Peer instruction

What peer instruction is and why we use it.

Peer instruction

Peer instruction refers to a planned process of having students engage with each other to learn in addition or as an alternative to what can easily be a very passive process of absorption from a lecturer or tutor.  Here we will concentrate on Eric Mazur's implementation of this idea in Physics, and what follows from it.  Aspects of his technique are in use by the School of Physics here. 

Before anything else,  anybody interested in thinking about the process of learning in science and maths to watch the video of Mazur's  talk "Confessions of a Converted Lecturer". 

My take on the main points of Mazur's programme is as follows.  It is based on the following observations which I believe are also wholly applicable to mathematics: 

• After conventional lecture courses, students are often quite good at exam questions which are formulaic in the sense of having enough cues as to the "correct" method to use or in being strongly related to previous exam questions or other material signaled as being "important" by the lecturer.  They can, however, perform very badly at what we would think of as easy questions on basic concepts - let us call such questions "conceptual".   (Two examples of conceptual questions in basic University maths are (a) True or False: 2≤3 and (b) How many tangents does the curve y=x have at the point (0,0)?) 

• In Physics at least, after conventional courses students' ability to do such conceptual questions does not improve very much. 

• The conventional lecture is very much directed to the transfer of information.   It becomes more and more difficult to make sense of that as information becomes more and more available.  

• Of course, there are benefits in the process of transcribing lecture notes (it would be surprising if the process had an entirely negative effect) but the question is whether this is really the bst use of valuable contact time.  (But according to Wieman who measures student's attitudes to the subject using the CLASS survey, the usual effect of a conventional introductory Physics course is that their outlook in fact regresses.) 

• The logical difficulties we have with the provision of lecture notes (to provide or not to provide, to hand out before or after the lecture, whether to follow them literally or do something different in lectures to the notes we have provided,...) suggest there is something wrong with the underlying idea. 

Mazur's proposed solution to these problems is essentially as follows: 

• Have a course textbook and set reading to be done before lectures. 

• Most of the time in lectures is devoted to "ConcepTests": sessions with clickers generally structured as follows:  

• A brief reminder from the lecturer of an important point from the reading. 

• A conceptual question posed to the class and students given 1-2 minutes to think about their answer to it.   (The general idea is that a conceptual question should be answerable with at most a trivial amount of computation.) 

• A "vote" taken on the answer by the class (with clickers) and the results noted by the lecturer but not made public. 

• A 3-4 minute discussion period where students are asked to discuss their answer with neighbors. 

• Another vote on the answer taken, the results announced and the lecturer briefly sums up. 

• Generally, if between 30 and 70 percent of the class get the right answer first time around, then there is a substantial improvement on the second vote.   (If more than 70% initially, best just to sum up straight away. If less than 30%, one needs to do something different.) 

• The assessment of the class is designed to reinforce the importance of conceptual understanding and of "doing the reading". 

This method has been studied carefully by Mazur and his co-workers and used also in other Schools across the US.  The results almost without exception are very good, with students showing a big increase in their ability with conceptual questions and a smaller but still significant gain in their ability with conventional questions.  It is important to realise that "conventional" questions still feature strongly in this system (being at last half the exam, etc) and that students' performance in them improves even though they will not have had many examples "worked through" in lectures. 

• In connection with this, it is instructive to put oneself in the position of a student able to do conventional questions well, but with little conceptual mastery. Presumably, they have a well-learned repertoire of methods, but no deep understanding of whether or why a given one works for a particular problem.  It must be rather confusing and dispiriting to apply what by pattern-matching looks to be a reasonable method and to get top marks some of the time and no marks at all at others. 

The huge issue in all this is how one persuades students to do the required reading.  Before listing some ways to proceed, it is worth noting that in non-science subjects it is completely routine that students are expected to read before lectures: a lecturer on Shakespeare would not read the play to the students in a lecture but would expect them to have read it first.  And if we do have some students not doing the reading then it is worth asking if they are worse off than students who have attended a conventional lecture, taking notes but not paying much attention and not reading them afterwards.   That said, here is how one could proceed. 

