Diagrama de temas

  • PREMISE

    1. Curriculum Structure

     

    «Mathematics curricula lay down all the essential learning aims and outcomes of mathematics education. In the past years, and especially since 2007, the great majority of European countries have revised their mathematics curricula, adopting an outcome-based approach whereby the focus lies on developing students’ competences and skills rather than on theoretical content. The amount of mathematics content in the curriculum has decreased while cross-curricular links, problem solving and the application of knowledge has increased. This integral approach tends to be more comprehensive and flexible in responding to the needs of a diverse range of learners, as well as to their ability to understand the purpose of mathematics applications in the real world» (The Education, Audiovisual and Culture Executive Agency, 2011. Mathematics Education in Europe: Common Challenges and National Policies. EACEA P9 Eurydice).

     

    What is described above is the approach to teaching mathematics at a European level and it is the one also adopted by the TELL ME project research team to teach maths to migrants.

    Thanks to the information gathered, the discussions and the processing by the RT after working with the focus groups, it was immediately decided to link the curriculum concept to the needs of adult migrants, placing particular emphasis on useful everyday life skills and those valuable for obtaining educational qualifications in the host country. The following fundamental skills were identified from the selection process conducted in the research phase which, it should be emphasised, have to be acquired in the host language.

    -        Utilising the symbols, techniques and processes of arithmetic and algebraic calculations;

    -        Reproducing, comparing and analysing plane and solid geometric figures and identifying their properties and relations;

    -        Resolving various types of problems by identifying appropriate strategies and, if possible, utilising graphic representations and calculation tools appropriately.

     

    From the needs analyses of the target group, it became evident that a structured learning path with standard modules and straightforward univocal sequences would not be appropriate because the target group that the TELL ME method is geared for is too heterogeneous to be satisfied by a singular product. It was therefore decided to go in the direction of building macro work areas that can be more or less explored depending on the needs of the members of the class and the level of maths literacy.

    The macro areas identified are: numbers, geometry and solving literal calculation, and within each area, activities were created in relation to the main arguments. The objective of the TELL ME methodology isn’t to make students understand a broad number of notions because it plays a complementary and support role to traditional teaching: the real objective of the methodology is to experiment with maths. The subject is approached from an unusual perspective; that of theatre workshops in which it is possible to play with and enter the world of mathematics in a global mind-body manner.

    The curriculum was developed with the idea of enthusing people about mathematics, in this way opening a door of understanding to the arguments addressed, which may then be benefitted from during frontal teaching in the classroom by deepening and consolidating the concepts introduced in the TELL ME activities.

    Due to the lack of a standard learning path, it was decided to describe some possible approaches that depend on the characteristics of the individual groups in §III.3 “Guidelines” in the Manual. For the same reason, it isn’t possible to quantify the hours necessary to carry out the curriculum. What can be generally acknowledged is that a subject addressed within a theatre workshop will require more time than that needed in a traditional frontal lesson because the heart of the activity is arrived at only after a preparatory phase which cannot be excluded at the risk of undermining the activity itself.

    The three main macro areas and related curricular subject areas of the TELL ME methodology that were deemed the most salient in assisting traditional maths instruction follow.

    – Arithmetic

    – Geometry

    – Literal calculation

     

    2. Guidelines

     

    2.1 - Who is the target?

    This result of the project is geared for teachers and educators who are engaged in mathematics literacy for foreigners.

    The activities described address specific mathematics topics and can be applied as they are described in the manual or adapted to the needs of the class.

    The guidelines don’t describe the activities necessary for building a group or managing and empowering group dynamics within a theatre workshop setting. This type of expertise can only be transferred to teachers through ad hoc training. For those who do not have any type of theatre experience and want to better understand how theatre workshops function, refer to §II.3, above.

    Where possible, it is recommended that teachers without experience in conducting theatre workshops have the support of an expert from the field. In considering cases where this is not possible, a dual use of the didactic materials was considered.

    The work sheets can be used employing alternative approaches according to the experience and expertise of the teachers.

