Computational Thinking and Mathematical Problem Solving, an Analytics Based Learning Environment

About the project

There is increasing European concern over worsening student performance, in particular concern over PISA study outcomes, and the supply of engineering and scientific competence to fuel industrial competitiveness. The countries involved in this application have also been concerned over the supply of digital and engineering competence for some time. To address the situation several proposals have been made, including DigCompEdu 2.0, establishing digital targets for Europe 2030 (https://commission.europa.eu/strategy-and-policy/priorities-2019-2024/europe-fit-digital-age/europes-digital-decade-digital-targets-2030_en) and establishing guidelines for education in future https://education.ec.europa.eu/focus-topics/digital/education-action-plan).

Making careers requiring mathematical and computing profiles in compulsory schooling more accessible and attractive to young people is a key element to enhancing access to STEM careers. Teachers, however, report low levels of preparedness, and need for additional support to implement these ambitious
programmes. See the report “Digital Competence, Teacher Self-Efficacy and Training Needs” (Mannila et al., 2018, DOI:10.1145/3230977.3230993), for a discussion of the status and needs of the teaching profession. Leveraging digital transformative technologies CT&MathABLE project provides teachers with new approaches to developing
Algebraic Thinking (AT) and Computational Thinking (CT) competencies in a way that is individually tailored to the learner. CT&MathABLE is going to achieve this through a novel architecture which supports individualized development paths and seamless
integration with competency and assessment frameworks. This approach builds on the previous joint work of partners VU, KTH, and UTU in the current consortium.

CT&MathABLE is about creating learning approaches more appropriate to those who are traditionally disadvantaged and helping them to benefit from CT and AT and thus STEM careers, contributing to a stronger and more egalitarian society. In addition the outcome strengthens the partners national capacity in terms of highly qualified STEM citizens who will contribute to technical development and sustainability as well as broadened participation and inclusion.
The project delivers new tools to teachers, teacher educators, education providers and individual schools, and contributes to the goal of achieving sustainable quality in education. CT&MathABLE combines a unique learning resources and learning analytics with expertise from leading research groups developing curricula and resources to support teaching CT and AT in all age groups. Drawing on our prior track record in
competency frameworks for the computing curriculum and innovative pedagogy we are uniquely positioned to develop a learning and assessment architecture which combines learning analytics and competency frameworks to support individualised learning trajectories for a CT and Maths Able society.

Objectives of the project

CT&MathABLE makes specific contributions to empowering citizen agency in STEM, with the objective of strengthening sustainable competitiveness, ensuring social fairness, facilitating access to education. While doing so, the partnership we have forged also addresses other overarching EU actions, such as the European Digital
Strategy, the Industrial and Small and Medium Enterprise Strategy, the Recovery Plan for Europe, and increased support for youth employment. In particular with a focus on technical and engineering pathways and competitiveness. These elements should be addressed in particular through the intensified activities to develop problem solving, algebraic and computational thinking skills and competencies, to develop collaborative educational programmes across the project partner countries, and engage with local educational systems and education providers.

CT&MathABLE main objective is to support digital transformation of students in multiple dimensions:
1) Improve school students digital skills and self-awareness based on learning-analytics;
2) Enhance computational thinking (CT) and algebraic thinking (AT) through the interactive tasks;
3) Integrate the STEM approach for task-based learning;
4) Create instruments for CT Assessment with learning-analytics, and
5) Provide the interactive tasks and assessment instruments in a format that can be integrated with various learning management systems.

The project aims to provide a learning-analytics based framework to support individualized learning trajectories for students in ages 9-14 across Europe. In this way, all children in ages 9-14 will be able to strengthen their Computational and Algebraic Thinking skills, which are among the key competencies of the 21st century, with Computer Science and problem solving tasks.

The project also has specific objectives in terms of teachers, instructional designers and school curricula. One of them is through the implementation of the CT&MathABLE system, teachers will experience the integration of technology into classroom settings as well as observe the effect of personalized instruction accompanied with the formal curricula. This implementation process is expected to work in a blended learning approach which again will make teachers to think and adopt appropriate pedagogical strategies for the use of interactive tasks through collaborative learning.

