Education and New Developments

2017

Edited by

Mafalda Carmo

Published by InScience Press

Copyright © 2017 InScience Press

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ISSN: 2184-044X

ISBN: 978-989-99864-3-5

Legal Deposit: 428062/17

Printed in Lisbon, Portugal by GIMA - Gestão de Imagem Empresarial, Lda.

iii

BRIEF CONTENTS

Foreword v

Scientific Committee vii

Keynote Lecture xi

Index of Contents xv

Author Index

vii

SCIENTIFIC COMMITTEE

Conference and Program Chair

Mafalda Carmo

World Institute for Advanced Research and Science (WIARS), Portugal

International Scientific Committee

Abdurrahman Guelbeyaz, University of

Salahaddin – Erbil, Irak

Adri Vermeer, Utrecht University,

The Netherlands

Adrian Rosan, Babes-Bolyai University,

Romania

Agnė Juškevičienė, Lithuanian University of

Educational Sciences, Lithuania

Aharon Gero, Technion – Israel Institute of

Technology, Israel

Ahrar Husain, Jamia Millia Islamia, India

Aistė Bartkevičienė, Mykolas Romeris

University, Lithuania

Ali Baykal, Bahcesehir University, Turkey

Anastasia Hadjiyiannakou, European

University Cyprus, Cyprus

Anca Draghici, Politehnica University

Timisoara, Romania

Anca-Olga Andronic, Spiru Haret University, Romania

Andrea Hathazi, Babes-Bolyai University,

Romania

Ângela Carrancho da Silva, UERJ / Fundação

Cesgranrio / Fundação CECIERJ, Brazil

Angela James, University of Kwazulu-Natal,

South Africa

Angela Piu, University of Valle d’Aosta, Italy

Annalene Van Staden, University of the Free

State, South Africa

Bernard Mulo Farenkia, Cape Breton

University, Canada

Binnur Yeşilyaprak, Ankara University,

Turkey

Brigita Janiunaite, Kaunas University of

Technology, Lithuania

Çağla Atmaca, Pamukkale University, Turkey

Carolina Bodea Hategan, Babes-Bolyai

University, Romania

Cezar Scarlat, University “Politehnica” of

Bucharest, Romania

Charalampos Karagiannidis, University of

Thessaly, Greece

Charles Elkabas, University of Toronto,

Canada

Christine Besnard, Glendon College,

York University, Canada

Christine Robinson, The University of Notre

Dame, Australia

Christopher Fowler, University of Essex,

United Kingdom

Claire Schonaerts, Northern Arizona

University, USA

Cristiano Luchetti, American University of

Sharjah, United Arab Emirates

Daniela Pasnicu, Spiru Haret University,

Romania

Dario Ianes, Free University of Bozen, Italy

David Aparisi, University of Alicante, Spain

Dee O’Connor, The University of Notre Dame,

Australia

Dejan Hozjan, University of Primorska,

Slovenia

viii

Denise Whitelock, The Open University,

United Kingdom

Diane Boothe, Boise State University, USA

Dominique Kern, University of Haute Alsace

(UHA), France

Donata Puntil, King’s College London,

United Kingdom

Dorina Anca Talas, Babes-Bolyai University,

Romania

Douglas Baleshta, Thompson Rivers

University, Canada

Ellen Whitford, Armstrong State University,

USA

Erik F. Överland, Free University of Berlin,

Germany

Esther Laslo, Technion – Israel Institute of

Technology and Zefat Academic College, Israel

Evridiki Zachopoulou, Alexander

Technological Educational Institute of

Thessaloniki, Greece

Gabriel Dima, Innovate4Future, Center for

Advances Educational Solutions and University

Politehnica of Bucharest, Romania

Georgios Zarifis, Aristotle University of

Thessaloniki, Greece

Gilles Sagodira, University of Réunion Island,

Reunion

Gina Chianese, Free University of Bozen, Italy

Grainne M. O’ Donnell, University College

Dublin, Ireland

Haim Shaked, Bar Ilan University, Israel

Hanife Akar, Middle East Technical

University, Turkey

Harvey Oueijan, Notre Dame University,

Lebanon

Helin Puksand, Tallinn University, Estonia

Ilijana Cutura, University of Kragujevac,

Serbia

Ioana Velica, Babes-Bolyai University,

Romania

Iulian Apostu, University of Bucharest,

Romania

Jana Kapounová, University of Ostrava,

Czech Republic

Jana Mazancová, Czech University of Life

Sciences Prague, Czech Republic

Janaina Cardoso, Rio de Janeiro State

University, Brazil

Jeannette Jones, Texas Lutheran University,

USA

Joanna Paliszkiewicz, Warsaw University of

Life Sciences, Poland

João Batista Bottentuit Junior,

Federal University of Maranhão, Brazil

Jose Augusto Oliveira Huguenin, Universidade Federal Fluminense (UFF), Brazil

Josef Trna, Masaryk University, Czech

Republic

Josep Sola Santesmases, Blanquerna –

University Ramon Llull, Spain

Juana Maria Sancho Gil, University of

Barcelona, Spain

Judith Szerdahelyi, Western Kentucky University, USA

Julia Haba-Osca, Universitat de Valencia,

Spain

Kadi Lukanenok, Tallinn University, Estonia

Karim Moustaghfir, Al Akhawayn University

in Ifrane, Morocco

Katerina Kabassi, Technological Educational Institute of the Ionian Islands, Greece

