IMYC2020 – Making the Mathematical Connection

Written by Lee Hendricks, International Curriculum Manager - IMYC

We are excited to announce that nine IMYC Big Ideas now feature support for Mathematics, developed in collaboration with Mathematics teachers within the IMYC network.

A range of optional tasks that cover IMYC mathematical strands have been created that provide authentic links to the nine IMYC Big Ideas. Our aim is for the Mathematics classroom in an IMYC school to feel more connected to the implementation of the curriculum.

The following nine IMYC Big Ideas now have mathematical support and activities:

• MY1: Adaptability
• MY1: Balance
• MY1: Discovery
• MY2: Courage
• MY2: Curiosity
• MY2: Relationship
• MY3: Challenge
• MY3: Development
• MY3: Identity

Each Mathematics addition has at least four optional tasks with Model-Eliciting Activities (MEAs). MEAs are open-ended activities designed for students to demonstrate their mathematical knowledge and are created to make deeper connections to the Big Idea. These tasks allow students to understand the real-life implications of the Knowledge, Skills and Understanding they are developing in the Mathematics classroom. It also allows them to show their reasoning and intuition related to the in-class skills they are continuously developing. By giving appropriate context to mathematical learning, students will have the opportunity to make personal meaning, understand why the Mathematical Learning Goals are purposeful to their daily life and due to this, avoid the “pruning” of information they view as irrelevant.

According to a recent blog from the Education Endowment Foundation (EEF), it is paramount that teachers and students alike make sense through modelling in the learning process. The EEF’s blog provides detail on modelling through their guidance report based on evidence found in England’s Key Stages 2 and 3 in Mathematics. EEF’s key findings were the following:

• Pupils should be taught to use and compare different strategies for approaching a mathematical problem;
• Teachers should use worked examples to enable pupils to analyse the use of different strategies;
• Initially, teachers may have to model metacognition by describing their own thinking; and
• We should provide regular opportunities for pupils to develop metacognition by encouraging them to explain their thinking to themselves and others. Pupils may need to be taught how to engage in effective discussion and teachers should model this.

In the nine IMYC additions to the Big Ideas, the use of Model-Eliciting Activities echoes the findings within the Education Endowment Foundation’s guidance report. The MEAs allow students to explore and use different mathematical strategies in realistic situations while engaging in group discussion and group work. Students are also encouraged to explain their methods and processes to how they found answers to MEA questions and scenarios. As an outcome, students should engage more with their critical and creative thinking along with taking risks as they are exposed to more MEAs within the classroom.

When to Use Model-Eliciting Activities (MEAs)
The timescale of each suggested MEA varies and it is suggested to view the available tasks to see if any would best fit the intended strand(s) covered during current practice. Some projects may take a single lesson, while others may require a larger time commitment but have the opportunity to yield a deeper understanding of the Mathematical Learning Goals covered. Most projects are designed to be flexible, based on the amount of information or pre-teaching provided for the students. If Mathematics teachers only have only one lesson for the MEAs, they will need to provide more data, give more examples, and do more pre-teaching. Ideally, finding time to commit to at least one Big Idea project per unit should help further the needs of the adolescent brain. Some suggestions on appropriate use are as follows:

• A collaboration with other subjects as part of a holistic Entry Point
• A hook to a new strand of learning
• To use as a formative skills assessment tool during a unit
• To provide the opportunity for students to demonstrate their understanding through the use of one of the suggested MEAs as a potential Exit Point project.

These projects will provide opportunities for making meaning, interlinking learning, collaborating with peers, student agency and taking supported risks throughout. To find the best results of these projects, blocking out a suitable amount of time for student investigation and exploration are expected. Additional needs such as resources, websites and other materials are often provided within each optional task.