    Teachers with theatre training and previous experience in conducting Social and Community Theatre workshops can use the TELL ME project work sheets included in the Manual, §III.4 (download: https://social.tellmeproject.com) within a more articulated workshop process that foresees an initial phase for building the group and conveying basic theatre skills. In the case of teachers who are experts in conducting Social and Community Theatre workshops, it is possible to consciously work with the participants on life skills, which respond to the needs identified in the Manual, §III.1, while teaching maths.

    For teachers with no experience in conducting theatre workshops and who cannot count on the assistance of an expert, it is in any case possible to use the TELL ME project work sheets (Manual, §III.4) as activities in and of themselves as long as they are carried out while paying attention to certain methodological aspects described below.

     

    2.2 - The TELL ME methodology

    The field of application that TELL ME must respond to is very vast and heterogeneous. Each class may contain, as was ascertained in the needs analysis, types of people and educational needs that are very different from one another.

    It is therefore impossible to define a distinct path that may be adapted to any group of student migrants, structured in a fixed number of lessons with each one addressing a precise topic in a pre-defined order. The proposed exercises cannot entirely substitute the classroom lesson but were conceived of as a tool that can interact with the frontal lesson and fill in gaps that groups of adult migrants may have in certain classroom learning situations.

    What the research team decided to do, based on previous experiences and the results of activities carried out over the two years of the project, was to create a “tool box”, didactic materials, which can be used at the discretion of the teacher depending on the particular group he/she is working with.

    The didactic materials may be used following different logics and we have identified some of them.

    The work sheets were created according to three categories, arithmetic, geometry and literal calculation.

    In the first one, we find all the topics that help to recognise and know how to write numbers, the four basic operations and then arriving at topics that are more arduous such as fractions, least common multiple and greatest common divisor, which may be useful for those hoping for an educational qualification in the host country.

    In the second category, geometry, we inserted basic activities that can be used to introduce or enhance many specific topics: from representing geometric forms to calculating the areas of plane figures up to expressing definitions and theorems of three-dimensional figures. In this section activities were inserted that were not actually geometry such as for example “Units of measure”. In the third section, literal calculation, three activities are evident which allow us to explore monomials and polynomials, the fundamentals of literal calculation, standard identities and first order equations.

    In addition, we developed differentiated learning paths according to the diverse categories of the subjects involved and present some of these paths as follows.

     

    Learning Path 1 - Linear usage

    Learning Path 2 - Basic literacy

    Learning Path 3 - Translating previous knowledge

    Learning Path 4 - Mathematics in daily life

    Learning Path 5 - Educational qualifications

     

    Each activity is intended for one or more specific topics. In the case of some activities, variations are also indicated and in general the activities described can be easily adapted and used to work on topics that are different from those indicated.

    How the main activity should be inserted into the work plan for the class, is up to the teacher because it can depend on many factors and a general rule cannot be applied. First of all, it is important to take into account the characteristics of the group: the composition, the level of literacy, and attitude toward non-frontal and theatre activities. Moreover, the choice must keep in mind the teacher’s expertise in leading groups in a non-frontal setting, her/his theatre skills as well as social theatre ones. For teachers who don’t have a great deal of experience in leading theatre workshops, we recommend trying the methodology starting from simpler exercises to learn how to manage the group while doing. A fluid and confident management of the group fosters the climate necessary for the successful realisation of the activities both in terms of content and relationships.

    The combination of these variables renders each situation unique. As an example, we describe the structure of the lessons that we used in April 2018 to test the methodology in Sweden with a group made up of women and men from Syria, Eritrea, Kosovo, Afghanistan and Philippines.

    The structure used, which lasted about two hours, is the following.

    1.                   Introduction.

    2.                   Opening up and warm up useful for the main activity.

    3.                   Main activity.

    4.                   Revisiting mathematical tools.

    5.                   Conclusions.

     

    The introduction is useful for welcoming the group into the relevant space and explaining the day’s proceedings, in terms of timing and the types of activities that will be carried out, to the participants.

    The second phase is very important because it prepares the group for carrying out the main activity. During this phase, the group is asked to get started, both physically and mentally, in order to be prepared for what will happen next. Normally, exercises that are preparatory to those that will follow are done. For example, if the main activity requires the use of objects and their transformation into something extraordinary, exercises that develop creativity and the use of objects will be proposed during the warm up phase.

