بررسی کتاب ریاضی پایه‌ هشتم بر اساس میزان برقراری ارتباط بین دانش رویه‌ای و دانش مفهومی

هدف پژوهش حاضر، تحلیل محتوای کتاب ریاضی پایه هشتم براساس میزان توجه به ارتباط بین دانش‌مفهومی و دانش‌رویه‌ای است، که برای انجام این پژوهش از شیوۀ تحلیل‌محتوا استفاده گردیده‌ است. جامعۀ آماری، کتاب ریاضی پایه‌ هشتم چاپ 1397 و کل محتوای این کتاب، تحلیل شد. ابزار پژوهش، فرم‌های تحلیل محتوای محقق‌ساخته است که به‌منظور اعتباریابی و روایی صوری و محتوایی ابزار از نظرات و دیدگاه‌های صاحب‌نظران، استادان آموزش ریاضی و معلمان باسابقه‌ ریاضی استفاده شد. همچنین، جهت اعتبار نتایج، ضریب توافق 81% از فرمول پایایی ویلیام اسکات به دست آمد. نتایج نشان داد که در تهیۀ‌ محتوای کتاب توجه کمی به برقراری ارتباط بین دانش مفهومی و رویه‌ای شده و در این بین بیشترین توجه به ارتباط بین دانش مفهومی و رویه‌ها در فعالیت‌ها و کاردرکلاس‌ها است، که البته این تعداد نیز چندان درخور توجه نیستند. بیشترین بخش مسائل کتاب نیز به دانش رویه‌ای اختصاص یافته است. در مجموع می‌توان گفت که محتوای کتاب نگاهی افراطی به آموزش رویه‌ها دارد. لازم است که مولفان و دست‌اندرکاران آموزشی در ارائۀ محتوا با توجه به نیازهای جامعه و دانش‌آموزان، فرصت‌هایی برای رشد و پرورش همه‌جانبۀ‌ آنان فراهم نمایند.

Evaluating 8th Grade Math Textbook Based on Conceptual and Procedural Knowledge conceptual knowledge

Introduction At the present time, students need to be equipped with knowledge and flexible attitudes to be able to adapt to  rapid changes in society. Mathematics is one of the most important sciences which can develop the power of thought.  One of the factors which can play a vital role in develping students’ mathematical skill is their mathematical knowledge. Considering this, it is believed that students need to improve both their canceptual and procedural knowledge of mathematics in order to be successful. Based on the previous research, conceptual knowledge involves awareness and skillful movement along special networks of  concepts, rules, algorithms, procedures, and so on. In other words, not only is conceptual knowledge concerned with what is known, i.e. knowledge of concepts, but also it can be helpful  in learning  key concepts and their  connections. Procedural knowledge is the knowledge of the steps involved in achieving different goals and is concerned with the use of skills, algorithms, techniques and methods. Indeed, procedural knowledge is a chain of sequential actions which can be taken to solve a problem and can be developed through practicing and solving specific problems. Although the two types of knowledge seem to be independent, they are in fact interrelated. In other word, these two kinds of knowledge are part of an interconnected chain, and can never be separate from each other, and are located at both ends of the knowledge spectrum. The Furthermore, they cannot develop independently and affect each other. Regarding these, many attempts have been made to investigate the relationship between the two types of knowledge. Some scholars have also been interested in exploring the causal relationship between the two, i.e. in understanding which one causes the other. For instance, theorists who believe that concepts are first formed in the mind claim that individuals acquire conceptual knowledge before procedural knowledge. In contrast, there are some other theorists who believe procedures develop before concepts and state that individuals first learn procedures for solving a problem and then the structure of concepts. Therefore, two approaches, namely the educational approach and the developmental approach, have been proposed regarding conceptual and procedural types of knowledge and the relationship between the two. It is noteworthy, however, that each approach can be considered as appropriate in teaching particular types of skills and concepts. Proponents of the educational approach believe that conceptual knowledge leads to procedural knowledge and Proponents of the Developmental approach believe that procedural knowledge leads to conceptual knowledge. Due to the fact that the ecucational system im Iran is od a centralized type,  a main criterion for improving mathematics education in the country can be curricula development and textbook authoring based on the particular needs which arise. With regard to recent changes in the content of in the 8th grade math textbookand concerning the faxtthat the textbook is used by all Iranian 8th grade students, a thorough evaluation of the textbook seems necessary.   Research Questions 1.         Which types of conceptual or procedural knowledge do the various sections of the 8th grade math textbook embody/pay more attention to?what is the distribution of the use of conceptual and procedural knowledge among the various sections of the 8th grade math textbook? 2To what extent is the 8th grade math textbook focused on the connection between conceptual and procedural knowledge? 3 Is the 8th grade math textbook’s overall approach to knowledge  of an educational or a developmental type?   Research materials and method This study aimed at evaluating content of the 8th grade mathematics textbook in terms of the amount of attention paid to each of conceptual and procedural types of knowledge. Accordingly, content analysis was used in order to conduct this study. The research material was the 8th grade mathematics textbook. Sample size was exactly the same as population size. In other words, i.e content analysis was done in relation to content of the whole book. Research instrument was a researchermade content analysis scale. Then, the views and opinions of experts, maths instructors and teachers were sought in order to examine content validity of the developed scale. To assess reliability of the scale, the percentage of agreement among the coders was determined through the use of Scott’s pi(B)coefficient and the reliability coefficient value of 0.81 was obtained.         Results Based on the the results, textbook authors had paid little attention to the connection between conceptual and procedural knowledge in the main texts, and more attention to the connection between conceptual and procedural knowledge in the activities and classroom exercises, which, of course, did not seem to be enough. Furthermore, most of the textbook’s problems had also focused on the improvement of procedural knowledge.   Discussion In summary, the 8th grade math textbook has held an extreme view of teaching procedures, and in most cases the emphasis has been put on increasing procedural knowledge. In addition, little attention has been paid to the connection between conceptual and procedural types of knowledge. Therefore, textbook authors need to emphasize the connection between the two types of knowledge in designing textbook activities On one hand, paying attention to the connections between familiar procedures and new concepts can help students acquire a better understanding of the concepts. On the other hand, the education system can achieve one of its major goals, i.e. making people more reflective, through helping students in development of their understanding. It is recommended, thus, that textbook authors and educators design more effective textbooks through both community and student needs assessment.