Have an intent and be intentional.

I’ve told this tale for years and have no idea where it came from (I do know I didn’t make it up):

A king is riding with his men through a forest and they come upon a grove of trees.  High and low, near and far, they see that on the trees there are tiny circles of paint and in the center of each circle there is an arrow.  The king is amazed and proclaims (as one does in such a story), ”Whoever shot these arrows is the greatest archer and, if found, will be given great riches and the hand of my daughter in marriage.” The king and his entourage continue riding along and come upon a young boy with a bow, a sling of arrows and a bucket of paint. After confirming that the boy is the source of all the arrows the king has seen, he reveals his proclamation and takes to boy back to his kingdom.  On the way, the king asks the boy how he came to hit all those targets so accurately and the boy responds, “I shoot the arrow first.”

There are lots of uses for this, but today the relevance is that as a teacher I can be like the boy carefully and forcefully shooting my arrows of knowledge, and then make claim of my great success by being the one to draw the target after the fact.  Instead, I try to plan out my targets ahead of time and then carefully and forcefully attempt to hit them.  I try to take this one step further, adding in a bit of accountability, by announcing my intent to my class (or to other teachers).

I think we hear too much about how important it is to have an intent for a class or activity (or call it an objective or code it as an SLO (student learning outcome)).  I agree that such are a valuable part of course design, but I think we miss a great opportunity when we don’t take advantage of having an intent and letting the students (and others) know about it.  Besides accountability/pressure to actually do the thing you say, you gain partners and some grace in getting it done. I am always amazed how accepting, supportive and agreeable students are to new ideas and methodologies when I’ve taken the time to respect them and let them know something about what I’m doing and why I’m doing it. Besides getting something done, a strange thing happens: it actually makes an impact.


Canon Fodder: Learning Theories

Is there a canon for education? Sort of.

Coming late to the theory and literature of learning after years of a life saturated with mathematics, I always wanted learning to follow the same path of development that I loved from math.  I wanted a set of classic ideas (and books) from which all of the modern learning theory was derived (deductively, if I’m allowed to dream).  I was always asking my colleagues in Math Education, “What books or articles should someone new to learning, read first?”  I never got satisfying answers. I did realize that there were some basic theories and there were names spoken with reverence, e.g. Piget, Vygotsky, and Bloom.  There were other characters I heard and read about: Freire, Skinner, Gardner, Dewey, and others, but I couldn’t tell if they were major or minor players, or heretics.

I haven’t forgot my quest for a canon, and so I was glad to come across the following. Apparently back in April, Howard Rheingold (@hrheingold) tweeted a link to this awesome mindmap (sorry it is so small, link to original is broken):


This looks to be a great resource and way to see various theories and how they are connected. I’ve just started to look through it carefully and I hope to be able to say more about it later.

Quick update: In searching for references to this map, I came across the blog for Donald Clark Donald Clark Plan B in which he did posts on all the learning theorists (and more) and either was the source for much of  the map or the makers of the map used the same sources as him.  Either way, I encourage you to visit his blog and read in more detail about the various learning theorists.

3 Ts for Change

3Ts = Think, Talk and Try

I can’t say exactly when it happened, maybe it was always there, but one day I realized that learning wasn’t really happening in my classroom. I started looking around to see what sort of changes I could (and should) make.  I’ll write later about what I’ve done in different cases, but for this entry I want to write about one my early principles from that early time. This is the 3Ts: Think, Talk and Try.

Think – The first step is to think (or reflect or study or research) about teaching in general, your teaching, and what’s going on (and should be going on) in your classroom. I usually start with thinking about some short or long term goals (learning objective, if you wish).  I then move to thinking about different practices, activities, course structures, etc.  My favorite approach is to take lunch at a quiet place with a notebook and my Pentel (0.7mm) or my signature1 green pen and write and think my way through some ideas about a specific course or issue.

Talk – The next step is to talk out the goals and the possible practices with someone.  It doesn’t have to be an expert or anyone especially knowledgeable about teaching or the content area. You just want a chance to talk out the ideas, get a reality check, and get some feedback from a different perspective. I’ve used colleagues, students (former and current), and family members. The conversations that go on on the websites of other educators can also be used for the process.

Try – The last step is the put together a plan and to implement some of the ideas you’ve come up with. The more extensive the idea, the more preparation that is needed. I’m probably much more willing to try something even if it hasn’t been fully developed and am willing to deal with failure, than most. You should try things that you feel comfortable enough with. (It is important to not be too honest with students about the experimental nature of the activity your are trying; you should act like its a great and well thought-out idea)

An Example: For an advanced numerical analysis class (senior and graduates in STEM fields) I was teaching, I had the issue that the students needed to know some specific prerequisite material for each of the topics that we would be exploring in the class.  Some of the students would be prepared, some would not (but could be, with study), and I didn’t want to spend much class time or grading effort on firming up their backgrounds. The book I was using had most of the elements that they needed or at least enough of a specific reminder that they could go and find it. So I headed to my favorite lunch spot (good food, not too busy, far enough away that I wouldn’t see people I knew), ordered a #5 and sat with my notebook and pencil.  I brainstormed some ideas, first breaking down the different types of problems the students could do (background practice, new material practice, projects, etc.) and then looking at how the students might get to where they can do these problems (book, in-class, online, etc.).  I thought it made sense to try to move this background material outside of the classroom (flip). I talked to some colleagues and read some ideas about flipping the classroom. I decided that for the background material, I would assign specific readings from the book (and other sources as needed), and then follow up with a short online quiz which might include some basic problems and some concept questions every week.  I also included some open-ended questions in the quiz where students could ask questions or give me feedback about their background on the material.  Fall semester, I put it in place.  I had to adjust it a little by putting in more direction for the readings, e.g. ‘In Section 2.1, focus on … and just lightly scan …’, and besides answering questions in class, I started posting the questions with answers online. Overall, as long as I kept to the schedule, it was successful in helping the students review or know what to review, and for me to know what they already knew or needed more work with.

Note A: In its current form the 3 Ts has really become the 4 Ts, with the 4th T being Technology, in which I look for ways to leverage technology in implementing the idea.

Note B: This blog is driven by this principle in that I have thought long about extending my conversations about teaching and learning, and having read many blogs, felt ready to try it. However, this blog also represents an incomplete application of the principle, if you take what I write as a result of thinking and half of talking (one sided, so far).  Thus, I hope for (yet fear) responses to what I write.


1Aside: for years when I had administrative duties, I had a green pen that I used for all my official signatures. I had/have horrible handwriting and an almost unreadable signature, but people knew my green scrawl. I was very protective of the power of that green pen and would confiscate green pens from others in the department.

The First Post

In which I establish the fabulous context for all my future postings.

I started this blog because I think way too much about teaching and learning in higher education, especially about what happens in my mathematics classroom and I need space to document those thoughts.  Just like the ubiquitous +C of integral calculus, I expect my thoughts to be a necessary (for me) addition to a much more valuable and interesting collection of thoughts on learning and teaching that exists on the web.