Investigating+Mathematics

This area of the RGHS wiki is dedicated to Mary Barnes and Malcolm Swan. Thank you for the inspiration. Through shared exploration and problem solving, students build deep and rich understanding. Skills proficiency will follow so long as we supplement with directed practice.
 * Thinking about Mathematics || [[image:rghs-mathematics/under_construction.jpg width="58" height="58" align="left"]] Some resources to help explore what mathematics is, what mathematicians actually do and how they do it. A look at the Proficiencies and why we might want to consider other approaches to learning mathematics. Guidelines for doing mathematics. Guidelines for group work. //Based on work from Mary Barnes, Malcolm Swan and Peter Sullivan.// ||
 * Investigating Coordinate Geometry with GeoGebra || [[image:rghs-mathematics/under_construction.jpg width="58" height="58" align="left"]] A set of guided discovery activities designed to teach introductory concepts: midpoint, distance, linear equations, and at the same time develop student skills using GeoGebra. ||
 * Investigating Functions || Developing idea of functions and families of functions (the "Function Zoo"). Based on Mary Barnes' Investigating Change books 1 & 2. Designed for use with Mathematics/Extension1 topic "4. Real Functions and their graphs" ||
 * Investigating Change || [[image:rghs-mathematics/under_construction.jpg width="58" height="58" align="left"]]Developing ideas of rates of changes. Based on Mary Barnes' books. ||

Philosophy
//Through exploration, problem solving and communication, students build deep and rich understanding of mathematical concepts and representations. Skills proficiency will follow so long as we supplement with directed practice.//
 * Understanding is best gained through personal exploration and discovery - concepts will be more deeply embedded and retained.
 * By exploring as a group, students //communicate// their understanding and reasoning to each other. This deepens and refines their understanding as well as supporting and extending their peers.
 * Misconceptions are exposed and dealt with - used as learning experiences.
 * Exploration is not random - it is guided - the teacher is actively involved (even if they often choose not to contribute answers)
 * Investigation lessons produce tangible assessable output: students summarise their learning at the end of each session.
 * Mathematics becomes enjoyable and meaningful, creating a positive environment conducive to learning. Risk taking and errors are encouraged.
 * Understanding and reasoning are reinforced and complemented by individual directed practice to ensure required skills are developed at high fluency levels.
 * With clear understanding of the big picture concepts, students can meaningfully learn and engage with precise and accurate mathematics formalism.
 * **A pragmatic approach**: Not every lesson will be group discovery work! Indeed, perhaps the majority of lessons will continue to be more traditional, transmissive style and text book based lessons. An initial approach for 2012 will be do to conduct one "Investigation" style lesson per week, during the double period on Wednesday.

External Resources
Malcolm Swan describes his approach in A Designer Speaks. His 2005 report "Improving Learning in Mathematics: challenges and strategies " is a detailed and highly readable description of a different way to teach and learn mathematics.

A valuable set of resources is the "Improving Learning in Mathematics " kit. The resources were developed from the work of Susan Wall, a Gatsby fellow working at Wilberforce College, Hull and Dr Malcolm Swan from Nottingham University. The underlying principles to Malcolm's and Susan's approaches are identical, and built on research evidence of the last 30-40 years, which suggests that learning mathematics is far more successful if learners are actively engaged, encouraged to think mathematically and to see links and connections. The first few pages of Mary Barnes' "Investigating Change Volume 1" which describe her approach are available on Google books. The full kit of 10 books + 2 teacher guides is available for purchase at @http://www.curriculumpress.edu.au/main/goproduct/13056

Peter Sullivan's 2011 ACER report "Teaching mathematics : using research informed strategies" is a high quality and inspiration review of current issues and research in mathematics education.

Charles Lovitt and Doug Clarke describe their philosophy in [|The features of a rich and balanced mathematics lesson: Teacher as Designer]

Nordin Zuber's relections on the profiencies at http://exzuberant.blogspot.com/2011/10/working-mathematically-picture-essay.html and http://kangaroopie.wikispaces.com/The+Proficiency+Strands