Presentation: "Formative, Summative, and Cooperative Clicker Instruction in Astronomy" (Cosmos in the Classroom 2007)

Workshop presented at the Astronomy Society of the Pacific Cosmos in the Classroom National Symposium on Teaching Astronomy for Non-Science Majors, August 5, 2007, 2:00-3:00 PM, Session H3 in Hahn 108, Pomona College, Claremont, CA.


Experience using electronic response pads ("clickers") in a classroom setting as students would, and also see first-hand how different reward structures stimulate collaborative interaction between students.

Tips and tricks for successful collaborative review sessions will be discussed, along with preliminary education research results, and a question/answer session.

By the way, hopefully the student depicted above is not a common occurrence in your classroom; but student inattentiveness and disengagement are exactly what clickers can address.


The Classroom Performance System (CPS) radio frequency (RF) pads used in this workshop have been provided by eInstruction.com. Each clicker has a unique number. By selecting your response and pressing enter, you should see your clicker number light up on the response grid projected onscreen. You can always change your response as time allows. The CPS Chalkboard is a wireless trackpad and pen that is optional.


Formative questions come at the start of a learning cycle, and get students engaged with (new) material. Students are rewarded for clicking in, regardless if whether their response is correct or incorrect; obviously, they cannot receive credit if they are inattentive or absent.

Example questions:

F1. Why are you interested in this clicker workshop (H3)?

1. Never used clickers before; would like to learn about them.
   
2. Already use clickers; would like to learn more.
   
3. Every other workshop at this time is too crowded.
   
4. Selected this workshop at random.
   

F2. Which one of the following choices best describes the glowing colors of light emitted by a "blackbody" (such as a charcoal briquette glowing in the dark), as it is gradually heated up from a warm temperature to a very hot temperature?

1. Dark gray, medium gray, light gray, white.
   
2. Red, blue, yellow, white, violet.
   
3. Red, orange, yellow, white, blue.
   
4. Blue, green, yellow, orange, red.
   

F3. Consider a 1.0 M_Sun giant and a 4.0 M_Sun main sequence star in a close pair ("mass-exchanging") binary star system. Which star is older?

1. The 1.0 M_Sun giant.
   
2. The 4.0 M_Sun main sequence star.
   
3. Both stars have the same age.
   
4. (The ages of these stars cannot be determined, without knowing how much mass has been exchanged between them.)

These questions are meant to survey student opinions, preconceptions, pre-reading comprehension, or bridge new material with previously discussed concepts.


In contrast, summative questions come in the middle or near the end of a learning cycle, and assess student understanding on their consolidation of the material. Students are still rewarded for clicking in, regardless if whether their response is correct or incorrect. A summative question can be asked again to form a "think-pair-share," after students see their initial responses, and attempt to discuss amongst themselves to reach a (correct) consensus.

Example question (results from this question as a "think-pair-share" are discussed in the previous post: Astronomy clicker question: the Stefan-Boltzmann law):

S1. Why is a white dwarf star known to be smaller than a main-sequence star that has the same white-hot color?

1. It is less luminous than the main-sequence star.
   
2. It is more luminous than the main-sequence star.
   
3. It is cooler than the main-sequence star.
   
4. It is hotter than the main-sequence star.

Collaborative questions are asked as a set in a "review session" at the end of the class just before an quiz or a midterm. In contrast to student-student interactions that may occur during formative and summative clicker questions, collaborative questions are designed such that the entire class must interact and reach a consensus, due to the drastically different reward structure. Students are still rewarded for responding as before, regardless if their response is correct or not, but if the cumulative class score for the entire review session is 80% or higher, then all participation points are doubled for that review session.

Example questions, for a sample review session:

C1. Which one of following statements best explains why white dwarfs are known to be smaller in size than red dwarfs?

1. They have the same temperature as, but are more luminous than red dwarfs.
   
2. They have the same temperature as, but are less luminous than red dwarfs.
   
3. They have the same luminosity as, but are hotter than red dwarfs.
   
4. They have the same luminosity as, but are cooler than red dwarfs.
   
5. (None of the above choices (A)-(D), as white dwarfs are actually larger in size than red dwarfs.)
   