Kerstin Junge, The Tavistock Institute of

Human Relations, United Kingdom

Konstantinos Kalemis, National and

Kapodistrian University of Athens / National

Centre for Local Government and Public

Administration, Hellenic Ministry of Education,

Greece

Kyparisia Papanikolaou, School of Pedagogical and Technological Education,

Greece

ix

Ladário da Silva, Universidade Federal

Fluminense (UFF), Brazil

Laura Rio, University of Salerno, Italy

Laurent Moccozet, University of Geneva,

Switzerland

Leela Ramsook, University of Trinidad and

Tobago, Trinidad and Tobago

Lefkothea Kartasidou, University of

Macedonia, Greece

Liliana Dozza, Free University of Bozen, Italy

Liliana Milevicich, Universidad Tecnologica

Nacional, Argentina

Lina Kaminskienė, Vytautas Magnus

University, Lithuania

Lipaz Sahmoa-Nir, Zefat Academic College,

Israel

Longzhi Yang, Northumbria University,

United Kingdom

Loredana Terec-Vlad, Stefan cel Mare

University from Suceava and Lumen Research

Center in Social and Humanistic Sciences,

Romania

Lorna M. Dreyer, Stellenbosch University, South Africa

Luca Refrigeri, University of Molise, Italy

Lucía Casal de la Fuente, University of

Santiago de Compostela, Spain

Luminita Cocarta, Al. I. Cuza University of

Iasi, Romania

Maria Moundridou, School of Pedagogical and Technological Education (ASPETE),

Greece

Maria Schwarz-Woelzl, Zentrum Fuer Soziale

Innovation Gmbh, Austria

Maria Carme Boqué Torremorell, Ramon

Llull University, Spain

Marielle Patronis, Zayed University,

United Arab Emirates

Marta Cabral, Columbia University, USA

Mdutshekelwa Ndlovu, Stellenbosch

University, South Africa

Melissa Caspary, Georgia Gwinnett College,

USA

Meral Aksu, Middle East Technical University,

Turkey

Metaxia Pavlakou, Oxford Brookes University,

United Kingdom

Michał Pietrzak, Warsaw University of Life

Sciences, Poland

Milan Kubiatko, University of Zilina, Slovakia

Naseer Ahmed, Al Ghurair University,

United Arab Emirates

Nazario Zambaldi, Free University of Bolzano,

Italy

Nikolaos Marianos, Neuropublic SA /

University of the Aegean, Greece

Nina K. Buchanan, University of Hawaii, USA

Olga Chis, Babes-Bolyai University, Romania

Paraskevi Chatzipanagiotou, European

University Cyprus, Cyprus

Pascal Marquet, University of Strasbourg, France

Pascalia Patsala, University of Sheffield

International Faculty, Thessaloniki, Greece

Pedro Canto, Universidad Autónoma de

Yucatán, Mexico

Petros Kefalas, University of Sheffield

International Faculty, Greece

P. K. Paul, Raiganj University, West Bengal,

India

Pule Phindane, Central University of

Technology, South Africa

Rasa Nedzinskaite, Lithuanian University of

Educational Sciences, Lithuania

Rashid Jayousi, Al-Quds University, Palestine

Rawad Chaker, Lebanese University, France

x

Razvan-Lucian Andronic, Spiru Haret

University, Romania

Robert A. Fox, University of Hawaii, USA

Romano Martini, Niccolò Cusano University,

Italy

Rosanna Tammaro, University of Salerno,

Italy

Rosemary Papa, Northern Arizona University,

USA

Seán Doyle, UCL Institute of Education,

University College London, United Kingdom

Seppo Sirkemaa, University of Turku, Finland

Sercan Sağlam, Anadolu University, Turkey

Seweryn Spalek, Silesian University of Technology, Poland

Shakila Singh, University of Kwazulu Natal,

South Africa

Sheryl Williams, Loughborough University,

United Kingdom

Silvia Pokrivčáková, Trnava University,

Slovakia

Simon Richir, Arts et Metiers Paristech (ENSAM), France

Sonia de Almeida Pimenta, Universidade

Federal da Paraiba , Brazil

Stephanie Linek, ZBW – Leibniz Information

Centre for Economics, Germany

Steven Malliet, University of Antwerp,

Belgium

Surendra Pathak, IASE Deemed University,

India

Susie Ruston McAleer, 21c Consultancy,

United Kingdom

Suzie Savvidou, The University of Sheffield

International Faculty, CITY College, Greece

Tatjana Portnova, Russian Center of the

University of Granada, Spain

Tintswalo Manyike, University of South

Africa, South Africa

Tony Toole, University of Wales, Trinity Saint

David, United Kingdom

Tracy Treasure, The University of Notre

Dame, Australia

Ulas Basar Gezgin, British University Vietnam

& Staffordshire University, United Kingdom

Valerie Hascoet, Dublin Institute of

Technology, Ireland

