Prospective teachers’ attention on geometrical tasks

Abstract

This study investigates early childhood prospective teachers’ attention to geometrical tasks while designing and using them in the classroom. This is explored in the context of the teaching practice of 11 prospective teachers who taught geometry in early childhood classrooms during the last semester of their university studies. The teaching practice was organized into four stages: design of a lesson plan; classroom implementation; discussion of the lesson with the school practice instructor; and self-assessment report and revision of the lesson. Analysis of data using the Teaching Triad framework (Jaworski, 1994) shows that although the prospective teachers attended to issues of mathematical challenge, sensitivity to students, and management of learning in their planning, in their actual teaching and after class reflection, their attention was focused mainly on management issues. The findings also show that prospective teachers’ attention on geometrical tasks can be developed through a process of reflection on their teaching.

Appendix

Part of a teacher’s profile

Prospective teacher: Elina

Mathematics content: Geometry circle

Age of children: 5 years

• Teacher’s lesson plan

  • The objectives of the lesson focus on processes such as recognizing and identifying circles amongst other shapes and also on the characteristics of the circle (equidistance from the center and curviness).

  • She starts her lesson by providing a letter where somebody asks for help in order to tidy some objects. She asks the children to identify what is common about these objects in order to put a label on the box. We can see here that she uses a realistic situation (a kind of connected mathematics with reality or even modeling) in order to motivate children and encourage them to concentrate on the shape.

    …

• Classroom observation

  • In her first and also last evaluation activity, she does not refer to the distinction between two- and three-dimensional circular shapes. For example, children who identified cylinders as circles were told that they were correct.

  • In the second activity, she uses too much time for writing down the shapes that children have recognized, but she does not use this list. Although she wrote each child’s answer in a table, she did not refer back to it.

    …

• Interview

  • She argues that, in general, her lesson plan was good because there was a hierarchy. Thus, she concentrates on the didactic side of the lesson. She also comments on the methodological issues and states that it was good that she had asked children to “cooperate” and “discover.”

  • She reflects on the level of difficulty and on the way that she was asking the questions.

  • She refers to the difference between theoretical and practical activities and states that it was valuable that she gave practical activities so the children could build the concepts (i.e., cars).

    …

• Self-assessment report

  • What she finds as positive points:

    • The letter was interesting for the students.

    • She told them that the activity was tricky and this motivated them to respond.

    • The cars were interesting and also related to the children’s everyday experience.

      …

  • What she thinks was negative:

    • The inclusion of cylinders, and that is why she suggests taking them out. It is interesting that instead of finding a way to incorporate the cylinders so as to help children to make the distinction between two- and three-dimensional shapes, she decides to take them out in order to avoid possible confusion.

    • The large amount of time that she took to make a table using all the children’s responses, which she eventually did not use.

      …