    The main activity consists of the maths topic that the teacher intends to address and is proposed only when he/she considers the group has acquired the necessary theatre skills to proceed without worrying about the performance component. A clear signal that the theatre element has been internalised, is evident when the trainer’s proposals are carried out without embarrassment or hesitation, on the contrary, participants immerse themselves in the activity, allowing themselves to be transported into theatre play. The performance moment sustains the mathematics component rendering it playful and fun.

    At the end of the main activity, we move to a more analytical phase in which, with the help of the group, we discuss the maths topic addressed. It is further analysed in an in depth manner and formalised on the flipchart so that the shift from the theatre activity to the abstract concept necessary to understand the topic is clear to everyone. Finally, the activity is concluded with a formal moment for saying goodbye which functions as the closure of the work session just completed.

    Moreover, a work sheet was created for each activity destined for the students. The sheet serves as a reminder of the work done and can be used by the teacher at the end of the lesson to review what was done previously and also evaluate how much the student has learned.

    In the first square at the top, is a vignette that represents the activity being carried out which serves to link the experience lived to the content that will be listed below.

    Space is left in the middle part so the student can write the title of the activity and the key words linked to the main topic in order to establish a minimum of useful vocabulary related to the topic being addressed. For example, if the title of the activity is “Fractions”, the key words connected to it that could emerge during the lesson are: numerator, denominator, simplification, reduction, etc...

    The last square at the bottom is left empty and may be used at the teacher’s discretion for students to do a useful brief maths problem to verify whether the topic has been learned at the end of the lesson. Referring back to the fraction example, the assignment given could be:

    «Draw three cakes. Each cake is made up of 12 slices. Colour the quantity that corresponds to 1/2 in the first cake, 1/3 in the second and 5/12 in the third».

     

    2.3 - Work principles

    What the work team did was to highlight an approach that can be used with any class group, both with teachers who have theatre skills and those who do not.

    With the aim of guaranteeing the high quality of the activities proposed, we believe it is important to stress a series of issues that the trainer must take into account, whether he/she is an expert of theatre workshops or not. We have articulated the following series of principles that are applicable even to those who decide to use the TELL ME activities without employing a theatre workshop approach.

     

    Progression from theatre to mathematics

    It is essential that participants feel comfortable using the theatre language proposed in the maths and theatre activities. In order for students to concentrate on the mathematics side of the activity, it is important that the theatre language be acquired and a source of fun instead of stress or embarrassment, as could be the case with a shy person or someone unused to theatre.

    To meet this requirement, which can be considered a starting point for introducing mathematics into the activity, it is recommended that the first meetings be predominantly just theatre activities aimed at acquiring a common theatre language. Only subsequently, when the theatre foundation is more structured, can the maths activity component be added. To understand the typology of the progression, we can refer to the example of the theatre workshop process described in the Manual, §II.3.

     

    Absence of judgement

    It is crucial that the entire process be lived by the participants in a manner which allows them to fully explore what is being proposed by the trainer. The activities should never be judged in terms of right or wrong, but be presented as experiences to live together from which we can learn; also and most importantly from our own mistakes. One factor linked to the absence of judgment is the importance of not instilling competition between students. When we begin to play with the maths concepts, it is very easy to slip into contests between participants. It is up to the trainer to maintain a playful milieu and, even if the game in itself may have a competitive component, to tone down the moments that could be sources of comparison between participants in terms of right/wrong or better/worse.

     

    Playing

    Playing is one of the foundations of theatre which allows participants to easily access a dimension that is outside the daily one.

    Playing is transcultural: from what we were able to observe during the TELL ME workshops, a playful environment and attitude, and an equally playful trainer, become compelling regardless of cultural origins.

    Starting and stopping a game is easier than starting and stopping a more structured theatre activity so creating a climate of trust in the initial work phase with the group is recommended to allow for subsequently moving toward the action of theatre.

