Ebenezer Owusu

Abstract Despite decades of effort to improve mathematical outcomes, studies examining the integrated roles of affective dimensions such as confidence, perceived value, and motivation in relation to mathematics achievement among Senior High School students in Ghana remain relatively limited. In this study, confidence was operationalised through items reflecting students’ domain-specific mathematics self-efficacy beliefs. This study examines the structural associations of confidence, perceived value, and motivation with self-reported mathematics achievement among final-year students in a selected Senior High School in the Atwima Nwabiagya North Municipal Assembly of Ghana. A quantitative descriptive correlational design was employed, and data were collected from 296 students using a structured questionnaire. Self-reported mathematics achievement was measured using students’ responses to items concerning their perceived achievement in mathematics, rather than standardised test scores or school achievement records. The hypothesised structural relationships among confidence, perceived value, motivation, and self-reported mathematics achievement were examined using structural equation modelling (SEM). Within the participating school, the results showed that confidence, perceived value, and motivation were each positively and significantly associated with self-reported mathematics achievement, with confidence having the largest standardised coefficient, followed by motivation and value. Given these findings, instructional practices that support students’ confidence may be considered in mathematics teaching. Likewise, opportunities to connect mathematics with real-world applications may help students recognise its value, while supportive learning environments may provide conditions conducive to sustained engagement with mathematics learning.

This study examined pre-tertiary students’ geometric problem-solving performance, the distribution of their errors across Van Hiele levels of geometric reasoning, and the nature of these errors using Newman's Error Hierarchical Model. A descriptive quantitative research design, complemented by qualitative content analysis of students’ written responses, was adopted. The sample comprised 300 final-year students selected through stratified random sampling. Data were collected using a researcher-designed Geometry Problem-Solving Test consisting of twelve open-ended items aligned with the senior high school geometry curriculum. Students’ responses were analysed using frequency and percentage distributions, while error patterns were classified using Newman's framework and mapped onto Van Hiele levels. The findings showed generally low performance in geometry problem solving, with most students scoring within the lower performance range. Error analysis indicated that students at lower Van Hiele levels, particularly visualisation and analysis, exhibited higher frequencies of comprehension and transformation errors. In contrast, students at higher reasoning levels showed fewer conceptual and representational difficulties but continued to experience process skills and encoding errors. The findings indicate different patterns of problem-solving errors observed among students demonstrating different levels of geometric reasoning. The results demonstrate the value of interpreting students’ geometric problem-solving through both the Van Hiele and Newman frameworks, providing complementary perspectives on students’ reasoning and the errors evident in their solution processes.

این مطالعه به بررسی عملکرد حل مسئله هندسی دانش‌آموزان پیش‌دانشگاهی، توزیع خطاهای آنان در سطوح استدلال هندسی ون هیله و ماهیت این خطاها با استفاده از مدل سلسله‌مراتبی خطای نیومن پرداخت. طرح پژوهش کمی توصیفی، همراه با تحلیل محتوای کیفی پاسخ‌های کتبی دانش‌آموزان، اتخاذ شد. نمونه شامل ۳۰۰ دانش‌آموز سال آخر بود که به روش نمونه‌گیری تصادفی طبقه‌ای انتخاب شدند. داده‌ها با استفاده از آزمون حل مسئله هندسه طراحی‌شده توسط پژوهشگر، متشکل از دوازده سؤال بازپاسخ منطبق با برنامه درسی هندسه دبیرستان، گردآوری شد. پاسخ‌های دانش‌آموزان با استفاده از توزیع فراوانی و درصد تحلیل گردید و الگوهای خطا با چارچوب نیومن طبقه‌بندی و بر سطوح ون هیله نگاشته شد. یافته‌ها نشان داد که به طور کلی عملکرد حل مسئله هندسی پایین بوده و اکثر دانش‌آموزان در دامنه عملکرد پایین قرار گرفتند. تحلیل خطاها نشان داد که دانش‌آموزان در سطوح پایین‌تر ون هیله، به ویژه تجسم و تحلیل، فراوانی بیشتری از خطاهای درک مطلب و تبدیل را نشان دادند. در مقابل، دانش‌آموزان در سطوح بالاتر استدلال، دشواری‌های مفهومی و بازنمایی کمتری داشتند اما همچنان با خطاهای مهارت فرایندی و رمزگذاری مواجه بودند. یافته‌ها نشان‌دهنده الگوهای متفاوت خطاهای حل مسئله در میان دانش‌آموزانی است که سطوح مختلفی از استدلال هندسی را نشان می‌دهند. نتایج ارزش تفسیر حل مسئله هندسی دانش‌آموزان از طریق چارچوب‌های ون هیله و نیومن را نشان می‌دهد که دیدگاه‌های مکملی درباره استدلال دانش‌آموزان و خطاهای آشکار در فرایند حل آنان فراهم می‌کند.