Methodology

Ideas for consideration

Control, Questions, Exploring, Collaborating, Going global, Outcomes, Choices, Differences

Students should, to a greater extent, be controlling their own learning.

They should be learning to learn - and learning about learning. They should be formulating probing and provocative questions. (McKenzie, J. 2000) They might ask;

Why are people out there creating artworks and what inclines them to share it via the www with others? Perhaps their answers might come from making contact - try asking the artists themselves?

The beginning of the unit should be 'hands-on' and explorative with concrete materials, and gradually the content should shift to innovate and creative endeavours for the students. 

Shifts in the nature of education and what classrooms look like have been following the transitions in the table below;

Many theorists support a move to a more student centred, collaborative, exploratory, cooperative curriculum which caters for a range of abilities and learning styles and is innovative and forward thinking.

The presentation of the unit of work to students in an interesting and vital format is essential - It should allow for increased levels of student determination of the path of exploration. 

Sharing with students the how and why the unit was created in this way, should form part of the process, and the evaluation of the unit - it was created to allow a global view of who has created and is creating tessellation art and why?

Students should also be encouraged to provide criticism and aesthetic appraisal of this 'work' - that is, the 'unit'.

ICT skills continuum

The continuum of ICT skills by the Tangara consortium - what is missing? The continuum explores Communication and Information Technologies but does not really explore the 'embedding' of the tools into existing curricula. Teaching the skills in isolation without clear purpose or productive intent may leave students lacking direction. Planning effectively for questioning, information and research processes to be integrated effectively with existing statement and profile outcomes, and within the guidelines of the new SACSA frameworks, is the challenge.

Across all States and Territories, the Commonwealth and non-government school education authorities, there is a shared vision of:

• Improving student outcomes through the effective use of information and communication technologies in teaching and learning (Edna 2000)

Student choice should be included in determining methods and software choices - decisions about the right tools for the task should be encouraged.

Individual differences need to be considered - learning at their own pace - this does not necessarily refer the computer as 'tutor' model in this situation but for the purposes of this unit the computer is a 'tool' for the information and creative processes. 

Students should be active participants/decision makers in the processes of the unit as well as the product - we need to scaffold experiences in these type of decisions so that decisions are made from an informed and experienced position. As learning managers, teachers must make decisions about the quantity and quality of their intervention in the learning process. As Jonassen, D (1996) explains 

Scaffolding is a cognitive apprenticeship technique in which the instructor performs or supports the performance of parts of a task that the learner is not yet able to perform. When students are stuck, suggesting a solution or performing that step for them before they give up will help them complete the task and gain the confidence to try other problems. The student and the teacher work cooperatively to solve the problem together. It is important that the teacher encourage students to assume as much of the responsibility for completing the process as they are able to, and scaffolding should be faded out as soon as possible. 

I would also argue that other students may, through collaboration, support one another in such scaffolding. 

Differences in Teaching

Who 'teaches' or implements the unit may also matter as teaching and learning styles and preferences may vary. It is highly recommended that this be approached as a team teaching situation where planning for the unit and the integration of it into the classroom is a team effort. 

The third lesson - How to tessellate using MS Word drawing tools, is a good indicator of the variation in teacher style. As evidenced in appendix A, different teachers and also different students may approach the same task in a different way. Appendix A is the instructions created by a teacher who has already taught a unit of work similar to this one. As a logical sequential thinker, her approach is often methodical and step by step. While doing the task herself she recorded each step and presented this as a series of instructions to students. 

As an abstract random learner with preferences for kinaesthetic learning, I would encourage students to learn by doing. My personal preference for approaching the same task is a 3 step one and is indicative of my beliefs about students varying abilities and the open ended nature of a task. 

	1. Demonstrate the task once, quickly (allow for students to begin straight away if they feel they know what to do or are ready to explore their own process to achieve the same product). Suggestions can be made about further activities for those who finish.
	2. Go through the process slowly, step by step for those who need this prescriptive direction
	3. Provide assistance one to one for those still exploring or finding difficulty with the process and the product

Through this 3 step process students can begin straight away if their skill levels are higher

	some - get going now exploring for themselves
	others - follow their lead, observe, then try
	still others - race ahead then teach others what they find out!

An old Latin proverb says

"By learning we teach...by teaching we learn"

The retention of information for students is much greater when they are encouraged to teach the skill to others. This philosophy also underpins the 'presentational' aspects of this unit of work where the teacher is not the 'sage on the stage' but the 'learning manager' (McKeown, 2000) who values the knowledge and opinions of all participants in the learning process and enables celebration of the learning of all participants.

The Lessons

1. Quick Quiz - evidence of learning by pre-testing and post-testing knowledge acquisition. Although I am theoretically opposed to such testing there is some merit in doing such testing for example...

1.a) Provide some necessary definitions - polygons, regular, tessellation, symmetry, rotation, translation, reflection

1.b) What regular polygons will tessellate and why? What regular polygons will not tessellate and why? (See Fathauer lessons for exact explanations - Appendix B and available on-line at www.tessellations.com/Polygons1.html and  www.tessellations.com/Polygons2.html  )

2. The Art exploring the mathematical art of Escher (poster book samples) and online - see links on main page and on 'cool' page. What looks 'good' and why? Why is clever art groovy? Emphasis on cultures and exploring real life tiling with tessellations.

3. Drawing Tools and Tessellations - Students choose which way to begin - follow the modelling or follow the instructions. (See above)

4. Art lesson using templates - 

	See 'how to' on student's site Link to it
	OR create own template from regular polygon either on computer or by hand
	OR make a puzzle from Fathauer templates 1. triangle to square or 2. dodecagon to hexagon
	OR experiment with the tangram puzzle from Erica Shadiac's book

5. Make and Create;  Discuss outcomes and assessment rubric at commencement of creation - begin development of criteria for assessment. Explicit understanding of expectations is valuable in the determination of the process AND therefore the product.

	Create a PowerPoint presentation to share your findings and your creations with the class
	OR Create a PowerPoint for younger children to teach students about tessellations - flips, slides, turns.
	OR Make a web site using Front Page which does either of these things

6. Continue with '5' - allow time for homework, class-work and group collaboration. Work together on the final stages of the assessment rubric.

7. Share, Evaluate and Assess - students present their work to peers as audience and their class mates use the class designed rubric to evaluate one another's product and the inherent process.