The concept of Last name forms the basis of the mathematics, Being therefore its acquisition the foundation on which mathematical knowledge is built. The concept of number was conceived as a complex cognitive activity, in which different processes act in a coordinated way.
From the youngest age, children develop what is called intuitive informal mathematics. This development is due to the fact that children show a biological propensity to acquire basic arithmetic skills and to stimulate the environment, as children from an early age find quantities in the physical world, counting quantities in the social world and mathematical ideas in the world. history and literature.
Learn the concept of number
The evolution of the number depends on education. Teaching in early childhood education to classification, serialization and number retention it produces gains in reasoning ability and academic performance that are maintained over time.
Difficulties in counting in young children interfere with the acquisition of math skills later in childhood.
From the age of two, the first quantitative knowledge begins to develop. This development is completed by the acquisition of so-called proto-quantitative diagrams and the first digital skill: explain.
Diagrams that allow the child’s “ mathematical mind ”
The first quantitative knowledge is acquired through three proto-quantitative schemes:
- The proto-quantitative scheme comparison: Thanks to this, children can have a series of terms that express quantity judgments without numerical precision, such as larger, smaller, more or less, etc. Using this scheme, language tags are assigned to the size comparison.
- The proto-quantitative increase-decrease scheme: With this diagram, three-year-olds are able to reason about the changes in quantities when adding or removing an item.
- Ethe proto-quantitative scheme in part: Allows preschoolers to accept that any room can be broken into smaller parts and if we put them back together they give birth to the original part. They may think that when they put two quantities together, they get a larger quantity. Implicitly, they begin to know the auditory property of quantities.
These diagrams are not sufficient to deal with quantitative tasks, so they must use more precise quantification tools, such as counting.
Counting is an activity that to an adult may seem simple but which requires integrating a number of techniques.
Some consider the count as a memorized and meaningless learning, in particular of the standard numerical sequence, to gradually endow these routines with a conceptual content.
Principles and skills needed to improve in the counting task
Others consider that the count requires the acquisition of a series of principles which govern the capacity and allow a progressive sophistication of the count:
- The principle of individual correspondence: Involves labeling each element of a set only once. It is the coordination of two processes: participation and labeling, by partitioning, they control the elements counted and those which are missing to count, while having a series of labels, so that each corresponds to an object of the set. counted, even if they do not follow the correct sequence.
- The principle of established order: It states that in order to explain it is essential to establish a coherent sequence, although this principle can be applied without the need to use the conventional digital sequence.
- The principle of cardinality: Defines the last label of the numeric sequence to represent the cardinality of the set, the number of elements that the set contains.
- The principle of abstraction: Determine that the above principles can be applied to any type of set, both with homogeneous elements and with heterogeneous elements.
- The principle of irrelevance: Indicates that the order in which the items are listed for the first time is unrelated to their cardinal designation. They can be counted from right to left or vice versa, without affecting the result.
These principles define the rules of procedure for how to count a set of objects. From his own experiences the child acquires the conventional numerical sequence and will allow him to establish the number of elements of a set, that is to say to master the counting.
On many occasions, children develop a belief that some non-essential characteristics of the count are essential, such as standard direction and adjacency. It is also the abstraction and irrelevance of order, which serve to guarantee and soften the scope of the above principles.
The acquisition and development of strategic skills
Four dimensions have been described through which the development of students’ strategic competence is observed:
- Policy Directory: Different strategies used by a student to do his homework.
- Frequency of strategies: How often each of the strategies is used by the child.
- Effectiveness of strategies: Precision and speed with which each strategy is executed.
- Selection of strategies: Ability of the child to select the most adaptive strategy in each situation and which allows him to be more efficient in performing tasks.
Prevalence, explanations and manifestations
The different estimates of the prevalence of math learning difficulties differ due to the different diagnostic criteria used.
The DSM-IV-TR indicates that the prevalence of computer disorders has only been estimated in about one in five cases of learning disabilities. It is assumed that about 1% of school-aged children suffer from a computer disorder.
Recent studies indicate that the prevalence is higher. About 3% have concurrent difficulties in reading and math.
Difficulties in math also tend to persist over time.
How Do Children Have Difficulties Learning Mathematics?
Many studies have noted that basic number skills such as identifying numbers or comparing the magnitude of numbers are found intact in most children. Difficulties in learning math (Hereinafter, DAM), at least in terms of simple numbers.
