At national level, mathematics is a compulsory subject, whose study involves following a standard curriculum for each grade. The use of IT tools is a methodological suggestion and it is up to each teacher the extent to which these are used during classes.
In 2002, the Romanian Ministry of Education financed an extensive project of providing schools with computers and e-learning resources. There is an on-line platform containing over 100 lessons and mathematics tests (not up-dated) for secondary school students.
The educational policy of our school encourages the use of IT tools in teaching and learning mathematics. The classes of students, by teachers’ request, have access to the IT laboratories in the school. Approximately a quarter of the classrooms are endowed with a video projector. All teachers have tablets. The teachers, students and parents have access to an on-line platform called Adservio, which offers email communication, resource sharing and an electronic roll. In order to increase the extent to which IT tools are used, the Math teachers have granted their students the permission to utilize their smartphones in class.
In A.T.Laurian National College the subject of mathematics is studied 4-5 classes per week. The IT resources are utilized sporadically, especially during the classes in which projects are being done, this method being used at least once per semester.
The target group consists of 73 students aged 12-14, from the 6th to 8th grade, from our lower secondary classes. These students have a compulsory curriculum until the end of the 8th grade, when they have to pass a national exam. After this exam, based on their results in Mathematics and Romanian, they can choose an upper secondary school specialization (e.g. mathematics and informatics)
The Romanian teachers of Mathematics who are members of the TEMP project team are Dorica Alexe, Liliana Tomita, Ciprian Apetrei and other two collaborating teachers of Laurian (Liliana Pricope and Geanina Tudose). The Computer Science teachers in the team are Daniela Cerasela Cardas and Carmen Afrodita Giocas, and the English teachers participating in TEMP project are Ionela Florentina Iacob and Nicoleta Saramet.
The students targeted by the research belong to two age-groups. There are approximately 72 students in the 6th and 7th grade (aged 13-15) and 30 students in the 11th grade (aged 17-18).
How can we increase the students’ understanding of elementary geometry by using IT tools?
The first problem identified in the case of lower secondary school students was the low degree of understanding of some geometrical concepts. Not all students understood the theoretical concepts from the “Important Lines in a Triangle” unit. The students’ imagination, creativity, ability to generalize and think in abstract terms differed a great deal.
In this case, the intervention consisted of learning activities planned for the first 6 months of the project. The problem was identified through direct observation of the teachers during the mathematical discussions in the classroom. There were students who did not participate in the discussions or gave incorrect answers to the assessment questions, either written or oral.
The progress from concrete thinking, from the palpable representation of things to formal, abstract thinking does not occur at the same pace for all students. The traditional learning/ teaching methods (creating a drawing on the board and explaining it) are not sufficient. For instance, when a section of a cube is to be determined, the cube is not literally sliced, we merely imagine, intuit this section and then we demonstrate it.
This problem can be alleviated by utilizing as many IT tools as possible in order to represent geometrical 3D-shapes which are moving or which can be moved easily in any direction. To this end we used an educational software entitled “The Congruence of Triangles”.
An initial evaluation test was taken by the 7th graders, containing topics learnt during the previous school year. These mathematical concepts were presented again during 6 consecutive classes, by using GeoGebra, video projectors and laptops. The students did not have access to computers during these classes. After the class discussion, the lessons were uploaded onto the class group and on the web platform of the school so that the students could access them at home and learn at their own pace. After participating in these 6 maths classes the students took an assessment test.
The maths classes were more dynamic, as among the participating students were also those who usually became bored easily or had problems concentrating. The geometrical shapes which could be easily altered helped the students to understand and learn the mathematical concepts.
- an on-line test of initial evaluation was applied;
- after the 6 technology-based revision lessons, a Google Forms assessment was conducted in January 2016;
- the students responded to on-line questionnaires, the data was collected in Google Data Sheets and then analysed by teachers.
Two impact studies were conducted, at the end of each semester of the first year.
They contain statistical data, diagrams and data interpretation. Both for the initial and the other tests, the students’ results were calculated and divided into 3 groups.
The number of students who took the initial test was 47. It can be noticed that the average grades, between 5-6.99, are the most numerous (61.67%). In the same test, two students (4.25%) obtained scores above 9 and four students (8.51%) between 8-8.99.
In the final tests, there was a slight increase in the results obtained by the students who scored between 7-10.
The number of students who took the initial test was 48. The grades between 5-6.99 are the most numerous (54.16%). There was an increase in the number of grades between 7-10.
The number of lessons during which the teacher conducted the intervention, lack of prior teacher training regarding how a research study is carried out, the students did not have laptops, the classes were taught by using a video projector, the assessment of the students involved special access to the computer laboratories. In building C of the school,where lower secondary students study, there is no Wi-Fi connection, only about 50% of the students there possess smart phones with an Internet connection.
How can we improve the students’ Mathematics learning performances in doing the homework using ICT and multimedia resources?
