his book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. There are problems that some people will solve quickly, and there are problems that will take days of thought for everyone. Probably the best way to use this book is to work on a problem until you feel you are not making progress and then go on to the next one. Think about the problem you couldn’t get as you do other things. The next chance you get, discuss the problem you are stymied on with other members of the class. Often you will all feel you’ve hit dead ends, but when you begin comparing notes and listening carefully to each other, you will see more than one approach to the problem and be able to make some progress. In fact, after comparing notes you may realize that there is more than one way to interpret the problem. In this case your first step should be to think together about what the problem is actually asking you to do. You may have learned in school that for every problem you are given, there is a method that has already been taught to you, and you are supposed to figure out which method applies and apply it. That is not the case here. Based on some simplified examples, you will discover the method for yourself. Later on, you may recognize a pattern that suggests you should try to use this method again.
In courses and programs with community-sponsored or industry-sponsored projects, the handoff between the design team and the sponsoring partner is a particularly vulnerable transition. Innovations with the potential for impact fail shortly after the handoff for myriad reasons, including: inadequate resource allocation (time, money, skills); no clear institutional champion; inadequate institutional will to see the concept through further trial, iteration, and growth; and more. What might it look like to design the handoff? This lesson prompts design students (high school through graduate school) to begin a design project within a design project: to empathize with the handoff’s stakeholders; to define the handoff’s key needs and opportunities; to ideate novel handoff artifacts, strategies, and processes; to prototype improvements to their intended handoff strategy; and to test these strategies before the class or program ends so they can make adjustments and improvements.
Purpose and audience. The Pathways to Impact lesson is designed for participants who want to have greater impact on a societal issue than they currently do but who aren’t sure how. The lesson helps participants discover directions (“pathways”) they might wish to pursue and identify small next steps to take in two or three of those directions.
Although this lesson was first created in a course for young alumni, the materials are applicable to many audiences. We encourage you to adapt and use the following lesson plan as you see fit; and please don’t hesitate to reach out to us for support.
Structure at a glance. In the first part of this activity, participants will identify a pressing societal issue that they wish to address. They will next be introduced to seven broad ways to have impact (the “pathways”) and asked to brainstorm several ways to have impact within each of the pathways.
In the second part of this activity, participants will select two or three ideas to which they feel most drawn. Next, in small groups, they will help each other identify the “smallest next step” that they might take towards each. Lastly, they will commit to taking two or three of these actions within the next week.
Context, purpose and audience. There are two broad types of assumptions that designers must identify and address: the first type are assumptions they, as designers, have as they begin a project; the second type are assumptions that are ambient in the project context–assumptions that many of the project stakeholders either hold or frequently experience. In both cases, naming the assumption and developing an articulation for how that assumption can be reconsidered can help direct a project toward greater impact.
This lesson is designed to help participants reframe these two types of assumptions. It can be used with design students from high school to continuing (adult) education. It is best delivered towards the end of the initial phase of design research (“Empathize” phase, to use the parlance of Stanford), after students have conducted interviews and other forms of research.
The lesson offers five reframe patterns. These are meant to help students identify particularly powerful articulations of reframed assumptions by providing five different jumping-off points for ideation. The patterns are best introduced and used lightly: as provocations rather than as a formula to rigidly follow.
We illustrate these reframe patterns using examples from disability studies. Thus, this lesson also serves as a “trojan horse” to infuse core design justice concepts.
This document includes a set of policies that are designed to provide efficient ways for instructors to implement pedagogies of care. The principle of “rigorous care” is informed by research on learning, accessibility, and mental health. The idea of “early warnings” is meant to help students identify their needs and seek support before problems become unmanageable. Both ideas respect the fact that both students and instructors work under enormous pressure.
Each policy statement is preceded by a brief framing justification and followed by a selected bibliography of the research and testimonials that have informed the policy.
This lecture covers some history of the psychology of learning and introduces some of the primary theories of learning from antiquity to the modern age.