Mathematics is very closely related to life situations. It teaches different ways of solving tasks and constantly reminds us that the individual parts must eventually come together into a coherent whole. This approach is not only suitable for solving tasks, but also for writing an article, cooking or planning an event. Vilnius University Researcher of the Institute of Educational Sciences of the Faculty of Philosophy, Assoc. Dr. Vaiva Grabauskienė and asst. Dr. Oksana Mockaitytė-Rastenienė develops the mathematics teaching methodology MATEMA, which draws inspiration from the environment around us, looking for ways to convey this educational subject as comprehensibly as possible to children.
LEGO blocks also help to learn mathematics
Assoc. Dr. V. Grabauskienė says that the idea of MATEMA was born together with the "Robotics Academy" during the implementation of the European Social Fund Agency (ESFA) funded project "I create, construct, discover mathematics with LEGO", the aim of which was to improve mathematics teaching.
"The original idea was to create a convenient set of LEGO blocks for the primary school teacher, which consists only of the parts necessary for learning mathematics. We developed this methodology while working with teachers from four schools in Vilnius," says the docent.
Combining the application of the LEGO set with the learning system of mathematical reasoning, the assistant Dr. O. Mockaitytė-Rastenienė notes that this partnership has brought tangible benefits. This set is convenient for teachers, because the amount of tools needed for learning mathematics is minimized, and students acquire other abilities in addition to knowledge of the content of mathematics.
"It is not enough for children to memorize and apply formulas. With a LEGO set, they can communicate, cooperate with each other, choose the right way for themselves and build an understanding of mathematics through their experiences," says the researcher.
"During the project period, we wanted to cover all the mathematics content of grades 3-4, so there were certainly topics where LEGO was not very suitable. We had to turn our heads properly to use LEGO to teach the decimal system or to construct geometric bodies. The LEGO brick set was the very beginning and our current MATEMA is already a long way from that. At the moment, we are mostly concentrating on the methodology of learning mathematical reasoning itself, when mathematics can be explained using various tools", adds Assoc. Dr. V. Grabauskienė.
The importance of mathematical reasoning
Scientists unanimously agree that the earlier we provide children with the conditions to reason, the stronger their knowledge and abilities are. Research shows that the formation of mathematical reasoning skills helps to move more smoothly to more complex mathematical topics, apply calculation procedures, and interpret content.
"MATEMA methodology helps to develop many important abilities - the ability to analyze, find regularities, generalize - and accelerates decision-making. A lot of attention is also paid to learning to communicate about mathematics," says the assistant. Dr. O. Mockaitytė-Rastenienė.
Students do not dare or are not able to talk about mathematics using the terms of this field. Teachers notice that children intuitively sense the answer to the task, but are unable to explain in words how to solve it. "A child must learn and dare to talk about mathematics. He must cooperate with his classmates, but at the same time have the opportunity to express himself as he wants. In the MATEMA methodology, we use visualization for this. At first, the child illustrates the mathematical situation with a realistic drawing and tries to explain it, and later the explanation is supplemented by drawn diagrams. Therefore, the methodology frees the child's imagination, allows him to use everything he wants, and thus increases the child's motivation", says Assoc. Dr. V. Grabauskienė.
The methodology is adapted to students of different abilities
Asst. Dr. O. Mockaitytė-Rastenienė notes that usually in mathematics textbooks, children are used to stricter schemes and templates, but by implementing the MATEMA methodology, she allowed the students to visualize the tasks the way they wanted.
"Our methodology is special in that it simultaneously adapts to students of various styles and abilities. Each child can draw his own picture and explain his own solution to the problem to the other children as best he can. A sense of freedom and creativity is important. Of course, I show the children different ways of visualizing before starting the tasks, but I also let them create their own. The main thing here is the structure. By preserving the structure characteristic of the representation of the addition or subtraction action, the child can choose the elements as he wants," says the researcher.
It is also very important that when using the MATEMA methodology, students are tried to access information in a variety of ways. Children draw, talk, depict using material means.
"Teachers often explain the tasks in one style, but we try to include different styles because it makes the children feel good. Mathematics is characterized by different ways of expressing ideas, so with MATEMA we try to present them", says Assoc. Dr. V. Grabauskienė.
The goal of the researchers is that MATEMA and different ways of expressing ideas in mathematics accompany students not episodically, but throughout the entire learning period, especially since the results of children who studied according to this methodology are better than the national average.
"We used this methodology in schools at a time when 2nd graders were taking standardized national math tests. in 2019 according to the results of the standardized tests, second graders could fall into three groups. The entire class I taught was in the highest, third group. Equally important is the fact that the cognitive abilities of these children were significantly higher than the average for the whole of Lithuania," the assistant shared the results. Dr. O. Mockaitytė-Rastenienė.
