Abstract:

The programme we present in this paper is aimed at developing cognitive strategies for change and combine problem-solving in children in their last year of Pre-School Education, the first cycle of Primary Education and/or children with mathematics learning difficulties.

The programme consists of 14 lessons in which children work on 6 types of change and 2 types of combine problems, which are all of additive structure.

The programme includes:
a) A “Teachers’ Guide” which, in addition to presenting the theoretical basis of the problems, provides a teaching guide for each of the 14 lessons.
This guide starts with the objectives for each lesson, the materials needed and the teaching procedure. This starts with a full group activity in which the teacher presents the task to be carried out and outlines the pair work and individual activities.
b) The “MATHS PROBLEMS FOR CHILDREN” Cd-rom. This CD-ROM contains a presentation that serves as a graphic support to the teacher’s explanations regarding the tasks to be undertaken.
c) The student’s workbook, “PROGRAMME FOR CHANGE AND COMBINE MATHS PROBLEM-SOLVING” includes the 6 types of change and 2 types of combine problems to be worked on during the 14 lessons. No problem involves numbers greater than 15. The teacher can change this according to students’ level of ability.
The level of difficulty depends on: a. the numbers used; b. whether there is a graphic representation of the problem or not; c. the different types of canonic sentence used (A±B=C); d. the presentation of a sentence for subsequent problem construction.

The analysis of the programme’s effectiveness was undertaken via the use of a pilot study. The participants were 48 second-year Primary School children, with an average age of 6 years and 10 months from two schools in the Bahía de Cádiz school district. The study was carried out during the second and third terms of the academic year. After the programme had been applied, the possible changes in cognitive strategies for the resolution of change and combine problems were analysed. A improvement in the level of problem-solving was confirmed.