Child and problem solving. The role of the school
At first glance, the school plays an important role in teaching the child about problem solving. An adult may ask, slightly , “Isn’t that what he does at school all day? Solve problems! ”
But we ask ourselves: is the fact that he asked, over and over again. To solve problems in textbooks and collections to help the student to be able to solve the problems. He will face later in life? We must know that life will never give the child of today (and the adult of tomorrow) problems. That have another algorithm to solve between the pages of a book. The child must learn that when he becomes an adult. He must do much more, understand the phenomenon in its complexity. Find data, information, build strategies, come up with solutions – all this alone. Without the help to any teacher.

Seven Important Steps

Arnold Goldstein offers us even seven important steps for the child to teach him. How to solve these complex problems when he encounters them in his life:
  1. First of all, it is important for our student to learn to analyze the situation well. To realize what he is dealing with;
  1. only secondly should the problem identified and defined. It must said that often the problem is not very clear and a good analysis of the situation will give us the key to understanding where the problem really is;
  1. the third step is to gather information from the child’s point of view (even if we are dealing with opinions, facts and information known or unknown at the moment);
  1. an important step is this moment: the child must go beyond his point of view. And gather information from the point of view of other people. (on several levels what they see.What they believe and what they feel);
  1. in life there is rarely a single solution to the problem: this is why it is important to consider alternative strategies, to think about what barriers / obstacles we might encounter and to “open our eyes” to opportunities and challenges;
  1. step number six draws our attention to the fact that it is not enough to reach a result; it is equally important to think as a whole, to think about the consequences, to anticipate the reactions and consequences that the implementation of that result might have;
  1. an in-depth analysis of the entire approach taken so far contained in step number seven. It is about going beyond the tendency – natural – to limit oneself to the first solution that seems to work, to persevere, to look carefully until the best solutions identified that offer the safest and most efficient solution to the problem.
Analyzing the seven steps above can we say that our school offers such a resolute path for students? Are they ready to apply such an approach to the problems they will encounter beyond the boundaries of the school?

Preschool Children Solving Additive Structure Problems: What Strategies?


Kindergarten Children Solving Additive Problems: Which Strategies?



Studies carried out in different contexts highlight the ability of children to correctly solve addition and subtraction problems, even before these operations are formally taught. The study described here seeks to understand how children from 4 to 6 years old (N=90) understand the problems of additive structure. To this end, it tries to answer the following questions: 1) What performances do children have when solving problems of additive structure? 2) What strategies do you use to solve additive structure problems? A quantitative methodology was adopted that analyzes children’s performances and strategies when they solve 28 problems of additive structure, presented from individual structured interviews.


A few examinations report small kids’ capacity to take care of expansion and deduction issues prior to getting any conventional guidance. This study centers around how 4-6-year-old kids (N=90) get added substance structure issues. It resolves two inquiries: 1) How do kids perform while tackling added substance structure issues? 2) What systems do kids utilize while taking care of added substance structure issues? Quantitative techniques were utilized to break down youngsters’ exhibition and systems while taking care of 28 added substance structure issues introduced to them utilizing individual meetings. Results propose that kids effortlessly tackled the given issues utilizing satisfactory procedures, some might count and depend on mathematical realities.
 Informal knowledge
During preschool age, children develop a large amount of knowledge as a result of their daily experience, understood as informal knowledge. Not disregarding informal knowledge such as that which is developed on a daily basis, outside of school, or even at school without being “taught” (BECKER & SELTER, 1994), the definition of Baroody and Ginsburg (1986), which refer to informal knowledge as the knowledge that the child develops daily, before formal schooling, and that later transports to the learning process. Some authors suggest that Mathematics Education should be built on the informal knowledge of children (see BAROODY & GINSBURG, 1986;RESNICK, 1989).

Logical Principles

This informal knowledge is so rich that Nunes, Bryant e Watson (2009)they even suggest that some of the intuitive models that children use translate the understanding of logical principles that allow them to appropriate mathematical notions.
Ginsburg e Seo (1999)understands that youngsters’ casual arithmetic contains, at a certain level, a considerable lot of the numerical thoughts that instructors need to advance at a formal and unequivocal level.
Resnick (1989)states that one way to understand the development of the concept of number in children is to analyze the use of counting in informal and invented strategies when solving problems. When the child shifts from “counting all” to “counting from” it is a sign that children relate their knowledge of part-whole relationships to the counting sequence, demonstrating an initial understanding of the additive composition of number (NUNES; BRYANT; WATSON, 2009). Thus, the way children use counting to solve problems of additive structure reflects the changes that occur in their reasoning.

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