Scholarlink

<p>Geometry is among the most challenging domains in middle school mathematics. While geometric problem solving depends on students’ spatial abilities and logical reasoning, problem complexity may also arise from task characteristics beyond students’ competencies. This study examines two diagram-related factors: field-(in)dependency (FID) and (a)symmetry (SYM). We hypothesize that geometry problems with identical conditions and goals become more complex when involving field-dependent (FD) rather than field-independent (FID) diagrams, and asymmetrical (ASYM) rather than symmetrical (SYM) diagrams, as reflected in behavioral measures and ERP amplitudes. Fifty-four Taiwanese high school students (Grades 10-11) solved geometry problems with different FID and SYM combinations while event-related potentials (ERP) were recorded to capture neurocognitive correlates of diagram complexity. The study findings supported our hypotheses: Students achieved higher accuracy with SYM or FID diagrams than with ASYM or FD diagrams. Response times were significantly longer for FD diagrams. As hypothesized, FD conditions elicited higher P100 amplitudes and greater mean amplitudes in the 250-500&#xa0;ms window during the question stage (S2). SYM diagrams elicited higher P100 amplitudes during S1, whereas ASYM diagrams produced larger amplitudes in the 250-500&#xa0;ms window during S1 and the answer verification stage (S3), indicating increased cognitive load for FD and ASYM diagrams. Moreover, exploratory analysis of scalp topographies revealed FID-SYM dependent differences in frontal attentional networks and posterior visual-processing areas, indicating higher cognitive load associated with FD and ASYM conditions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Complexity of geometrical problems as a function of field-(in)dependency and (a)symmetry of geometry diagrams: an ERP study

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月9日

查看全文
  • Roza Leikin,
  • Hui-Yu Hsu,
  • Ilana Waisman,
  • Chen-Yu Yao

摘要

Geometry is among the most challenging domains in middle school mathematics. While geometric problem solving depends on students’ spatial abilities and logical reasoning, problem complexity may also arise from task characteristics beyond students’ competencies. This study examines two diagram-related factors: field-(in)dependency (FID) and (a)symmetry (SYM). We hypothesize that geometry problems with identical conditions and goals become more complex when involving field-dependent (FD) rather than field-independent (FID) diagrams, and asymmetrical (ASYM) rather than symmetrical (SYM) diagrams, as reflected in behavioral measures and ERP amplitudes. Fifty-four Taiwanese high school students (Grades 10-11) solved geometry problems with different FID and SYM combinations while event-related potentials (ERP) were recorded to capture neurocognitive correlates of diagram complexity. The study findings supported our hypotheses: Students achieved higher accuracy with SYM or FID diagrams than with ASYM or FD diagrams. Response times were significantly longer for FD diagrams. As hypothesized, FD conditions elicited higher P100 amplitudes and greater mean amplitudes in the 250-500 ms window during the question stage (S2). SYM diagrams elicited higher P100 amplitudes during S1, whereas ASYM diagrams produced larger amplitudes in the 250-500 ms window during S1 and the answer verification stage (S3), indicating increased cognitive load for FD and ASYM diagrams. Moreover, exploratory analysis of scalp topographies revealed FID-SYM dependent differences in frontal attentional networks and posterior visual-processing areas, indicating higher cognitive load associated with FD and ASYM conditions.