow student and was approved by both the classroom teacher and university staff prior to the commencement of the lessons. We were allocated a group of Prep and Grade 1 students who required a focus on the number sequence 11-20.
This article describes the processes we undertook, observations made, and lessons learned as a result of this experience.
Beginning the program
Early in the semester, pre-service teachers were allocated to teams of approximately three people and each team was assigned a colleague teacher with whom to collaborate. The first meeting with the colleague teachers was held at the university and discussion occurred around the classroom context, the focus group of students, relevant behavioural and health issues, students' family dynamics, and their learning needs. This meeting was followed by another at the school, where we met senior school staff and teachers. They shared their whole school goals and philosophy regarding mathematics teaching and learning, including their school mathematics curriculum. Of particular interest was their commitment to use standardised vocabulary for mathematics across the school. This strategy was aimed at reducing confusion and easing transitions from one grade to the next. During this meeting we arranged a time to meet the focus students in their classroom.
To begin the sequence we were required to plan and implement an assessment of the students' current understandings of the numbers 11-20. Collaborative planning led to the identification of the following learning outcomes:
1. Students will match the numbers 10-20 to a collection of the same number of objects.
2. Students will correctly represent the numbers 10-20 through written oral and visual forms.
3. Students will match the numbers 10-20 with appropriate dot arrays/numbers of objects.
4. Students will correctly count and order the numbers 10-20 both forward and backwards.
5. Students will recognise the relationship between 10 and the numbers 11-20.
The assessment of current knowledge was based on these learning outcomes and conducted with students individually. Observations were recorded on a checklist, along with anecdotal notes. Although time consuming, this approach resulted in rich data on which to base future planning and provided an opportunity for detailed observation.
The pre-teaching assessment revealed common difficulties with the following:
* representing the numbers (11-20) in text;
* making collections to represent a given number (11-20);
* drawing arrays (11-20). Other observations included:
* some students exhibited competence in one-one correspondence;
* others forgot the size of the required collection and continued counting;
* when asked to count individually, many students skipped some numbers or said them out of sequence;
* all students could pronounce the numbers correctly;
* all but two students exhibited significant difficulty with recognising the words for the numbers 11-20.
After a review of the pre-teaching assessment data, it was determined that the planned learning outcomes remained appropriate for the target learners.
Developing the learning sequence
From these data, the learning sequence was developed. Constructivist theories informed our planning and this teaching experience provided a rich …