Introduction Level-2 visual perspective taking (VPT-2) reflects children’s ability to understand others’ visual experiences. However, the effects of viewing angle and task materials on 4-year-olds’ performance remain unclear. Methods Using a picture-taking (“photographer”) task, this study examined the effects of test tool and rotation angle, as well as egocentric error patterns, among 163 four-year-old children from Hainan, China. A 2 (test tool: Lego figurines vs. geometric solids) × 3 (rotation angle: 0°, 90°, 180°) within-subjects design was used. The formal test comprised 18 four-alternative trials, with three trials in each Tool × Angle condition; each correct response scored 1 and each incorrect response scored 0. Performance was assessed using raw correct scores and the proportions of egocentric errors. Results Rotation angle significantly affected performance in a nonmonotonic pattern: raw correct scores were highest at 0°, followed by 180°, and lowest at 90°. The main effect of test tool was significant, with higher raw correct scores in the Lego figurine condition than in the geometric solids condition. The Tool × Angle interaction for raw correct scores was not significant. The proportions of egocentric errors showed significant main effects of test tool and rotation angle, as well as a significant Tool × Angle interaction. Egocentric errors were most pronounced in the geometric solids condition at 180°. Supplementary analyses revealed no significant sex main effect or sex-related interactions. Discussion These findings indicate that 4-year-olds’ VPT-2 performance varies across rotation angles and test materials. Performance differences between material conditions may be associated with differences in task structure, stimulus discriminability, social cues, and spatial-relational judgment demands, whose independent contributions could not be isolated in this study. Because the analyses relied on raw correct scores and error-type data, the findings should be interpreted as differences in behavioral performance rather than direct evidence about processing strategies or cognitive mechanisms.
Angle is a fundamental concept that students need to learn correctly, as it is one of the building blocks of geometry and is embedded in many geometry topics. This study aimed to determine seventh-grade middle school students’ concept definitions and concept images of angle, as well as the ways in which they associated their concept definitions with their concept images. Adopting a qualitative research method, a form consisting of 23 open-ended questions was prepared by taking into account most of the angle-related learning outcomes up to the seventh grade. The form was administered to 168 seventh-grade students attending two state middle schools; after the written data were analysed, clinical interviews were conducted using the same form with 9 participants selected through criterion sampling. The data were analysed using qualitative data analysis and interpreted within Tall and Vinner’s concept image-concept definition framework. The findings showed that the participants held incorrect or incomplete images of angle and largely produced their personal concept definitions from their concept images. The participants could not define angle formally, confused angle with angle measure, and mostly emphasised the measure-related aspect of angle. They also had difficulty using the concept of angle in problem situations. The results point to the importance of learning environments in which the dynamic and static aspects of angle are associated and in which everyday-life contexts and dynamic geometry tools are used.
زاویه یکی از مفاهیم بنیادی است که دانش‌آموزان باید به‌درستی آن را بیاموزند، چرا که یکی از اجزای سازنده هندسه بوده و در بسیاری از مباحث هندسی جای گرفته است. هدف این پژوهش تعیین تعاریف مفهومی و تصاویر مفهومی دانش‌آموزان پایه هفتم متوسطه دربارهٔ زاویه و همچنین بررسی نحوه ارتباط تعاریف مفهومی آنان با تصاویر مفهومی‌شان بود. این پژوهش با اتخاذ روش کیفی انجام شد و فرمی شامل ۲۳ پرسش بازپاسخ با توجه به اکثر اهداف یادگیری مرتبط با زاویه تا پایه هفتم تهیه گردید. این فرم برای ۱۶۸ دانش‌آموز پایه هفتم که در دو مدرسه دولتی متوسطه تحصیل می‌کردند اجرا شد؛ پس از تحلیل داده‌های مکتوب، مصاحبه‌های بالینی با استفاده از همان فرم با ۹ نفر از شرکت‌کنندگان که به روش نمونه‌گیری مبتنی بر معیار انتخاب شده بودند، انجام گرفت. داده‌ها با استفاده از تحلیل داده‌های کیفی و در چارچوب تصویر مفهومی-تعریف مفهومی Tall و Vinner تفسیر شدند. یافته‌ها نشان داد که شرکت‌کنندگان تصاویر نادرست یا ناقصی از زاویه داشتند و عمدتاً تعاریف مفهومی شخصی خود را از تصاویر مفهومی‌شان استخراج می‌کردند. شرکت‌کنندگان قادر به تعریف رسمی زاویه نبودند، زاویه را با اندازه زاویه اشتباه می‌گرفتند و عمدتاً بر جنبه مرتبط با اندازه زاویه تأکید داشتند. همچنین در به‌کارگیری مفهوم زاویه در موقعیت‌های مسئله‌محور با دشواری مواجه بودند. نتایج بر اهمیت محیط‌های یادگیری که در آن‌ها جنبه‌های پویا و ایستای زاویه با یکدیگر مرتبط می‌شوند و از زمینه‌های زندگی روزمره و ابزارهای هندسه پویا استفاده می‌شود، تأکید دارد.
