Question 1

Describe how you would go about selecting and applying a range of instructional strategies and resources to a lesson in your main teaching area.

The instructional strategies I choose for lessons in mathematics vary depending on the students needs and the topic.

The context for my teaching is this: "The world is an amazing place, we are all students of it together".

My goal is for students to gain the deepest and most profound knowledge possible for where they are at. More specifically I aim for students to move in their understanding as high as possible through Bloom's taxonomy of cognitive outcomes. Students should be able to remember basic mathematical formulas and methods, They should be able to understand how to use them, they should be able to apply them to a range of problems.

The higher levels are more of a challenge. Ultimately students should be able to creatively analyse and work with mathematics in a way that goes beyond the discipline. One angle on this is starting to see the 'Meta' rules of mathematics - rules about rules. Another angle is to see the application of mathematics to the whole world, and to integrate mathematics into understanding of physical processes, biology, history, politics and society.

But I also must consider where students are at and what learning styles they have:

In the middle school students are hopefully transitioned or about to transition from concrete operational to formal operational thinking in the development of their Piagetian scheme of knowledge.

To assist with this transition I include content which challenges the concrete operational mind and creates some dissonance. Students should ultimately be comfortable with more abstract descriptions of the world and able to work with them. The application of algebra to geometry, trigonometry, indices, growth and other areas is a signpost to 'we can generalise - the abstract is more powerful than the concrete'.

Instructional Strategies?

Intro to the lesson: Build Motivation, settle the class, set the scene:

• stories from the real world - engineering/science/nature eg: development of the International Space Station, size of dinosaurs, life span of stars. (Glasser: Fun/learning)
  
• Contradicting sets of information
• Challenges: Here is a problem... can we solve it?
• Quiz or mini test of previous work
• Advance Organisers - overview/expository/graphic/mindmap (Ausubel)
  

Body of the lesson: Ask key question(s), Introduce new content, Get students thinking, talking and practicing:

• Demonstration of techniques on the board
• Group activity to solve a problem
• Sample problems
• Work sheet (not too many of these - once a fortnight)
• Problems from the Text - working in pairs
  
• Reverse problems - here is the answer - work out the question
• Practical activity - solve problems with paper, scissors, tape, timber etc

Conclusion of lesson: Revisit key points or key question

• Student summary
• Groups report back
• Revisit introduction

The resources required apart from the obvious ones of a well set out classroom that has heart and soul, are determined by the desired activities. For example a lesson exploring surface area of three dimensional shapes could include an exercise to build a whole range of prisms out of paper and sticky tape, and then calculate the areas of each part.

The selection of instructional strategies depends also on what the class is capable of, or is familiar with. The use of Jigsaw excercises would not suit my year 9 classes at present, as they have not been trained up in how to use them.

My choice of instructional strategies reflects my belief in constructivist education. It also reflects my desire to move towards a democratic/choice therapy discipline model with the teacher as leader and co-learner. Learning should be fun, challenging, interesting and students should be motivated to get involved.