mathscratch - bringing programming and

MATHSCRATCH - BRINGING PROGRAMMING AND MATHEMATICAL SKILLS INTO HIGHER EDUCATION E.Bigotte de Almeida1,3, A.Gomes1,2, F.Correia1,4 R.Almeida3 1

Instituto Superior de Engenharia de Coimbra/Instituto Politécnico de Coimbra(PORTUGAL) 2 CISUC - Center for Informatics and Systems of the University of Coimbra(PORTUGAL) 3 CASPAE-Centro de Apoio de Pais e Amigos da Escola(PORTUGAL) 4 IEETA- Institute of Electronics and Informatics Engineering of Aveiro(PORTUGAL)

Abstract According to some authors, the success of students’ integration in the courses of Differential and Integral Calculus all depends on their obtained basic knowledge in mathematics, which should have been acquired during the Secondary School. This knowledge is also essential for the first year in any Engineering Degree at the Superior level. It is from this compatibility that a better integration of students in the courses arises. A link between secondary and higher education is urgently needed, reducing the degree of demotivation that may lead to early school dropout with consequent implication in academic failure. However, a growing multiplicity in the basic training of students, with significantly different grades of access in mathematics, causes difficulties not only in Mathematics-based courses but also in courses of Introduction to Programming. Project members have already studied both problems. In this scenario, the integration of students in higher education, namely in Engineering degrees, is essential. Concurrently the recruitment of students to these areas of knowledge is in visible decline. Therefore, strategies to prevent students from deterring from these areas by introducing new processes of teaching and learning are needed. It is also important to draw a plan that fosters positive attitudes towards mathematics to reinforce self-efficacy. This intervention has to be carried out in higher education from a very early phase and has to gather a set of strategies that reverse the students' alienation in the areas of mathematics. Either by reorganizing the functioning and evaluation of courses or by constructing instruments that facilitate the learning process and that promotes student involvement. The “MathScratch” project aims at the creation of products (games/animations) on a Mathematics theme, in basic and elementary concepts that are considered essential for the integration of students in higher education in engineering degrees using Scratch programming. These resources will later be placed on a platform for the use of the 1st year students with difficulties in mathematics. We intend to support students and facilitate their integration into higher education by creating a sustainable structure that includes projects carried out through the 2016/2017 academic year, identifying the major difficulties experienced in areas of knowledge which are considered essential. Keywords: Scratch, Higher Education, Mathematics, Programming, Computational Thinking Skills.

1 DIAGNOSIS OF THE PROBLEM AND THE NEEDS TO WHICH THE PROJECT IS INTENDED TO GIVE ANSWER In Portugal, engineering degrees have been facing a decrease in demand, as verified by the Order of Engineers (in the academic year 2013/14, the demand for Civil, Electrical, Mechanical, Agricultural, Chemistry was 44% as opposed to 81% for Management, Law, Psychology and Economics courses). Therefore, it is urgent that Higher Education makes an effort to better adjust its degrees to the real needs of students and the country, in order to avoid that, in the near future, there may be a lack of professionals in the area of Engineering. The introduction of Mathematics and Physics as compulsory subjects in entrance examinations since 2012 for access to most Engineering courses was a measure that teachers have always certified as essential because they are the basic knowledge areas of Engineering. However, the lack of preparation of students during the secondary cycle of learning and the absence of student motivation

