The Students’ Perspective of Geometry Teaching and Learning in High School

The purpose of this article is to present the results obtained from a questionnaire applied to Costa Rican high school students, in order to know their perspectives about geometry teaching and learning. The results show that geometry classes in high school education have been based on a traditional system of teaching, where the teacher presents the theory; he presents examples and exercises that should be solved by students, which emphasize in the application and memorization of formulas. As a consequence, visualization processes, argumentation and justification don’t have a preponderant role. Geometry is presented to students like a group of definitions, formulas, and theorems completely far from their reality and, where the examples and exercises don’t possess any relationship with their context. As a result, it is considered not important, because it is not applicable to real life situations. Also, the students consider that, to be successful in geometry, it is necessary to know how to use the calculator, to carry out calculations, to have capacity to memorize definitions, formulas and theorems, to possess capacity to understand the geometric drawings and to carry out clever exercises to develop a practical ability.

Trees: radiocarbon and dendrochronology - together for the Resolution project

The year 14,226 BP marks an important border in the actual radiocarbon (14C) calibration curve: the high resolution and precision characterising the first part (0 – 14,226 BP) of the curve are due to the potential represented by tree-ring datasets, which directly provide the atmospheric 14C content at the time of tree-rings formation with high resolution. They systematically decrease going back in time, where only a few floating tree-ring chronologies alternate to other low-resolution records. The lack of resolution in the dating procedure before 14,226 years BP leads to significant issues in the interpretation and untangling of tricky facts of our past, in the field of Human Evolution. Research on sub-fossil trees and the construction of new Glacial tree-ring chronologies can significantly improve the radiocarbon dating in terms of temporal resolution and precision until 55,000 years BP to clear puzzles in the Human Evolution history. In this thesis, the dendrochronological study, the radiocarbon dating and the extrapolation of environmental and climate information from sub-fossil trees found on the Portugal foreshore, remnants of a Glacial lagoonal forest, are presented. The careful sampling, the dendrochronological measurements and cross-dating, the application of the most suitable cellulose extraction protocol and the most advanced technologies of the MICADAS system at ETH-Zurich, led to the construction of a new 220-years long tree-ring site chronology and to high resolution, highly reliable and with a tight error range radiocarbon ages. At the moment, it results impossible to absolutely date this radiocarbon sequence by the comparison of Δ14C of the trees and 10 Be fluctuations from the ice-cores. For this reason, tree growth analysis, comparisons with a living pine stand and forest-fires history reconstruction have made it possible to hypothesize site and climate characteristics useful to constrain the positioning in time of the obtained radiocarbon sequence.