Innovative aspects of the project

CT&MathABLE develops innovative educational approaches to classroom education and supports transdisciplinary and holistic learning. The partners promote a pragmatic approach to Computational Thinking integrated with Algebraic Thinking (Mathematics) as to a set of tools, techniques and approaches which enable a seamless transition from the early-aged learners unplugged activities to digital-based learning paths.

CT&MathABLE develops an innovative personalized digital learning trajectories. The resulting personalized learning architecture integrates digital transformation of learning process and assessment frameworks. Through CT&MathABLE school students in Europe will have access to new teaching and learning support enhancing learning outcomes in CT integrated with AT for learners of ages 9 to 14 and directly influencing key performance indicators such as national test results and PISA rankings.

The key innovations are:
- integration CT with AT;
- individual learning paths and assessment framework for interactive problem-based educational architecture, which increases student motivation via any gamified learning environment;
- linking competence frameworks with automated assessment so that learning analytics data will be interpreted using relevant learning theories;
- new approaches to empowering less motivated learners to succeed in the 21st century key skills by strengthening student self-awareness through the usage of learning analytics.

Problem solving skills development are based on evidence-based guidance system. Using student-cantered approach in an online environment, that aims students to overcome the weaknesses and misunderstandings leading to improve student key
competencies by solving interactive tasks based on CT with integration of AT, is another innovation of this project.

CT&MathABLE project is unique in terms of the creation of learning trajectories on CT integrated with AT which would lead to achieving personal outcomes of each learner.

 

Meetings

Kick-of meeting in Bilbao, 26-28 October, 2022

Overview of the project goals and special objectives, discussion and clarification of the target groups: teacher trainers, policy makers and politicians, presented by the project coordinator professor Valentina Dagienė, Vilnius University. Introductions by project partner institutions: Basque Country University, Vilnius University, Eötvös Loránd University, Turku University, KTH Royal Institute of Technology, Ankara University, Mamak Özkent Akbilek School, Türkiye, and Klaipėdos Gedminų Progymnasium, Lithuania.
Discussion about involving different disciplines teachers. D during the project activities, the main fucus should be on mathematics and informatics (computing, information technology) teachers but others like science or technology teachers could get involved at some point of projects, for example in piloting activities.
Partners have provided brainstorming on developing Learning Paths, many ideas were collected, overviewed and going to be implemented in work package 2 especially.
Intensive work was dedicated to revise the project reviewers recommendations, the assessment. All partners made comments on the project assessment sheet.

      

 

Meeting in Budapest 30-31 May - 1 June 2023

The 7th face-to-face CT&MathABLE meeting was held on 30-31 May - 1 June 2023 in Eötvös Loránd University, Faculty of Informatics, Budapest. 22 participants were attended from all project partner institutions. Main attention was paid to define the Learning Paths and the curriculum analyses of Algebraic Thinking (WP2), development of the COMATH assessment instruments (WP3), and the framework of the interactive tasks (WP4). The meeting was culminated in a successful Hungarian teachers' workshop  with focus on unplugged activities of Computational Thinking. Some unplugged ideas are shown in the presented photos. 

       

 

Online meetings – in the first week of each month

Regular monthly online meetings are organised in the first week of each month or as required.
In the first week of each month or as required, the partners meet to discuss the project's progress, main activities, and results. Agreements on what should be done further are discussed and confirmed.

7 December, 2022

 

10 January, 2023

 

8 February, 2023

 

7 March, 2023

 

4 April, 2023

 

2 May, 2023

 

27 June, 2023

 

22 August, 2023

 

19 September, 2023

 

16 October, 2023

 

14 November, 2023

 

12 December, 2023

 

9 January, 2024

 

20 February, 2024

 

12 March, 2024

    

 

Learning Paths for CT

Learning paths usually have three primary components: goals, developmental progressions of students’ thinking processes, and instructional activities that promote the development of students’ thinking along the progression. When learning paths
are used to guide lesson development, lessons are designed to build upon contiguous levels of instruction in a deliberate, consecutive manner because those lessons build on foundations set by previous lessons in order to avoid gaps in learning.

If instructions are based on digital target competencies and CT (for example, lessons on sequencing), we assume that students will be able to perform tasks associated (in this case to Mathematics - Algebraic Thinking) with that level of instruction as well as all previous levels. So, our interactive tasks must be designed to fit these different objectives: algebraic thinking concepts, computational thinking process, and digital competence.

