ConcepTests for Calculus

ConcepTests in your Classroom

Arlo in classroom explaining to students

Implementing ConcepTests in Class

There are a wide variety of ways to use ConcepTests in teaching.  The questions can be used for discovery or review, synthesis or challenge.  You can use many questions or relatively few.  Here are some examples:

  • When conducting a review prior to an exam, divide the review time into two blocks. Use a series of ConcepTests to review major ideas in the first block of time and then switch to another activity (examples at the board, group work, etc.) to review computational methods and facts.
  • Start a topic with an easy question, before discussing the material and see what the students do with it.  Since the distractors are based on common misconceptions, the student discussion is likely to be rich and may lead to the discovery of the correct idea.  Your lecture on the topic will then be actively received.
  • Break up the lecture into segments with questions.  Since human attention spans in minutes are roughly the same as age in years, college students can focus their attention well for about 20 minutes.  Lecture for 20 minutes, then implement a pair of ConcepTests, and then lecture for another 20 minutes.  The change of task for the students resets their attention and can improve comprehension of the latter 20 minutes of lecture.
  • Start class with a hard ConcepTest on prior material as an active method of summary prior to starting the day's topic.  This is similar to the technique of starting with a problem-of-the-day but limits the scope to ideas rather than ideas and computations which you may want to do later.

To use ConcepTests in your classroom, you will need a method of displaying the question slides and students will need a way of communicating their voted responses to you. 

Methods of Display

In ``smart'' classrooms, the questions can be loaded onto the classroom computer, or you can plug in a laptop or tablet via a VGA connection, and then the questions can displayed via the computer projector using a PDF viewer in full-screen mode.  If your classroom is not so equipped, you can request a projector on a cart from MediaOrder through I&IT.  The projector will be delivered to your classroom and picked up afterward by a staff member from I&IT.  Carts are available with computers attached or with just a stand-alone projector to which you can connect your laptop or tablet through a VGA connection.  You can also print the individual questions onto transparency slides and display them using an overhead projector, although black and white printing will lose the color information in graphics that was added to enhance clarity for some of the questions.

If the classroom computer is connected to the Internet (as in ``smart'' classrooms), or an Internet connection is available for your personal computer, we recommend that you upload the questions you plan to use to Blackboard prior to class.  Then you can open Blackboard and download a local copy of the question slide to use.  With this technique, the questions shown in class are then available to the students for download and study.  The question slides do not display the answer, so that participation in class or study-group discussion about the question is necessary.

It is a good idea to turn on the projector, load the slides to the computer, and test their display prior to class.  The projector can then be put on standby mode so that it can be quickly activated when you are ready to deploy the question.  Otherwise, you will spend several uncomfortable minutes after pausing your lecture getting the technology set up, and this can disrupt the momentum you were carrying into the activity.

Classroom Response Systems

There are a variety of ways of observing the votes of the students.  For small to medium size classes (under 60) you can simply ask the students to raise their hand as you read out the options, ``How many of you think the answer is A? B? ..." This disadvantages of this method are its sequential nature and publicity.  Since students can observe the votes of their peers and the votes are called in sequence, it is possible that student opinions will be influenced by their observation of the voting of their peers.  The technique works best when the students have an individual option for the first vote which is changed through reasoned debate with their classmates, and not changed just by a desire to be part of the majority. 

Flash Cards

Another method that allows the students to cast their vote simultaneously is to use flash cards.  Most of the questions have answers indexed by options A through D.  If you distribute to each student four index cards labeled A through D, then the students can cast their vote by holding up the appropriate card.  In this manner, the vote is simultaneous. In a pinch you could associate A through D with 1 through 4 and ask the students to hold up their hand showing the number of fingers for their vote.

If the cards are different colors, one color for A, one color for B, etc., then the distribution of responses is very easy to gauge from the front of the room.  The hope is to see a dappled mix of color on the first vote and a unity of color on the second vote.  You can also tell when the responses cluster.  For example, one half of the room may have one opinion and the other half of the room another.  In that case, it is advisable to ask the students to temporarily move in order to ensure the debate is rich and changes of opinion are then more likely to take place.  If you are interested in using flash cards as a response system, please make a request for the supplies from the department office.  The supplies are inexpensive and the department may be able to foot the bill depending on budget.  We recommend that you order enough cards for your typical roster size plus ten extra.

It is a good idea to to distribute the cards to the students at the beginning of class and collect them again at the end.  It is easy for the students to lose or forget some or all of the cards on any given day, which compromises their ability to participate in the questions.  Combating this tendency with course policies can indirectly degrade their participation. 

Clicker Systems

For large lecture classes, where distributing flash cards or even counting hands is logistically difficult, you can use a clicker system.  Cal Poly Pomona adopted the iClicker system.  More information about the system is available through the Faculty Center and I&IT.  The students are required to purchase an iClicker and bring it to class each day and keep it supplied with batteries.  Students vote their answers by clicking the appropriate button A through E on the iClicker.  The base station receives the votes when you activate it and then displays the statistical distribution of responses to you.  Each iClicker has a unique ID and if you record those ID's at the start of the quarter, the base station can actually export a spreadsheet of responses indexed by student. Some instructors use this to award credit for participation which is difficult to monitor in large classes.  Many of the students are required to purchase iClickers for introductory courses in physics, chemistry, and biology, so it is likely that many students in Calculus already own one.  The cost per unit is about $25 to each student.

Deploying a Question

When deploying a question, it can be hard to tell how long to wait before calling the initial vote or stopping the debate to call another one.  Here is a pacing method which is easy to use:

  1. Display the question.
  2. Walk slowly to the back of the room (adding time)
  3. Read the question and answers to yourself, word-for-word and symbol-for-symbol, as the students will.
  4. Decide on an answer to the question
  5. Walk slowly back to the front of the room (adding time).
  6. Call for the students to vote.  (Some instructors even say ``Let's vote in 5...4...3...2...1" in order to ensure simultaneity of responses).

After the initial vote, instruct them to turn to a partner and discuss their answers.  (Some instructors tell the students to explain to their partner why they are right and the other is wrong in order to encourage debate).   It is important to give them a definite period of time for this.  One to two minutes is usually sufficient.  Until the students get used to the ConcepTest process, the discussion may be slow to start.  Instructing them that they have exactly 1 minute for discussion gets them going.  When calling for the second vote, some instructors like to use language like, ``Okay, let's see if opinions have changed. What do you think is the answer now?"  This emphasizes that what you as the instructor are looking for is their ideas and evidence of their thinking and that this activity is designed to encourage their learning.