TITLE: CAT #24 “Application Cards”
Teacher:
M. Toran
Context:
The topic I based it on was surface area to volume ratio (SA:V), an important concept in Biology which they will see again and again in different units
Background:
The lessons are mainly lecture-based and sometimes feel like a guessing game where students have to complete the teacher’s sentences. . I was observing the lesson when the teacher went over surface are to volume ratio and they had talked about it in several lessons previously, they had also done a practical around the concept, so I knew they had covered it.
Task:
I modified CAT 24 for this class because the teacher warned me that I would probably only get a yes or no answer from them if any, so I tried to make the assessment more approachable for the lower ability student. Instead of making it completely free-response, I asked them 3 questions, two of which were multiple choice and one open-response item. I wanted to have at least one question they could all answer and gradually increase the level of difficulty so that the higher ability students could also show what they knew (Figure 1 shows the exact CAT questions).

1. Out of these three, solid, 3D shapes, which has the biggest surface area? ____
Which has the biggest volume? ____
Which has the biggest surface area to volume ratio? ____
2. Which of these animals has the biggest surface area to volume ratio?
1Giraffe 1Elephant 1Horse 1Hamster 1Don’t know
3. How is the job of the mitochondria improved by having an inner membrane with many folds?
Results:
Most of them did not understand the concept of surface area to volume ratio or they did not know how to apply it. I did a quick tally of the answers and found that only about a third of the class (4/15 students) identified the shape with the greatest surface area correctly (A), about two thirds (9/15 students) identified the greatest volume (B) and only one third (5/15) the largest SA:V (A). The students seemed the most confident with the idea of volume (probably because they have seen it more often in Math and it’s a more common unit of measurement in general, everyday use), although it was still only 60% of the class that got that question right.
Only 3/15 students (20% of the class) answered the second question correctly (the giraffe being the animal with the greatest SA:V). Around half of the class (7/15 students) thought the elephant had the greatest surface area to volume ratio. I can see why they would think this, because the ears and the trunk do add a lot of surface area to the animal. However, when probed further, they gave the fact that the elephant is bigger than the giraffe as the reason why they picked this answer, which also supports the fact that most of them don’t understand how to apply the concept of SA:V
Only one student in the class answered all the questions correctly
Closing the Loop:
I simply told them that their responses indicated that there was a general lack of understanding of surface area and SA:V and because it is an important concept in Biology we would spend some time going over it. I went over surface area, volume and SA:V using the ball and worm as visual aids.
Reflection:
Overall I felt the assessment went as I had planned. The assessment was somewhat limiting because I had to adapt it given the responses I was told to expect from this group of students. One way I would modify this particular CAT about SA:V I used in the future is by having the students write their definition of surface area, volume and surface area to volume ratio after their multiple choice answers for Question 1. One thing I was reminded of through this CAT, as I mentioned in the Analysis section is the importance of using a wide variety of methods to teach a difficult concept
Source:
Angelo, T.A. & Cross, P.K. (1993). Classroom Assessment Techniques (2nd ed.). San Francisco: Jossey-Bass.
Acknowledgement: The author completed this assessment while a student at Montana State University
Example Presentation: