# Conceptual Understanding Procedure

### What is a CUP?

A Conceptual Understanding Procedure, or CUP, is a teaching procedure designed to assist students to develop or consolidate their understanding of difficult concepts. The problems provided have been developed in a physics context but the procedure could be equally adapted for use in other areas of study such as chemistry, mathematics or biology.

They are constructivist in approach, i.e. they are based on the belief that students construct their own understanding of concepts by expanding or modifying their existing views. The procedure also reinforces the value of collaborative learning as it encourages students to share ideas and to reflect on and analysis the ideas of others. This procedure promotes students to play an active role in their own learning.

CUP problems are set in the 'real-world' rather than idealised or contrived situations so they encourage the learner to explore authentic contexts. For example, in the CUP's study of motion, students are expected to qualitatively consider; the friction between objects moving relative to one another, air resistance, and energy losses to the surroundings. They should not expect to assume that they are working in an idealised world where friction should be considered to be negligible. CUPs were developed in 1996 by Pam Mulhall and Brian McKittrick from the Faculty of Education, and David Mills and Susan Feteris of the Department of Physics, (now School of Physics) at Monash University.

### Student Worksheets - Examples

Master copies of both A4 and A3 problem sheets are provided in Adobe Acrobat (.pdf) format. (Acrobat Reader is available free on the Web.) These are suitable for senior high school, college or first year university students and may be copied and distributed for educational purposes without changes.

Title Worksheet Masters Concepts targeted
1. Driving to Hilary's A4 sheet, A3 sheet Displacement, velocity and acceleration in 1-D.
2. Throwing a hockey ball A4 sheet, A3 sheet Velocity and acceleration during vertical flight.
3. Hitting a golf ball A4 sheet, A3 sheet Action/reaction pairs (Newton's third law). Dependence of motion on net force.
4. Dropping a golf ball and a foam ball A4 sheet, A3 sheet Forces acting on falling objects.
5. Forces on a can of peaches A4 sheet, A3 sheet Forces on an object coming to rest on a surface.
6. Swinging the billy can A4 sheet, A3 sheet Forces on an object moving in a vertical circular path.
7. Rudolph's trouble with Newton's third law A4 sheet, A3 sheet The motion of an object depends on the net force on the object.
8. Hot stuff A4 sheet, A3 sheet Heating and temperature change.
9. What is the current? A4 sheet, A3 sheet The electrical current in basic series and parallel circuits.
10. What is the reading on the voltmeter? A4 sheet, A3 sheet The potential difference (voltage) between points in basic series and parallel circuits.
11. Energy of a soccer ball in flight A4 sheet, A3 sheet Conservation of energy.
12. Momentum and traffic accidents A4 sheet, A3 sheet Conservation of momentum.
13. Where did the light go? A4 sheet, A3 sheet Reflection and refraction of light at an interface

### What does a CUP consist of?

The procedure involves students exploring a qualitative problem (master sheets provided) requiring an answer in a diagrammatic form and has three distinct stages:

1. Individual student analysis
Each student thinks privately about their personal response to the question using diagrams drawn onto an individual A4 supplied sheet

2. Peer analysis in triplets
In groups of three, students discuss their responses and try to reach group consensus. The agreed group response is than annotated onto an enlarged A3 version, of the question supplied on the original A4 sheet.

3. Whole class analysis
The A3 sheets from each group are then collected and displayed so the whole class can view them. The teacher facilitates a whole class discussion in which groups explain, defend or modify their responses. The aim being to reach a whole class consensus as to an acceptable answer to the problem.

### How do I use a CUP with my class?

This guide will explain the procedure in detail describing how to best set up the room, select students for the triplets and to approach the class discussion in a way that encourages your students to do the thinking.

### FAQs - Frequently Asked Questions

1. What is the most demanding part of using a CUP?
2. What if my students don’t reach consensus by the end of the session?
3. What if my class reaches consensus but they’re wrong?
4. How do I overcome the temptation to just tell them the ‘right’ answer?
5. Won’t my students find it embarrassing having to explain their group’s response to the whole class?
6. Why not skip the initial working alone phase and just start with the small group discussions?
7. Won’t it take too long for students to learn this way?
8. Why do you suggest three as the optimum group size?

