Hasan Unal

Differences in learning geometry among high and low spatial ability pre-service mathematics teachers

The objective of this study was to investigate and characterize the geometric thinking and understanding of four pre-service middle and secondary mathematics teachers while considering their spatial ability levels. To investigate the differences, if any, that existed among these pre-service middle and secondary teachers with different spatial ability levels and understanding geometry, pre- and post-test designs were employed using Mayberrys (J. Mayberry. An investigation of the Van Hiele levels of geometric thought in undergraduate pre-service teachers, Unpublished Doctoral dissertation, University of Georgia, Athens, GA, 1981) protocol. Four contrasting cases in terms of spatial ability scores are examined using the van Hiele model to provide a description of geometric understanding. The study participants were chosen using the Purdue visualization of rotations test (ROT; G.M. Bodner and R.B. Guay, The Purdue visualization of rotations test, Chem. Educ. 2 (1997), pp. 1–18) from among a pool of pre-service middle and secondary mathematics teachers at a major research university in the southeast United States. The results were supportive of previous research in this area. Learners with low spatial abilities are more challenged geometry learners. While learners identified with mid-range spatial abilities showed the most change in van Hiele levels after instruction, the low spatial ability student showed the least amount of change. The student with high spatial ability showed some change after instruction. It was identified that instructional activities that afford opportunities for fostering spatial abilities must be included in pre-service programmes so that future teachers have a mathematical foundation from which to teach geometry.

Proof Without Words: A Formula of Hermann

Summary A visual proof of a formula for π proved by the Swiss mathematician Jakob Hermann in 1706.