for these subjects, leads our society to the traditional aversion to these areas, which require dedication, work, reasoning, but which undoubtedly enable young people to have a working future. In this context, Higher Education institutions have been pursuing a process for the recruitment of different types of students coming from Scientific-Humanistic Courses, Professional Courses, Technological Courses, Technological Specialization Courses or “Over 23”. This allows them to have more students. As a consequence the degrees have a very heterogeneous public with diverse personal, motivational and cognitive characteristics. Therefore, professors must diversify their method of teaching so that it is more appropriated for the admitted student profiles. It is therefore a priority that professors of mathematics in Engineering degrees, especially those who teach units in the first year, seek changes in their pedagogical practices that allow the adequacy of educational strategies to the characteristics of students, their modes of communication, difficulties, motivations and learning styles. This practice becomes a permanent challenge for the professors of Higher Education and launches to debate some important issues, namely with regard to the motivation, the success of the students and their way of learning. According to some authors [1] the success in the integration of students in the Differential and Integral Calculus (DIC) units is verified by the need to reconcile the basic knowledge in mathematics, acquired during the course in Secondary Education, with the knowledge considered essential for the first year of the degree in engineering. It is from this compatibility that the better integration of students in the Curricular Units (UC) arises. Therefore it is urgent that an articulation between secondary and higher education occurs, reducing the degree of demotivation to avoid early school dropout with consequent implication in academic failure. However, the increasing multiplicity of students' basic skills, with significantly different math scores, leads to difficulties not only in mathematics-based UC but also in Introductory Programming UC. Both problems have been the subject of several studies carried out by these researchers [2],[3],[4],[5]. In this scenario, the integration of students in higher education, namely in Engineering degrees, has led to a process so that, concurrently with the recruitment of students to these knowledge areas (in visible decline), strategies are defined in order to prevent students from being away from the processes of teaching and learning and to foster positive attitudes towards mathematics, reinforcing self-efficacy. This intervention has to be carried out in higher education from a very early age and has to gather a set of strategies that reverse the students' alienation in the areas of mathematics, either by reorganizing the functioning and evaluation of UC or by constructing instruments that facilitate the learning and that promote student involvement. It was based on these assumptions that a process of awareness of the educational community of ISEC (Higher Institute of Engineering of Coimbra) was initiated, for the implementation of a Center for Support to Mathematics in Engineering (CeAMatE) [6]. This project was presented to the Pedagogical Council, which approved it at a meeting held on May 29, 2013. CeAMatE is a structure dedicated to personalize support for students in learning mathematics in Engineering. It integrates a physical component (CeAMatE-in) and an E-learning component (CeAMatE-on). CeAMatE-in is a physical space, located in the Physical and Mathematical Department of ISEC. This space has resources enabling the development of activities, parallel to those developed in the classroom. They have a nonmandatory character, aiming at helping students in the overcoming the difficulties of mathematics essential to full integration in the UC-DCI. The aim is to provide a quality service and a wide range of learning resources in order to encourage students to overcome their difficulties, either through selfstudy or with the help of teachers. CeAMatE-on is an e-learning platform that consists of a moodle platform plug-in embodied in an intelligent system that accumulates knowledge resulting from the data provided by its users (successes and failures) and adapted to the learning preferences Of the student and their cognitive level. This Center has implicit some important peculiarities, such as the association between higher education and civil society and also the association to the educational community in which it is inserted. The lack of human resources and administrative difficulties in contracting, associated with the overload of teachers and the absence of reductions in service to follow up on these types of projects are constraints faced by Higher Education Institutions. The Institutions organized by Civil Society, as well as the Student Associations, also have as a mission promoting social responses, personal appreciation and well being, in a perspective of inclusion of the individual in society. From these intentions a partnership, with the Private Institution of Social Solidarity, CASPAE (a Portuguese

acronym of Social Support Center for Parents and Friends of the School) for the implementation of CeAMatE-in in ISEC, was born. Another substantial pillars of CeAMatE-in is the integration of students with proven success in DCI units, within the existing volunteer project in the IPCSer (a Portuguese name for a volunteer project of the Coimbra Polytechnic http://voluntariadoipc.wordpress.com/programas). The work of theses students will revert to the diploma supplement. as well as trainees of the Faculty of Psychology and Educational Sciences of the University of Coimbra, to support the team coordinating the structure as well as trainees of the Faculty of Psychology and Educational Sciences of the University of Coimbra, to support the team coordinating the structure.

