To support teachers, Bowland Maths includes five Professional Development modules which cover the main pedagogical challenges for this type of investigative, non-routine problem solving. The modules are activity-based and built around specific problems similar to those in the Case Studies, but short enough to fit into a single lesson.
Each module is designed as a three part “sandwich”:
|
• |
Introductory session - teachers are guided through a sequence of problem-based activities that raise issues related to the module challenge; they look at video of other teachers working on a chosen problem, together and in the classroom; teachers then prepare a lesson.
|
• |
Into the classroom - teachers teach the prepared lesson in which pupils tackle the same problem.
|
• |
Follow-up session - teachers report to each other on what happened in their lesson, reflect on a set of pedagogical questions, and consider further related issues.
|
|
Each module is self-standing and can be used on its own; the modules can also be used in any order. The modules are designed for teachers working in groups, but can also be used by a teacher working alone.
|
Each module includes an extensive description of its content and its pedagogical aims. The modules make extensive use of video, showing teachers trying new material with their classes and discussing the issues with colleagues. The software provides a step-by-step narration for those new to the material or working alone, while allowing confident session leaders quickly to choose which clips to use. The video is supported by handouts and guidance notes for teachers and session leaders, supplied in PDF form for printing or on-screen use.
|
The full PD package can be accessed via the Bowland Player;
to launch the Player, click here.
The following is an outline which provides a quick reference guide to the modules.
|
| 1. The Case Studies and Mathematics |
“Where's the mathematics in these Case Studies?”
The Case Studies offer pupils opportunities to develop the Key Concepts and Processes in the KS 3 Programme of Study for Mathematics; notably the ability to represent and then analyse situations using mathematics, interpret and evaluate the results, and communicate and reflect on the findings. This module is designed to help teachers consider how to integrate and develop these Key Concepts and Processes into their teaching.
|
| 2. Tackling unstructured problems |
“Do I just stand back and watch or intervene and tell them what to do?”
In mathematics lessons, pupils are usually told which prerequisite information they need and which techniques to deploy. If, however, pupils are to learn to use their mathematics outside the classroom, they also need opportunities to work on unstructured problems that require the selection and use of a wide range of mathematical techniques. This module compares structured and unstructured versions of problems and considers the demands and challenges they present to pupils and teachers.
|
| 3. Fostering and managing collaborative work |
“How can I get them to stop talking and start discussing?”
There is overwhelming evidence that mathematical discussion is beneficial for learning when pupils engage with each others' reasoning. This module is intended to help teachers:
• |
consider the characteristics of an effective pupil-pupil discussion;
|
• |
respond to some common objections to pupil-pupil discussion;
|
• |
explore techniques for promoting pupil-pupil discussion;
|
• |
discuss the teacher's role in managing pupil-pupil discussion.
|
|
| 4. ICT: Using resources effectively |
“How do I get them to stop playing and start thinking?”
ICT plays a central role in many of the Bowland Case Studies. This module explores the pedagogical and practical challenges that confront teachers as they help pupils to use ICT effectively in solving problems and learning mathematics. The role and significance of ICT in mathematics and its relationship to the traditional curriculum are discussed.
|
| 5. Questioning and reasoning |
“How can I get them to think, reason and explain?”
The Case Studies are intended to promote deeper and more extended chains of reasoning. This module is therefore intended to help teachers to consider:
• |
the types of questions that encourage pupils to think and reason;
|
• |
ways in which pupils can be encouraged to provide extended, thoughtful answers, without being afraid of making mistakes;
|
• |
the value of modelling reasoning by 'thinking aloud' with the whole class.
|
|
|
