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Supporting critical thinking in sequences and series through a problem-solving e-module with algebraic tasks

حمایت از تفکر انتقادی در دنباله‌ها و سری‌ها از طریق یک ماژول الکترونیکی حل مسئله با وظایف جبری

Nasrun Nasrun, Irwan Akib, Muhammad Ikram, Muhammad Muzaini, Rahmat Kamaruddin

Infinity Journal 2026 Vol. 15(4), pp. 1031-1060
https://doi.org/10.22460/infinity.v15i4.p1031-1060

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چکیده

Examining sequences and series often leads students to rely on formulas, especially when assignments require algebraic modeling and generalization. This condition may hinder the advancement of critical thinking, especially in evaluation, inference, and reasoning. This study examined the extent to which a problem-solving e-module with algebraic challenges enhanced students' critical thinking and identified the elements that best facilitated critical thinking during the learning process. The study used a sequential explanatory mixed-methods design. The quantitative phase encompassed 89 senior high school students from three classes. Students completed a pretest, engaged with an e-module featuring guiding questions, scaffolding, feedback, and reflection, and then completed a posttest. The quantitative data were examined utilizing descriptive statistics, normalized gain, pretest-posttest comparisons, and effect size analysis. Data were gathered from students' e-module assignments, classroom observations, written reflections, and task-oriented interviews. The data were examined using theme coding and synthesized with the quantitative results. The results indicated an improvement in overall critical thinking and across all metrics; however, the improvements were inconsistent. Evaluation and interpretation improved more significantly than explanation. Feedback, directed inquiries, scaffolding, and reflection facilitated critical thinking; however, argument quality and algebraic reasoning varied among students.

چکیده به فارسی

بررسی دنباله‌ها و سری‌ها اغلب منجر به اتکای دانش‌آموزان به فرمول‌ها می‌شود، به‌ویژه زمانی که تکالیف نیازمند مدل‌سازی جبری و تعمیم هستند. این وضعیت ممکن است پیشرفت تفکر انتقادی، به‌ویژه در ارزیابی، استنتاج و استدلال را مختل کند. این پژوهش میزان ارتقای تفکر انتقادی دانش‌آموزان توسط یک ماژول الکترونیکی حل مسئله با چالش‌های جبری را بررسی کرد و عناصری را که بیشترین تسهیل را در تفکر انتقادی طی فرایند یادگیری داشتند، شناسایی نمود. این مطالعه از طرح آمیخته تبیینی متوالی بهره برد. مرحله‌ی کمی شامل ۸۹ دانش‌آموز دبیرستانی از سه کلاس بود. دانش‌آموزان یک پیش‌آزمون را تکمیل کردند، با ماژول الکترونیکی که شامل پرسش‌های راهنما، پشتیبانی، بازخورد و تأمل بود کار کردند و سپس پس‌آزمون را انجام دادند. داده‌های کمی با استفاده از آمار توصیفی، بهره‌ی نرمال‌شده، مقایسه‌ی پیش‌آزمون-پس‌آزمون و تحلیل اندازه‌ی اثر بررسی شد. داده‌ها از تکالیف دانش‌آموزان در ماژول الکترونیکی، مشاهدات کلاسی، تأملات مکتوب و مصاحبه‌های مبتنی بر وظیفه گردآوری شد. داده‌ها با استفاده از کدگذاری تماتیک تحلیل و با نتایج کمی تلفیق گردید. نتایج نشان داد که بهبود در تفکر انتقادی کلی و در تمامی شاخص‌ها مشاهده شد؛ با این حال، این بهبودها یکنواخت نبودند. ارزیابی و تفسیر نسبت به توضیح، بهبود بیشتری داشتند. بازخورد، پرسش‌های هدایت‌شده، پشتیبانی و تأمل به تسهیل تفکر انتقادی کمک کردند؛ با این حال، کیفیت استدلال و استدلال جبری در میان دانش‌آموزان متفاوت بود.

ترجمه‌ی خودکار برای آشنایی سریع؛ برای نقل و ارجاع، متن اصلی ملاک است.

موضوع‌ها و کلیدواژه‌ها

استدلالدانش‌آموزانیادگیریAlgebraic numberArgument (complex analysis)Coding (social sciences)Critical reflectioncritical thinkingData collectionInterpretation (philosophy)Reflection (computer programming)

ارجاع

Nasrun, N., Akib, I., Ikram, M., Muzaini, M., & Kamaruddin, R. (2026). Supporting critical thinking in sequences and series through a problem-solving e-module with algebraic tasks. Infinity Journal, 15(4), 1031–1060. https://doi.org/10.22460/infinity.v15i4.p1031-1060

(Nasrun et al., 2026)

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قوانین پرسش و گفتگو
  1. با احترام و بدون توهین، تحقیر، برچسب‌زنی یا حمله‌ی شخصی با دیگران گفتگو کنید.
  2. از نوشتن هرگونه اطلاعات هویتی یا قابل‌شناسایی مراجعان، بیماران یا اشخاص ثالث، از جمله نام، شماره‌ی تماس، تصویر، نشانی، محل کار یا جزئیات منحصربه‌فرد پرونده خودداری کنید.
  3. اگر درباره‌ی یک تجربه‌ی بالینی سؤال می‌کنید، اطلاعات را تا حد ممکن بی‌نام و کلی بیان کنید تا امکان شناسایی فرد وجود نداشته باشد.
  4. این بخش برای یادگیری و گفت‌وگوی علمی است و جایگزین ارزیابی، تشخیص، مشاوره یا روان‌درمانی شخصی نیست.
  5. در شرایط بحران یا خطر آسیب به خود یا دیگران، به این بخش اتکا نکنید و برای دریافت کمک فوری با اورژانس اجتماعی ۱۲۳ یا صدای مشاور بهزیستی ۱۴۸۰ تماس بگیرید.
  6. انتشار تبلیغات، معرفی خدمات شخصی، شماره‌ی تلفن، شناسه‌ی شبکه‌های اجتماعی، پیوند تبلیغاتی یا درخواست جذب مراجع در این بخش مجاز نیست.
  7. در بیان ادعاهای علمی، به‌ویژه درباره‌ی اثربخشی درمان‌ها، تشخیص یا یافته‌های پژوهشی، تا حد امکان نام منبع معتبر، مقاله یا راهنمای علمی را ذکر کنید.
  8. از ارائه‌ی تشخیص قطعی، تجویز درمان یا دارو و توصیه‌های بالینی شخصی به سایر کاربران خودداری کنید.
  9. پاسخ‌هایی که کارشناسان فکر بنیان می‌دهند با برچسب «پاسخ فکر بنیان» یا «کارشناس فکر بنیان» نمایش داده می‌شوند و سایر نوشته‌ها بیانگر نظر کاربران هستند.
  10. گزارش نوشته‌ی نامناسب: اگر نوشته‌ای حاوی نقض محرمانگی، محتوای آسیب‌زا، توهین، تبلیغ یا تخلف از این قوانین است، گزینه‌ی «گزارش» را انتخاب کنید تا تیم سایت بررسی کند.

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