Provides additional knowledge for teachers as well
MATEMA methodology could be applied in more than one Lithuanian school, but it is necessary to prepare teachers for it. Assoc. Dr. V. Grabauskienė says that primary school teachers can get acquainted with the MATEMA methodology in the courses organized by VU and in author's seminars.
"We teach this methodology to VU Institute of Education students. At the university, we organize teacher training courses for primary school teachers, where we also discuss full-fledged mathematical education in preschool age. "Teachers can independently familiarize themselves with the report of our project "I create, construct, discover mathematics with LEGO", which is publicly available," the researcher presents the learning methods.
Asst. Dr. O. Mockaitytė-Rastenienė emphasizes that today many teachers are confused and do not know which teaching methods are optimal, so courses may not be enough for teachers as a simultaneous "injection" of knowledge. "We would like to strengthen the community of teachers. Of course, the most important thing is that teachers want to learn and learn something new," she says.
A version of the digital learning environment suitable for applying the methodology is being developed
The pandemic changed the scientists' approach to the MATEMA methodology after it became clear that LEGO bricks are not necessary for its implementation. When learning according to MATHEMATICS, you can put together pasta, acorns, and other objects available at home. The ability to manipulate tools on the computer screen is also important.
"The computerization of mathematics learning is a very specific topic and a significant number of mathematicians are hostile to the completion of numerical mathematical tasks. Despite the fact that there are currently quite a few websites, the information on them is very diverse and lacks systematicity," says Assoc. Dr. V. Grabauskienė.
The researchers received funding from the Innovation Fund of Vilnius University for the preparation of the "Possibilities study of MATEMA digitization of primary school mathematics learning methodology". This study helped refine the form and details of the digitized MATEMA methodology.
"We knew a few things while conducting a feasibility study for digitizing the MATEMA methodology. First of all, MATEMA will not be a simulator, because there are many apps of this kind. Second, we wanted to combine all the topics necessary for learning mathematics into a whole. Thirdly, we tried to familiarize ourselves with as many existing tools as possible, and we certainly found some that inspired us to choose advanced ways of presenting our methodology," says the researcher.
"Analyzing the possibilities of transferring the MATEMA methodology to the digital space, we once again made sure that this methodology cannot replace the teacher and his contribution is necessary. We have already planned digital tasks for the children, but presenting methodological materials to the teacher will be no less challenging. We hope that this digital tool will make it easier for teachers to explain tasks and for children to understand them," says Assoc. Dr. V. Grabauskienė.
In order to complete the implementation of this idea, it is necessary to obtain additional funding for software development work, to find programmers capable of implementing the requirements for the learning environment formulated in the digitization feasibility study. The authors of the methodology hope that in the long run they will be able to solve this puzzle as well.
Future plans include a methodical publication, and website
The researchers emphasize that when creating the MATEMA methodology, they wanted to help teachers, but did not seek to abandon what is currently used and effective. They do not rule out the possibility that, in the future, it would be possible to gradually switch to the use of only MATEMA methodology in schools.
"It is important to understand that in order to implement a new learning methodology, a unified approach at the level of the entire state is needed. The approach must be reflected in the training of teachers, the publication of textbooks and task sets. For now, the methodology we have developed is more of an encouragement, helping the teacher to explain the material," says the assistant. Dr. O. Mockaitytė-Rastenienė.
"For a long time we wanted to create a methodical publication for teachers with many examples and photos. We have already started to realize this by participating in the ESFA project "Optimization of the network of higher education institutions and improvement of study quality by connecting Šiauliai University to Vilnius University". It will not be long before the three "Sustainable Mathematics" tasks (for a child, a primary school student, a primary school student) and a three-part teacher's book, which we have just finished creating together with our co-authors, will be available online to the general public. In this way, we showed the commonality of the fundamental ideas studied in school mathematics and their expression in different educational centers, in different mathematical content. In the future, we would also like to prepare publications dedicated to explaining specific mathematics topics for teachers.
We are also considering an additional possibility of disseminating the MATEMA methodology - an online website for mathematics teachers. We hope that the material presented in this form will be easily accessible to teachers of all Lithuanian schools, and will encourage them to familiarize themselves with our methodology and apply it.
The MATEMA methodology developed by us could be interesting for educational technology companies, so we are open to cooperation. It will take a lot of effort to realize all the ideas, so first of all we wish to find time for ourselves to carry out the planned activities", says Assoc. Dr. V. Grabauskienė.
