STUDENTS’ GEOMETRIC THINKING ON TRIANGLES: MUCH IMPROVEMENT IS NEEDED

A look into students’ misconceptions help explain the very low geometric thinking and may assist teachers in correcting errors to aid students in reaching a higher van Hiele geometric thinking level. In this study, students’ geometric thinking was described using the van Hiele levels and misconceptions on triangles. Participants (N=30) were Grade 9 students in the Philippines. More than half of the participants were in the van Hiele’s visualization level. Most students had imprecise use of terminologies. A few had misconceptions on class inclusion, especially when considering isosceles right triangles and obtuse triangles. Very few students correctly recognized the famous Pythagorean Theorem. Implications for more effective geometry teaching are considered.

Networked Analysis of a Teaching Unit for Primary School Symmetries in the Form of an E-Book

In mathematics education, technology offers many opportunities to enrich curricular contents. Plane symmetries is a topic often skipped by primary teachers. However, it is important and may be worked in attractive ways in dynamic geometry software environments. In any regular classroom there are students with different levels of mathematical attainment, some needing easy tasks while others, particularly mathematically-gifted students, need challenging problems. We present a teaching unit for plane symmetries, adequate for upper primary school grades, implemented in a fully interactive electronic book, with most activities solved in GeoGebra apps. The book allows student to choose which itinerary to follow and attention is paid to different levels of students’ mathematical attainment. The research objective of the paper is to make a networked analysis of the structure and contents of the teaching unit based on the Van Hiele levels of mathematical reasoning and the levels of cognitive demand in mathematical problem solving. The analysis shows the interest of networking both theories, the suitability of the teaching unit, as the Van Hiele levels and the cognitive demand of the activities increases, and its usefulness to fit the needs of each student, from low attainers to mathematically-gifted students.

Modification of the geometry curriculum in relation to the curriculum reform in the light of the Van Hiele levels

In this paper the level of geometry education in mathematics education in Hungary is investigated. The relationship between the National Core Curriculum, the Framework Curriculum and the final exam is analyzed from the geometry point of view via the Van Hiele levels as a tool for comparison. It is observed that the geometry problems on the final exams do not follow the level prescribed by the National Core Curriculum. We compare these observations with the results of the Usiskin-test of first year preservice math teacher students.

PENGEMBANGAN PERANGKAT PEMBELAJARAN DENGAN PENDEKATAN KNISLEY BERORIENTASI PADA LEVEL BERPIKIR VAN HIELE DAN KEMAMPUAN PENALARAN ADAPTIF

<p class="AfiliasiCxSpFirst" align="left"><strong>Abstrak:</strong></p><p class="AfiliasiCxSpMiddle">Penelitian ini merupakan penelitian pengembangan perangkat pembelajaran geometri dengan pendekatan model pembelajaran matematika Knisley untuk meningkatkan level berpikir Van Hiele dan kemampuan penalaran adaptif siswa kelas VII SMP. Pengembangan perangkat pembelajaran ini didasarkan pada empat tahapan model pembelajaran matematika Knisley yang terdiri dari <em>allegorization, integrator, analysis</em>, dan <em>synthesis.</em> Penelitian ini menggunakan model pengembangan ADDIE. Instrumen penelitian yang digunakan adalah lembar validasi, lembar penilaian kepraktisan guru dan siswa, lembar observasi keterlaksanaan pembelajaran, tes level berpikir Van Hiele dan tes kemampuan penalaran adaptif. Perangkat pembelajaran dikatakan baik jika memenuhi aspek kevalidan, kepraktisan, dan keefektifan. Hasil penelitian menunjukkan bahwa perangkat pembelajaran memenuhi aspek kevalidan, kepraktisan, dan keefektifan dengan kriteria berikut 1) sangat valid menurut ahli dengan skor rerata 4,179 untuk RPP dan 4,230 untuk LKS, 2) sangat praktis menurut penilaian guru dengan skor rerata 5 untuk LKS dan RPP serta sangat praktis menurut penilaian siswa dengan skor rerata 4,538 untuk LKS, dan 3) sangat efektif berdasarkan level berpikir Van Hiele dengan banyaknya siswa pada level analisis mencapai 77% dan berdasarkan kemampuan penalaran adaptif dengan ketercapaian persentase ketuntasan 64,71%, rerata kelas 65,4 dan rerata skor 10,47 dengan kategori tinggi.</p><p class="AfiliasiCxSpMiddle" align="left"><strong> </strong></p><p class="AfiliasiCxSpLast" align="left"><strong>Kata Kunci</strong>:</p><p>Geometri, Kemampuan Penalaran Adaptif, Model Pembelajaran Matematika Knisley, Level Berpikir Van Hiele, Perangkat Pembelajaran</p><p class="AfiliasiCxSpFirst" align="left"><strong><em> </em></strong></p><p class="AfiliasiCxSpMiddle" align="left"><strong><em>Abstract:</em></strong></p><p class="AfiliasiCxSpMiddle"><em>This study </em><em>was a study of geometric instructional development with Knisley mathematics learning model approach to improved Van Hiele levels of thinking and adaptive reasoning skills of seventh’ grade Junior High School students. The development of geometric instructional based on four phases of Knisley mathematics learning model were </em><em>allegorization, integrator, analysis</em>, <em>and</em> <em>synthesis. This study used ADDIE’s model. The research instrumens were validation sheets, teacher and student practicality assessment questionnaire, observation sheets for learning implementation Van Hiele levels of thinking tests and adaptive reasoning skills test. The instructional package is good if fulfilled validity, practicality, and effectiveness aspects. This study result showed that the instructional package fulfilled the following criteria: 1) very valid according to the average score of 4,179 for RPP and 4,230 for LKS, 2) very practical according to the teacher’s assessment with mean score of 5 for LKS and RPP and very practical according to the assessment of students with an average score of 4,538 for LKS, and 3) very effective based on Van Hiele levels of thinking with the number of students at the analysis level reaching 77% and based on adaptive reasoning ability with completion of a classical was 64,71%, average grade was 65,4 and average score was 10,47 with high category.</em></p><p class="AfiliasiCxSpMiddle" align="left"><strong><em> </em></strong></p><p class="AfiliasiCxSpLast" align="left"><strong><em>Keywords</em></strong><em>:</em></p><p><em>Geometric, Adaptive Reasoning Skills, Knisley Mathematics Learning Model, Van Hiele Levels Of Thinking, Instructional Package</em></p>

VAN Hiele Level of Geometric Thinking among Secondary School Students

Geometric thinking plays an important role in geometric achievement. It is also important in other fields, such as architecture, engineering, film, science, graphics, and arts. However, in Indonesian education curriculum, teaching and learning geometry does not emphasise the geometric thinking skills. Several studies revealed that Indonesian students could not come out from the lowered zone of the International exam, such as Trends in International Mathematics and Science Study (TIMSS), which caused by van Hiele levels of geometric thinking. Therefore, the purpose of this study was to investigate the van Hiele levels of geometric thinking among secondary school students in Makassar, Indonesia. A total of 298 respondents randomly took part in this study. The van Hiele geometric thinking test was used to assess the student's level of geometric thinking. Data were in ordinal form analysed according to the weighted van Hiele geometric thinking test scores presented in the table. The findings showed that most of the students were at the lowest level of geometric thinking. Several 123 and 93 respondents were at Level 0 (Visualisation) and Level 1 (Analysis), respectively. Meanwhile, 70 respondents were lower Level 0 and only a few respondents were in the upper Level 1. The result might be used as a fundamental source to produce a learning strategy in elevating van Hiele levels of geometric thinking.