Section A.1 Problem Set Success Guide
What are Problem Sets?
The term Problem Set is used commonly in STEM courses at Brown and, generally, means some form of written assignment in which students solve problems. While this term may be familiar, the experience of working on a problem set varies greatly between courses because different courses may have different expectations for quality and style of writing, and there may be different expectations surrounding the types of problems that students are expected to solve.
The purpose of this brief guide is to clarify expectations around Problem Sets in this course. Your Problem Sets make up a significant portion of your grade and, as such, are expected to take a significant amount of time and effort to do well on them.
What Kinds of Problems Will Appear on Problem Sets?
Different types of problems assess different learning outcomes and promote the development of different skills and habits. To help you better understand the kind of problems that you will encounter your problem set (and why you are encountering them), it is instructive to examine the basic types of problems that make up this TBIL course, as described in Team-Based Inquiry Learning.
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www.tandfonline.com/doi/abs/10.1080/10511970.2019.1666440Broadly speaking, the problems that you encounter in this course (both inside and outside of the classroom) fall into the following types:
- Scaffolded Exploration problems introduce you to a new concept through a sequence of carefully scaffolded activities. These activities include exploratory activities to motivate an entire line of thinking; working a series of examples to have students realize the need for a new definition; and working a carefully scaffolded problem to develop a general algorithm for solving similar problems, for example.
- Fluency Builders are designed to help you develop fluency in a new concept. You will work on such problems both in-class with your teammates after learning a new concepts, but also outside of class while you study. All of the problems that you will see on Fluency Assessments are Fluency Builders.
- Flexible Extensions are problems that require you to apply a concept in a new setting. These problems can take a variety of forms and include: checking if something satisfies a new definition; extending an idea from its “natural” setting to something more general; or, a true application to another field or topic. In these activities, the emphasis is on developing a flexible mindset when faced with new problems.
The most common types of problems that you will work on in class are Scaffolded Explorations and Fluency Builders. In contrast, your Problem Sets will largely prioritize Flexible Extensions—because these are exactly the types of problems that allow you develop your ability to knowledge-transfer.
How Will You Be Evaluated?
Each Problem Set in this course will contain five (5) problems. For each problem, your task is to solve the problem and prepare a written solution to it. You will then upload your solutions to Gradescope as a single .pdf file, as instruced on Canvas.
Written solutions are more than just answers. A complete solution to a problem:
- clearly states what the answer to the problem is;
- explains why the claimed answer is indeed the correct answer;
- is grounded in sound mathematical reasoning that builds on and/or refers directly to results, Facts, or Activities that we have explored in class;
- is written for an audience of a typical classmate; that is, someone who is generally new to these ideas and has the resources and experiences provided in this Activity Book.
For each problem on your problem set, you will receive a total score of at most 5 points; three (3) of those points are for Problem Solving and two (2) of those points are for Communication.
- Problem Solving (3 Points)
- The solution uses methods covered in class, is grounded in mathematical reasoning, and solves the problem, when executed accurately.
- All key ideas required to solve the problem are introduced in a clear and concise manner.
- Communication (2 Points)
- The solution is well-written, audience appropriate, and follows principles of good mathematical writing (explained more below).
- Mathematical terms and notations are used correctly, and Theorem and Facts are cited appropriately.
- Solutions are uploaded to gradescope properly with all relevant pages selected for each question.
In order to grade your work fairly and consistently among our varied sections, the teaching team will meet prior to assessing the Problem Sets in order to decide how to interpret these criteria for each problem on your Problem Set.
After your Problem Set is returned to you, you will be provided an opportunity to reflect on the feedback that you were given and earn two (2) additional point on your Problem Set.
Writing Mathematics Well.
Writing Mathematics well is a skill that you can and will develop over time. Like other forms of writing, it will take a lot of practice, and the incorporation of feedback from peers and those with more expertise. While it may feel like it at the beginning, we want to stress that our goal is not to have you write the exact same way that we do. Rather, we want you to be able to express yourself precisely, so that you may share your ideas and perspectives accurately with the greater community.
The writing guide depicted below (by Francis Su of Harvey Mudd College) is a great resource that covers the basic principles of good mathematical writing. A PDF is also available. Use it a checklist when writing your solutions. Almost every deduction we give for communication is a result of work that violates at least one of these principles.
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https://tbil.org/external/custom/Su-MathWriting.pdfThe single greatest piece of advice I can give is: write for a hypothetical student who is anxious about the material. With this audience in mind, take care not ensure that all details are explained well and that you are using ideas and terminology that we have used in class. At the same, work to remove any unnecessary text that does not help with the readability.
This is a short guide to writing mathematics well by Francis Su (Harvey Mudd College). A PDF is also available. Use it a checklist when writing your solutions. Almost every deduction we give for communication is a result of work that violates at least one of these principles.
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https://tbil.org/external/custom/Su-MathWriting.pdfGetting the Most Out of Your Problem Sets.
Out of everything you do in this course, the Problem Sets will take up the most of your effort. They are also where the most significant and lasting learning will happen, provided that you invest the time and resources into yourself for this learning to occur. Take pride in the work you submit this semester—it represents the culmination of a lot of time, energy, and creativity on your part, even though you will inevitably experience the ebb and flow of joy and frustration as you get stuck on challenging problems.
Here are some tips to help you get the most of your experience:
- Begin your Problem Set early!
- They are designed with the intention of them being completed over a period of around 10 days.
- Identify key terms in each problem and locate the relevant Activity Book sections.
- Identify which learning outcome(s) are aligned with each problem.
- These alignments may help you solve the problem.
- Every problem you encounter will be aligned with at least one outcome—even if it doesn’t look like it!
- Practice getting unstuck:
- Go for a walk, grab a snack, or engage in a hobby.
- Talk to a friend, or member of the teaching team in Office Hours.
- Avoid external resources (like Youtube, etc.), and rely on internal ones.
- These problems are designed to be solved with the concepts and ideas that are introduced in class.
- While external resources can be helpful for learning, they may also serve as a crutch and rob you of an opportunity to strengthen an area of weakness.
