Using quadratic theory in CSI work

This is an interesting article to talk about the use of quadratic graphs:

http://sydney.edu.au/news/science/397.html?newsstoryid=2863
About how Physics provided the evidence to convict Gordon Wood of the murder of his girlfriend, model Caroline Byrne. Based on experimental data, the parabola that the body would have moved into cannot possibly land at the spot where she was found - she lacks the strength.

How do you count the number of people in a crowd?

I came across an interesting article in BBC news this morning. The link is here. The issue circling it was an insignificant one which most would not batter an eyelid. But when one is tasked to provide a 'reasonable' estimate of the size of the crowd that turned up at the protest site, how would one do it? This may be an interesting question to explore.

Is the essay 'Math-y' enough?

• How much Mathematics is considered sufficient in a Math IA essay?

There is no standard reference as to what constitutes 'sufficient' in a Mathematics essay. It is an issue of how much Mathematics one can understand and grasp within the timeframe and develop an essay. In a way, this is one of the alternative assessment modes in mathematics to ascertain your ability to cope with the 'unknown' and 'untaught' domains of mathematics.

• Do I need to 'invent' my own processes or come up with my own solution in the topics explored?

There is no expectation that your essay will contain original research or work. However, there is no stopping anyone from attempting to do so, as any mathematics teacher will welcome the valiant attempts of a student in coming up with a creative approach in solving a problem.

• My topic has a fair amount of literature and contains several approaches. Can I evaluate a few approaches and come up with my personal comments and conclusion?

Yes, you can. Do cite the necessary references. However, do note that your evaluation and analysis of the approaches will be important in deciding whether you understand and grasp the mathematics in the topic. You can consider giving your own examples to show your understanding and application of the ideas.

It's lovely to see everyone back in school TODAY!!

Welcome back to SOTA! It's been a long break and good to see everyone. Putting the haze aside, the June holidays have been lovely and we are roaring to go in this hectic 10 weeks.

To put everyone in the frame of mind, please refer to the Math IA rubrics whenever you feel lost or not sure whether your essay is heading in the right direction. A quick summary of the rubrics:

Math HL

• Criterion A - Communication [4] : The essay should have a concise introduction, explanation of the rationale of the topic, a detailed aim and conclusion of the essay. We are looking for coherence and a clear exposition and development of the topic. Having suitable headers and subheaders to guide the communication process is helpful.
• Criterion B - Mathematical Presentation [3] : We are assessing the use of appropriate symbols and notation in your communication of mathematical ideas. Using the correct symbols (for variables, lines, angles, etc) and using appropriate representations (graphs, diagrams, tables, etc) to show a deeper understanding of the topic will help to enhance the presentation of the ideas.
• Criterion C - Personal Engagement [4] : Personal engagement in the task or topic enables one to see it at a more conceptual level. In addition, a closer engagement will allow the writer to ask insightful and good questions that will greatly enhance the quality of the essay. We are looking for personal interest in the topic and also a display of creativity in the exposition of the idea. Presenting the idea differently and in your own way counts greatly in this criterion.
• Criterion D - Reflection [3] : Very often, writing mathematics require one to evaluate and assess the techniques and processes used in the problem. In this criterion, we are looking for evidence of the writer's ability to evaluate the exploration of the topic and have suitable conclusion or mini-conclusions in the essay. While it is often seen at the end of the essay, it can also be found at the end of each section, depending on the structure and outline of the development.
• Criterion E - Use of Mathematics [6] : One of the most difficult areas to assess is the level of mathematics that commensurate with the level of the course. Loosely, if the main topic area is found within the Math HL syllabus, it commensurate with the level of the course. However, the emphasis of the criterion here is beyond that. We are looking at the ability to demonstrate knowledge, understanding and exploration of the topic and ideas in the essay. It is the writer's responsibility to convince the marker that they have understood the topic explored and not the assessor's responsibility to highlight errors and mistakes in the essay.

Math Studies SL

• Criterion A - Introduction [3] : The essay contained a title and a clear exposition of the task/problem and a detailed plan of the essay. Whatever plan outlined in the essay must be carried out. There is no point outlining an ambitious plan that cannot be carried out adequately.
• Criterion B - Information / Measurement [3] : We are looking for the skills of organising the data in the appropriate forms and templates for analysis. In addition, we are also assessing whether the writer has able to determine the appropriateness of the quantity and quality of data collected or information generated. Hence, it is important to explain further for your decision to collect these data or to generate these information.
• Criterion C - Mathematical Processes [5] : We are looking for sophistication and variety of mathematical processes, methods and techniques in this criterion. Attention to accuracy and errors is encouraged. In addition, diagrams and graphs presented should give the teachers a peek into the attentiveness of the writer in the presentation of data. It is often the smallest of all things that reveal whether the writer has grasped the concept and be able to juggle comfortably with it.
• Criterion D - Interpretation of Results [3] : We are looking for the interpretation of the analysis in the essay and the writer's conclusion thereafter. Explaining the results of the mathematics and interpreting them in the context of the problem is what we are looking for in this criterion.
• Criterion E - Validity [1] : This refers to the part of the essay that explained the rationale for the use of a particular mathematical technique or to state the appropriateness of the mathematics used in the problem.  Discussion of the limitation of the mathematical techniques or software is assessed in this criterion.
• Criterion F - Structure and Communication [3] : We are looking for a definite structure and plan in your essay. It is important to ensure that your essay is coherent and communication is consistently clear throughout the essay. Have someone proofread and point out the areas that may be unclear to them.
• Criterion G - Notation and Terminology [2] : Make sure that you have defined and used the correct notation in your essay. This is especially so if you are using a word processor to type your Mathematical symbols. Calculator or spreadsheet notation is not acceptable.

Hope that above helps in clarifying your understanding of the Math IA criteria.

Alvin Soon

Creation of this blog

Dear all,

In creating this blog, I have many aims in mind, some personal and some for my students. First of all, the blog aims to share some of my thoughts and views on the Math IA during the process of supervision. In addition, I believe strongly that putting ideas into words is a clarifying process. It would enable me to think through these ideas in as much as I wish that the process of writing Mathematics would clarify your impressions and understanding of the Mathematics that you have been learning in the last decade or so.

Furthermore, I have made a conscious decision to blur the lines between a Math HL, SL and MS IA as the process of supervision is a similar one. Thus, the comments that I share here would apply to all in most cases.

Lastly, I am hoping that many of you will comment actively as you share your concerns and queries in this blog. This will create a more vibrant learning atmosphere and lead to a higher quality of essays being created by everyone in this community.

Alvin Soon
30 June 2013