1.1

Sample Characterization

One of the assumptions of the Bologna model and the recommendations of the A3Es-Agency for Evaluation and Accreditation of Higher Education is precisely in the sense that there is a higher concern in the planning of transversal competency training throughout the course. Thus, it is considered that the development of multidisciplinary projects may be a relevant strategy for the integration of students in higher education. As already mentioned, the students of Engineering degrees, namely Informatics, Electrotechnics and Mechanics, show great difficulties in integration in the UC-DCI, taught in the 1st year of the 1st semester, which implies demotivation and absence to the classroom. These behaviours inevitably lead to high dropout rates in assessments and increase the failure rates. Several studies carried out with the ISEC students show that one of the reasons for this scenario is explained by the poor knowledge of mathematics content, considered by teachers as basic and elementary when accessing higher education [7],[8],[9]. It is also observed that students of Biomedical Engineering do not show this "natural tendency" in lack of knowledge of mathematics but, undoubtedly, show weak skills for introductory programming disciplines. Consequently, in the 1st year/1st semester, a high failure rate in the UC of Introduction of Information Technologies is registered. The vast majority of students who have access to this degree come from the Science and Technological Area and have attended mathematics A, whose program content ensures the basic and elementary knowledge required in DCI. Since, all these students are in engineering degrees it seems fundamental that there be problem solving skills and the logic involved in the computational thinking that many students do not have. The studies point out that the difficulties come from this precise area, which constitute a barrier to the success in UC of programming. Confronted, on the one hand, with the lack of basic and elementary knowledge of mathematics that allows the full integration of 1st year students in Engineering degrees and, on the other hand, with the lack of problem solving skills and the logic involved in computational thinking, the professors in charge of the UC of Introduction to Information Technology (ITI) and Calculus I (CI) of the degree in Biomedical Engineering, decided to carry out the project "MathScratch". This project not only allows to develop the programming skills of these students but also to involve the participants of CeAMatE in the construction of pedagogical resources. These resources are related to mathematics subjects in which students have less knowledge or more difficulties. The idea is also to make them available, in a later phase, in the online platform that is under construction. An applied cooperative methodology would enable each member of the group to highlight each of their competencies while also being able to develop areas of knowledge converging to the resource production that could be used by all the community. "MathScratch" is part of a project to promote Scratch programming, aimed at students of various education levels, covering pre-school, primary school and higher education - "All in Scratch" promoted by CASPAE in Partnership with ISEC, the Faculty of Psychology and Educational Sciences of the University of Coimbra and the School of Education of the Polytechnic Institute of Setúbal.

2

DESCRIPTION OF THE OBJECTIVES AND THE ACTION PLAN

"MathScratch" project has the following objectives: • To allow the development of computational thinking skills that will help students in the various UC of their engineering course and in particular in the programming subjects of 1st year students of Biomedical Engineering. For this purpose, different learning strategies are used over the one-month course, with 2h weekly workshops in Scratch programming, as an extracurricular activity, supported by a technician assigned by the CASPAE partner institution.

• To involve students in the construction of their own pedagogical resources in mathematical subjects in which the majority of engineering students have less knowledge. The construction of these resources will also allow the development of abstract thinking and the ability to modularize, reducing a problem to simpler situations, representing problems in different ways, making analogies with similar problems and developing deductive thinking. This process allows the improvement of several problem-solving skills through the expansion of analytical, quantitative, analogical and combinatorial reasoning skills. The evaluation of these pedagogical resources will be carried out simultaneously in two UC of the degree in Biomedical Engineering (CI and ITI), in a transdisciplinary way, which will allow the direct integration of students in the construction process. Based on realized studies [10] it is easily demonstrated that the use of Scratch makes it possible to learn mathematical basic concepts in a constructive manner and awakens student interest and motivation to this knowledge area. Thus, one of the objectives of the "MathScratch" project is to stimulate students in areas such as mathematics in order to develop their own taste for learning. Felleisen and Krishnamurthi [11] emphasized the concept of "imaginative programming", considering its importance as an element of programming because of its close relationship between mathematics and computation. In this context, we have used Scratch, a programming environment that allows its users to learn programming concepts while developing resources that can explain math content. The "MathScratch" Project was divided into several phases that were developed during the first semester of the current academic year (2016/2017): First phase - Accessibility and Diagnostic Assessment - is about raising awareness about the Scratch platform: how it should be used, what its potentialities are, what students can and can not develop, and how they can do it. For the multidisciplinary team, it is a phase of diagnostic evaluation, perceiving the major students difficulties, the areas that should be more worked, the projects they like to develop, where the motivation is greater. Second phase - Motivation, Autonomy in Problem Solving and Challenges - this is a learning phase of the platform, where students learn to develop projects effectively with different levels of complexity, including the logic of programming, solving problems and developing autonomy of work. Third phase - Final Project - students have full autonomy to build the project, following previously established guidelines, in groups of 2 elements, which must be presented at the end of the semester. At this stage, the team members who were present at the Workshops act as job coaches, intervening only when requested by the students, providing autonomous learning based on trial and error. The various projects developed are educational games or animations inspired by mathematical themes where students have more difficulty. Fourth phase - Preparation of the final report and a final presentation – the presentation is done in public discussion with the teachers of the two UC and the technician who accompanied all students in extracurricular activities. In this context and with this approach of interdisciplinary projects the authors intend to evaluate, in a first phase, the satisfaction of the students of Biomedical Engineering of ISEC, in relation not only to the use of Scratch software but also to the importance of carrying out a project work developed jointly in the two UC (CI and ITI).

