As we look more carefully at mathematics

We have read several texts – “Think Maths” by Ian Stewart; “Why is math so useful?” by Michael Lemmonick, and an excerpt from a ToK text called “Discovered or invented?”.  Today, we watched a video about Fractals – “Fractals, the colors of infinity“.  The multiple choice questions for your final will come from this video.

Beyond this, it is worthwhile for you (especially those of you who enjoy math) to consider some of the following:


Revisions to the calendar and the rubric for the Manifesto are in Blue

[The rubric for this project is linked here.]

There has been much discussion this campaign year about issues that relate to the duties and obligations we have to each other.  The Tea Party’s anger with the growing National Debt, the Occupy Wall Street movement’s outcry over the distribution of wealth have raised questions about the role of government in society.  Given that our economic system contains many free-market elements as well as social programs and government regulations, there is a great opportunity for discussion regarding both in terms of ethics.  Your Manifesto Assignment, should you choose to accept it, is to create the moral blueprint for a solution to one of the following vexing problems:

The intertwined issues of a burgeoning national debt, a growing disparity in wealth, and an overly complex tax code.

In your Manifesto on the economy (assuming you choose this topic), you must consider what duty we have, if any, to other citizens, and how wealth should be distributed.  You may choose for the focus of your Manifesto, specific programs like the ‘Bush Tax Cuts’ or the current proposals of Republican candidates and the incumbent President.  Regardless of your proposal, you must specify the scope of your Manifesto to tackle a particular problem.  Is it the National Debt?  The excessive taxes?  The lack of health care for many Americans?  You must decide.

Once your decision has been made, you will have to clarify how your proposal stands firmly on a set of ethical assumptions and how the problem you seek to solve will be solved by the particular solutions you propose.  You must do more than argue for a particular political policy or change in law – you must argue that the moral foundation of the country will be strengthened and that a better, more just society will result.  Good Luck.

Alternately, you may choose to write your Manifesto considering the difficult question of Justice in the case of Robert Bales, a U.S. soldier stationed at Fort Lewis, Washington.  Bales is accused of murdering 17 Afghani citizens.  From many initial reports, it appears the killings were premeditated.  It should be a simple case.  Alas, it is not.

A manifesto that considers the full range of opinions on the matter of Justice in this case would surely consider the events themselves, a soldier’s duty to serve one’s country, a country’s request that a soldier serve four tours of duty in a short range of time, the military’s choice to medicate soldiers while on duty, the personal history of Robert Bales, the significant loss of life,  the unnecessary harm done to the several families in Afghanistan, and the choice to try the soldier on American soil – rather than in an Afghani courtroom.  Once a clear definition of Justice has been provided, a quality Manifesto will explore the many facets of Justice in this case – as well as provide clear direction as to what steps should be taken to ensure that Justice is served in this case.  PLEASE BE CAREFUL to recognize that this is NOT a legal manifesto.  Regardless of which laws apply in this case, your task is to define justice, establish the facts in the case, and explain how to best ensure that a just process and verdict can be meted out in this highly-politicized case that has caused a further rift between two countries.

In order to accomplish your assignment, you will need to include the following elements in your Manifesto:

  1.  The assumptions relevant to your topic. Some or all of the following may apply:  [Multi paragraph essay #1] 
  • What is human nature?
  • What constitutes moral behavior? Who defines “good”?  What is ‘Justice’?
  • Do we have a duty to others?  What obligations are parts of that duty?
  • What obligations, if any, does the government have to its citizens?
  • (How) do people know (or learn) to be moral?
  • How is knowledge (especially moral knowledge) gained?   What do the experts say?  Distinguish your views from theirs.

2.   The problem [3+ paragraphs]  *Current problem(s) explained and supported*

3.   The solution explained and argued (with support) [Multi-paragraph essay #2]

  • Given the problem, what moral situations must individuals be prepared to face? Why?
  • What are the steps?  What (moral content) needs to be learned?  Why?
  • Links made to both assumptions about human nature [#1] as well as current problems [#2].
  • How will moral learning be known?
  • How will the plan encourage the moral development [given the problems in #2]?
  • What makes you think it will work?

