Algorithms for Del Pezzo Surfaces of Degree 5 (Construction, Parametrization)

It is well known that every Del Pezzo surface of degree 5 defined over k is parametrizable over k. In this paper we give an efficient construction for parametrizing, as well as algorithms for constructing examples in every isomorphism class and for deciding equivalence.Comment: 15 page

EXPLORING PROSPECTIVE ELEMENTARY MATHEMATICS TEACHERS’ KNOWLEDGE: A FOCUS ON FUNCTIONAL THINKING

The importance of students being acquainted with algebraic ideas before secondary education has been revealed in the research literature. It is therefore essential that prospective elementary teachers (PTs) be prepared to instill an early algebra perspective in their teaching. However, PTs often show difficulties in algebra content knowledge, which need to be diagnosed aiming to assist them in developing the required knowledge to teach according to that perspective. This study aims to understand what aspects of functional thinking Spanish and Portuguese elementary PTs exhibit at the beginning of their teacher education program. The findings show that although PTs from both countries use different strategies to generalize functional relationships, the occurrence of successful strategies is low. Also, most participants provide local approaches in their interpretation of relationships between variables and reveal difficulties in understanding and connecting different representations of functions. These difficulties show that PTs lack important knowledge about functional thinking. By providing a framework concerning the functional thinking required for PTs to teach within an early algebra perspective, we shed light on a necessary step for teacher education programs to diagnose PTs’ functional thinking and to assist them in developing the needed mathematical knowledge to teach accordingly

Teaching multiplicative word-problem solving to a student with autism spectrum disorder

This work has been supported by the project with reference PID2019-105677RB-I00 funded by MCIN/ AEI /10.13039/501100011033

Ruled quartic surfaces, models and classification

New historical aspects of the classification, by Cayley and Cremona, of ruled quartic surfaces and the relation to string models and plaster models are presented. In a ?modern? treatment of the classification of ruled quartic surfaces the classical one is corrected and completed. The string models of Series XIII of some ruled quartic surfaces (manufactured by L. Brill and by M. Schilling) are based on a result of Rohn concerning curves in P1 × P1 of bi-degree (2, 2). This is given here a conceptional proof.The authors thank the referee for his very useful remarks

Multiplicative problem-solving strategies used by students with autism spectrum disorder

Students with autism spectrum disorder (ASD) are found to use less efficient problem-solving strategies than their typically developing peers. This work examines the strategies used by 17 first-to-fourth graders with ASD without intellectual disability when solving multiplicative equal-groups problems. The participants mainly resorted to incorrect or low-level strategies, such as modelling. Within the first-to-third graders, all the strategies observed were low-level ones. Within the fourth graders, four of the eight students used operation strategies to solve the multiplication problem and only three to solve the partitive division one. The measurement-division problem was the most difficult for them to solve. These results highlight the difficulties faced by students with ASD when solving multiplicative problems and could guide future design of specific instruction.This work was supported by the research projects PID2019-105677RB-I00 (funded by MCIN/AEI/10.13039/501100011033) and SUBVTC-2022-0004, and by a "Concepción Arenal" grant (funded by the Gobierno de Cantabria, Spain