1) What is the most demanding part of using a CUP?

Most teachers find the third stage, the interpretive discussion, to be the most challenging to conduct. You need to facilitate the class discussion of the group understandings shown on the A3 sheets rather than simply telling the class the correct scientific view. The potential for students to develop a strong conceptual understanding of the ideas is more likely to be realised when they have had a chance to grapple with the range of ideas advanced in the class. This requires the teacher to relinquish familiar techniques of leading students straight to the accepted scientific view or confirming correct ideas by an agreeing nod or other non verbal body language. Look to delay your judgement of the ideas being advanced to promote a rich discussion.

Another challenging stage can occur when you put up all the A3 sheets and wonder “What I am going to do with such a wide range of ideas?” Two possible suggestions:

• A valuable preparation before commencing the CUP session, is to spend some time thinking through the range of conceptions that your students are likely to provide.
• As you move around the room during the small-group discussions, observe the similarities and differences the groups are recording on their A3 sheets and begin to prepare your response to unpacking the ideas.

2) What if my students don’t reach consensus by the end of the session?

In such a case, students will probably leave the class dissatisfied unless you provide some reassurance that you will return to the problem next class. Summarise the stage reached, e.g. “We haven’t reached agreement yet and that’s OK. You’re at the stage where four groups think A … and the other groups think B … Think a bit more about these options before our next class. We will complete the discussion then.”

3) What if my class reaches consensus but they’re wrong?

As the designers of CUPs, we are yet to hear of a whole class reaching an incorrect consensus, although of course it may be possible. In that case, rather than just telling the class that they are wrong and giving them the accepted scientific view, you may need to devise other strategies, e.g.

• present an idea or analysis, with which they are likely to agree but which challenges the incorrect class view currently reached,
• show a relatively straightforward demonstration which might produce a cognitive challenge to the view that may advance their questioning,
• do some direct teaching that addresses, in a different situation or context, the concept that poses a stumbling block.
The time students have already invested in thinking about the CUP exercise means they are likely to be highly receptive to approaches that promote alternative ways of engaging with the concepts involved.

4) How do I overcome the temptation to just tell them the ‘right’ answer?

Some examples of non threatening approaches you could use to help the groups to continue to think about their present understanding of the situation:

• “Karen's group said that the graph here should be horizontal, but Daniel's group have drawn it sloping down. Daniel could you tell us your groups reasoning for this?”
• “Hongming your group’s first ammeter pointer is further to the right that your second pointer. Could one of you please explain why you chose to draw it this way?”
• “Four groups have the arrow pointing downwards, but the other groups have it pointing upwards. Can any group tell us why they believe it should be pointing downwards?”
• “Vinh your group thinks the other groups are all wrong? Could you explain Vinh why your group thinks the other have it incorrect?”
• “Claire, you just said you’ve changed your mind. Could you tell us why?”

5) Won’t my students find it embarrassing having to explain their group’s response to the whole class?

Some of the more timid students may struggle. Teachers using CUPs report this occurs much less than they expected, probably due to the students supporting the ideas of their group, and not having direct ownership of the ideas. However, it is important to encourage an atmosphere of trust where all initial contributions are considered equally important and respected. The teacher needs to lead by example here.

6) Why not skip the initial working alone phase and just start with the small group discussions?

It is essential that students have time alone to really consider their understanding of the situation presented so that they can formulate a personal view which can then be presented and tested by argument in the subsequent group discussion.

7) Won’t it take too long for students to learn this way?

While CUPs employ valuable learning procedures that you probably use on other occasions, it is envisaged that CUPs would be used only occasionally, as they may take 40 to 60 minutes to successfully implement. However, teachers using CUPs tend to report that the time is well spent as the students are often highly engaged and frequently achieve greater understanding of the concepts. The vast majority of students find a well managed CUPs exercise challenging, rewarding and most enjoyable.

8) Why do you suggest three as the optimum group size?

Research suggests that three is the optimum size for effective, engaged small-group discussion. Where the class size is not a multiple of three, four is preferable to two. Researchers also found that involvement increases when the group is of mixed ability and for female students to form a triplet or for a triplet to have at least two female students present.