Vassilis Argyropoulos, University of Thessaly,

Greece

Verica Babić, University of Kragujevac, Serbia

Virginiya Zhelyazkova, VUZF University,

Bulgaria

Yakim Kitanov, VUZF University, Bulgaria

Yonghuai Liu, Aberystwyth University,

United Kingdom

xv

INDEX OF CONTENTS

ORAL PRESENTATIONS

Teachers and Students

The teaching excellence project as a framework for leading integrative change and quality

learning in technological and vocational education

3

Hua Hui Tseng

Teaching strategies of dictation in music education 8

Aynur Elhan Nayir & Nurtuğ Barişeri Ahmethan

Internationalization of teaching in higher education: case of Turkish universities and

academics

12

Fugen Toksoz

What if our schools are working? Base, superstructure, and hegemony in global education

reform

16

Alan Singer & Felicia Hirata

Not so fast: a case against leaving liberal arts behind in the rush to STEM education 17

Michael Telafici

Designation of cognitive structures associated with the concept of folk song of the

candidate teachers of music

22

Vahide Bahar Yiğit & Sema Sevinç

Investigating the classification performances of support vector machines and logistic

regression: a case study on Pisa 2012

27

Ersoy Oz, Serpil Kilic Depren, & Oykum Esra Askin

Sensual experience in design: seeing and imagination in studio environment 32

Elif Aktaş Yanaş

Decision tree approach for predicting students’ mathematics achievement of TIMSS study 37

Oykum Esra Askin, Ersoy Oz, & Serpil Kilic Depren

Crucial variables in developing a proactive attitude to improve society 42

Maria Cerrato-Lara, Mary Deane, & Carlos Fresneda-Portillo

Comparing data mining methods for classification of students’ science success 47

Serpil Kilic Depren, Oykum Esra Askin, & Ersoy Oz

Supporting STEM teachers’ learning: lessons from a newly established school in the

Middle East

52

Cory A. Bennett, Beverly B. Ray, & Mona Fairley-Nelson

Class climate from the perspectives of students with migration background and special

educational needs

57

Friedrich Linderkamp

Transforming distance education cognitive distribution - Co-teaching and co-evaluation 58

Felipe Tirado & Guillermo Santos

xvi

Developing and assessing the generic problem-solving skills of undergraduate students 63

Andis Klegeris

Identifying students-at-risk in schools and what next? Promoting remediation in the

school leadership programme

68

Disego Vincentia Thobejane & Kgomotlokoa Linda Thaba-Nkadimeng

Defining the pre-vocational curriculum: A case study in the design of the BTEC Level 1

introductory qualification

72

Hayley Dalton & Eleanor Andressen

Reasons why students lost interest in studying 77

Hideyuki Kumaki

Bilingual Latino teachers: Experiences of language shame and loss in the teaching of

ELLs

82

Lisa Winstead & Congcong (Penny) Wang

Youth bulging in South Africa: The role of entrepreneurship education in the schooling

systems

83

Disego Vincentia Thobejane & Kgomotlokoa Linda Thaba-Nkadimene

Using an app as a log to collect data about the feedback perceptions of first year EAL

(English as an additional language) undergraduate students

87

Karen Olave

Examination of the employment hope levels of Turkish conservatory students 90

Mürvet Nevra Küpana

SEN and mainstream teachers’ perception of giftedness in Italian middle schools do they

evaluate gifted students in the same way?

95

Clarissa Sorrentino

Pre-service teachers perceptions of cooperative and individual-learning 100 Michal Nachshon & Amira Rom

Eyes wide open: Exploring faculty perceptions about student progression and retention in

higher education

105

Angeliki Papakonstantinou & Suzie Savvidou

Whole school systems for engaging students in learning and improved behaviour 110

Judith Foggett, Robert Conway, & Kerry Dally

Dynamics of peer tutoring in a higher education program in Trinidad and Tobago 115

Michele Taylor & Vimala Judy Kamalodeen

The neglected twin: Numeracy pathways to critical thinking 120

Maura Sellars

Analyzing western choir education courses in music departments of fine arts high school 124

Sema Sevinç & Vahide Bahar Yiğit

Students' perceptions of cooperative-learning 127

Michal Nachshon & Amira Rom

Deaf-blind students are perceived to have low abilities due to limited language skills 132

