Tasks Types and Mathematics Learning research project

Project description

Monash University Project Reference: LP0775375
Monash University SCERH Reference: CF07/606-2007/0173

Tasks Types and Mathematics Learning (TTML) project examines the relationship between the documented curriculum, classroom tasks, and the learning of mathematics.

It is a research partnership between the Department of Education, the Melbourne Catholic Education Office, Monash University, and Australian Catholic University.

This research project will investigate the learning prompted by different types of mathematical tasks. Our research questions are as follows:

• If teachers use models, examples, or explanations that elaborate or exemplify mathematical principles and connections: what are the characteristics of learning that is fostered; what constraints are experienced by teachers; and what are the most appropriate pedagogies?
• If teachers situate mathematics within contextualised practical problems: what are the characteristics of the learning that is fostered; what constraints are experienced by teachers; and what are the most appropriate pedagogies?
• If teachers use content specific open-ended mathematical tasks: what are the characteristics of the learning that is fostered; what constraints are experienced by teachers; and what are the most appropriate pedagogies?
• If teachers use tasks designed to foster multi domain perspectives: what are the characteristics of learning that is fostered; what constraints are experienced by teachers; and what are the most appropriate pedagogies?
• How are each of these types of tasks best described?
• What is the most appropriate mix of the four types of tasks?

Types of mathematical tasks

Essentially the project focuses on the following four types of mathematical tasks:

Type 1: Teacher uses a model, example, or explanation that elaborates or exemplifies the mathematics - definition and examples

Type 2: Teacher situate mathematics within a contextualised practical problem to engage the students but the motive is explicitly mathematics - definition and examples

Type 3: Students investigate specific mathematical content through open-ended tasks - definition and examples

Type 4: Multidomain investigation - definition and examples (pdf 18KB)

The four types of tasks are designed to represent potentially successful task types. Our goals are to describe in detail how the tasks respectively contribute to mathematics learning, the features of successful exemplars of each type, constraints which might be experienced by teachers, and teacher actions which can best support students’ learning.

Each of the chief investigators (CIs) will take responsibility for one cluster, will support them actively through teacher professional development and the creation or sourcing of the respective tasks matching the teachers’ curriculum, and will oversee the data collection at each phase. There will be initial teacher development sessions that will include some data collection, and subsequent teacher development meetings (at least two per term) and data collection will be based around the phases as described above. The teacher development will focus on the nature of the respective task types, the associated pedagogies, ways of addressing key constraints, such as diversity in culture and language background and readiness to learn, and student assessment.

The participating teachers will receive professional development on the theoretical rationale of and usage of the respective task types, the expected student responses, the associated pedagogies, and the processes for constructing such tasks and matching them to the Standards.

Propositions for discussion

Some general propositions about tasks or teaching

• Experiences should ensure that most of the class are working on tasks which will take them beyond their current levels of thinking.
• Opportunities for student to make their own decisions on pathways, strategies and destinations are engaging.
• It is better to plan sets of experiences rather than individual lessons, with the sequencing of tasks providing foundational skills as well as leading towards generalisation (or abstraction, or pattern identification, etc).
• All students should progress through learning experiences in ways that allow them to feel part of the class community and contribute to it, including being able to participate in reviews and class discussions about the work.
• Teachers should make explicit for all students the usual practices, organisational routines, and modes of communication that impact on approaches to learning.
• Rather than assuming student prior knowledge, teachers should adapt their responses to the way the students engage with the tasks.
• Tasks should not be isolated from on-going experience and be followed by opportunities for reinforcement and incorporate explicit prompting for transfer and connections.

Project partners