Most secondary students have very little or no experience in formal writing tasks in which they discuss and analyze mathematical ideas. They have completed countless hours of doing mathematics - e.g. doing homework exercises, showing algebra working on assessments, etc - but they often lack significant practice in writing about mathematics. I truly wish my students will derive some pleasure from completing the internal assessment (IA) requirement for Maths SL & HL - the Exploration*. And I think that there is a greater chance of this occurring if clear and effective support and encouragement is provided to the students. [ * when the word "Exploration" is capitalized and italicized it refers to the required IA task for Maths SL & HL ]

Students need to be guided and encouraged by their teacher at all stages of completing their Exploration. I believe that this is most crucial in the first two stages - the introduction / preparation stage, and the topic choice stage.

There are two simple but effective activities that I think students should do during the intro/prep stage: (1) read short articles that are examples of good writing about a mathematical topic at a suitable level for Maths SL and/or Maths HL, and (2) read past student Explorations - preferably with some information on how well the Exploration addressed the assessment criteria.

For the intro/prep stage, it's not particularly easy to find mathematical articles that satisfy the three ingredients of (i) not too long and not too short (roughly 6-12 pages; like an Exploration), (ii) demonstrate a good quality of writing with appropriate mathematical working, explanations and diagrams embedded in the writing, and (iii) that the level of mathematics is at the right level (commensurate) for Maths SL and/or HL - not too basic and not too advanced. I have managed to collect a few articles that I think include these three ingredients and there are link to them below. I am also in the process of writing my own articles that are not Explorations but present interesting (at least, I find them interesting) mathematical topics that I believe could provide teachers and students with ideas appropriate for developing into a good student Exploration. I am calling these articles of mine, Exploration Starting Points. I'm writing them with both teachers and students in mind. As mentioned, my intention is not for them to be examples of an Exploration (maybe somewhat) but more to present some thoughts about a mathematical topic sufficiently constrained and focused to make it a good 'starting point' for an Exploration.

Take a look at my first Exploration Starting Point, "Building Parabolas" - which looks at constructing parabolas from linear and non-linear functions, and considers how to go about finding the vertex and axis of symmetry of a rotated or non-standard parabola (non-vertical, non-horizontal). It's certainly takes more effort and thought than finding the vertex and axis of symmetry of a standard parabola. My hope is that this 8-page paper might contain some ideas for starting and developing a student Exploration.