How to Use Model-Eliciting Activities (MEAs)
By offering a range of suggested investigations and modelling projects for the provided Big Ideas, teachers can select suitable projects to use in conjunction with the current material and Learning Goal coverage that is taking place in typical day-to-day lessons. The projects may suit multiple Big Ideas, even ones not currently provided. By looking through the provided documentation, teachers can assess the best tasks for their school’s Route Plan. Although the tasks for the MEAs suggest the goals that may be covered during the project, different goals may end up being the focus as students are following their own lines of enquiry. Planning can reflect this after students have presented their solutions. The role of the teacher during these projects is that of a facilitator, starting the project with a discussion or activity hook that will engage the learners with the ideas around the project. From there, as the MEA is presented, the teacher should take the role of asking probing questions to help guide learners in their journey. The aim is not to provide direct answers but rather to ask questions that can support the learners in finding the right direction for the task. The projects provide some anticipated questions and useful resources that can be provided to the learners to help them during the project, depending on the need. As many MEAs involve group work, the best way to ensure active participation from all group members is through ensuring that all members of the group have assigned roles and are ensuring to focus on these roles. Groups may find some tasks challenging to begin but suitable scaffolded questioning should help with engagement.

The Six Core Model-Eliciting Activities (MEAs)
The Model-Eliciting Activities can be viewed under six core strands:

• The Model Construction Principle - Students create a mathematical model to apply to a given situation. Through the process, students will create a hypothesis, as well as testing and revising their model.
• The Reality Principle - Tasks that allow students to use Mathematics to make sense of real-world problems. These tasks are aimed to suit the interest of the learners and the needs of the local community. Tasks do not need to match real-life situations but should apply skills realistically.
• The Self-Assessment Principle - Tasks designed for students to check the validity of their solution themselves.
• The Construct Documentation Principle - Tasks designed for students to create documentation to demonstrate their mathematical thinking in a clear manner.
• The Construct Shareability and Reusability Principle - Tasks designed so the students' solution can be applied in addressing similar situations used by others.
• The Effective Prototype Principle - Tasks are designed for the students to design a solution that they can reuse themselves. This differs from the previous principle as the purpose is for the students to continue using their solution instead of being designed for others.

All provided tasks will address one or more of these principles.

Structure of the Model-Eliciting Activities (MEAs)
The structure of each of the nine mathematical additions to the Big Ideas is as follows:

• The potential Learning Goal coverage for the project. Teachers can modify any project but must review whether this changes the goal coverage and update as appropriate.
• An overview of the Big Idea and how the task connects to that idea.
• Suggested projects, investigations or modelling questions that connect the Big Idea. These will be linked to the appropriate strands. Each project will link to one or more of the MEA strands but these may vary depending on each learners’ lines of enquiry and teacher direction for the project.
• A reflection on the MEA and the overall process to find solutions to the questions.

Special thanks to Colin Gear and Pamela Naylor for collaborating, researching and writing the MEA Mathematics activities featured in our nine IMYC units.

Additional Resources
For further information on Model-Eliciting Activities (MEAs), please click on the links below:

• EEF Blog: Integrating evidence into mathematics teaching – Making sense through modelling – Blog on modelling from a monthly series by the Education Endowment Foundation that supports teachers and maths leads in implementing the evidence from the EEF’s Improving mathematics in Key Stages 2 and 3 guidance report.
• Math class needs a makeover – Tedx Talk on the importance of building enquiry and resilience in Mathematics learners by Dan Meyer.
• Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity – Journal article from the European Journal of STEM Education explaining the purpose of MEAs and with a provided case study.
• Examples of MEA projects for further understanding – Examples provided by Pedagogy in Action – SERC-Carleton.
• Model-Eliciting Activities Presentation – Video overview explaining MEAs by James Fields.

We would love to hear your ideas and feedback on our new Model-Eliciting Activities, featured as Mathematics additions to the nine IMYC Big Ideas. Please send us an email to contribute@fieldworkeducation.com or pin your thoughts to the MyFieldwork Pinboard to share with the learning community.