# data[].attributes.body
The Irish Experience of Assessing Mathematics Using a Competence-Based Approach

Changes to assessment We had two major aims in mind when it came to assessment:
1. That formative assessment would be more of a feature of the day to day practice in the classroom and it would support the development of mathematical proficiencies.
2. That the final examinations would be less predictable than they were in the past and they would include a section on problem-solving and applying knowledge to unfamiliar situations.

To improve the use of formative assessment in the classroom, much of the teacher Continuous Professional Development (or CPD), focused on analysing student’s responses and written work. The emphasis was on looking for evidence of what the student understood, rather than focusing on right answers, judging what students misunderstood and providing supportive feedback to help them develop mathematical proficiency.

# data[].attributes.body
Assessing collaborative problem solving

We now examine each of these broad areas of skill in detail and identify the sub skills and evidence that we would be seeking when monitoring students working together in a collaborative problem-solving context.
- Collaborative problem solving and reasoning
- The role of collaboration in collaborative problem solving
-  CPS as a target skill:
-  CPS as an enabling skill
-  Described scales (Development Progressions)

Collaborative problem-solving – dimensions and elements
We now we will explore each of the social and cognitive dimensions in some detail and identify the kinds of skills and behaviours that we would need to observe to enable us to conclude that students are demonstrating a specific level of competence.
Social components of collaborative problem-solving
For the purpose of assessment, these could be described using a rubric of social skill capabilities such as participation, perspective-taking, and social regulation. Within each capability we can define a series of elements and the evidence or indicative behaviour that would be needed in order to conclude that the student was exhibiting the capability. Finally, we explore the indicative behaviour and differentiate between students on the basis of how well they exhibit that behaviour in terms of a series of quality criteria.
Participation skills
Action
Interaction
Task completion skills
Perspective-taking skills
Responsiveness
Audience awareness skills
Social regulation skills
Metamemory
Transactive memory
Negotiation skills
Responsibility
Cognitive domain of collaborative problem-solving
-  Task Regulation Skills
Problem analysis
Goal-setting
Resource management
Flexibility skills
Collecting data
Systematicity
-  Knowledge Building Skills
Relationships within the data
Contingencies
Hypotheses

Overview of cognitive domain
So the cognitive domain collaborative problem-solving is a complex, coordinated cognitive activity among two or more people. It is evident that efficient problem-solving does not rely on any single or uniform skill, but rather a set of distinguishable sub-skills or capabilities, some of which are deployed in accordance with situational needs. The evidence of these capabilities being deployed can be accumulated in a number of ways. And it is beneficial to identify how well each of these capabilities and indicative behaviours are being demonstrated.

Two dimensions - social and cognitive dimensions

# data[].attributes.body
Good practice in assessing key competences
Tools and practices to support assessments of transversal competences, such as creativity, initiative and the constructive management of feelings.
Innovative tools, such as portfolio assessments, ICT-based assessments and simulations.

# data[].attributes.body
The Principles of Assessing Key Competences

Summative assessment, also referred to as assessment of learning.
Formative assessment, this is sometimes referred to as assessment for learning.

Both summative and formative assessments are focused on whether students have achieved the learning objectives outlined in curriculum and standards.

Student self-assessment, also known as ipsative assessment, which focuses on the student’s personal development.

Any kind of assessment, including summative assessment will be most effective when based on multiple measures over time. This is because no single test or classroom interaction on one day can really capture what a student is able to do.

# data[].attributes.body
Examples of project-based learning

eTwinning
In eTwinning a project is usually founded between two teachers from different European countries.
Once it is registered the two founding teachers are then free to invite other teachers to join the project and all the work is carried out in an online workspace, called a TwinSpace
eTwinning Project – Rainbow Village:
https://www.etwinning.net/en/pub/projects/project.cfm?id=58043
eTwinning Project – Let Your Passions Shine
https://www.etwinning.net/en/pub/projects/project.cfm?id=82576
eTwinning Project – Health 4 Life
https://www.etwinning.net/en/pub/projects/project.cfm?id=79799
Virtual Guide to Entrepreneurial Learning: http://theentrepreneurialschool.eu/

# data[].attributes.body
A Teacher’s Experience of using Project-Based Learning to Teach Mathematics

Many teachers had to completely review how they understood their role in the classroom.
We chose to embrace the challenges, and we were able to meet them thanks to five effective strategies.
1.  collaboration among the department
2.  intensive school support
3. supportive leadership
4. Team teaching
5. use of IT to support learning

On the basis of my experience of using a skills-based approach and project-based learning in the maths class, my top four tips to teachers would be the following.
1. Use project-based learning.
2. Create an environment where students can make connections across the subject
3. Create rich tasks and encourage students to use different strategies.
4. Encourage students to discuss maths and justify their solutions.

