بررسی تاثیر تدریس معادلات دیفرانسیل بر اساس رویکرد مدل سازی در عملکرد حل مسئله دانشجویان فنی و مهندسی

هدف: مدل‌‌ سازی ریاضی که فرآیند دو سویه ترجمه بین مسائل دنیای واقعی و ریاضیات است، می‌‌تواند برای ایجاد انگیزه، رشد توانمندی‌های شناختی و ارتقاء توانایی انتقال دانش ریاضی به حوزه‌های دیگر همچون علوم مهندسی به کار رود. این پژوهش با هدف بررسی تاثیر تدریس معادلات دیفرانسیل بر اساس رویکرد مدل‌سازی در عملکرد حل مسئله دانشجویان فنی و مهندسی در مقایسه با تدریس سنتی انجام پذیرفت.روش: در این پژوهش از روش شبه‌آزمایشی با طرح پیش‌آزمون-پس‌آزمون با گروه کنترل استفاده شد. دانشجویان دانشکده فنی و مهندسی واحد تهران مرکزی دانشگاه آزاد اسلامی جامعه آماری این پژوهش را تشکیل دادند. نمونه آماری در دسترس و شامل دو گروه هر یک با 33 دانشجوی مهندسی بود. معادلات دیفرانسیل مرتبه اول تفکیک‌پذیر، خطی و همگن در گروه آزمایش با رویکرد مدل‌سازی و در گروه کنترل به روش سنتی تدریس شد. تلفیقی از نتایج آزمون تعیین سطح ریاضی عمومی و پیش‌آزمون مدل‌سازی به‌عنوان متغیر مداخله‌گر در آزمون تحلیل کوواریانس به کار گرفته شد.یافته‌ها: داده‌های مستخرج از آزمون‌ها با نرم‌افزار spss  نسخه 26 تحلیل شد. نتایج این پژوهش نشان می‌دهد که تدریس معادلات دیفرانسیل بر اساس رویکرد مدل‌سازی علاوه بر افزایش توانمندی به‌کارگیری دانش ریاضی در حوزه‌های مهندسی، به‌صورت معناداری می‌تواند عملکرد حل مسئله دانشجویان را بهبود بخشد.

investigating the effect of teaching differential equations based on the modeling approach on the problem-solving performance of technical and engineering students

objective: mathematical modeling is an interconnecting process between mathematics and real-world problems that, as a tool, can be applied to increase motivation, develop cognitive competencies, and enhance the ability to transfer mathematical knowledge to other areas such as engineering disciplines. this study aimed to investigate the effect of applying the modeling approach on the problem-solving performance of engineering students during a differential equation course and compare the results with those of traditional teaching.method: a quasi-experimental method with a pretest-posttest design comprising a control group was applied in this study. the statistical population was 1225 engineering students of the islamic azad university central tehran branch. the available statistical sample contained two experimental and control groups, each comprising 33 engineering students who randomly attended the course. the modeling approach was applied to teach the first-order separable, linear and homogeneous differential equations in the experimental group, whereas, in the control group, the traditional approach was used. since the antecedent knowledge of calculus directly affects the ability of students to learn differential equations, a placement test was first applied to both groups. a combination of the results derived from the placement test and the modeling pre-test was used as the covariate in the analysis of covariance (ancova) test, and the modeling performance of both groups and their problem-solving skills were eventually examined.findings: the data extracted from pre-test and post-test results were analyzed using the spss version 26. the results of this study indicate that apart from the fact that teaching differential equations based on the modeling approach can increase the ability to apply mathematical knowledge in the field of engineering, it also can significantly improve their problem-solving performance. in contrast, in the traditional approach, students cannot transfer the knowledge attained from the course to applied and real-world problems. the research findings can be used in reviewing the differential equation syllabus.abstract (extended): due to the lack of connection between real-world applications that students encounter in their future careers and the knowledge attained from traditional mathematics courses at the university, students are virtually incapable of interpreting complex structural systems as the future workforce. therefore, the primary purpose of introducing major mathematics courses in the engineering curriculum should be to prepare students for mathematical reasoning on the issues they will face in their related engineering courses and/or real-world applications. studies over the past few decades have shown that mathematical modeling as an interconnecting tool between mathematics and real-world problems can help students fulfill this goal effectively.