Julia Laderer Young

xvii

Understanding multi-grade teaching within South African context 137

Kgomotlokoa Linda Thaba-Nkadimene, Raesetja Letjobana Cathrine Lekgothoane,

Disego Vincentia Thobejane, & Mavhungu Samuel Nkadimene

Participation in extracurricular activity: Distinctions caused by cultural and social status

of families

140

Sergey Kosaretsky

Investigating the use of virtual environments in education to enhance students’

performance in the kinematics graphs

143

Itumeleng Phage

Projects and Trends

Potential or problem? Analysing secondary school teachers’ causal attributional outcomes

of students with learning disabilities

148

Stuart Woodcock

Inclusiveness in the online classroom: A strategic planning approach 149

Neil M. Alperstein

The neoliberal revolution in education: Three instruments for diagnosing and addressing

the problem

154

Johannes L. van der Walt

The common core debacle: Failed school curriculum reform in the United States 159

Alan Singer & Felicia Hirata

Professional teaching practices transformation from the use of TELESSALATM

methodology: Case study of autonomy programme

160

Ana Teresa Pollo Mendonça & Ariana Cosme

Outdoor learning in the Czech Republic – Confrontation between plans and reality 165

Hana Svobodová, Eduard Hofmann, & Radek Durna

Gamification in learning Chinese: Using Kahoot to motivate non-Chinese speaking high

school students

170

Lih-Ching Chen Wang, Xiongyi Liu, & Chia-Ying Hsu

Digital learning solutions: Are we designing assessment for learning? 175

Colette McCreesh & Karen Fraser

Learning from visions of the past for visions of the future: Some pedagogical implications 180

Anneli Martin & Juliet Dawnay

Arts education and cultural understanding: A pedagogical framework 185

Ilana Morgan

Teaching cultural competence in the foreign language classroom: Meeting the other 186 Charles Elkabas

An innovative methodological approach based on collaborative learning projects in higher

education

187

Pilar Alberola Colomar & Raquel Iranzo Fons

Flipped classrooms, flipped homes? Tending to students’ personal competencies 192

Eva N. Patrikakou

xviii

Technology in translation training 197

Iulia Mihalache

The creative development from the application of urban sketching in the academic

context

198

Adriano de Almeida Ferraiuoli

Remote access to a physical laboratory 202

Ulrich Borgolte, Michael Gerke, & František Jelenčiak

Massification of higher education in Botswana: Opportunities and challenges 207 Jane Iloanya & Abbas Lusenge

A pedagogic innovation in teamwork 212

Renée-Pascale Laberge

Robotics as means to increase students’ STEM attitudes 216

Marievie Panayiotou & Nikleia Eteokleous-Grigoriou

Teaching verbal behaviors to children with autism 220

Nurgül Akmanoğlu & Esin Pektaş Karabekir

Universal instructional design for accessibility and inclusivity: Supporting learners with

challenges

221

Peter Fenrich & Tim Carson

Unpacking the experiences of teachers transitioning to blended learning in Trinidad

and Tobago

226

Sharon Jacqueline Jaggernauth

Effectiveness of the multidimensional curriculum model in developing high order

thinking skills in elementary and secondary students

231

Hava Vidergor

Marking for the masses when timely feedback is important 232

Angela Allen, Philip Hanna, Darryl Stewart, & Andrew McDowell

Employers as individuals, employers as organisations: The continued influence of

employer behaviours on policy success

237

Eleanor Andressen & Hayley Dalton

Engaging students for the learning and assessment of the advanced computer graphics

module using the latest technologies

238

Yonghuai Liu, Longzhi Yang, Jiwan Han, Bin Lu, Peter Yuen, Yitian Zhao, & Ran Song

The impact of trailblazer standards on the delivery of apprenticeships 243

Eleanor Andressen, Hayley Dalton, & Irene Custodio

How can the technology introduction foster educational innovation in vet centers?

A comparative case study

248

Marco Perini & Arianna Costantini

Effects of the neonatal hearing screening program in a school for hearing impaired in

Turkey

253

Zerrin Turan & Nagihan Baş

Euro4Science 2.0: Spinoff of a forensic science educational strategy 256 Luís Souto, Helena Moreira, Sandra Vieira, & Rosa Pinho

xix

Effective practices promoting aboriginal communities’ school success 260

Mirela Moldoveanu, Marilyn Steinbach, Maryse Potvin, Naomi Grenier, Élian Boco,

& Chantal Viens

Using Google classroom to reinvent science education 265

Julie Smith

Increasing labour market success potential of young university graduates through

project-based education

270

Grażyna Budzińska & Marta Kędzia

Educational functions of museums and music in museum 274

Ali Öztürk

Use of mixed reality in design studio to enhance creativity of design students 275

Ahmet Fatih Karakaya

Developing a graduate employability profile: How do we ensure we deliver what we

promise?