• Explain carefully and repeatedly to students what we expect and why we expect it. 

• Make it clear that all (set) material in the book is assessable and examinable and make sure this actually happens.

• Set short assessed tests (via Maple TA or a system associated with the book where such exists) of a couple of basic questions on the reading with a due date before the lectures where the material will be discussed. 

• Introduce some measure of self-assessment on whether students have done the reading. 

Resources 

• Mazur's original book on the method is in the JCM library. 

• An experiment with Peer Instruction in Mathematics at Cornell is reported in this preprint. The authors have shied away from Mazur's terminology of "conceptual questions" and "ConcepTests" and instead have the idea of "Good Questions".  A lot of their questions are rather good, but the terminology seems to suggest a lack of clarity in purpose: are they good for discussion, or good for conceptual learning or are they good in some general abstract sense?  This may reflect the nature of the experiment where different instructors of different sections of a calculus class (with the same exams) chose to use these questions for peer instruction to greater or lesser degrees.   Thus the class assessment was not designed around the use of peer instruction.  

• The quest project:  Conceptests for Mathematics. 

• A case study by Wieman of the process of transforming a quantum mechanics course.   The systematic analysis and careful iterative correction using observations of the effectiveness is impressive.  

What is Peer Instruction (PI)? 

How does one work on understanding in lectures?  It seems clear that lecturing in the form of something close to a monologue of explanation is not going to work.  Most "flippers" use Eric Mazur's method of Peer Instruction for a large proportion of the time.  His account of the system and how he came by ("Confessions of a Converted Lecturer") is a very entertaining and instructive story and nobody should try PI without watching it.  (I'm tempted to say that nobody should teach in Higher Education without watching it.) 

The idea is this.  Students have before class read a section of the textbook and come to class with some mechanism for voting on the answer to multiple-choice questions, typically "clickers". Peer instruction then consists of a succession of cycles of the following form. 

1. Lecturer briefly reminds the class of an important concept or point from their prior reading. 

2. Lecturer poses a multiple choice question on that concept and asks the class to think quietly on their own and then vote for their preferred answer. 

3. Lecturer looks at the voting results but does NOT show the class. 

4. Normally (see below) the lecturer invites the class to "turn to their neighbor" and discuss the question for 2-3 minutes. During this period the lecturer circulates around the class, listening and promoting discussion. 

5. Class votes again and lecturer shows the class the results. 

6. Resolution: the lecturer sums up, explaining the question and its solution. 

A magical thing usually happens:  if before the group discussion phase 45% of students get the answer right, after 70-90% are now correct.  

If in the initial vote more than about 75% of the class are correct then the discussion phase is omitted and one goes straight to the resolution.  On the other hand, if less than about 35% of the class are right discussion does not usually improve things and so one has to take an alternative line. 

This phenomenon of increased understanding happening without the lecturer saying a word is magical. But it is important to understand its purpose and meaning if it is to be educationally successful. 

The key points about PI 

What makes a good question for PI ? 

• The question should generally be answerable without calculation.  It should usually require the student to think about a concept and gain understanding.  It should have plausible "wrong answers" (or "distractors" as they are called in the PCQ world) but should not (usually) be a trick. Addressing a common misconception is a very constructive thing to do. 

What is the purpose of the PI questions? 

• The most important point is that the purpose is NOT for the lecturer to have a quick check on comprehension before moving on.  It is certainly true that if you employ PI you are in touch with what the class understands to a potentially almost frightening degree, but that is a beneficial side effect rather than the main purpose. 

• The central purpose is that the process of working on and talking about the questions is itself an extremely effective educational process for the class.  It is there that most of the learning happens.  (But because students are heavily invested in the question by the time one gets to the resolution, those two minutes are often spent explaining to a very interested and engaged class.) 

• Other benefits of PI are: 

• Students gain experience of talking about mathematics. 

• The act of recalling information improves memory of it.  (In fact, for promoting long-term memory a recall test after reading new material is more effective than spending the same time rereading it or taking notes on it.)