The main results of Work Package 2:
- Learning outcomes for the two age groups separately (9-11 and 12-14): what students should know, be able to do as a result of participating in this project. Learning outcomes play an important role in assessment and evaluation, making clear
what knowledge learners should have upon completion of the learning activity.
- The activity plan. Learning objectives are passed to the outcomes and design the activity plans. The activity plan is based on and paired with Bebras activities (used in partner countries) and contain online, interactive activities and unplugged extending activities, as well.
- Tasks on CT with integrated AT. Tasks are practical, current, and can be used as a basis for digital competence development in any schools. The activities are integrated into an analytics based learning ecosystem linked with an assessment framework. At least 100 activities will be developed, translated and integrated.
- Materials. The following materials will be translated into partner countries’ languages where associated school will participate in pilots: the texts of activities integrated into the ecosystem and used in 1) the pilot questionnaires, 2) forms for feedback, 3) teachers guides - if needed.
- Piloting works. The feedback and questionnaire give the basis of each partner’s
pilot reports.
- Teacher workshop. The learning paths and the plans of earning activities will be discussed in a Teacher workshop, in Budapest with the partners and teachers from associated schools in Hungary. This involves the final improvement of the learning activities.

 

CT&Math Assessment Frameworks

To teach the 21st century skills of Computational Thinking (CT) and Algebraic Thinking (AT) by integrating them is unique. As CT and AT share some subskills, intertwining them should benefit the development of both CT and AT. Thus the shared subskills of CT and AT, most importantly algorithmic thinking and problem-solving skills, will be utilized whilst developing the assessment instruments for CT&MathABLE. There is currently a lack of assessment instruments for CT integrated with AT, but teachers certainly need instruments to assess their students’ learning progression and to discover whether additional support is needed.

Two valid and reliable assessment instruments of CT and AT for use with students from age 9 until age 11 will be developed: (COMATH1) and from age 12 until 14 (COMATH2). The need for two separate assessment instruments arises from the
different development phases of the students. The students of the first age group are in the early phase of learning CT and AT whereas the second age group has progressed to more advanced content.

The main results of Work Package 3:
- Based on the definition of learning outcomes of CT (WP2) and the systematic review, assessment instruments for CT and AT skills, COMATH1 and COMATH2, for two different age groups will be developed. COMATH1 and COMATH2 will be of high validity and reliability as they are theoretically grounded and guided by well-established design frameworks, thus fully unravelling the complexities of students’ digital skill development and capturing the level of students’ CT and AT thinking skills.
- Short and clear guidelines for teachers on how to use the assessment instruments. Teachers need them to ensure the correct use of the assessment instrument for 9-11 and 12-14-year-olds.
- Short and clear guidelines for teachers on how to interpret the results of students’ performance.
- The guidelines for teachers will be developed in English and then translated into partner’s languages.

 

Developing Interactive Tasks

The goal of Work Package 4 is to develop a set of interactive task and design/program a tool for creation interactive tasks for the CT integrated with AT skills development. The created interactive tasks and tool will be integrated into the ecosystem with
learning analytics.

The main results of Work Package 4:
- A set of classified interactive tasks according to the concepts of computer science / CT integrated with AT;
- A framework of interactive tasks - it can serve for creating new interactive tasks on CT;
- A tool for creating interactive tasks will be designed and programmed, additionally templates for type of interactivity, criteria for interactive tasks, etc. will be developed. All classified tasks would be presented using the tool and the ability to create new tasks will be provided (templates for type of interactivity, criteria for creating interactive tasks)
- A set of interactive tasks for implementation using the developed tool will be created. This set will be piloted in partner schools as well as in the project associated schools and feedback how to improve will be collected;
- The integration of the tool into an analytics based learning ecosystem. Also functionality for the students to solve those interactive tasks will be implemented in the learning ecosystem together with the tool.
- Translation of the created interactive tasks and organizing workshop held in Klaipeda Gedminai Progymnasium for piloting the interactive tasks and tool.
- Research on the usability of the learning tasks. Through observing user experience based on evidence, interaction design will be improved throughout the tasks.

