Noticing mathematical potential – A proposal for guiding teachers

International audienceIt has been shown to be problematic for teachers to use Krutetskii´s definition of mathematical abilities to recognize mathematically highly able pupils (MHAPs). Aiming to concretize what teachers can notice in pupils’ problem-solving processes, we connect a 10-year-old boy’s problem-solving process to some of the abilities defined by Krutetskii. The results give clear descriptions of what teachers can observe in pupils’ mathematical activities to notice their mathematical potential. We concretize, for example, how a pupil’s abilities to grasp a problem’s formal structure and to generalize can be observed. To be able to notice MHAPs, teachers need research-based support on how and what to observe in their pupils. Our proposed guide needs to be tested and validated to explore if it will help teachers to notice MHAPs s and subsequently support their learning

Améliorer l’enseignement des mathématiques

L’article présente le plan d’action suédois pour les mathématiques lancé par le gouvernement suédois en 2003 et qui couvre l’ensemble du système éducatif : préscolaire, enseignement obligatoire, secondaire supérieur, secondaire pour les adultes, enseignement supérieur général et formation des adultes. Ce plan vise à développer l’image des mathématiques et l’intérêt pour la discipline ; à former et à renforcer les compétences des enseignants qualifiés grâce à la formation initiale et continue ; à accompagner les enseignants et les établissements pour améliorer leur enseignement et l’apprentissage ; à mettre constamment l’accent sur les objectifs, les finalités, les contenus et les évaluations de l’enseignement des mathématiques. Plusieurs actions et initiatives ont été engagées au niveau national. Les mathématiques y sont conçues comme un pont vers de nombreux autres éléments de l’enseignement scientifique. Les auteurs s’attachent à montrer l’apport des mathématiques dans l’apprentissage.This article presents the Swedish action plan for mathematics: the reasons for launching it, its main objectives, and how it was carried out. The authors put forward a fresh view of what mathematics can contribute at school. The action plan aims to generate interest in mathematics among both pupils and the general public. The authors present the actions taken since the action plan was introduced, along with examples of ongoing initiatives.Este artículo presenta un plan de acción sueco para las matemáticas: los motivos de su lanzamiento, sus principales objetivos y su implantación. Los autores proponen una visión renovada acerca de todo aquello que pueden aportar las matemáticas a la escuela. Pretende fomentar el interés de los alumnos y del público de cara a las matemáticas. Presentan las acciones realizadas desde la implantación del plan de acción y ofrecen ejemplos de algunas iniciativas en curso

Assessing mathematical creativity : comparing national and teacher-made tests, explaining differences and examining impact

Students’ use of superficial reasoning seems to be a main reason for learning difficulties in mathematics. It is therefore important to investigate the reasons for this use and the components that may affect students’ mathematical reasoning development. Assessments have been claimed to be a component that significantly may influence students’ learning. The purpose of the study in Paper 1 was to investigate the kind of mathematical reasoning that is required to successfully solve tasks in the written tests students encounter in their learning environment. This study showed that a majority of the tasks in teacher-made assessment could be solved successfully by using only imitative reasoning. The national tests however required creative mathematically founded reasoning to a much higher extent. The question about what kind of reasoning the students really use, regardless of what theoretically has been claimed to be required on these tests, still remains. This question is investigated in Paper 2. Here is also the relation between the theoretically established reasoning requirements, i.e. the kind of reasoning the students have to use in order to successfully solve included tasks, and the reasoning actually used by students studied. The results showed that the students to large extent did apply the same reasoning as were required, which means that the framework and analysis procedure can be valuable tools when developing tests. It also strengthens many of the results throughout this thesis. A consequence of this concordance is that as in the case with national tests with high demands regarding reasoning also resulted in a higher use of such reasoning, i.e. creative mathematically founded reasoning. Paper 2 can thus be seen to have validated the used framework and the analysis procedure for establishing these requirements. Paper 3 investigates the reasons for why the teacher-made tests emphasises low-quality reasoning found in paper I. In short the study showed that the high degree of tasks solvable by imitative reasoning in teacher-made tests seems explainable by amalgamating the following factors: (i) Limited awareness of differences in reasoning requirements, (ii) low expectations of students abilities and (iii) the desire to get students passing the tests, which was believed easier when excluding creative reasoning from the tests. Information about these reasons is decisive for the possibilities of changing this emphasis. Results from this study can also be used heuristically to explain some of the results found in paper 4, concerning those teachers that did not seem to be influenced by the national tests. There are many suggestions in the literature that high-stake tests affect practice in the classroom. Therefore, the national tests may influence teachers in their development of classroom tests. Findings from paper I suggests that this proposed impact seem to have had a limited effect, at least regarding the kind of reasoning required to solve included tasks. What about other competencies described in the policy documents? Paper 4 investigates if the Swedish national tests have had such an impact on teacher-made classroom assessment. Results showed that impact in terms of similar distribution of tested competences is very limited. The study however showed the existence of impact from the national tests on teachers test development and how this impact may operate

Noticing pupils’ mathematical potential: A proposal for guiding teachers.

It has been shown to be problematic for teachers to use Krutetskii´s definition of mathematicalabilities to recognize mathematically highly able pupils (MHAPs). Aiming to concretize whatteachers can notice in pupils’ problem-solving processes, we connect a 10-year-old boy’s problemsolvingprocess to some of the abilities defined by Krutetskii. The results give clear descriptions ofwhat teachers can observe in pupils’ mathematical activities to notice their mathematical potential.We concretize, for example, how a pupil’s abilities to grasp a problem’s formal structure and togeneralize can be observed. To be able to notice MHAPs, teachers need research-based support onhow and what to observe in their pupils. Our proposed guide needs to be tested and validated toexplore if it will help teachers to notice MHAPs s and subsequently support their learning

Noticing mathematical potential – A proposal for guiding teachers

International audienceIt has been shown to be problematic for teachers to use Krutetskii´s definition of mathematical abilities to recognize mathematically highly able pupils (MHAPs). Aiming to concretize what teachers can notice in pupils’ problem-solving processes, we connect a 10-year-old boy’s problem-solving process to some of the abilities defined by Krutetskii. The results give clear descriptions of what teachers can observe in pupils’ mathematical activities to notice their mathematical potential. We concretize, for example, how a pupil’s abilities to grasp a problem’s formal structure and to generalize can be observed. To be able to notice MHAPs, teachers need research-based support on how and what to observe in their pupils. Our proposed guide needs to be tested and validated to explore if it will help teachers to notice MHAPs s and subsequently support their learning