# data[].attributes.body
Developing learners’ collaborative problem solving skills
What are the capabilities that have been identified and defined as 21st century skills? One view is that any skills that are essential for navigating life in the 21st century could be classed as 21st century skills. This does not mean that many familiar skills of the 20th and preceding centuries are no longer needed. But there are new skills emerging as increasingly important.
Competence therefore can be regarded as the ability of the person to adjust the skill performance to the demands of the context.
The skills were identified as those which would enable people to demonstrate new ways of thinking, ways of working, tools for working and living in the world that had emerged as a result of technology.
Ways of thinking were conceptualised to include creativity and innovation, critical thinking, problem-solving, and learning to learn and the development of metacognition.
Ways of working was conceptualised to include communication, collaboration and teamwork.
Tools for working involved information and ICT literacy.
Living in the world involved changing emphases on local and global citizenship, aspects of life and career development, and personal and social responsibility.
The Delors’ Report (1996) marked the beginning of UNESCO's 21st century competence learning discourse - with learning to know, learning to do, learning to be, and learning to live together - forming the four pillars of learning.
Collaborative problem solving is a complex skill requiring both social and cognitive competencies.
Hesse et al (2015) conceptualised collaborative problem solving as consisting of five broad strands - participation, perspective taking, social and task regulation, and knowledge building.
Collaborative problem solving is a set of skills that we need to rely on when the capacities or resources of just one person are not sufficient to solve the problem.
The Nature of collaborative problem solving
The primary distinction between problem-solving by an individual and collaborative problem-solving is its social nature - the need for communication, exchange of ideas, shared identification of the problem and its elements, and negotiated agreement on connections between problem elements and relationships between actions and their effects.
Collaborative problem solving requires that the people combine their resources and their strategies in order to reach a common goal. The assumption here is that collaboration is essential because the task is too complex for a person to work through it alone.
Collaborative problem-solving has these two main components. The collaborative, sharing or social aspects and the knowledge, strategic, problem-solving or cognitive aspects.
The essential aspect of the collaborative problem-solving task or a collaborative problem based learning project is that each participant in the group possesses or controls unique knowledge, expertise, experience, materials or objects that are essential to the completion of the task, the project or the problem solution. Without every individual contributing their specific resource project cannot be completed; problem cannot be solved; the task cannot be done. Collaborative problem-solving demands that every participant contributes to the work of the group and is able to understand and explain to their collaborators their role and the importance of their contribution to the solution of the task.

Two areas of skill.
The students working together must have the capacity and skills that enable them to work collaboratively and to share their knowledge, expertise and suggestions of strategy. They must also have the cognitive skills that enable them to understand the problem and analyse its tasks and specific requirements.
So in designing a collaborative problem based task or project there are several steps:
1. Define the problem or collaborative project.
2. Identify project elements and components in detail; 3. for each component identify the resources that are essential. These can be; a. knowledge b. materials c. strategies d. experience e. equipment;
4. Allocate to each participant non-overlapping, unique sets of resources necessary to be contributed to the project completion or problem resolution. Divide the resources amongst the participants with no shared or common resources.
5. Clearly state the goals of the task or problem solution and observed to students procedure in the task.
6. Explain to the participants that they must identify the problem, sort out a strategy to resolve the problem or complete the task
7. The students also need to develop a means of keeping records of their decisions and discussions. For face-to-face attempts at collaborative problemsolving or collaborative project work keeping records is an essential aspect of the assessment process.

# data[].attributes.body
How to design project-based learning.

Project-based learning is an approach which uses methods such as inquiry-based learning and problem-based learning to develop students’ competences.
The Inquiry-based learning method
Inquiry is "a seeking or request for truth, information or knowledge". Inquiry-based learning starts with questioning, continues with exploration and investigation and ends with finding a solution, drawing a reasonable conclusion, making a substantive decision or applying new knowledge or skills.
In the traditional classroom it is the teacher who asks questions to which answers can easily be found and which usually do not go beyond the immediately available information. In an inquiry-driven classroom, it is not only the teacher who asks open-ended questions, but also students themselves. Students are encouraged to question arguments, information, ideas, opinions and viewpoints, to go deeper and generate new questions, which will lead them to new knowledge.
The problem-based learning method, which is more practical.
Students are given a real life problem to investigate, which can be described as an authentic problem and have to come up with possible solutions. It may be widely applied to all kinds of real life problems. The solutions can then be discussed and tested to see which will work best in a given situation, for example.

