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:

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:

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:

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:

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: