Asymmetry in student achievement on multiple choice and constructed response items in reversible mathematics processes

In this paper we report the results of an experiment designed to test the hypothesis that when faced with a question involving the inverse direction of a reversible mathematical process, students solve a multiple-choice version by verifying the answers presented to them by the direct method, not by undertaking the actual inverse calculation. Participants responded to an online test contain- ing equivalent multiple-choice and constructed-response items in two reversible algebraic techniques: factor/expand and solve/verify. The ndings supported this hypothesis: Overall scores were higher in the multiple-choice condition compared to the constructed-response condition, but this advantage was significantly greater for items concerning the inverse direction of reversible processes compared to those involving direct processes

The problem of assessing problem solving: can comparative judgement help?

This definitive version of this paper is available at Springerlink: http:dx.doi.org/10.1007/s10649-015-9607-1School mathematics examination papers are typically dominated by short, structured items that fail to assess sustained reasoning or problem solving. A contributory factor to this situation is the need for student work to be marked reliably by a large number of markers of varied experience and competence. We report a study that tested an alternative approach to assessment, called comparative judgement, which may represent a superior method for assessing open-ended questions that encourage a range of unpredictable responses. An innovative problem solving examination paper was specially designed by examiners, evaluated by mathematics teachers, and administered to 750 secondary school students of varied mathematical achievement. The students’ work was then assessed by mathematics education experts using comparative judgement as well as a specially designed, resourceintensive marking procedure. We report two main findings from the research. First, the examination paper writers, when freed from the traditional constraint of producing a mark scheme, designed questions that were less structured and more problem-based than is typical in current school mathematics examination papers. Second, the comparative judgement approach to assessing the student work proved successful by our measures of inter-rater reliability and validity. These findings open new avenues for how school mathematics, and indeed other areas of the curriculum, might be assessed in the future

Synthesis and characterization of TiO2-incorporated silica foams

Titania-incorporated silica (TiO2–SiO2) porous materials have great applications in diverse areas. In this work, TiO2–SiO2 porous materials with tunable Si/Ti molar ratio (R) have been successfully prepared through a one-pot method under a near-neutral condition. With decreasing Si/Ti R, a phase transition from a macroporous foam-like structure to mesostructure is observed. The resultant TiO2–SiO2 porous materials possess large surface areas and high pore volumes. In addition, the titania species are homogenously dispersed in silica matrix when Si/Ti R ≥ 10. Our contribution provides a convenient method to synthesize TiO2/SiO2 porous materials with very large pore size, high pore volume, and relatively high titania content well dispersed in the silica wall framework