3

RESULTS 3.1 Methodology

After defining the main objective of this investigation, we tried, using a qualitative approach, to understand the perceptions of students in relation to the importance of conducting an interdisciplinary project developed as a curriculum complement and with the use of Scratch programming software. Qualitative research is a methodology of study, which focuses on the question of how to interpret and give meaning to the experiences, allowing further variables in study, exploring and bringing a variety of possibilities for the interpretation of the phenomena under discussion.

3.2 The sample The study focused on students of the Biomedical Engineering degree, given at ISEC, enrolled in courses of ITI and/or CI, in the first semester of the school year 2016/2017. The sample consists of 33 students, 11 male and 22 female, and 72.4% were between the ages of 18 and 20 years.

3.3 Data collection instruments The objective was to analyse the satisfaction of students of Biomedical Engineering of ISEC in two aspects. Firstly, in relation to the use of Scratch software. Secondly, to validate the importance of the undertaking a project developed jointly in two UC (ITI and CI). For this, at the time of presentation by various groups, corresponding to phase 4, a questionnaire designed to gather information about the students perspectives was answered by them. The used format of the scale was a five-point likert type, which depended on the student degree of agreement, where 1 was the minimum value and 5 was the maximum value. The questionnaire was divided into 2 groups of questions: • “The utilization of Scratch tool ", that includes the 7 items. • "The work done together in two courses (CI and ITI)”, that integrates 2 open-response items.

3.4 The procedure The questionnaire was applied in the first semester of the school year in progress (2016/2017) to students who performed a public presentation/assessment of their final work, after the joint and shared debate of the project. In order to develop complementary studies in the context of the contribution of this action for the improvement of the performance of students in ITI and CI, which permits a better understanding of each student trajectory, student identification was requested, but not mandatory, guaranteeing the confidentiality in the treatment and disclosure of the data.

3.5 The results For data analysis we opted for a simple approach using only the descriptive statistics, treated with the IBM SPSS Statistics. The measure of location used was the median since the data collected corresponded to ordinal variables, reporting the respective distribution for each question, during the analysis process. For the question "I've enjoyed working with the tool Scratch", 69.7% of students agreed with the statement and 24.2% agreed totally agreed from what in general we may conclude that it was a good option to have introduced this software as a complement to the curriculum. When questioned about the difficulty, 42% revealed they had difficulties, while 21% assumed they did not have any great difficulties. The assessment that students made about “The final outcome of the project was what they expected", 57.6% said that the final project was very close to the expected, 21.2% answered that the project was exactly what they envisioned, with the percentage of respondents who disagreed with the statement being only 3%. The motivation to work with this tool accompanied 72.7% of respondents having only 6.1% sense opposite feelings. One of the goals of the implementation of the "MathScratch" in higher education context was to allow developing computational thinking skills that will help students in the various courses of engineering degrees and in particular in programming courses. Through the students' responses to the questionnaire 69.7% of respondents expressed their agreement with the item “I developed my programming skills”, 84.8% recognizes in Scratch “Important features for those who start programming”, and 60.6% understand that it is “Important for all biomedical engineering graduates to receive training in this programming tool”. In conclusion, only 15.1% of students wouldn’t work in a professional context with Scratch, but 57.6% agreed to use this tool in the future. In relation to the work performed together in the two courses (CI and ITI) the analysis of the open answers given by the students induce, in general, the acquisition of skills at the level of programming. However, no great transformations in terms of obtaining basic knowledge of mathematics were seen. These results were not surprising since students of Biomedical Engineering do not reveal any great

difficulties at the level of mathematic. Therefore their full integration in the course of DCI is not an issue. With regard to the level of programming in this project, the following advantages were identified, using the open answers given in the questionnaire, in terms of: • Structuring and organization of the program, as well as the logical reasoning behind its construction; • Understanding programming structures and their use; • Understanding the C language that is taught at the ITI course, through the translation and concrete visual representation of the used structures, contributing to the improvement of the ability of abstraction inherent in a programming language; • Acquisition of skills that generate the feeling of real programmers and content producers and at the same time contributing to the development of their creativity. Students when regarding the achievement of this project did generally not identify disadvantages. Some students actually stated that there were no disadvantages. Although the "MathScratch" had been properly planned so as to contemplate a weekly support which was permanently provided until the completion of the project, proved to be indispensable by students, nevertheless they highlighted this as a disadvantage, mainly because of the increased amount of time necessary to the implementation of their works.

