خلاصة:
One of the factors influencing students' mathematical performance is their mathematical knowledge. In recent years, the model of mathematical knowledge, like many other topics in mathematics education, has evolved. The present article reviews and examines important research and theoretical perspectives regarding mathematical conceptual knowledge and procedural knowledge. The results of the review identified three fundamental perspectives in this field. First, a one-dimensional model of mathematical knowledge was presented, such that this knowledge was (initially) categorized based on type into conceptual and procedural knowledge. With the passage of time and the need to change this model, a two-dimensional model of knowledge based on type and quality was suggested, and finally, a three-dimensional model of knowledge based on type, depth, and readiness for learning was proposed. Furthermore, different ideas regarding the relationship between these two types of knowledge have been raised, the most important of which are: the inactive view, the simultaneous action view, the dynamic interaction view, the developmental view, and the reciprocal view. Examining existing theoretical perspectives as well as the results of the present research shows that the three-dimensional model of mathematical knowledge, compared to other models, and also the reciprocal view regarding the relationship between conceptual and procedural knowledge, compared to other views, provides a more complete implication.
ملخص الجهاز:
Reviewing existing theoretical perspectives as well as the results of the present research shows that the three-dimensional model of mathematical knowledge, compared to other models, and also the reciprocal perspective regarding the relationship between conceptual and procedural knowledge, compared to other perspectives, provides a more complete implication.
Different studies in the field of conceptual knowledge and procedural knowledge 1 are also conducted to increase students' mathematical knowledge and ultimately enhance their learning and understanding.
Skills/Procedural knowledge 1 (Papert 2, 1980); *Words specifying concept-processes/Mental images 3 (Tall, Vinner 4, 1981); *Hierarchies of cognitive units-Condition-Action rules 5 (Anderson, 1983); *Understanding and comprehension-Algorithmic performance 6 (Nesher 7, 1986); *Conceptual competence-Procedural competence 8 (Gelman, Mack 9, 1986); *Rich vs.
Relational mathematical learning involves creating a conceptual structure such that the holder of the schema can produce an unlimited number of maps to go from any starting point to any end point; for example, Skemp (1976), (translated by Heydari and Gouya, 1984), states that for students, learning that "the area of a triangle is equal to half the product of the base and the height" (instrumental understanding) is easier than learning the reason for its correctness.
The authors of the article believe that in order for a student to reach the required understanding of concepts and procedures, their knowledge must first become deep and then reach the experienced level in the dimension of readiness for learning.
Subsequently, Hessenberg's (2006) model of mathematical knowledge is discussed based on type (conceptual versus procedural), quality (surface versus deep), and readiness for learning (novice versus experienced), which adds another dimension to Star's model.
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