280

Ioanna Stamatopoulou, Anna Sotiriadou, & Petros Kefalas

Teaching English as a foreign language by adapting materials according to student’s

learning styles

285

Júlia Hong Ventayol Alsina

Enhancing creativity and fostering education to enable community development.

Case study in Favara (Sicily – Italy)

290

Carla Cardinaletti

Changing the paradigm. The empathetic approach to problem solving in engineering

education

295

Grażyna Budzińska

Challenges in higher education: Involving students in the dynamics of scientific

knowledge production

300

Ana Capelo & Isabel Cabrita

Maximizing self-confidence, linguistic assimilation and cultural awareness using

interactive exchanges in the French language classroom

305

Ana Fonseca Conboy & Joseph Conboy

Design in concrete and abstract landscapes in architectural education 310

Hacer Mutlu Danaci, Elif Çelebi Karakok, Ayşe Şekerci, & Berk Saatci

Strengthening computer science students’ entrepreneurial skills: A step forward 313 Dimitris Dranidis & Thanos Hatziapostolou

Critical media literacy in communication space of historical film exhibition 318

Jakub Jiřiště, Terezie Křížkovská, & Adéla Mrázová

Teaching and Learning

Student teachers approach on using indigenous languages as LOLT in teaching science in

primary schools

321

Pule Phindane

Perceptions of music students for effective group working 326

Nurtuğ Barişeri Ahmethan & Aynur Elhan Nayir

xx

The teacher as a qualified interlocutor: Educational implications, conditions and

opportunities

327

Cristiana Cabreira & Rui Trindade

Implications of sexual development of LGBT children and youth for sex education

curriculum

332

Angela Hovey & Susan Scott

Are illustrations and texts in picture storybooks innocent? Natural environment messages

transmitted

333

Burcu Cabuk, Tugba Bas, & Nergiz Teke

First language versus first additional language(s) teaching in foundation phase in

South African schools

338

Takalani Mashau, Matodzi Muremela, Humbulani Mutshaeni, & Fhatuwani Ravhuhali

Development of functional thinking in primary school children using early algebra 343

Felipe Tirado & Ana Medrano

Mental health literacy development in pre-service teacher education 348

Wendy Carr, Yifeng Wei, Stan Kutcher, & Amy Heffernan

Enhancing cognitive development among undergraduates in the biology classroom by

active learning the principles, logics, and rationales that drive the information explosion

in modern (molecular) Biology

352

George M. Malacinski & Brian Winterman

Tackling econometrics teaching challenges: The use of Unicode in higher education 356

Julio Abad-González, Ana Pardo-Fanjul, & Luis E. Pedauga

The difficult second album: Why we must start teaching computer science in secondary

education again

360

Neil Anderson, Matthew Collins, Aidan McGowan, Angela Allen, Philip Hanna, & John Busch

Integrating laptop computers: A learning process for biology teachers 364

Morag S. Gundy & Marie-Josee Berger

Religious diversity in a multicultural society: What we can learn from the history and

Mandarin textbooks in Taiwan

369

Chuen-Min Huang

Exploring the transitional experience of BTEC students from post-16 study into an

undergraduate degree

374

Irene Custodio

The effect of using metacognitive strategies for solving mathematical word problems 379

Eda Vula, Rrezarta Avdyli, Valbona Berisha, Blerim Saqipi, & Shpetim Elezi

Foundations of education: From secondary to higher education. Identities and

(des)continuities

384

Emanuel Oliveira Medeiros

The pedagogical orientation of preservice teachers in teaching physics 388

Sam Ramaila & Umesh Ramnarain

Reducing public speaking classroom anxiety through the use of masks 392

Mine Ataş & Aynur Kesen Mutlu

University physics students’ views about scientific inquiry 397

Sam Ramaila & Umesh Ramnarain

xxi

Unplugged tools for building algorithms with Sprego 401

Piroska Biró & Mária Csernoch

Developmental dysgraphia and its prevention. What educational activities? 406

Angelo Luigi Sangalli, Angelo Lascioli, & Andrea Lascioli

Promoting the research knowledge mobilization through a collaborative action-research

project in two disadvantaged school settings in Quebec (Canada): Challenges and success

conditions

411

Naomi Grenier & Mirela Moldoveanu

Fostering critical thinking in teacher education 412

Ginette D. Roberge

Integration of civil technology theory content: Students’ practical work perspective 417

Khojane Mokhothu & Joseph Ramathibela Maimane

The relationships between number sense and mathematics achievement 422

Sinan Olkun, Yılmaz Mutlu, & Mehmet Hayri Sarı

Organizational Issues

Leadership for school reform: A case study from a New York city renewal school 427

