Dig Deeper!
Try Oral Assessments
(AMATYC 2013)
Seth Daugherty, STLCC Forest Park: sdaugherty@stlcc.edu
______________________________________________________________________
MOTIVATION
O “I know this stuff, but I’m not a good test-taker.” An oral
exam or presentation gives them an opportunity to ‘prove
it’.
O Written exams test recollection of facts, rule-following,
imitative reasoning [D’arcy, 4]. Are they following rules
blindly, or have they really learned something?
O Oral exams allow us to better determine what students
understand and where their misconceptions lie…we will
know what concepts need to be explained better
individually or for the whole class [Nelson, 50].
O Students explaining their thinking and defending their
positions with each other and/or with the instructor can
enable them to apply what they have learned more
‘flexibly’ [Nelson, 58].
O Many European nations use oral assessments as a major
component of their mathematics courses [Iannone &
Simpson, 179].
O Providing a verbal explanation of work…could be an
essential work skill.
OPTIONS
O For Starters:
O Try adding an oral component to one of your exams
(75% written exam/25% oral exam).
O All In?
O Try the Collaborative Oral Take Home Exam (COTHE)
HOW IT WORKS (COTHE)
O
O
O
O
O
O
O
O
O
Test has 4 or 5 problems, not typical ‘test questions’
Test given in groups of 3-4 students
Groups have 3-5 days to work on the test
Each group given a 40-50 minute “interview”
Students take turns presenting one of the problems
Other students in the group are asked follow up questions
Every group member provides input for every problem
All group members receive the same grade
Groups receive instant feedback
FROM THE STUDENT PERSPECTIVE
O PROS:
O Collaborative Learning…on a Test!
O Problems given ahead of time…no surprises*
O Feedback given right away; no waiting for the
exam to be graded and handed back
O CONS:
O Oral Math Exam…doesn’t sound too fun!
O More challenging problems
FROM THE TEACHER’S PERSPECTIVE
O PROS
O More challenging problems on the test truly
assess students’ understanding of the concepts
(not their ability to follow a routine)
O Stronger students are challenged to help the
weaker students understand the concepts
O Weaker students are given the extra help and
extra time they need
O No papers to grade!
O No review sessions
O Teach during the test.
O CONS
O More prep-work than traditional test.
O Takes an extra class day in most cases.
O Students may be concerned with receiving a
group grade.
Survey Results
(Disclaimer: I should have much more data, but I do not always remember to give
the survey!)
O To prepare for this exam, I spent ________ time than I
normally spend preparing for a typical math exam.
O More 33
O Less 10
O Same 4
More Survey Results
O I liked this exam because…
O “We worked as a team; similar to a real job
setting scenario.”
O “I realized that I didn’t know something as good
as I thought I did.”
O “It felt like the collaboration of the group helped
me to understand the material better; also it
O
O
O
O
O
O
O
O
helped to foster some interaction between us
since before we really hadn’t been speaking.”
“Hearing different approaches to the same
problem and deliberating over the most elegant
or logical method gave better insight into the
concepts.”
“Some of us decided that we are going to meet
sometimes to study together for future tests.”
“I was able to explain my understanding to
others and see other’s point of view.”
“Less intense studying.”
“The feeling of not letting down your fellow man
as well as the feeling that your associates are not
going to let you down is rewarding.”
“It gave me a chance to get to know my
classmates; it was fun.”
“I liked the fact this exam was to show that we
knew the information not just be able to do the
problems.”
“I just love this game!!!”
O I did not like this exam because…
O “Not everyone puts in the same effort.”
O “I was nervous about what questions would be
asked.”
O “I don’t like having to rely on others, or have
others rely on me for grades.”
O “Because giving speeches in front of people
makes me uncomfortable to the point that I
sometimes blackout.”
O “It can be frustrating having your grade partially
depend on other people’s knowledge.”
O “Its harder for me to answer questions when
they are not written down.”
O “Didn’t have to learn the material as well.”
O “Not a fan of working in groups, but I think that
is a personal issue.”
O “My answers could reflect negatively on my
peers.”
O “We got into a lot of arguments.”
YOU CAN ALSO TRY…
O Oral Component to Written Exam
O Written Exam 75 points/ Oral 25 points, for
example
O Give students ‘bank’ of 6-8 potential oral exam
questions.
O Students sign up for interview time.
O Student draws a card 1-8 to determine which
problem they will present.
O Student presents/explains their solution and
answers follow up questions.
Example of COTHE for a Calculus III class:
Collaborative Oral Take-Home Exam (Chapter 14)
The following exam consists of five problems, each problem worth up to 20 points. On test day,
your group will be scheduled for a 50 minute “interview”. Each person in your group will
present one of the five problems (if your group has fewer than five students, one or two people
will have to do two problems). You may use your notes. During the presentation of each
problem, three follow-up questions pertaining to the problem will be asked of other members
of your group. The correct solution for each problem is worth 5 points. Your group’s ability to
answer each of the three follow up questions is also worth 5 points, for a total of 20 points per
problem.
Scoring breakdown: Problem 1 solution
- 5 points
Question 1
- 5 points
Question 2
- 5 points
Question 3
- 5 points
Problem 1 Total:
20 points
Exam Total = 20 points X 5 problems = 100 points
In order to do well on this exam you must make sure that you have correctly solved all five
problems, and you must make sure that you (and all other members of your group) understand
well enough to answer any questions about each problem. All members of the group will
receive the same score.
Here are the problems.
1)
For r(𝑡) = (5𝑡) 𝐢 + (cos(𝜋𝑡)) 𝐣 + (sin(𝜋𝑡)) 𝐤, find 𝐓(1) × 𝐍(1).
