Successful Strategies of Primary School Students in Proportional Problems

Magina, Sandra Maria Pinto; Lautert, Sintria Labres; Santos, Ernani Martins dos

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OTHER THEMES • Educ. Real. 45 (4) • 2020 • https://doi.org/10.1590/2175-623696023 copy

Successful Strategies of Primary School Students in Proportional Problems

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract:

The article investigates the successful strategies mobilized by students in the literacy cycle when solving problems of simple proportion. 483 students from the 1st to the 3rd grade of Brazilian Elementary Education, were asked to solve six problems of proportion, and the responses of 182 students who had successful strategies were analyzed. When comparing school grades, there is an increase in hits from year to year, in the class of situations one-to-many, which cannot be said about the class for many, which remained stagnant. From the results obtained, it is possible that the multiplicative structure is being little discussed in the first three grades of elementary school.

Keywords:
Simple Proportion; Multiplicative Conceptual Field; Problem Solving

	1st grade (n=22)			2nd grade (n=45)			3rd grade (n=115)						Total
	E1	E2	E3	E1	E2	E3	E1	E2	E3	E4	E5	E6
P1	3 (of 22)	6	0	9 (of 45)	16	3	17 (of 115)	30	18	7	16	0	125 (of 182)
P2	1 (of 22)	3	1	5 (of 45)	9	0	14 (of 115)	35	1	0	5	0	74 (of 182)
P3	7 (of 22)	1	0	5 (of 45)	0	0	25 (of 115)	7	1	0	4	0	50 (of 182)
P4	0 (of 22)	0	1	1 (of 45)	0	0	6 (of 115)	0	0	0	0	2	10 (of 182)
P5	7 (of 22)	0	0	5 (of 45)	0	0	11 (of 115)	0	0	0	0	0	23 (of 182)
P6	0 (of 22)	0	0	2 (of 45)	0	0	4 (of 115)	2	0	0	0	2	10 (of 182)
TOTAL	18 (of 132)	10	2	27 (of 270)	25	3	77 (of 690)	74	20	7	25	4
%	14	8	1,5	10	9	1	11	11	3	1	4	0,5

Universidade Federal do Rio Grande do Sul - Faculdade de Educação Avenida Paulo Gama, s/n, Faculdade de Educação - Prédio 12201 - Sala 914, 90046-900 Porto Alegre/RS Brasil, Tel.: (55 51) 3308-3268, Fax: (55 51) 3308-3985 - Porto Alegre - RS - Brazil
E-mail: educreal@ufrgs.br

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[1] Sandra Maria Pinto Magina has a bachelor’s degree in Psychology, a PhD in Mathematical Education from the University of London, a post-doctorate from the University of Lisbon. Professor in the Department of Exact Sciences and Technology, and member of the collegiate bodies of the Graduate Programs in Mathematics Education and in Education at UESC / BA. ORCID: http://orcid.org/000-0003-0383-9744 Email: sandramagina@gmail.com

One-to-many	Many-to-many
P1. Joana knows that, in a package, there are 6 cookies. She has 5 packages. How many cookies does Joana have?	P4. To make 3 costumes, 5m of fabric is required. Ana has 35m of fabric. How many fantasies can she make?
P2. A supermarket did a promotion: “Take 4 liters of juice for only 12 reais”. How much will each liter of juice cost?	P5. Caio bought 9 boxes of juice and paid 15 reais. If he bought 3 boxes of juice, how much would he need to pay?
P3. Escola Recanto will host a party for 36 guests. At each table, there will be 4 guests. How many tables will the school need to rent?	P6. In a contest at Escola Saber, every 3 laps running on the court, the student scored 4 points. Alex ran 15 laps on the court. How many points did he score?

Scores	One situation	Two situations	Three situations	Four situations	Five situations	Six situations
Classes	One situation	Two situations	Three situations	Four situations	Five situations	Six situations
The two classes (n = 182)	108	46	21	5	2	0
One-to-many (n = 161)	96	44	21	0	0	0
Many-to-many (n = 40)	36	4	0	0	0	0