Felicia Hirata & Alan Singer

Teaching in a global world: How economy defines educational policies 428

Daniel Carlos Gutiérrez Rohán & Bárbara Torti

Controversies surrounding sex education: A case study 432

Susan Scott & Angela Hovey

The arduous journey of the high functioning autistic/Asperger syndrome individuals from

the school system to the workplace: A Canadian model

433

Christine Besnard

Internationalizing allied health curriculum 434

Peggy R. Trueblood & Nancy Nisbett

Developing effective university governance in knowledge based society 435

Verica Babic & Marko Slavkovic

A research on third-party word-class university evaluation institutions in China and all

around the world

440

Baoyu Guo & Zhuolin Feng

Development of Fintech and importance of financial education 445

Suguru Yanata, Takao Nomakuchi, & Inga Malinauskaite

Not the “French-French”: Issues of inclusion and identity for non-Europeans after

Charlie Hebdo

449

Lisa Winstead

Transformation and social justice challenges facing South African higher education 450

Naziema Jappie

Leadership for teacher professional learning in Shanghai schools 455

Nicholas Sun-Keung Pang

xxii

Exploring professional learning practice in South African school leadership programmes

between 2008-2013

456

Kgomotlokoa Linda Thaba-Nkadimene, Disego Vincentia Thobejane, & Cathrine Lekgothwane

Methods used for determining of economical efficiency of selected activities for high

school students

460

Karel Kolar

THE RELATIONSHIPS BETWEEN NUMBER SENSE AND MATHEMATICS

ACHIEVEMENT

Sinan Olkun

1, Yılmaz Mutlu

2, & Mehmet Hayri Sarı

3

1Primary School Education, TED University (Turkey)

2Primary Mathematics Education, Muş Alparslan University (Turkey)

3Primary School Education, Nevşehir Hacı Bektaşı Veli University (Turkey)

Abstract

Number sense has been found to be relevant for measuring mathematics achievement in the elementary

school years. However, there are conflicting or at least different ideas as to what constitutes number

sense. Two basic systems of number have been identified: Approximate and exact number systems. This

paper evaluates the approximate number system. There are mainly two types of task used in measuring

the approximate system: pure quantity estimation and number line estimation. The purpose of this paper

is to determine which type of tasks is more relevant to measuring mathematics achievement in the early

years of schooling. A curriculum based math achievement test (MAT), calculation performance test

(CPT), Raven Standard Progressive Matrices Test (RSPMT), 2 Mental Number Line Tests (MNL-10 and

MNL 100), and Pure Quantity Comparison Test (Panamath) were used in collecting the data. Participants

were 323 second graders recruited from schools located in low-middle socioeconomic areas of 2 mid

Anatolian cities. In the analysis, lower 10% of the students in Raven SPMT were excluded from the

analysis to avoid low general intellectual abilities. Outliers were also removed before the analysis. Final

analysis was performed on 274 students. MNL-100 explained 12% of the variance while Panamath

explained an additional 2% of the variance in curriculum based math achievement (MAT). On the other

hand, MNL-100 has explained only 6% of the variance while Panamath explained an additional 10% of

the variance in calculation performance (CPT). When it comes to MNL-10, which is considered to be

small numbers for second graders, it explained 28% of the variance and Panamath contributed to an

additional 4% of the variance in CPT. These results showed that the relationships between number sense

and what considered to be math achievement and calculation performance is more complex than we

expected. Relatively small numbers seem to be more associated with calculation performance while MNL

with larger numbers were more associated with general math achievement which includes but not limited

to numerical problem solving and estimation.

Keywords: Number sense, math achievement, calculation performance.

1. Introduction

Calculation ability represents a very complex type of cognition, including linguistic (oral and

written), spatial, memory, body knowledge, and executive function abilities (Ardila, Galeano & Roselli,

1998). Children with developmental dyscalculia have tremendous difficulties in calculation and other

numerical skills. Two hypotheses have been proposed regarding the causes of mathematics learning

difficulties (Henik, Rubinsten, & Ashkenazi, 2011; Vanbinst, Ghesquiere, & De Smedt, 2014). First

hypothesis is domain-general cognitive deficits; the second is the domain-specific deficits hypothesis.

Domain-general hypothesis suggests that children with mathematics learning disorder have deficits in

intelligence, language skills, working memory, executive function, attention control, semantic memory

and data processing speed and these affect mathematical performance (Andersson & Östergren, 2012).

The second assumes deficits in number sense (Dehaene, 1997). It is suggested that number sense consists

of two subsystems (Carey, 2001; Feigenson, Dehaene, & Spelke, 2004). One of the two sub-systems

which is called approximately number systems is used to determine the approximate number of the

magnitude while the other is called exact number system that helps to determine the exact number of the

magnitude (Izard, Pica, Spelke, & Dehaene, 2008).

