YuMi Deadly Maths (YDM) is a unique mathematics pedagogical approach developed across 2010–12 to improve capacity to teach mathematics. It aims for the highest level of mathematics understanding through activity that engages students and involves parents and community. YDM aims to empower teachers to prepare effective mathematics lessons.

Originally designed for Indigenous students, YDM has been successfully adapted to low-SES students and mainstream schools. With a focus on how to teach, an emphasis on big ideas and connecting mathematics topics, and a special pedagogy that starts and ends with students’ reality, it is effective for all students*.* YDM follows the *Australian Curriculum: Mathematics* and fits in with or extends many existing programs and teaching approaches.

YDM has been effective in improving student attendance, engagement and performance, and in empowering teachers to go beyond their training and take control of planning and designing their own sequences of mathematics lessons. The YDM approach is unique in its focus on creativity, structure and culture with regard to mathematics and on whole school change with regard to implementation. It never limits the type of mathematics experience the students are to receive. We believe all students should receive the same mathematics as in elite schools. YDM provides practical and active ways to enable this to happen for all students, particularly Indigenous and low-SES students.

Information on YDM is included on the Teach Learn Share website of the Australian Government Department of Education.

YuMi Deadly Maths on Teach Learn Share websiteThe YDM approach has four components: mathematics, mathematics learning, mathematics teaching, and school–community connections.

## Mathematics

**Mathematics is a living, growing, creative act in which all students can excel.**

YDC’s view of mathematics is illustrated in the diagram below. It shows the relationship between perceived reality and invented mathematics and is adapted from Matthews (2009). It has three tenets:

- Mathematics is a cultural and contextual abstraction of reality based on symbols.
- Mathematics reflects back on reality and empowers people to solve problems in their own lives.
- This abstraction and reflection is a creative but also a culturally biased act.

This model emphasises mathematics as a sequenced and connected structure, a life-describing language and a tool for problem solving, and leads to a focus on big ideas – mathematical ideas that hold across topics and across years.

## Mathematics learning

**Mathematics learning is undertaken through active participation – relating kinaesthetic activity to mental models, through a sequence of body → hand → mind.**

Although YDC believes that clearly stating what we intend to do is important, and that whole-class teaching is effective, the belief at the basis of YDM is that the big ideas of mathematics can only be learnt when constructed anew and individually by each learner from work across representations (materials, language, pictures and symbols) and discussion with teachers and peers.

This is because the big ideas go beyond stimulus-response learning. For example, two of many objects (fingers, arms, chairs, and so on) can be shown and described, but the ‘twoness’ that is the commonality in the examples and the meaning behind the symbol ‘2’ must be constructed by each learner and cannot be told to them.

Through such self-construction, mathematics knowledge can be learnt in integration with each student’s existing knowledge and constructed into a rich schema. Such schema contains a complete definition of the idea (often multi-faceted), all applications of the idea, all connections to related ideas, and the experiences of the learner with respect to the idea.

Such schema comes from connecting different representations and enables the learner to have a deep understanding of mathematics ideas and apply the ideas to their own world.

## Mathematics teaching

**Mathematics teaching is seen as more powerful if it reveals the underlying structure of mathematics and relates it to the mathematics knowledge within local cultures and communities.**

YDC believes that effective teaching requires students to interact with activities, teacher questions and discussion to build, consolidate and extend mathematical ideas. The YDM pedagogy is based on the Matthews (2009) diagram and views teaching as a cycle through four phases: reality, abstraction, mathematics, and reflection (RAMR).

RAMR with Matthews framework RAMR with Matthews framework PDFThis view of teaching translates into a pedagogical framework for planning and delivering learning experiences for students that:

- begins from the context of the students’ real world
- actively abstracts ideas through body to hand to mind experiences
- consolidates the ideas with formal language and symbols and connects to other ideas
- extends upon and reflects the ideas back to real-world contexts.

YDM is not a scripted program; it relies on teachers being equipped with the necessary knowledge of mathematics, mathematics education and lesson planning to be able to construct their own scripts so that they can make teaching decisions based on the needs of their students. It focuses on the **how** of mathematics teaching and places teachers and their teaching as the major determiner of learning.

As a result, the YDM approach has shown itself to be effective for differentiating curriculum in the classroom.

## School–community connections

**Mathematics improvement is enhanced if it is accompanied by community involvement and whole-of-school programs to improve attendance and learning.**

The YDM approach is strongly influenced by the philosophy of the Stronger Smarter Institute (C. Sarra, 2003). It encourages schools to involve parents and community in mathematics learning. It aims to develop not just new capabilities but also shifts in thinking individually and collectively.

This is because the approach works best with *Strong and Smart* style whole school change achieved through:

- strong community–school partnerships
- embracing local leadership within school and community
- development of positive identity and pride in heritage
- high-expectation relationships with respect to attendance, engagement and performance.

These four imperatives are particularly important for Aboriginal, Torres Strait Islander and minority people.