Cinzia Bonotto

How to Replace Word Problems with Activities of Realistic Mathematical Modelling

In this contribution we want to discuss some classroom activities, whose overall aim is to change pupils’ conceptions and beliefs of the role of real-world knowledge in mathematical classrooms activities, and to develop in them a positive disposition toward more realistic mathematical modelling. These activities make extensive use of cultural artefacts that could prove to be useful instruments in creating a new tension between school mathematics and the real world with its incorporated mathematics.

How to connect school mathematics with students' out-of-school knowledge

In this paper we present an explorative study for which special cultural artifacts have been used, i.e. supermarket receipts, to try to construct with 9-year old pupils (fourth class of primary school) a new mathematical knowledge, i.e. the algorithm for multiplication of decimal numbers. Furthermore also estimation and approximation processes have been introduced, procedures that are not commonly used in ordinary teaching activity. In our study the receipts, through some modifications, have become more explicitly tools of mediation and integration between in and out-of school knowledge, so they can be utilized to create new mathematical goals, thus becoming real mathematizing tools and constituting a didactic interface between in and out-of-school mathematics. In agreement with ethnomathematical perspective we deem that it is a task for the teacher to know, in order to be able to profitably take account of the teaching, the life experienced by the pupil. Future mathematics teachers should be prepared a) to see mathematics incorporated into real world, b) to investigate mathematical ideas and practices of their pupils, and c) to look for ways to incorporate into the curriculum elements belonging to the sociocultural environment of the pupils, as a starting point for mathematical activities in the classroom. In this way the motivation, interest and curiosity of the pupils will be increased and the attitude towards mathematics of both pupils and teachers will be changed.

Realistic Mathematical Modeling and Problem Posing

In this paper I present a teaching experiment characterized by a sequence of activities based on the use of suitable cultural artifacts, interactive teaching methods, and the introduction of new socio-mathematical norms in order to create a substantially modified teaching/learning environment. The focus is on fostering (i) a mindful approach toward realistic mathematical modelling, and (ii) a problem posing attitude. I argue for modelling as a means of recognizing the potential of mathematics as a critical tool to interpret and understand the communities children live, or society in general. Teaching students to interpret critically the reality in which they live and to understand its codes and messages so as not to be excluded or misled, should be an important goal for compulsory education.

On the Relationship Between Problem Posing, Problem Solving, and Creativity in the Primary School

Problem posing is a form of creative activity that can operate within tasks involving semi-structured rich situations, using real-life artefacts and human interactions. Several researchers have linked problem-posing skills with creativity, citing flexibility, fluency, and originality as creativity categories. However, the nature of this relationship still remains unclear. For this reason, the exploratory study presented here sought to begin to investigate the relationship between problem-posing activities (supported by problem-solving activities) and creativity. The study is part of an ongoing research project based on teaching experiments consisting of a series of classroom activities in upper elementary school, using suitable artefacts and interactive teaching methods, in order to create a substantially modified teaching/learning environment. In addition, the study provides a method for analyzing the products of problem posing that teachers could use in the classroom to identify and assess both the activity of problem posing itself and students’ creativity in mathematics.

How it is Possible to Make Real-World Mathematics More Visible: Some Results from Two Italian Projects

The first project described in this contribution regards the primary school level and is articulated in some teaching experiments aimed at showing how an extensive use of suitable artifacts could prove to be useful instrument in creating a new tension between school mathematics and real world with its incorporated mathematics. The main purpose of the second project is to encourage high-school graduates entering Universities to apply for degrees in the “hard” sciences, including Mathematics, Physics, and Chemistry