Quality Assurance

The Quality Assurance Plan (QAP) is developed in compliance with the Project CT&MathABLE description and all applicable rules and guidelines.

Quality Assurance measures in a project ensure the quality of the project results and the quality of the methods and procedures used to manage the project lifecycle and to develop these results. The QAP defines the specific measures to be followed by the project partnership to ensure the effective management of the project and the conformity of Project deliverables with the expectations and objectives of the project.

The Quality Assurance Plan outlines the indicators, methodology and procedures for evaluation of project activities and results. It contains a set of scheduled activities and defines the objectives, roles and responsibilities. It is a primary concern that the approach to evaluation and review should be simple, flexible, relatively easy to implement, and certainly improvement oriented.

In this research project, partners will be able to avoid the possible distraction of the complexities of the technology by combining unplugged and plugged-in Computational Thinking (CT) exercises embedded with Algorithmic Thinking (AT) into an analytics based learning framework: CT&MathABLE. In doing so, we are able to offer a novel way to familiarize students with CT and AT with a learning framework which is not that distractive for students as they are familiar with the learning environment already via using it in other school subjects. In addition, in this way we are able to avoid the traditional approach “first-arithmetic-then-algebra”, which does not support the development of students’ AT skills effectively enough. In many countries, early algebra skills are not emphasized which leads to difficulties later when algebra is introduced as a separate topic. According to some authors, teaching Mathematics and Information and Communication Technology, especially in combination with algebra, would benefit the students, but the teaching needs to be carried out in a multifaceted way as will be done within the CT&MathABLE.

CT&MathABLE project aim is to make the benefits of CT skills in mathematics explicit. The focus is especially on early algebra and AT since it shares many traits with computational thinking such as abstraction, generalization, pattern matching and structuring operations. We use the Bebras competition as a model for our intervention. It is hard to change national curriculums, instead we introduce additional activities that can be incorporated into the mathematics lessons by the teacher. These activities are CT problems integrated with AT, and they are fitted to the current mathematical context with an eye on developing both CT and AT in parallel. The problems are structured based on subskills of CT (e.g., data and information, algorithms) and, thus, require the use of selected CT skills embedded with AT for the solution. The correct answer is also provided with an explanation how this problem relates to computer science and AT.

In addition to the learning activities, an assessment tool for CT and AT will be developed, because the teachers need a framework to assess how students CT and AT skills are developing. Using the assessment tool they can plan support activities for a student who needs help in his/her learning.

From the future perspective, making careers requiring mathematical profiles in compulsory schooling more accessible and attractive to young people is a key to enhancing access to STEM careers. Leveraging digital transformative technologies the project provides new approaches to developing algebraic and computational thinking competencies in a way that is individually tailored to the learner. CT&MathABLE achieves this through a novel instructional architecture which supports individualized development paths and seamless integration with competency and assessment frameworks. Direct contribution to education for all, broadened participation and inclusion, the goal is to achieve sustainable quality in education.

Dissemination

Teacher Workshop

Whitepapers

CT&MathABLE Whitepaper 1

CT&MathABLE Whitepaper 2

Newsletters

CT&MathABLE Newsletter 1, October 2022

CT&MathABLE Newsletter 2, May 2023

CT&MathABLE Newsletter 3, February 2024

CT&MathABLE Newsletter 4. April 2024

CT&MathABLE Newsletter 5, October 2024

 

Project Consortium

 

	VILNIAUS UNIVERSITETAS Vilnius, Lithuania www.vu.lt
	EOTVOS LORAND TUDOMANYEGYETEM Hungary www.elte.hu
	UNIVERSIDAD DEL PAIS VASCO / EUSKAL HENRIKO UNIBERTSITATEA Spain www.ehu.eus
	KUNGLIGA TEKNISKA HOEGSKOLAN Sweden www.kth.se
	GEDMINŲ PROGIMNAZIJA Klaipėda, Lithuania gedminai.lt
	TURUN YLIOPISTO Finland www.utu.fi
	ANKARA UNIVERSITESI Türkiye en.ankara.edu.tr
	OZKENT AKBILEK ORTAOKULU Türkiye ozkentakbilekoo.meb.k12.tr