### Feedback - What do teachers and students say about using CUPs?

These quotes from teachers and students were recorded during research into the use of CUPs at senior high schools and first year university level classes (where "T" indicates teachers and "S" students).

• Working alone ( individual phase )

S: Normally when we get asked something most people don’t think about it. They just say “We don’t know” and you just get told by the teacher, but in CUPs you’ve got time to think about it.

T: One of the best parts to the CUP format was that the students had time to sit down individually and sort out what they were thinking before I led them to a discussion, and that allowed real insight.

• Working in small groups (triplet phase)

S: If we were just one big group then I’m sure some people just wouldn’t say anything. With the triplets you had to say something.

• Whole-class interpretive discussion

S: When you were in the whole-class discussion it’s not as intimidating because it’s not just you ... because you have a combined opinion on your A3 sheet.

T: I reckon you get a really good insight into what they’re thinking. … All sorts of kids [contributing] that don’t normally… It’s quite a non-threatening sort of process.

T: Normal class discussion is just one way. You’re directing it whereas this way they’re telling you what they really think.

T: I don’t think it hurts to have a touch of confusion. You often learn best, don’t you, when you realise there’s something not quite right here!

• Engaged active learning by the students

S: Everyone usually got their say about what they thought was right … You had to understand it a bit better to be able to answer questions people asked you.

S: Yeah, you had to actually think in class (laughs)!

S: That’s the hardest I’ve had to think in any subject this year [this was two-thirds through the academic year] and it was great.

S: You get different ideas. … Where as if you just get told it and write it down … you feel “Yeah, sure, whatever.”

T: You actually got to hear what the kids were thinking, whereas in a normal class discussion you leap on the first person that says something right, whereas in this you heard all those misconceptions. I found it really valuable to hear those things that they were thinking that I’d forgotten they would think, because I don’t think like that any more.

T: Seeing them get that passionate about a discussion in physics was good.

• Trusting atmosphere

T: There was a sort of intimacy in the whole-class discussion. All the different [students contributing] … and obviously not being threatened about it, and also enjoying it.

T: The second CUP was easier because they knew there wasn’t going to be that embarrassing feeling of “I’m going to be put on the spot; I’m going to be laughed at.”

• Enabling formative assessment

T: For me the CUPs were very important in a formative sense of trying to … determine where … the greatest needs lie and how … to adjust my classes over the next few weeks to address some of those needs. And … recognising where the shortfalls were in … kids’ understanding of problems.

• Enjoyment

T: I was delighted, absolutely delighted! At recess they were still going, no one moved.

T: At the end of the class they did not want to leave until they had the right answer.

• Challenges for the teacher

T: Not telling them the right answer!

T: Thinking on your feet when you put all the A3 sheets up, “What am I going to do with all this variation?”

T: [From using CUPs] I became very much more aware that normally you’re forcing your agenda on the kids, so you’ve got to try to avoid that, that’s the hardest thing.

### Relevant articles and websites

• Mulhall, P., & McKittrick, B. (2010). Using discussion to improve students’ understanding of electric circuits. Lab Talk, 54(3), 17-22.
• Gunstone, R., McKittrick, B., & Mulhall, P. (1999). Structured cognitive discussions inn senior high school physics: Student and teacher perceptions. Research in Science Education, 29(4), 527-546.
• McKittrick, B., Mulhall, P., & Gunstone, R. (1999). Improving understanding in physics: in effective teaching procedure. Australian Science Teachers' Journal, 45(3), 27-33.
• Mills, D., McKittrick, B., Mulhall, P., & Feteris, S. (1999). CUP: Cooperative learning that works. Physics Education, 34(1), 11-16.iopscience.iop.org/0031-9120/34/1/013/pdf/0031-9120_34_1_013.pdf
• A comprehensive website on ‘alternative conceptions’ with other useful related links at the Australian Institute of Physics (Victoria) Education Committee’s website: www.vicphysics.org/misconceptions.html

### Who to contact about CUPs?

For further informationabout CUPs contact Pam Mulhall at the Faculty of Education, Monash University.