Both of these approaches focus on developing problemsolving, critical thinking and information-processing skills. They also work best when students have to work in small teams or groups. The two methods are closely related to each other and often overlap. It is also interesting to note that in this approach, there are not necessarily right or wrong answers. Each solution may have merits and demerits and the students have to analyse and judge.
"Tell me and I forget, show me and I remember, involve me and I understand". This is the basic tenet of PBL. It is of course more demanding on both student and teacher, but it is also more rewarding.
Implementing the PBL approach in your teaching requires you to bear in mind a few practicalities before you start. Here are a few pointers you need to think about, which you can consider as a preliminary checklist:
 What is your project idea?
 What is the time frame proposed?
 Is the project idea manageable?
 Is it a project just between you and your class or will you collaborate with other teachers in your school or in other countries
 If it involves partners from other countries, what is the language proposed?
 What subjects could be integrated into this project?
 What technical tools, if any, will you use?
 How does your project fit with the school planning and calendar?

Once you have fulfilled the basics you are ready to start. If you bear in mind the following 7 steps then you are well on your way…
Step 1. Involve your students from the very beginning. Start with a guided exploration of some topics you have in mind as a whole class; but also be prepared to change if better ideas are emerging from the class. It is important to establish certain ground rules regarding behavior with them in advance.
Step 2. Having defined the topic, in discussion with the class break it down into different tasks. Discuss which technologies to use and how they will be integrated
Step 3. Plan well, set goals, define outcomes. Above all be concrete, students need goals to work towards and responsibility of tasks in order to achieve them
Step 4. Proceed to put pupils into small groups with responsibilities for a particular task. Encourage pupils to ask personally relevant and socially significant questions regarding the topics chosen. Work to the strengths of each pupil.
Step 5. Create a tangible artifact that addresses the issue, answers questions, and makes learning visible and accountable.
Step 6. Arrive at a conclusion...take a stand...take action.
Step 7. Document, justify, and share conclusion with larger audience. (parents, school etc)
Build in presentation of the outcomes or artifact to different audiences as a key part of the project. Presentation of ideas to others consolidates the learning for the students. When you actively engage the student in their learning activities and find these activities to be meaningful with a tangible outcome, their attitude to learning will undoubtedly change for the better. Learning becomes fun.

# data[].attributes.body
Irish case study: Key Skills in the Irish Curriculum & Project Maths.

In Ireland  The key skills are based on the competences set out in the European Framework for Key Competences for Lifelong Learning, but are adapted to suit the Irish context.
The approach is an integrated approach with the competences embedded into the learning outcomes of the formal curriculum and assessment.
Currently, the curriculum and its assessment for lower secondary education (or what we call in Ireland, junior cycle, which includes students aged between 12 and 15) is being reformed and as part of that reform literacy, numeracy and six key skills have been identified as being central to teaching and learning.
You can see here the six key skills of the Junior Cycle, and it is clear that the focus is on learning to learn, working with others and being reflective, creative and innovative.
At Senior Cycle (which includes students aged between 16 and 18) a framework sets out how Key Skills can be embedded in teaching and learning and the learning outcomes associated with each skill. You can see here the five key skills of Senior cycle education in Ireland.
One of the main aims of the initiative was to improve skills such as reasoning, sense-making and problem-solving.
We wanted our students to be able to think creatively and use maths to think critically, to develop a set of transferrable skills which meant they could apply their knowledge beyond the classroom and to unfamiliar situations. We wanted them to learn collaboratively, to analyse each other’s strategies, problem-solve in groups and use technology to support their learning. In this way they would be more equipped with skills for living in the world and for further study in the area of maths. Internationally, the move has been towards an emphasis on problem-solving, modelling and maths in real life contexts, and this approach was largely absent in the previous mathematics curriculum in Ireland.

