NotesFAQContact Us
Search Tips
Back to results
Peer reviewed Peer reviewed
PDF on ERIC Download full text
ERIC Number: EJ1198045
Record Type: Journal
Publication Date: 2019
Pages: 17
Abstractor: As Provided
ISSN: EISSN-2148-9955
Facilitating Pre-Service Mathematics Teachers' Understanding of Directly and Inversely Proportional Relationships Using Hands-On and Real-World Problems
Arican, Muhammet
International Journal of Research in Education and Science, v5 n1 p102-117 Win 2019
The purpose of this study was to examine four pre-service middle and high school mathematics teachers' understanding of the directly and inversely proportional relationships presented through hands-on and real-world missing-value word problems. The problems included single and multiple proportions, and the PSTs were provided with plastic gears and a mini number balance system in the hands-on problems. A case study methodology with multiple cases was used in designing this study. Analysis of the semi-structured interviews revealed that for the PSTs, identifying directly proportional relationships was easier than identifying inversely proportional relationships. The PSTs recognized inversely proportional relationships in the hands-on problems but had difficulty recognizing them in the missing-value word problems. Therefore, the inclusion of the hands-on problems appeared to facilitate the PSTs' understanding of the inversely proportional relationships. When forming multiplicative relationships between quantities, they mostly reasoned about within measure spaces. Furthermore, when determining directly and inversely proportional relationships, they usually attended to the qualitative relationships and constancy of the rate of change. In the multiple proportions problems, the PSTs had difficulty finding a mathematical formula that expressed relationships between quantities compared. This result suggested possible constraints in their understanding of the multiplicative relationships when more than two quantities were present.
International Journal of Research in Education and Science. Necmettin Erbakan University, Ahmet Kelesoglu Education Faculty, Meram, Konya 42090 Turkey. e-mail:; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education; Secondary Education; Middle Schools; Junior High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A