ANNEX 1. Abel’s case

Below, we present a situation concerning a permanent teacher training seminar. The seminar is related to the learning and teaching of subtraction. One of the teachers, Abel, who participated in the seminar talked about a situation he is currently going through with one of the groups of pupils he is working with.

Analyze the situation and give your opinion afterwards about the case described.

Abel, third grade teacher in an elementary school

Currently, I am working with a group of third grade pupils. This year, my pupils are having lots of trouble learning subtraction.

In previous years, I haven’t had these problems, because, generally, I used to start working with the same group of children beginning in second grade and continued to work with them in third grade.

I have a few cases like the ones that follow:

A) When I suggested the following problem, Ana solved it in the following way:

B) Compared with the previous problem, Carlos solves it orally following these steps:

C) Finally, there is Beatriz who solved the problem in the following way:

Script of the case discussion

In relation to situation A.

a) Have you ever faced a similar situation?
b) Do you think that what is occurring in this situation could be due to a teaching problem? Why?
c) What do you think is the reason for Ana’s difficulty?
d) What recommendations would you give the teacher to help Ana in this situation?

In relation to situation B.

a) Do you consider that this situation is problematic? Why?
b) According to you: what is Carlos thinking about in order to solve the problem the way he did?
c) Do you think it is advisable for children to use informal or non-conventional strategies to solve subtraction problems? Why?
d) What would you do in such a situation?

In relation to situation C.

a) What is Beatriz’s problem?
b) What would you advise the teacher to do to solve this situation?
c) Describe the subtraction procedure that seems to you to be the most appropriate to teach children in this school grade.
d) What do you think of the problem proposed by the teacher?

Abel’s colleagues have suggested the following pedagogical intervention options:

Option 1

Use coins of different denomination as an aid so the children can solve the operation (200-125).

Option 2

Teach the children the conventional method for subtraction through a sequence of numerical exercises, gradually increasing the difficulty of the operation and the size of the numbers involved.

Option 3

Use multibase material as an aid for the comprehension of each step in the conventional subtraction procedure.

Option 4

Starting from the setting forth of problems related with the children’s everyday life and then letting them free to solve it using either an informal procedure or the conventional one.

Option 5

Reinforce the learning of the conventional procedure for subtraction, explaining every step more clearly to the children and giving them many numerical exercises so they can learn to dominate it.

a) Among the didactic options described above, which seems to you to be the most adequate to teach subtraction? Why?
b) Which didactic option seems to you to be the least adequate? Why? What suggestion would you make to teach subtraction, but which, for some reason, is not , or cannot be, carried out in school?