# data[].attributes.body
Competence-based education in Europe today

Several European countries, including Austria, Bulgaria, the Flemish Community of Belgium, Finland, France, Norway, Spain, Portugal and Poland, have introduced new legislation or amended existing legislation to set out goals and frameworks for integrating key competences into school education.
Most European countries have also introduced key competences and related learning outcomes into their national curricula for compulsory education, during the last decade.
While no country has made a complete shift to competence-based education, several countries have made significant progress. In addition to introducing legal and curricular frameworks for key competences, countries have used various strategies to foster a competence-based approach in the classroom.
Norway’s Cultural Rucksack Programme is a good example of a national initiative which has used an innovative partnership between the educational and cultural sectors.
Another example of a large-scale initiative which engages schools with the broader community, is the Global Enterprize project, which teams up students with professionals from the business sector.
Some countries have invested in intensive professional development when introducing new competence-based initiatives, like Project Maths in Ireland
https://www.youtube.com/watch?v=RlSQwYbpcSc
Some education systems have also provided centrally-developed tools to help teachers implement this new approach to teaching and learning.

# data[].attributes.body
Key Points on Assessing Key Competences

Assessment of key competences should reflect these new ways of teaching and learning.
This means that teachers will need to develop new approaches to assessment.
Summative assessment
Formative assessment
Student self-assessment of progress toward the transversal competences.
An important thing to keep in mind is that assessment of key competences is very different than in courses where the focus has been on learning specific content.
Assessments need to provide ways for students to demonstrate that they can use knowledge, skills and attitudes to reason, solve problems and so on. New tools such as portfolios and e-assessments will be very useful for teachers.

# data[].attributes.body
Key Points on Teaching Key Competences

Educational research by Dewey and Vygotsky promoting a social and constructivist approach to learning emphasizes the importance of competence development within a social learning context, where learners are engaged in active learning in real life situations. Simulating real world contexts has three main purposes: it can motivate learners more than traditional approaches, learners are more likely to remember concepts they discover on their own, and it provides a meaningful context for problem-based learning
Project-based learning is a particularly well suited method for the development of pupils’ competences.
Project-based learning is a particularly well suited method for the development of pupils’ competences.
Let’s now look at  eight key principles for teaching key competences effectively:
Firstly, teaching should be task-based. Learners should develop key competences through active, authentic, collaborative tasks based on problem-solving. Problems should be complex and with multiple solutions, allowing students to produce the solution in a variety of forms.
Secondly, teaching should be interdisciplinary.
Thirdly, learning should be both collaborative and individualised: Learners must collaborate to develop social and communicative competences, but also be able to act autonomously and self-manage.
Fourthly teaching needs to be both learner- and teacher-led.
Fifthly, teaching and learning where possible should be technologically innovative.
The sixth principle is that teaching and learning of key competences should take place both inside and outside of school.
The seventh teaching principle is that teachers should collaborate with the wider community including the social, cultural and business sectors to create more opportunities for real world learning.
Lastly, the teaching of key competences requires teachers to pay closer attention to the social and emotional aspects of learning, including the quality of relationships between and among teachers and learners.

# data[].attributes.body
The importance and definition of competences

Some skills, such as numeracy and literacy, are just as important today as they were in the past, other more transversal and higher order skills, such as collaborative problem-solving are increasingly valuable for citizens to be able to effectively take part in life today.
New technologies are constantly changing the way we learn, work, live and function in a digital and knowledge based society.
But what exactly are the competences, and which ones should we be focusing on?
A useful definition is given by Hoskins and Crick who state that a ‘competence’ can be defined as :
‘a complex combination of knowledge, skills, understanding, values, attitudes and desire which lead to effective, embodied human action in the world in a particular domain’.
In other words, being competent means being able to effectively apply a combination of knowledge, skills and attitudes to successfully react to a situation or solve a problem in the real world.
The ATC 21st century skills framework which includes four dimensions: ways of thinking; ways of living in the world; ways of working; and tools for working.
The European Union Framework, developed by the European Commission in consultation with all member states, includes the following 8 Key Competences:
- Communication in the mother tongue
- Communication in foreign languages
- Mathematical competence and basic competences in science and technology
- Digital competence
- Learning to learn
- Social and civic competences
- Sense of initiative and entrepreneurship
- Cultural awareness and expression.
‘Learning to learn’ competence, as it is the foundation of all learning.
In terms of the essential knowledge related to this competence, learning to learn requires an individual to know and understand his/her preferred learning strategies, and the strengths and weaknesses of his/her skills and qualifications.
In terms of the essential skills related to this competence, learning to learn firstly requires the acquisition of the fundamental basic skills such as literacy, numeracy and ICT skills that are necessary for further learning.
The essential attitudes related to this competence include the motivation and confidence to pursue and succeed at learning throughout one's life. A problem-solving attitude supports both the learning process itself and an individual's ability to handle obstacles and change.

# data[].attributes.body
My name is Romina Durante, I teach Italian, History and Geography at Istituto Comprensivo Ezio Franceschini , a middle school in Rho.