2)
The position of a particle moving through space is given by:
1
r(𝑡) = 𝑡𝐢 + 𝑡 2 𝐣 + 2 𝑡 2 𝐤 , where distance is given in centimeters and time in seconds.
Find the following:
a) The speed function for the particle, and the particle’s speed at location (4, 16, 8).
b) The curvature function for the particle, and the curvature of the particle’s path at
location (4, 16, 8).
c) The point on the particle’s path with maximum curvature.
3)
The outer edge of a spiral staircase is in the shape of a helix of radius 2 meters. The
staircase has a height of 2 meters and is three-fourths of one complete revolution from
bottom to top.
Find a vector-valued function for the helix.
If a beetle travels up along the outer edge of the staircase to the top, how far does the
beetle travel?
4)
A projectile is fired from ground level at an angle of elevation of 30 degrees. Find the
range of the projectile if the initial velocity is 75 feet per second.
Set up an integral to determine the actual distance traveled by the projectile from the
time it is fired to the time it hits the ground. Use Mathematica to approximate the
distance.
5)
Stanley B. Manley is attempting to break the world record in the shot put. The current
WR is 23.12 meters. If Stanley throws the shot at an angle of 45 degrees to the
horizontal, and it leaves his hand 2 meters above the ground, with what initial speed
must Stanley throw the shot in order to match the world record?
Grading Rubric for Collaborative Oral Exam (Chapter 14)
Group Members:
Problem One:
Problem Two:
Solution
________ /5 points
Question 1
________ /5 points
Question 2
________ /5 points
Question 3
________ / 5 points
Solution
________ /5 points
Question 1
________ /5 points
Question 2
________ /5 points
Question 3
________ / 5 points
Problem Three:
Problem Four:
Problem Five:
GROUP SCORE:
Solution
________ /5 points
Question 1
________ /5 points
Question 2
________ /5 points
Question 3
________ / 5 points
Solution
________ /5 points
Question 1
________ /5 points
Question 2
________ /5 points
Question 3
________ / 5 points
Solution
________ /5 points
Question 1
________ /5 points
Question 2
________ /5 points
Question 3
________ / 5 points
EXAMPLE of ORAL Final Exam component for a Calculus class:
MTH 210 Final Exam, Spring 2013
Part One: Written exam, 90 points. Wednesday May 8 from 12:00 – 1:50.
Part Two: Oral, 10 points. By appointment.
For the Oral Portion of the exam, you will need to do the following:
1) There is a sign-up sheet on the wall next to my office door (C-322). You need to sign up for a 20minute time slot ASAP (time slots are available on a first-come, first serve basis).
2) Work on the six problems found on the back of this sheet. You will be presenting your solution
to one of these problems when you arrive for your oral exam (but you will not know which one
until you arrive for your appointment). So, you should be well-prepared to present any of the 6
problems!
3) The first thing you will do when you come to my office is draw a card from a set numbered 1-6;
the card you draw will correspond to the problem I will ask you to present. You will present
your solution on the white board in my office, without notes if possible. Your solution is worth 4
points. If you require your notes to solve the problem, points will be deducted.
4) You will then be asked three follow-up questions pertaining to the problem, each worth 2
points. A correct answer to a follow-up will get you 2 points, a partially right answer will get you
1 point, and an incorrect answer will get you 0 points. In order to be prepared to answer the
follow-up questions, you need to be sure you really understand how the problem works (once
you have the solution worked out, ask yourself questions like ‘Why?’ or ‘What If?’).
Your score on the Oral Portion of the exam will be calculated as follows:
Solution (0-4 points) + Follow-Up 1 (0-2 points) + Follow-Up 2 (0-2 points) + Follow-Up 3 (0-2 points),
for a possible total of 10 points.
Possible Oral Exam problems:
1) Find a polynomial function 𝑓(𝑥) that satisfies all of the following:
a. Concave up on (−∞, 0) and Concave down on (0, ∞).
b. Decreasing on (−∞, −2) ∪ (2, ∞) and Increasing on (-2,2).
c. 𝑓(0) = 10
𝑥
2) Find the location of any inflection points for 𝐴(𝑥) = ∫3
𝑡
𝑡 2 +1
dt. (x-
coordinates only).
3) Use the Shell Method to find the volume of the solid obtained by
revolving the region between 𝑦 = 𝑥 2 and 𝑦 = 𝑚𝑥 about the 𝑥-axis.
4) Use the Washer Method to find the volume of the solid obtained by
revolving the region between 𝑦 = 𝑥 2 and 𝑦 = 𝑚𝑥 about the 𝑥-axis.
5) A car traveling 84 ft/s begins to decelerate at a constant rate of 14 ft/s 2 .
After how many seconds does the car come to a stop and how far will the
car have traveled before stopping?
6) The base x of a right triangle increases at a rate of 5 cm/s, while the
height remains constant at h = 20 cm. How fast is the angle Ө changing
when x = 20 cm? (see figure)
20 cm
Ө
x cm
FOR YOUR REFERENCE:
O Crannell, Annalisa. “Collaborative Oral Take- Home Exams”,
Assessment Practices in Mathematics, MAA Notes 49 (1999) 143–
145.
O D’Arcy, A. “Look who’s talking – incorporating oral presentations
into mathematics”, Conference Proceedings of ICME 11 Conference,
http://tsg.icme11.org/document/get/549
O Iannone, P. & Simpson, A. “Oral assessment in mathematics:
implementation and outcomes”, Teaching Mathematics and Its
Applications, 31, (2012) 179-190.
O Nelson, M. “Oral assessments: improving retention, grades, and
understanding”, PRIMUS, 21 (2011) 47-61.
Questions? sdaugherty@stlcc.edu