In this section (as well as in section 1), you must rely on a range of support:

  • Expert testimony/support from texts you have read (not just an online quote mill)
  • Personal experience
  • The experience of one of your peers
  • Related modern examples

Additional Elements [these can go anywhere in the work, but most will probably work best in the solution]:

  • A cover that visually represents the moral issues and societal pressures facing individuals in our society
  • A paragraph on the back cover that explains the collage
  • A table and a lengthy caption
  • A visual representation of how the plan should work.  The visual should symbolically represent the influences on the ideal citizen as well as the skills and content necessary to deal with the influences.
  • A caption will explain the visual
  • A statement of purpose – what is your philosophy in a nutshell?
  • A text box inserted into your work for visual effect
  • A Works Cited Page that accurately uses MLA format  [Obviously, this means there will be in-text quotations and citations that follow appropriate MLA formats.]

The primary learning objective is that students must form THEIR OWN ideas regarding a solution to the problem.  With this in mind, finding that some online source has said what you want to say is, perhaps, the most defeating find one could make.  With this in mind STAY AWAY FROM OPINION PIECES ON THE INTERNET UNTIL YOU HAVE FORMED YOUR OWN IDEAS.  If you have ever done ‘research’ by typing a question into Google and printing out the first link you found, you must reform your ways.  Don’t dare go to Wikipedia, avoid asking Jeeves or Yahoo!, and stay away from  The rubric will punish those student ‘authors’ who submit work heavily influenced by another source – because the point of the whole exercise is for you to think and to create your own philosophical scaffolding.  The rubric will reward thinkers who have managed to see the range of views, created a space for his/her own ideas, and established a well-crafted argument with support for those ideas.

Another of the learning objectives for the project is that the student author must demonstrate an understanding of the range of philosophical positions in the field of ethics.  With regard to this, students should work to incorporate the views of authors we have discussed in class – Mill, Bentham, and Kant – as either support or counter-arguments.  In the critical portion of your project [#s 1 & 3], you will include analysis (not just random quotes found online, but rather excerpts and analysis to explain that expert’s views on morality) from expert sources that we have studied in TOK as well as sources you have uncovered on your own.  It is imperative that you justify and defend your opinions using expert testimony; additionally, it is crucial that you address the counter-arguments to your positions.  These parts [#1 & 3] should read as an essay; an expository rubric will be applied.  Neither the rubric nor the evaluator will not look fondly upon manifestos from authors who fail to demonstrate an understanding of the implications and the underlying assumptions inherent in their plan.

In addition, I will not accept plans that fail to use in-text citations and a Works Cited Page as demonstrated in Write for College or Writer’s Inc. which can be checked out in the Skyline High School Library.

All plans will be of professional-calibre; have a beginning, middle and end; and include a cover sheet and integrated visuals.  All Manifestos will be submitted in both paper form and digital form – the digital form will be submitted to  In addition, all drafts and peer editing must be kept and submitted.  A grade will be given for process points.  A quick review of the calendar [as shared in class April 30 and modified May 13th] for the Manifesto project is as follows:

May 7th – Project explained; in-class time to work on Manifesto – Start drafting part one above.  For homework, research the problem [part two].

May 8th – in-class time to draft Manifesto – Work should be invested into the solution [part three].  For homework, students should edit and revise work if they have finished the draft.

May 9th – a rough, bare-bones draft of the complete Manifesto will be ‘submitted’ (shown) to the teacher to demonstrate that productivity has been achieved.  Peer editing of this draft will happen in class.  ***This is the final day to request a revised calendar***  Seniors who fail to submit a draft or submit an alternate calendar will be in danger of not passing the course. 

May 10th – in-class time to work on Manifesto – as well as time to meet with the instructor and answer questions regarding student drafts

May 11th – in-class time to work on Manifesto – as well as time to meet with the instructor and answer questions regarding student drafts

Wednesday, May 16th, (not May 14th) – 2nd draft brought to class for peer editing – draft is shown to instructor.  Peer editing in class.

Friday, May 18th Beginning of class (not May 15th) – Manifesto is due in paper form as well as in digital form submitted to  All drafts and peer editing will be submitted in class.

Experts read in class:

Bentham (secondary source), Mill, Kant (Categorical Imperative and Velazquez Excerpt)

Experts mentioned in class:

Aristotle, Plato, The Bible, Gandhi, Thoreau, and Marx

Choose two of the following:

Sartre – One, Two, Three & Four; Locke; Hobbes (‘state of war’ and benefits of society) ; Nietzsche Page One & Page Two; Kohlberg; and Machiavelli.

*An alternate problem for the Manifesto may be proposed, but it must be signed-off by the instructor prior to May 15 and should address similar, if not identical, questions in parts one and three.