The second problem was the lack of motivation in doing homework, given the fact that the 8th grade students are preparing for the national mathematics examination, which is part of the admission to the Romanian upper secondary education.
The problem was identified through systematic observation and periodical homework check. Also, during classes, the accuracy of the way the homework was done was also checked by verifying samples of homework.
Some causes of this problem could be the fact that some students may not have understood the lesson in class, their poor ability to work individually, lack of communication outside the classroom between teachers and students.
In order to solve the problem we created a collection of solved mathematical problems, of self-assessment tests and simulated exams on the on-line platform ATLmath. By using these web resources, the students have access to support for a deeper understanding of mathematics lessons, to assessment, self-assessment and result-monitoring tools. We also utilised this platform during the assessment classes by organising in the computer science laboratories simulations of the national exams. For current evaluations, the students accessed the platform from their mobile phones, in their classrooms.
As part of the intervention, in February 2016 we created an interactive educational software within the learning unit of “The Congruence of the Triangles”. The students were instructed how to use the application on their computers at home, and used it as a learning resource, as well as of self-evaluation and homework completion resource. During classes were discussed the problems faced by students. The intervention was conducted during 4 Maths classes and 4 hours of individual study.
The students solved the problems contained by both the software “The Congruence of Triangles” and the ATLmath website (http://mate.laurian.ro/) . The students responded to the satisfaction questionnaire in the first semester of the first year of the project.
The students simulated the 8th grade national mathematics examination on the ATLmath platform. Their results were analysed by using diagrams (pie charts).
Based on the question: “Do you always do your math homework?” it was observed that 7th graders generally do their homework. When asked “To what extent did using IT tools help you to do your homework? “, the majority of students answered “A lot.”. There was a minimal percentage of students who answered “At all”, which means that they may not have used use the resources they had. After simulating the 8th grade national math exam on the ATLmath platform it was observed that prior to taking the simulated exam, the students had accessed the section of “Problems solved”, the evidence being the high percentage of correct answers.
The students discovered the excitement of using portable gadgets on educational purposes. They become accustomed to utilising digital resources alongside textbooks and the traditional notebooks. The self-assessment tools to which they had access become learning tools, due to frequently-repeated utilisations. The communication among students improved, owing to the on-line groups. The task assigned by teachers for students to use these types of software led to arousing their interest in the discovery and utilisation of other learning platforms.
It was noticed that the quality of the semestrial school subjects done by the students from the target group had increased, as the method used within the project is one of summative evaluation, applied at least once per semester. This may be accounted for by an increase in the students’ ability to analyse and select the learning resources.
Reflections on the collaborative process
Our partners in the TEMP project were the Vasteras Kommun in Vasteras, Sweden and the UCL Academy-London. We shared experiences and examples of good practice during the transnational meetings. Also, we participated in a training course on Classroom Response System organized by our Swedish partners.
We communicated with our TEMP partners through emails, Facebook groups, we shared the resources created for the project on Google Drive and the TEMP project website, projecttemp.org.
The main benefits for us are the fact that we have exchanged information about IT tools and pedagogical methods used by our own partners, websites and innovative applications utilized in the UK and Sweden. Also, we have discovered useful research articles of mathematical pedagogy regarding the manner in which IT tools can be used in teaching mathematics.
Moreover, through this project we have been challenged to design, implement and analyse an intervention as part of a European research study related to using IT in teaching mathematics. Another important benefit is the interaction with researchers from UCL Academy, Vasteras and Mälardalen from whom we have learnt about reflecting on the process of teaching/ learning mathematics. These, in turn, have been reflecting on the process of teaching/ learning mathematics in A.T.Laurian National College, in Botosani county and in Eastern Romania and will influence this process in the years to come.
Utilising IT tools in teaching mathematics has contributed to:
- enhancing the students’ understanding of complex mathematical concepts which are fairly abstract;
- developing the students’ creativity and innovative skills;
- increasing teacher-student and student-student interaction;
- changing the focus of the teaching/ learning process from teaching to learning;
- reducing the students’ learning time and increasing the time dedicated to deepening the knowledge of mathematical concepts;
- increasing the students’ motivation to study mathematics;
- increasing the formative potential of assessment, due to instant feedback given by IT evaluation tools, as compared to the traditional types of assessment;
- increasing the number of students who do their homework.
- We will use IT tools in our future mathematical classes.
- We will participate in professional development courses.
- We will involve more students in creating software to be used in the maths classes.
- We will attempt to purchase more IT equipment.
- We will further develop the ATL Math platform.
The project will be shared with other teachers of mathematics, as follows:
- we will use demonstrative lessons based on IT tools at the professional development meeting of Maths teachers;
- we will disseminate the TEMP project at the Society of Mathematical Sciences –the Botosani county branch.
How can we create connections between Mathematics and other subjects in an interdisciplinary approach?