7/31/2019 PerContare Project & Activities

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• to develop appropriate teaching strategies andmaterials for teachers of grades 1-3 to help allchildren build numerical competence;

• to support teachers in learning to use thesestrategies and materials effectively;

• to develop early screening tools to be used ingrades 1, 2, and 3;

• to develop intensive training tools for childrenwho continue to exhibit difficulties in buildingbasic number competence.

The Project1:

Proposed Teaching Strategies and Some Developed Materials

Starting from year 3 of primary school developmentaldyscalculia (DD) can be diagnosed, and according tointernational data the estimated population affected isbetween 2% and 6% (Butterworth, 2004; Badian,1983; Gross-Tsur et al., 1996; Kosc, 1974). Moreover,in Italy, about 20% of children in the first year ofprimary school present learning difficulties inmathematics (Lucangeli, 2005). Therefore, to lowerthe number of children with learning difficulties inmathematics, and to avoid the diagnosis of “false positives” in early dyscalculia screening tests, it isimportant for teachers to offer all children adequateresources for developing numerical competence.

Results and Conclusions

Anna Baccaglini-Frank & Maria G. Bartolini Bussi

Università di Modena e Reggio Emilia 

Hands and the “FingerCounter” 

In the present poster we intend to describe someactivities that have seemed to be particularly

successful during their pilot-testing. It is prematureto discuss other preliminary results of the study.PerContare is an innovative project with greatpotential, as it is characterized by the fruitfulcollaboration of cognitive psychologists andmathematics educators who are attempting to finda combined approach for successfully overcominglearning difficulties in mathematics.

Objectives

PerContare is currently in year 1 (of 3). Each year

teaching materials are developed and pilot-tested in15 classes (we refer to these as basic experimental classes ); the following year the most recent materialsdeveloped are tested in new experimental classes  whose results are compared with those of the samenumber of control classes .The project will be able to complete two cycles: onefor a package of materials for grade 1, and one for apackage of materials for grade 2. In addition apackage for grade 3 will be prepared and pilot-tested.

The teaching strategies and materials to developchildren’s numerical competence involve the use ofthe activities and artefacts described in the followingsections.

ReferencesBadian, N.A. (1983). Dyscalculia and nonverbal disorders of

learning. In H.R. Myklebust, Progress in Learning Disabilities Volume 5 . New York: Stratton. pp. 235-264.

Bartolini Bussi, M.G. & Mariotti, M.A. (2008). Semioticmediation in the mathematics classroom artifacts andsigns after a Vygotskian perspective. In L. English (Ed.),Handbook of international research in mathematics education (2nd ed). New York: Routledge. pp. 746-783.

Bartolini Bussi, M.G. & Boni, M. (2009). The EarlyConstruction of Mathematical Meanings. LearningPositional Representation of Numbers. In O.A. Barbarin &B.H. Wasik (Eds.), Handbook of Child Development and Early Education: Research to Practice. New York: TheGuilford Press. pp. 455-477.

Butterworth, B. (2005). Developmental Dyscalculia. In, J.I.DCampbell (ed.), Handbook of Mathematical Cognition . NewYork: Psychology Press. pp. 455-467.

Butterworth, B., Varma, S., & Laurillard, D. (2011).Dyscaclulia: From Brain to Education. Science, 332 (27May 2011), 1049-1053.

Gross-Tsur V, Manor O, Shalev RS (1996). Developmentaldyscalculia: prevalence and demographic features.Developmental Medicine & Child Neurology, 38 , 25-33.

Kosc L. (1974). Developmental Dyscalculia. Journal of Learning Disabilities, 7, 164-177.

Lopez, M. & Stella, G. (2004). Lo Studio del Calcolo Mentalenella Scuola Elementare. Dislessia, 1(2), 219-236. 

Lucangeli, D. (2005). National survey on learning disabilities .Rome: Italian Institute of Research on Infancy.

