An A Priori Measure of Visual Difficulty of 2-D Sketches Depicting 3-D Objects

Aiming to enhance understanding of visual obstacles inherent in two-dimensional (2-D) sketches used in high school spatial geometry instruction, we propose a measure of visual difficulty based on two attributes of the sketches: potentially misleading geometrical information (PMI) and potentially helpful geometrical information (PHI). The difficulty of 12 normatively oriented cube-related sketches was theoretically ranked according to their ratios, #PHI/#PMI. The ranking was compared to the actual visual difficulty as measured by the percentage of correct or desired comprehension, individual spatial ability, and study-time allocation. This procedure was repeated for unnormatively oriented sketches, obtained by vertically flipping the original sketches. In both cases, the findings substantiate #PHI/#PMI as an a priori measure of visual difficulty. Practical, theoretical, and methodological implications are inspected and discussed.

Transforming Middle School Geometry Instruction

Students move from slides, flips, and turns into reasoning about the characteristics of rigid transformations.

“Sliding” into an Equitable Lesson

A kindergarten teacher uses Gutièrrez's Four Dimensions of Equity to design and facilitate geometry instruction.

Pembelajaran Geometri Berbantuan Geogebra dan Cabri Ditinjau dari Prestasi Belajar, Berpikir Kreatif dan Self-Efficacy

Penelitian ini bertujuan untuk mendeskripsikan dan membandingkan keefektifan pembelajaran geometri berbantuan Cabri dan pembelajaran geometri berbantuan Geogebra ditinjau dari prestasi belajar, berpikir kreatif, dan self-efficacy siswa SMP. Penelitian ini adalah penelitian eksperimen semu desain pretest-posttest non equivalent group design. Penelitian ini menggunakan dua kelompok eksperimen tanpa kelompok kontrol. Populasi penelitian ini mencakup seluruh siswa kelas VII SMP Santa Maria Banjarmasin. Sampel terdiri dari dua kelas, yaitu kelas VIIA dan kelas VIIB yang dipilih secara acak. Kelas VIIA menggunakan pembelajaran geometri berbantuan Cabri dan kelas VIIB menggunakan pembelajaran geometri berbantuan Geogebra. Hasil penelitian ini menunjukkan bahwa ditinjau dari prestasi belajar, berpikir kreatif, dan self-efficacy siswa (1) pembelajaran geometri berbantuan Cabri efektif; (2) pembelajaran geometri berbantuan Geogebra efektif; (3) terdapat perbedaan keefektifan pembelajaran geometri berbantuan Geogebra dan Cabri; (4) pembelajaran geometri berbantuan Geogebra lebih efektif dari pada pembelajaran geometri berbantuan Cabri.Kata Kunci: Cabri, Geogebra, prestasi belajar, berpikir kreatif, dan self-efficacy Geometry Instruction Using Cabri and Geogebra in Terms of Achievement, Creative Thinking, and Self-Efficacy AbstractThis study aimed to describe and to compare the effectiveness geometry instruction using Cabri and Geogebra in terms of the achievement, creative thinking, and self-efficacy of the students junior high schools. This research was a quasi-experimental research with the pretest-posttest non-equivalent group design. This study used two experimental groups without control groups. The population of the study was all grade VII students of Junior High School Saint Mary Banjarmasin. The sample of two classes (class VIIA, and class VIIB) was established randomly. Class VIIA got geometry instruction with Cabri and class VIIB got geometry instruction with Geogebra. The results show that in terms of students’ academic achievement, creative thinking, and self-efficacy: (1) geometry instruction using by Cabri was effective; (2) geometry instruction using by Geogebra was effective; (3) there was a difference in the instruction using Cabri and that using Geogebra; (4) geometry instruction using Geogebra was more effective than geometry instruction using Cabri.Keywords: Cabri, Geogebra, academic achievement, creative thinking, and self – efficacy