ISSN:2184-044X ISBN:978-989-99864-3-5 © 2017

422

The Approximate Number System (ANS) is a primitive mental system of nonverbal

representations that supports an intuitive sense of number in human adults, children, infants, and other

animal species. The numerical approximations produced by the ANS are characteristically imprecise and,

in humans, this precision gradually improves from infancy to adulthood (Mazzocco, Feigenson

& Halberda, 2011). There are mainly two types of task used in measuring the approximate system: pure

quantity estimation and number line estimation. In pure quantity estimation tasks either the number of

dots in a pile is estimated numerically or two piles of dots are compared. A hallmark feature of ANS is

that the imprecision in its representations increases as numerosity grows. As a consequence, the

discriminability between two approximate number representations is determined by the ratio between

them, not by their absolute difference (such performance is also commonly described as adhering to

Weber’s law) (Libertus, Feigenson & Halberda, 2013) In number line estimation tasks children are asked

to estimate either the relative place of a given number or the number that corresponds the hash mark

placed on empty number line that has 0 on the left and 10 or 100 on the right).

It was revealed that infants could recognize numerosities three hours after they were born (Izard,

Sann, Spelke, & Streri, 2009). Moreover, the differences in unlearned approximate number sense partly

explains some of the differences in mathematics achievement (Halberda, Mazzocco, & Feigenson, 2008).

Numerical acuity of individuals who have mathematics disorder is problematic to the highest degree

when it is compared to their peers (Piazza et al., 2010). Libertus, Feigenson & Halberda, (2013) found

that early ANS acuity predicted math ability six months later, even when controlling for individual

differences in age, expressive vocabulary, and math ability at the initial testing. In addition, ANS acuity

was a unique concurrent predictor of math ability above and beyond expressive vocabulary, attention, and

memory span. These findings of a predictive relationship between early ANS acuity and later math ability

add to the growing evidence for the importance of early numerical estimation skills.

Many studies confirmed that approximate number system is not independent of educational and

cultural inventions (Gordon, 2004; Halberda ve Feigenson, 2008; Nys, Ventura, Fernandes, Querido,

& Leybaert, 2013). Obersteiner, Reiss, and Ufer (2013) examined the effect of training intended for

enhancing first grade students’ basic number processing and arithmetic skills on their approximate mental

number skills. The improved number sense acuity of students with math disorder enabled them to perform

arithmetic operations much more easily (Kucian et al., 2011; Obersteiner et al., 2013). Group and

individual results indicate that children with math disorder mainly relied on an immature and

biased-logarithmic mapping compared to typically developing children. Half of the children with DD

showed a logarithmic and less accurate mapping on both interval sizes (Sella, Lucangeli, Zorzi

& Berteletti, 2013).

To our knowledge the relevance of number line estimation or pure quantity estimation to

mathematics achievement and calculation performance has not been compared yet. The present study

aims at determining either the pure quantity estimation or number line estimation is more relevant to

measuring mathematics achievement in the early years of schooling.

2. Methods

2.1. Participants Participants were 323 second graders recruited from schools located in low-middle

socioeconomic areas of 2 mid Anatolian cities. In the analysis, lower 10% of the students in Raven SPMT

were excluded from the analysis to avoid low general intellectual abilities. Outliers were also removed

before the analysis. Final analysis was performed on 274 students. There are approximately equal number

of boys and girls in the study. The mean age was 8.3 for all the participants, 8.1 for girls and 8.4 for boys.

2.2. Data Collection Tools Five different tests were administered to the participants; a curriculum based math achievement

test (MAT), calculation performance test (CPT), Raven Standard Progressive Matrices Test (RSPMT),

2 Mental Number Line Tests (MNL-10 and MNL 100), and Pure Quantity Comparison Test (PanaMath).

Mathematics Achievement Test: MAT, Mathematics Achievement Tests was developed by Fidan

(2013) for grades 1-4 based on the number domain of the Turkish national education math curriculum.

It includes numbers, counting, number patterns, four arithmetic operations, and fractions. KR-20

coefficients of the tests were .92 for second graders. The administration of the test took one class hour.

Mental Number Line Test (MNL) was developed by (Olkun & Sarı, 2016) and consisted of

number placement tasks. A typical number line is a horizontal or vertical line with zero on the left end

and 10 or 100 on the other end. Students are requested to place the numbers shown one at a time on the

number line by drawing a hash mark on the number line (see Figure 1). No timing was recorded for this

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test. Only the absolute values of the difference between the estimation and to be estimated numbers were

recorded in number to position tasks.

Raven Standard Progressive Matrices (RSPM): The test has 5 subtests each of which has 12

items progressively increasing in difficulty. In each item a figure is given with a missing part. Participants

are required to find the shape that fits the missing part.

Figure 1. Sample items from the MNL 1 and MNL 2.

The Calculation Performance Test (CPT): It is developed by De Vos (1992) and adapted by

Olkun, Can, and Yeşilpınar (2013) into Turkish. It has five columns of basic arithmetic operations written

in Arabic numerals and arithmetic operation symbols. Each column has 40 operations. In the original

study, the KR-20 coefficients were .95 and .98 for the timed and untimed administrations of CPT. The

students were given one minute for each column. The main difference between MAT and CPT is that

MAT has open-ended word problems while CPT has only arithmetic operations with Arabic numerals.