Many children with DAM they have difficulty understanding certain aspects of the count: Most understand stable order and cardinality, at least fail to understand one-to-one correspondence, especially when the first element counts twice; and they consistently fail in tasks that involve understanding the irrelevance of order and adjacency.
The greatest difficulty for children with AMD is in learning and memorizing number facts and in calculating arithmetic operations. They have two major problems: procedural and MLP fact finding. Knowing the facts and understanding the procedures and strategies are two separate issues.
Procedural issues are likely to improve with experience, but your recovery difficulties will not. This is so because procedural problems arise from a lack of conceptual knowledge. Auto-retrieval, on the other hand, is a consequence of semantic memory dysfunction.
Toddlers with ADD, however, use the same strategies as their peers They depend more immature counting strategies and less fact retrieval of memory than his peers.
They are less effective at performing different fact-counting and collecting strategies. As age and experience increase, those who have no difficulty perform recovery more accurately. Those with DAM show no change in the accuracy or frequency of using the strategies. Even after a lot of practice.
When they use the memory facts retrieval is usually inaccurate: they make mistakes and take longer than those without DA.
Children with AMD have difficulty retrieving digital facts from memory, having difficulty in automating this retrieval.
Boys with DAM do not adaptively select their strategies Children with DAM perform worse in frequency, effectiveness, and adaptive selection of strategies. (Referred to the count)
The impairments observed in children with AMD seem to respond more to a model of developmental delay than to a deficit model.
Geary devised a classification in which three subtypes of DAM are established: procedural subtype, subtype based on semantic memory deficit, and subtype based on visuospatial skills deficit.
Subtypes of Children Who Have Difficulty in Mathematics
The research identified three subtypes of DAM:
- A subtype with difficulty performing arithmetic procedures.
- A subtype with difficulty representing and retrieving arithmetic facts from semantic memory.
- A subtype with difficulties in visuospatial representation of digital information.
Working memory is an important component of mathematics performance. Working memory problems can lead to procedural errors, as can actually recovery.
Students with language learning difficulties + DAM they seem to have difficulty remembering and retrieving math facts and problem solving, Both vocabulary and complex or real life, more severe than students with isolated DAM.
Those with isolated DAM have difficulty with the visuospatial diary task, which required memorizing information with movement.
Students with DAM also have difficulty interpreting and solving verbal math problems. They would have a hard time detecting relevant and irrelevant information about issues, constructing a mental representation of the issue, remembering and performing the steps involved in solving a problem, especially multi-step issues, by using cognitive and metacognitive strategies.
Some suggestions for improving math learning
Solving problems requires understanding the text and analyzing the information presented, developing logical plans for the solution, and evaluating the solutions.
requires: cognitive demands, such as declarative and procedural knowledge of arithmetic and the ability to apply this knowledge to word problems, Ability to perform a correct representation of the problem and the ability to plan to resolve the problem; metacognitive demands, such as knowledge of the solution process itself, as well as strategies for controlling and monitoring its performance; and emotional conditions such as a favorable attitude towards mathematics, a perception of the importance of problem solving, or confidence in one’s own abilities.
There are many factors that can affect math problem solving. It is increasingly evident that most students with DAM have more difficulty in the processes and strategies associated with constructing a representation of the problem than in performing the operations necessary to solve it.
They have problems with knowing, using and controlling problem representation strategies, to grasp the contours of different types of problems. They propose a classification differentiating 4 main categories of problems according to the semantic structure: change, combination, comparison and equalization.
These superschimas would be the knowledge structures that are brought into play to understand a problem, to create a correct representation of the problem. From this representation, we consider the execution of the operations to arrive at the solution of the problem by memory strategies or from the immediate recovery of long-term memory (MLP). Operations are no longer solved in isolation, but as part of solving a problem.
- Cascallana, M. (1998) Introduction to mathematics: teaching materials and resources. Madrid: Santillana.
- Díaz Godino, J, Gómez Alfonso, B, Gutiérrez Rodríguez, A, Rico Romero, L, Serra Vázquez, M. (1991) Field of didactic knowledge of mathematics. Madrid: Editorial Síntesi.
- Ministry of Education, Culture and Sports (2000) Difficulties in learning mathematics. Madrid: summer classes. Higher institute and teacher training.
- Orton, A. (1990) Didactics of mathematics. Madrid: Ediciones Morata.