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Big Picture assignment items for MTH 225 (Discrete Structures for Computer Science 1).

MTH 225 Big Picture Items

The Big Picture category consists of items that will address the following learning goals of our course:

  • Students will describe the uses of mathematics as a way of knowing in computer science and mathematical proof as a way of establishing knowledge in math and computer science.
  • Students will identify and describe connections between the mathematical content of the course (sets, counting, logic, proof, probability) and the elements of computer science (algorithms, data structures, programs).

Big Picture items can also be used to show that you are thinking carefully about your work (particularly any failures that you encounter while learning) and about the way that you learn.

In order to certify at Level 2 on any of the five learning bundles, you will need to complete an item that demonstrates evidence that you have satisfied at least one of these two learning goals. Note that in order to earn a C or higher in the course, you must certify at Level 2 on at least one bundle.

Choosing and completing a Big Picture item

At the end of this document is a list of four Big Picture items. Each of these is to be done as an add-on to the work you are already doing for Level 2 certification in a bundle. Select one (1) of these items and complete it customizing the content of the response to the particular bundle you wish to attach it to.

The four items fall into four categories: Connections, Mathematics as a Way of Knowing, Productive Failure, and Learning How to Learn. Each category has a general description of what the items in that category should try to accomplish and especially a question (or group of questions) to address. To complete the Big Picture item, address the questions that are being asked.

The standard way to complete the item is to produce written work in the form of a short essay in which you address the questions. If you choose this route, your work must satisfy the following specifications:

  • The work must be typewritten using a word processor or typesetting system, saved as a PDF, and submitted to the professor as an email attachment (talbertr@gvsu.edu).
  • The work must employ clear and correct English. In particular, the following are considered syntax errors: misspelled words, incomplete sentences, subject-verb disagreements, and failure to use correct capitalization and punctuation rules. Excessive instances of these will downgrade the work.
  • The work should be between 700 and 800 words long. This is roughly equivalent to about 1-2 pages. Here is a file consisting of 750 words of lorem ipsum text for reference.
  • The work needs to address the core question(s) directly and in a thoughtful and significant way. Responses that include excessive "filler", or do not get to the point, or are merely superficial will not be given a Pass rating.

A written essay must satisfy all of the above specifications in order to receive a Pass rating.

However, writing an essay is not the only way you may address the item. You can create a response in any medium you wish, provided it addresses the item in a significant and thoughtful way. Some alternative ways of responding to a Big Picture item might include:

  • A blog post or series of blog posts.
  • A video (posted to YouTube, Instagram, etc.) that addresses the item in a way equivalent to an essay.
  • A photo essay.
  • A song or a musical. (Don't laugh -- it's been done before.)

The important thing is that you are free to address the questions in each item in any way you wish, so long as you are providing evidence of significant and careful thought about the question.

If you choose a non-standard means of addressing an item, you are required to consult with me (Prof. Talbert) first so that your idea can be approved and so that we can negotiate a mutually acceptable set of specifications for Pass level work.

Submissions of Big Picture items that are exceptionally insightful or creative may be awarded an extra token in addition to a Pass grade. There is no rubric for this; it will strictly be a judgment call based on my reaction to your response.

Finally, note that Big Picture items that do not receive a Pass rating can be revised and resubmitted with no limitations on number or frequency and without having to spend tokens.

Big Picture items

Category: Connections

In the learning bundle for which you are choosing this Big Picture item, think about one or more of the big ideas of that bundle. For example, logical equivalence of propositions is a big idea of the Logic bundle; mathematical induction is a big idea in the Proof bundle. Having chosen those ideas, address the following question:

What are the connections between my big idea(s) and computer science?

For example, you could address connections between logical equivalence and some aspect of data structures; or mathematical induction and some aspect of algorithm design.

Category: Mathematics as a Way of Knowing

In the learning bundle for which you are choosing this Big Picture item, think about one or more of the mathematical processes that have been used. Be careful not to select merely a "topic" (e.g. Bayes' theorem, set unions, etc.) but rather a way in which knowledge in mathematics is constructed. Those "ways of knowing" could include proof techniques, mathematical solution strategies, computational processes, and so on. Then, with that process chosen, address the following question:

How does the process that I chose, which produces knowledge in mathematics, aid me in constructing knowledge in computer science?

For example: You might choose proof by induction as a mathematical process; this is a way of constructing knowledge in mathematics because it is used to argue for the truth of a proposition which we can then use as a fact. How does this "way of knowing" in mathematics help me to build knowledge in computer science? (For example, what are some instances where proof by induction could be used to verify the performance of an algorithm?)

Category: Productive Failure

In the learning bundle for which you are choosing this Big Picture item, find an instance of your work that did not receive a Pass rating, but which you eventually went on to re-work and achieve a Pass rating. This can be a certification assessment or a Homework B. (To avoid last-minute submissions of this item, you may not use a recertification for this task.) That is, find an instance of work at which you initially failed, but then used that work and the experience behind it to improve, so that your failure was "productive".

Then, answer the following questions in a response:

  • Where did you go wrong? What factors contributed to the initial failure on the work you chose?
  • When you received the feedback on your work, what was your reaction?
  • After you received feedback, what insights did it provide on your work and on the way you approached your work that allowed you to improve it?
  • What exactly did you do with the feedback and your initial work to improve?
  • How did this experience contribute to having a "growth mindset" versus a "fixed mindset"? (See: http://mindsetonline.com/whatisit/about/)

Category: Learning How to Learn

In the learning bundle for which you are choosing this Big Picture item, think about how you approached learning the material in this bundle. Take everything into account: the activities you did, both those prescribed for you by assignments and activities you undertook on your own; the assumptions that you held about yourself and the work you were doing; the experiences you had while learning; and so on. Then address the following questions:

  • What did you learn about how to be a good student in MTH 225?
  • What did you learn about how to learn mathematics (generally speaking, not necessarily just the math that is in this class) effectively?
  • What did you learn about how to become a self-directed learner in this subject --- that is, how to make an agenda about what you need and want to learn, how to make a plan for learning those things, and how to be a person who does not need a professor present in order to learn new things?
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