4

FUTURE WORK

The main idea underlying the "MathScratch" is the sharing of knowledge that stimulates the creation of new information and improvement of performance among all the involved people. Therefore, in the second semester of this school year, the group intends to progress with the project in the following ways. • To make available the products developed on the online platform (CeAMatE-on) which is under construction. The functioning of the CeAMatE-in structure will ensure the validation of these pedagogical resources. This is accomplished by testing these resources with students from other degrees in engineering, with knowledge gaps in math skills which will enable the survey of suggestions/changes/adaptations. • To involve students in higher years and other degrees in projects of interest to ISEC which may associate transversal skills important to the integration into the labour market. This objective will be achieved by the students’ integration of Human Computer Interaction course of the 2nd year of the Informatics Engineering degree. It should be done by analysing the usability and improvements of the educational resources developed, in line with the tests carried out. The multidisciplinary aspect of the project allows, once again, the involvement of a greater number of students, fostering the association of transversal skills that are so important to the integration of these students into the labour market. • To analyse the influence of learning this tool with the results obtained throughout the semester in ITI. It is also intended to understand what the acquired mathematical skills are in students that both show the ability to ask and answer questions with math and also to relate and deal with the language of mathematics and the tools.

ACKNOWLEDGES The authors would like to thank all students that participated in the studies and to the teachers and people that allowed their realization.

REFERENCES [1]

M. E. Bigotte, C. Fidalgo, J. R. Branco and V. Santos, “ACAM – Competency Assessment/Improvement Actions: Diagnose to guide,” in Proc. of the 17th SEFI MWG Seminar Mathematical Education of Engineers, 2014.

[2]

M. A. Barbosa, “O insucesso no ensino e aprendizagem na disciplina de cálculo diferencial e integral [The failure in teaching and learning in differential and integral calculus course, in english],” Dissertação de Mestrado [Master’s thesis], PUCPR, Brasil, 2004.

[3]

W. M. Resende, “O ensino de Cálculo: Dificuldades de Natureza Epistemológica [Teaching Calculation: difficulties of epistemological nature, in english],” Tese de Doutorado em Educação [Ph.D. thesis], Faculdade de Educação, Universidade de São Paulo, USP, Brasil, 2003.

[4]

A. Gomes, and F. Brito Correia, “Errors to avoid in Programming Teaching and Learning,” in Proc. of 7th International Conference of Education, Research and Innovation, Seville, Spain, November 2014.

[5]

A. Gomes and F., Brito Correia, “Programming Education Strategies,” in Proc of 7th International Conference of Education, Research and Innovation, Seville, Spain, November 2014.

[6]

M. E. Bigotte and A. Gomes, “The CeAMatE-on project: an online Mathematical Support Center in Engineering,” in Proc of XVII Simpósio Internacional de Informática Educativa, 2015, pp. 169175.

[7]

O. Gill and J. O’Donoghue, “The mathematical deficiencies of students entering third level: An item by item analysis of student diagnostic tests,” in Proc. of Second National Conference on Research in Mathematics Education, Dublin, UK, 2007, pp. 228–239.

[8]

M. Cardella, “Which mathematics should we teach engineering students? An empirically grounded case for a broad notion of mathematical thinking,” Teaching Mathematics and its Applications, vol. 27, no 3, pp. 150-159, 2008.

[9]

O. S. Rosa, “Aspectos Motivacionais do Cálculo Diferencial e Integral [Motivational aspects of Differential and Integral Calculus, in english],” Programa de Pós-Graduação Stricto Sensu, Mestrado Profissional em Educação Matemática, Universidade de Severino Sombra, Brasil, 2011.

[10]

L. Calao, J. Moreno-Leon, H. Correa, G.Robles,” Developing Mathematical Thinking with Scratch An Experiment with 6th Grade Students”, G. Conole et al. (Eds.): EC-TEL 2015, LNCS 9307, pp. 17–27, 2015.

[11]

M.Felleisen,S. Krishnamurthi, “Safety in Programming Languages”,Sixth ACM-SIGSOFT Symposium on the Foundations of Software Engineering, November 1998.