Panamath: This is the test used for measuring pure numerical estimations. Participants were

asked to decide which side has more dots in a given box that has blue and yellow dots (see Figure 2). The

ratio between the number of blue and yellow dots ranged from XXX to YYY. There are different sizes of

dots in each side and the place and color of larger side randomly changed. Both accuracy and latency

scores were recorded in a database.

Figure 2. Two sample tasks in Panamath.

2.3. Analysis The lower %10 (32 students) in the RSPMT was excluded from the analysis. Outliers (17 students)

were also removed from the data. The final sample consists of 274 participants. Row scores were used for

MAT, CPT and RSPMT. Total absolute errors were calculated for MNL 10 and MNL 100 (Booth

& Siegler, 2008). Weber fraction calculated by the Panamath software has been used as the score for pure

quantity estimation. Correlations among the tests were calculated. Stepwise multiple regression analyses

were performed to calculate the explanatory power of Panamath Weber and MNL test scores on

estimating MBT and CPT test scores.

3. Results

First of all, correlations among the tests were calculated. The highest correlation was calculated

between MNL 10 and CPT scores, MAT and Raven scores. Another interesting finding of the study is

that while RSPMT was strongly, significantly correlated with MAT it was only moderately correlated

with other tests. It is also surprising that there is virtually no correlation between Weber fraction scores

and MNL 100. This may mean these 2 test measures different aspects of the numerical cognition. All

other correlations are statistically significant (see Table 1 for details).

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424

Table 1. Correlations among the tests used in the study.

MAT CPT MNL-10 MNL-100 Weber RSPMT

MAT - .39* -.22* -.31* -.15* .53*

CPT - -.54* .23* -.30* .19*

MNL-10 - .19* .23* -.18*

MNL-100 - .02 -32*

Weber - -.18* *p<.01

Gender analysis showed that there were no statistically significant differences between boys and

girls in MAT, CPT and MNL 10 however boys did statistically significantly better on both MNL 100 and

Weber fraction. See Table 2 for further details.

Table 2. Gender differences.

Gender MAT CBT MNL-10 MNL-100 WEBER

N Mean Mean TAE TAE Mean

Girls 122 11.81 50.09 26.75 451.56 .266

Boys 152 11.68 50.28 25.00 406.59 .296

p .713 .942 .322 .043* .029* *p<.05

In order to determine the explanatory power of MNL 10, MNL 100, and Weber fraction on

mathematics achievement measured by MAT, a linear regression analysis (enter method) was performed.

Results showed that MNL 10 (R= 0.216, R2= 0.047) explained 5% of the variance (F(1-271)= 13.280,

p< .01) in MAT. Similarly MNL 100 (R= 0.311, R2= 0.097) explained 10% of the variance

(F(1-272)= 29.143, p< .01) in MAT. Both variables (R= 0.350, R2= 0.123) explained 12.5% of the variance

(F(2-271)= 18.927, p< .01) in MAT together.

Another linear regression analysis was performed to see if MNL 10, MNL 100 and Weber

fraction explains any variance in CBT. MNL-10 (R= 0.535, R2= 0.286) explained 29% of the variance

(F(1-272)= 109.11, p< .01). Similarly, MNL 100 (R= 0.231, R2= 0.054) explained 5% of the variance

(F(1-272)= 15.383, p< .01) in CPT. Both variables together (R= 0.632, R2= 0.400) explained 40% of the

variance (F(2-271)= 90.285, p< .01) in CPT.

In order to see if Weber fraction scores explain any variance in MAT and CPT, a linear

regression analysis was run. Results showed that Weber scores (R= 0.149, R2= 0.022) explained 2% of

the variance (F(1-271)= 6.175, p< .01) in MAT while they (R= 0.302, R2= 0.091) explained 9% of the

variance (F(1-272)= 27.253, p< .01) in CPT.

Taken together, Weber fraction and MNL 10 (small numbers) contributed more to arithmetic

performance as measured by CPT than mathematics achievement as measured by MAT. On the other

hand, MNL 100 (large numbers) contributed more to mathematics achievement than arithmetic

performance.

4. Conclusion

The results of this study showed that the relationships between number sense and what

considered being math achievement and calculation performance is more complex than we expected.

Relatively small numbers seem to be more associated with calculation performance while MNL with

larger numbers were more associated with general math achievement which includes but not limited to

numerical problem solving and estimation. Pure numerical estimation or quantity comparison skills on the

other hand contributed more to mathematics achievement than calculation scores although we used

relatively large numbers of dots to be compared in this test.

Results of this study also showed that the skills measured by pure numerical comparison tasks or

analog quantity comparison with dots as measured by Weber fraction score have more to do with small

with arithmetic performance than mathematics achievement.

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