• School Mathematics
• /
• v.11 no.1
• /
• pp.147-164
• /
• 2009

This study investigated the development of geometrical thinking levels of the under achievers at mathematics through supplementary classes according to van Hiele's learning process by stages using mathematical journal writing. We selected five under achievers at mathematics among the fourth graders. We examined their geometrical thinking levels in advance and interviewed them to collect basic data related to their family backgrounds and their attitude toward mathematics and their characteristics. Supplementary classes for the under achievers were conducted a couple of times a week during 12 weeks. Each class was conducted through five learning stages of van Hiele and journal writing was applied to the last consolidating stage. After 12th class had been finished, posttest on geometrical thinking levels was conducted and the journals written by the pupils were analyzed to find out changes in their geometrical thinking levels. The result is that three out of five under achievers showed one or two level-up in their geometrical thinking levels, though the other two pupils remained at the same level as the results by the pretest. Moreover we found that mathematical journal writing could provide the pupils with opportunities to restructure the content which they study through their class.

• Education of Primary School Mathematics
• /
• v.13 no.2
• /
• pp.85-97
• /
• 2010

The purpose of this study is to develop a teaching program in consideration of the geometrical thinking levels of students to make a contribution to teaching figures effectively. To do this, we checked the geometrical thinking levels of fourth-graders, developed a teaching program based on van Hiele's theory, and investigated its effect on their geometrical thinking levels. The teaching program based on van Hiele's theory put emphasis on group member interaction and specific activities through offering various geometrical experiences. It contributed to actualizing activity-centered, student-oriented, inquiry-oriented and inductive instruction instead of sticking to expository, teacher-led and deductive instruction. And it consequently served to improving their geometrical thinking levels, even though some students didn't show any improvement and one student was rather degraded in that regard - but in the former case they made partial progress though there was little marked improvement, and in the latter case she needs to be considered in relation to her affective aspects above all. The findings of the study suggest that individual variances in thinking level should be recognized by teachers. Students who are at a lower level should be given easier tasks, and more challenging tasks should be assigned to those who are at an intermediate level in order for them to have a positive self-concept about mathematics learning and ultimately to foster their thinking levels.

• Research in Mathematical Education
• /
• v.15 no.1
• /
• pp.81-91
• /
• 2011

The aim of this study was to explore the grade 1-3 students' geometrical thinking level descriptors based on van Hiele level descriptors. The data were collected through collection of geometric curriculum materials such as indicators and learning standards in Basic Education Core Curriculum and mathematics textbook for grades 1-3. The findings were found that 1) Inconsistency between descriptors appeared on mathematics curriculum and Thai mathematics textbooks. 2) Using topics on textbooks as criterion for exploring 5 of 7 descriptors appeared on Thai mathematics textbook indicated geometrical thinking levels based on van Hiele's model merely level 0 (Visualization) across textbooks for grades 1-3.

• Research in Mathematical Education
• /
• v.18 no.2
• /
• pp.103-128
• /
• 2014

This paper presents the Global van Hiele (GVH) questionnaire as a tool for mapping knowledge and understanding of plane and solid geometry. The questionnaire facilitates identification of the respondents' mastery of the first three levels of thinking according to van Hiele theory with regard to key geometrical topics. Teacher-educators can apply this questionnaire for checking preliminary knowledge of mathematics teaching candidates or pre-service teachers. Moreover, it can be used when planning a course or granting exemption from studying in basic geometry courses. The questionnaire can also serve high school mathematics teachers who are interested in exposing their students to multiple-choice questions in geometry.

• Education of Primary School Mathematics
• /
• v.14 no.1
• /
• pp.13-26
• /
• 2011

The purpose of this research is to analyze geometrical level and the justification process in the proofs of construction by mathematically gifted elementary students. Justification is one of crucial aspect in geometry learning. However, justification is considered as a difficult domain in geometry due to overemphasizing deductive justification. Therefore, researchers used construction with which the students could reveal their justification processes. We also investigated geometrical thought of the mathematically gifted students based on van Hieles's Theory. We analyzed intellectual of the justification process in geometric construction by the mathematically gifted students. 18 mathematically gifted students showed their justification processes when they were explaining their mathematical reasoning in construction. Also, students used the GSP program in some lessons and at home and tested students' geometric levels using the van Hieles's theory. However, we used pencil and paper worksheets for the analyses. The findings show that the levels of van Hieles's geometric thinking of the most gifted students were on from 2 to 3. In the process of justification, they used cut and paste strategies and also used concrete numbers and recalled the previous learning experience. Most of them did not show original ideas of justification during their proofs. We need to use a more sophisticative tasks and approaches so that we can lead gifted students to produce a more creative thinking.

• Journal of Educational Research in Mathematics
• /
• v.16 no.4
• /
• pp.327-344
• /
• 2006

This study examined the proof levels and understanding of constituents of proving by three mathematically gifted 6th grade korean students, who belonged to the highest 1% in elementary school, through observation and interviews on the problem-solving process in relation to constructing a rectangle of which area equals the sum of two other rectangles. We assigned the students with Clairaut's geometric problems and analyzed their proof levels and their difficulties in thinking related to the understanding of constituents of proving. Analysis of data was made based on the proof level suggested by Waring (2000) and the constituents of proving presented by Galbraith(1981), Dreyfus & Hadas(1987), Seo(1999). As a result, we found out that the students recognized the meaning and necessity of proof, and they peformed some geometric proofs if only they had teacher's proper intervention.