C2. Which one of the following statements best describes how the blackbody (continuous) spectrum of a solid object would change as it is gradually cooled down from a very hot temperature to a warm temperature? On this intensity versus wavelength graph, spectrum W and spectrum X have their peaks at the same wavelength of 480 nm; spectrum Y and spectrum Z have their peaks at the same wavelength of 1,070 nm.

1. Spectrum W will gradually become spectrum X.
   
2. Spectrum W will gradually become spectrum Y.
   
3. Spectrum W will gradually become spectrum Z.
   
4. Spectrum Y will gradually become spectrum X.
   
5. Spectrum Y will gradually become spectrum Z.
   

C3. Which one of following sets of parameters best describes the minimum information required to determine the radius of a star?

1. The distance from the Earth to the star, and its apparent magnitude.
   
2. The surface temperature of the star, and its parallax angle.
   
3. The surface temperature of the star, and its luminosity.
   
4. The parallax angle of the star, and its apparent magnitude.
   
5. The parallax angle of the star, and its luminosity.
   

C4. Which one of the following statements best describes the relationship between a main sequence star and a supergiant that have the same luminosity?

1. The main sequence star is cooler and smaller than the supergiant.
   
2. The main sequence star is cooler and larger than the supergiant.
   
3. The main sequence star is hotter and smaller than the supergiant.
   
4. The main sequence star is hotter and larger than the supergiant.
   
5. (None of the above choices (A)-(D), as it is not possible for a main sequence star to have the same luminosity as a supergiant.)
   

Refer to the table below in answering the following question (C5).

	Surface temperature, in Kelvin	M absolute magnitude	m apparent magnitude
Shaula	25,000 K	–5.0	+1.6
π Puppis	4,300 K	–5.0	+2.7
β Muscae	25,000 K	–1.8	+3.0
Minkar	4,300 K	–1.8	+3.0

C5. Which one of the following choices best explains which star is the largest in size, according to the Stefan-Boltzmann law?

1. Shaula.
   
2. π Puppis.
   
3. β Muscae.
   
4. Minkar.
   
5. (Not enough information is given to determine which of the above stars (A)-(D) is the largest in size.)
   

Successful collaborative clicker questions should keep the class "in play" throughout the review session, such that every question until the last counts towards reaching the 80% threshold. Students will not be able to attain this by splitting their answers; they must reach a consensus as much as possible. You can give gentle hints, or remove a choice when class discussion has gone completely astray.

Throughout a review session, encourage students to talk and listen, and even shout and demand accountability from each other--that is what these collaborative questions are designed to do! Emphasize "high-energy" interaction; by the end of the semester students engage in enthusiastic class-wide debates, resort to shouting out their answers, and even try to steer the class by pointing on the overhead projector screen with laser pointers.

If it is not mathematically possible for the class to reach the 80% threshold even with the last question being 100% (this corresponds to a cumulative score of less than 75% before the last question is asked), offer the class a "deal" where if students respond correctly and unanimously to the last question, then they will awarded the doubling of their participation credit (no matter their actual cumulative score), in order to keep the students actively engaged to the very end.


A preliminary study has been done in Fall 2005, on a small number of students (N = 36), supported by an @ONE Scholar Fellowship, and published in the Astronomy Education Review vol. 5, no. 2, p. 5. As opposed to formative and summative questions, collaborative questions in a review session had a higher average rate of correct responses, and a higher rate of self-reported cooperation, where the number of students who took others' responses into consideration while responding increased from 13 to a nearly unanimous 35 out of 36 students.

Due to the small population of this study, future research will look at several years of accumulated data, and investigate whether the inclination to individually answer or cooperatively respond to formative and summative questions is correlated with previous background in science, attitudes towards astronomy, and/or personal motivation for acting alone or interacting with others.

[Acknowledgements to the workshop participants for their suggestions in improving the wording of the clicker questions!]

Questions posed by workshop participants are answered in a subsequent post: Formative, Summative, and Cooperative Clicker Instruction in Astronomy (Q & A), while further discussion on the results of research on this topic are discussed in the subsequent post: Formative, Summative, and Cooperative Clicker Instruction in Astronomy (research results).