Diagnostics and Diagnosis
Douglas Quinney
University of Keele
A level results.
1992: 35% got A &B
2007: 35% didn’t get A&B
A level questions
Diagnostic Results
Diagnostic results at Keele
2009-2010 Reorganization
2009 6 modules 10 credits
• MAT10014 Math Methods -10 credits
• MAT10030 Fundamental Techniques - 5
credits
2010 4 module 15 credits
• MAT10025 Math Methods -15 credits
2009
2010
100 students
180 students
System Requirements
• Variety of QA Questions correctly
checked
• Additional resources
• Direct text Links
• Ease of generation of assignments
• Grade book – linked to VLE
• System support, extensibility, portability
WileyPlus.
WileyPlus.
WileyPlus.
WileyPlus.
WileyPlus.
WileyPlus.
WileyPlus – Student Results.
P1.1
P1.2
T1
P2.1
P2.2
T2.1
T2.2
P4.1
T4
P5.1
T5
70%
50%
90%
10%
80%
70%
90%
95%
15%
95%
5%
95%
60%
60%
90%
10%
85%
60%
95%
90%
5%
90%
<5%
90%
WileyPlus - Evaluation.
Hauk et al (2005), Zerr (2007)
Lenz (2010), La Rose (2010)
 Diagnostic Test Results
 Comparison within 2010
 Comparison with 2009
 Examination performance
 Follow students through 2 years
WileyPlus - Results.
• Greater engagement
• Better retention
• Reduced marking loads
WileyPlus- Student feedback
 “Great because I can keep trying until I get it right.”
 “Opportunity to practice before I try the assessed work is brill.”
 “Before I only had one chance to get it right”
 “Getting immediate feedback is the best part – I don’t have to
wait 2 weeks”
 “OK, its ok for basic stuff but how will it help me prove
theorems?”
WileyPlus - Who is it for?
–Administration?
–Academic leaders (Deans)?
–Academics?
–Students?
Part II - Diagnosis
•
•
•
•
Do we understand our students?
Do our students understand us?
Are we asking the right questions?
Do students know what questions to ask?
Simple experiment
1. Tabulate the function
and use the result to plot this function. Find the slope of the curve at x=0.5 and comment on
the result.
2. Find two positive real numbers that have product 100 and minimum sum.
3. Classify all the turning points of the function
where A, B and C are all positive.
4. A cylindrical can has radius r and height h. If the can is to hold 250 cubic units and has
minimum surface area, show that the height is twice the radius.
5. The cost of keeping a car is the sum of insurance and running costs. Daily insurance cost is
inversely proportional to the age of the car. Daily running cost is the sum of a fixed cost,
including tax, and a maintenance cost that is proportional to the age of the car. For what
age of car is the total daily cost smallest?
Simple experiment – Q1
1. Tabulate the function
and use the result to plot this function. Find the slope of the curve at x=0.5 and
comment on the result.
Therefore x=0.5 is a
turning point of the
function f(x).
f’(0.5)=0 curve has no gradient
Gradient=0  does not exist
Simple experiment – Q2
2. Find two positive real numbers that have product 100
and minimum sum.
Simple experiment – Q3
3. Classify all the turning points of the function
where A, B and C are all positive.
Simple experiment – Q4
4. A cylindrical can has radius r and height h. If the can
is to hold 250 cubic units and has minimum surface
area, show that the height is twice the radius?
Simple experiment – Q5
5. The cost of keeping a car is the sum of insurance and running
costs. Daily insurance cost is inversely proportional to the age of
the car. Daily running cost is the sum of a fixed cost, including
tax, and a maintenance cost that is proportional to the age of the
car. For what age of car is the total daily cost smallest?
Results
Students
Q1
Q2
Q3
Q4
Q5
Total
17.0
9.4
9.0
7.2
6.2
48.8
Q1
Q2
Q3
Q4
Q5
Total
Staff
18.9
16.1
18.1
14.0
10.1
77.3
SD
3.5
4.2
3.5
5.1
3.6
Q1
Q2
Q3
Q4
Q5
Total
BAMC
12.8
9.84
12.7
8.2
8.2
52
SD
3.4
3.5
3.1
3.5
3.6
Student Attitude Survey
1. At school /college we were
encouraged to work in groups.
2. At school /college we were
encouraged to discuss mathematical
ideas. .
3. I had opportunities to discuss
mathematics outside the classroom.
Student Attitude Survey
7. I found the questions easy
8. I was comfortable with the questions
and the mathematics involved.
9. The level of the questions is
appropriate for students starting a
Mathematics Degree.
Results
Quinney D.A: MSOR Connections Vol 8 No 3 August – October 2008
Comparison by A level grade
Comparison by FM Grade
Comparison by A level board
1
2
3
Using formula
from Q2
Principle of Blinded Reflectiveness
buffalo buffalo buffalo buffalo buffalo
Buffalo buffalo buffalo, buffalo Buffalo buffalo
MSOR Year 1 conclusions
1. Group activities
2. Conceptual sophistication.
MSOR Year 2 – Group Work
MSOR Year 2 – Conceptual
Conclusions – Good Practice
Know your students
Practice & Rapid Feedback
Discussion groups
Group working