Our evidence-informed approach

Designing for teacher learning

The reSolve digital educative teaching resources (dETR) have been designed and developed to be educative for teachers as well as students (Ball & Cohen 1996). They are intended to support teacher learning both as a teaching resource and learning resource. They do this through evidence-based professional learning (PL) which is embedded into online teaching sequences.

The resources deliver a range of professional learning which focuses on content and practices which are embedded in the teaching sequences and ‘Teaching with Intent’ elements.

The dETR supports teachers to develop their:

• Mathematical knowledge for teaching (MKT) - PL content is situated in practice, active teacher learning, use of models, focus on student learning, focus on teacher-student relationship (Ball et al., 2008).
• Pedagogical design capacity (PDC) - PL connects evidence with practice, to makes teaching sequences’ design decisions visible and clarifies criteria to develop capacity to adapt and modify resources without compromising intended learning outcomes (Remillard, 2018).

The dETR are delivered in digital formats online to teachers, making it possible for anyone, anywhere, to access them free of charge. They have been designed to be scalable, as the intent is that they can be used by individual teachers in the classroom, by school leaders working with staff, by the whole school and by the broader system. They also use digital communication as a platform for curated ‘live’ interactions with teachers to provide access to reSolve expertise.

Features of effective professional learning

Designing for student learning

Realistic Mathematics Education (RME) 

RME theory influences the design of our teaching sequences. RME emerged through the work of the German-born Dutch mathematician, Hans Freudenthal (1905-1990), who saw mathematics as a human activity. Freudenthal believed that students should be active participants in the process of learning mathematics (Van den Heuvel-Panhuizen, 2003). As students engage in tasks, they develop their own tools and strategies as they solve experientially real problems. Students form and organise new knowledge and develop their own mathematical insights (Van den Heuvel-Panhuizen & Drijvers, 2014), a process called mathematisation.  

Students’ progressive mathematisation is supported through the use of three design heuristics:  

• Experientially real contexts for learning: Realistic contexts are used as a starting point for learning new concepts. These contexts need to be easily imagined by students, whether real, fantasy or even taken from the abstract world of mathematics (Van den Heuvel-Panhuizen, 2003), as long as the situation is real in the minds of the students. 
• Guided reinvention: Tasks are designed so students reinvent important mathematical concepts and strategies for themselves with active teacher guidance. 
• Emergent modelling: In RME, models (such as concrete materials or visual representations) are deliberately not provided for students. Model are developed through the context and, ideally, is created by the students themselves. It is not the model itself that develops mathematical understanding but students’ modelling activities within the sequence context. 

Teaching sequences and task structure 

Mathematical tasks are central to the learning of mathematics, however, one task on its own cannot teach students everything they need to learn about a concept. We use carefully sequenced mathematical tasks and activities to build learning over time.  

Each task in our sequences generally use a Launch Explore Connect instructional model: 

• Launch: The task is introduced without telling students how to solve the problem. 
• Explore: Students explore the task and important mathematical ideas that task addresses, by themselves or in small groups. 
• Connect: This is the most important phase where the teacher carefully orchestrates a whole-class discussion to make connections; connections between the different strategies used by students and connections to the main learning goal of the lesson.