Wilson, A.J., Dehaene, S., Pinel, P., Revkin, S.K., Cohen, S.,& Cohen, D. (2006). Principles underlying the design of “The Number Race”, an adaptive computer game for 

remediation of dyscalculia . Behavioral and BrainFunctions, 2006, 2:19. Retrieved online September 1,2011 from:http://www.behavioralandbrainfunctions.com/content/2/1/19

Wilson, A. & Dehaene, S. (2007). Number Sense andDevelopmental Dyscalculia. In D. Coch, G. Dawson, & K.Fischer (Eds.), Human Behavior, Learning, and the Developing Brain: Atypical Development . New York:Guilford Press. pp. 212-237.

AbstractPerContare is a 3-year project aimed at developingeffective inclusive teaching strategies and materials tohelp primary school teachers (in grades 1, 2, and 3)address learning difficulties, especially of studentswho are potentially at risk of being diagnosed withdevelopmental dyscalculia. The teaching strategiesand materials developed involve the use of digital andphysical artifacts to help students constructmathematical meanings in a solid way. Each year thematerials developed are pilot-tested in 15experimental classrooms, and tested the year after in5 new experimental classrooms whose results arecompared with those of control classrooms. In thisposter we describe some of the proposed teachingstrategies and material that has been developed withinthe project.

Methods

Straws

The field of cognitive psychology has studied theincidence and characteristics of developmentaldyscalculia and has developed computer-basedtraining tools for remediation of dyscalculic learners(for example, Wilson et al., 2006; Butterworth et al.,2011). On the other hand, mathematics educatorshave developed theories and teaching strategies thatenhance students’ construction of mathematicalmeanings (for example Bartolini Bussi & Mariotti,2008; Bartolini Bussi & Boni, 2009). However the twofields have seldom related to one another andenriched the others’ perspective. In this context, thescientific directors of the PerContare project1 (seepercontare.asphi.it), Maria Giuseppina Bartolini Bussi,and Giacomo Stella of the University of Modena andReggio Emilia (Italy) decided to collaborate andreceived a 3-year funding to guide the PerContare

Project, aimed at achieving the following goals:

Fig 1: The “finger -counter” built by a

first grade class.

Most activities make use of a number line. We usean evolution of different representations as shownbelow (the last representation is extended to 20).

ASPHIFondazione Onlus

We propose aseries of activitiesthat involve allfingers and use ofa “finger -counter”, cardboard handswith fingers thatcan be raised andput down torepresentnumbers andcomputations.

Number Lines

The Abacus

Children construct their ownabacus out of play-doh,wooden skewers and pasta,and/or they use amonochromatic plastic abacusof the teacher’s, as

The Pascaline2

We introduce the pascaline, as a tool for counting,

representing numbers, and understanding additionand subtraction.

1 The project is directed by Fondazione ASPHI onlus; supervisedscientifically by the Università di Modena e Reggio Emilia; and withsupport from Compagnia di San Paolo and Fondazione per laScuola della Compagnia di San Paolo.2 For more information visit page 19 of the Quercetti catalogue at:http://issuu.com/arcastudio/docs/cat_scuola2011_12?viewMode=magazine&mode=embed3 See http://www.tts-group.co.uk/shops/tts/Products/PD1723538/Bee-Bot-Floor-Robot/ orhttp://www.terrapinlogo.com/bee-botmain.php

Notes

Bee-bot  (Fig.7) is aprogrammable robot thatcan also be used in avirtual version on acomputer and/or aninteractive white board(Focus on Bee-Bo tsoftware, see Figs 8,9).

Bee-Bot3

One of the games we propose is “memory withhands” in which pairs are made with any two cardsthat represent the same number.

Fig 2: The “memory with

hands” played at recess in

first grade class.

Fig 3: Examples of pairs ofcards from the “memory with

hands” game constructed for 

first grade classes.

We use straws tointroduce counting by10, place value, andaddition and subtractioncalculations.

The abacus is used to discussplace value, and addition andsubtraction algorithms. Theseare developed by the childrenand shared during classroomdiscussion before beingformalized.

Fig 4: the abacus usedin one of our classes.

During discussions this tool is compared to the useof straws or of the abacus.

Fig 5: the pascaline.

Fig 6: a first grade childexplaining her understanding ofhow the pascaline works.

Fig 8: The virtual world “Focus on Bee-Bot”. 

Fig 7: Bee-Bot

Fig 9: the “shapes activity map”.

We proposeindividual andwhole-classactivities thatinvolve planningand programmingthe real and virtualbee-bot.