    «From this point of view it [play] contributes exactly because of its mysterious qualities and the fact that it evades any definition, being part of theatre workshops, which are almost like a sort of neutral place, an ‘already but not yet’, a decompression room, allows for a gradual passage and painless experience from the reality often lived on painful or conflicting terms by the subjects involved in socio-educational theatre, to the new adventure of group theatre.»  (Pontremoli A., 2005. Teorie e tecniche del teatro educativo e sociale. Turin: Utet Libreria).

    Play, done seriously like children know how to do, requires very deep involvement which helps participants forget everything else and remain in the here and now. In this sense, playing with mathematics has proved to be very important in allowing participants who are afraid to make mistakes forget their fear and thus has fostered effective training in putting the brakes on inhibitions.


  • ARITHMETIC

    The topics in this area, especially the first 13 on the list that follows, were considered in order to provide a minimal maths foundation to any student. This base is functional both for the translation of basic concepts in the host language, and therefore in moving studies forward, as well as for the use of mathematics in everyday life; for example to read and understand phone bills or understand the percentage of a discount.

    1.            Numbers

    2.            Counting

    3.            Assembling numbers

    4.            Writing numbers and symbols

    5.            Place values

    6.            Counting times tables

    7.            Times tables

    8.            Factors

    9.            Addition

    10.          Subtraction

    11.          Multiplication

    12.          Division

    13.          Fractions

    14.          Calculating in your head

    15.          Least common multiple

    16.          Greatest common divisor


  • GEOMETRY

    The topics of this area were considered to introduce geometry to students who intend to continue their studies by creating a basic vocabulary in the host language and, where required, an understanding of the units of measure in the host country.

    1.            Plane geometry

    2.            Perimeters and areas

    3.            Solid geometry

    4.            The Cartesian plane

    5.            Expressing definitions and theorems

    6.            Sexagesimal system

    7.            Units of measurement


  • LITERAL CALCULATION

    This topic was considered specifically for those who intend to obtain school qualifications in the host country and must, therefore, integrate literal calculation into their educational path to arrive at first order equations. As we shall see below, the lessons in this area are easily adaptable to other topics of literal calculation.

    1.            Representing monomials and polynomials

    2.            Operations between monomials

    3.            Equations


  • PATHS

    Learning Path 1 - Linear usage

    The exercises were placed in a particular order within each category that assured the preceding ones were preparatory to those that followed. Thus, a first approach is to propose the sequence of exercises to the group as they are presented in the manual. This progression can be useful in a homogenous class with whom the intention is to do a global overview of the programme proposed or a session of one of them.

     

    Learning Path 2 - Basic literacy

    This path was intended for those who do not have maths literacy, even in their language of origin, and thus need to start with the basics, that is recognise and know how to write numbers, understand the place value of a digit and do the four basic operations.

    For this path we recommend the following sequence of activities.

    Arithmetic - activities 1, 2, 3, 4, 5, 9, 10, 11 and 12.

    Geometry - activities 17, 18 and 23.

     

    Learning Path 3 - Translating previous knowledge

    This path is intended for those who have good maths literacy in their language of origin and need to translate the basic concepts already learned into the host language.

    For this path we recommend the following sequence of activities.

    Arithmetic - activities 1, 2, 6, 7, 8, 9, 10, 11, 12 and 13.

    Geometry - activities 17, 19, 20 and 23.

     

    Learning Path 4 - Mathematics in daily life

    This path is intended for those who need to learn the basic useful skills of everyday life but do not wish to obtain educational qualifications in the host country.

    For this path we recommend the following sequence of activities.

    Arithmetic - activities 1, 2, 6, 7, 8, 9, 10, 11, 12, 13 and 14.

    Geometry - activities 17, 22 and 23.

     

    Learning Path 5 - Educational qualifications

    This path is intended for those who intend to obtain an educational qualification in the host country. It is a process that provides the basics of the three trajectories for more in-depth study. We imagine this aimed at people who had minimal mathematics skills in their language of origin.

    For this path we recommend the following sequence of activities.

    Arithmetic - activities 1, 2, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 16.

    Geometry - activities 17, 18, 19, 20, 21, 22 and 23.

    Literal calculation - activities 24, 25 and 26.