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How to Generate Personalized Tasks and Sample
Solutions for Anonymous Peer Review in Electrical
Engineering using L
A
TEX, PGFPLOTS and CircuiTikZ
Doctoral Student Meeting 2021
IEEE German EMC Chapter
Mathias Magdowski
Chair for Electromagnetic Compatibility, Institute for Medical Engineering
Otto von Guericke University, Magdeburg, Germany
November 9, 2021
License: cb CC BY 4.0 (Attribution, ShareAlike)
Motivation Implementation in L
ATEX Evaluation and Discussion
Organizational Matters
Slides:
yes
Personalized Engineering Tasks in L
ATEX 2
Motivation Implementation in L
ATEX Evaluation and Discussion
Organizational Matters
Slides:
yes
Recording:
no
Personalized Engineering Tasks in L
ATEX 2
Motivation Implementation in L
ATEX Evaluation and Discussion
Organizational Matters
Slides:
yes
Recording:
no
Questions:
with pleasure
Personalized Engineering Tasks in L
ATEX 2
Motivation Implementation in L
ATEX Evaluation and Discussion
Overview
Why all this?
How are the tasks generated in L
A
TEX?
Topic „Charge and Current“
Topic „Nodal Analysis“
What has come out of it?
Personalized Engineering Tasks in L
ATEX 3
Why all this?
Motivation Implementation in L
ATEX Evaluation and Discussion
Traditional Performance Assessments
Source: https://pixabay.com/de/photos/taschenrechner-notizblock-1687962/
Personalized Engineering Tasks in L
ATEX 5
Motivation Implementation in L
ATEX Evaluation and Discussion
Demands in the Working World
Source: https://pixabay.com/de/arbeitsplatz-team-gesch%C3%A4ftstreffen-1245776/
Personalized Engineering Tasks in L
ATEX 6
Motivation Implementation in L
ATEX Evaluation and Discussion
Classical E-Learning Tasks
Personalized Engineering Tasks in L
ATEX 7
Motivation Implementation in L
ATEX Evaluation and Discussion
Free Handwritten Solution
Personalized Engineering Tasks in L
ATEX 8
Motivation Implementation in L
ATEX Evaluation and Discussion
Free Handwritten Solution
Personalized Engineering Tasks in L
ATEX 9
Motivation Implementation in L
ATEX Evaluation and Discussion
Examples of Student Misconceptions
Specification of Fourier coefficients in V and V ◦
:
also see: https://twitter.com/LehrstuhlEMV/status/1257605076308426753
Personalized Engineering Tasks in L
ATEX 10
Motivation Implementation in L
ATEX Evaluation and Discussion
Examples of Student Misconceptions
Complex impedance converted to time function:
€ #ß
= 2.42Mt
8,411J
--
ZAB
=
81751 "
Sin Iwtt 73,95 ) I 8,751 .
ewtt 73,95
-
also see: https://twitter.com/LehrstuhlEMV/status/1264294433027174401
Personalized Engineering Tasks in L
ATEX 11
Motivation Implementation in L
ATEX Evaluation and Discussion
Idea
Personalizable tasks for handwritten solution:
▶ handwritten −→ authentic, low-threshold for formulas, schematics, diagrams,
misconceptions become visible
▶ personalized −→ no plagiarism possible
▶ peer review −→ no correction effort −→ good ready-made personalized
sample solution
▶ via Moodle and e-mail −→ scalable, no „red tape“
Personalized Engineering Tasks in L
ATEX 12
Motivation Implementation in L
ATEX Evaluation and Discussion
Creation and Sending of the Tasks
Registration
MAT-
LAB
LaTeX
Matriculation
No.
PDF
Task
Sample Solution
Folder
Personalized Engineering Tasks in L
ATEX 13
Motivation Implementation in L
ATEX Evaluation and Discussion
Submission and Distribution of the Solutions
ZIP File
MAT-
LAB
Folder
Sample Solution
Form
Personalized Engineering Tasks in L
ATEX 14
Motivation Implementation in L
ATEX Evaluation and Discussion
Mutual Correction and Completion
2 Reviews
Sample Sol.
Folder
ZIP File
Score
List
MAT-
LAB
Sample Solution
Personalized Engineering Tasks in L
ATEX 15
How are the tasks generated in L
A
TEX?
Motivation Implementation in L
ATEX Evaluation and Discussion
1. Task (same for all)
The displayed time curve shows the current i as a function of time t. The charge
Q(t) is searched for the four sections
1. 0 s ≤ t ≤ 1 s,
2. 1 s < t ≤ 2 s,
3. 2 s < t ≤ 3 s and
4. 3 s < t ≤ 4 s.
The initial charge is Q(t = 0) = 0.
Calculate the charge Q(t) for each section as a formula by integrating the current
over time and draw the corresponding time curve.
Personalized Engineering Tasks in L
ATEX 17
Motivation Implementation in L
ATEX Evaluation and Discussion
Diagram (for Matriculation Number 123 456)
1 2 3 4
−4
−3
−2
−1
1
2
3
4
t in s
i(t) in A
Personalized Engineering Tasks in L
ATEX 18
Motivation Implementation in L
ATEX Evaluation and Discussion
Diagram (for Matriculation Number 123 457)
1 2 3 4
−4
−3
−2
−1
1
2
3
4
t in s
i(t) in A
Personalized Engineering Tasks in L
ATEX 19
Motivation Implementation in L
ATEX Evaluation and Discussion
Diagram (for Matriculation Number 123 458)
1 2 3 4
−4
−3
−2
−1
1
2
3
4
t in s
i(t) in A
Personalized Engineering Tasks in L
ATEX 20
Motivation Implementation in L
ATEX Evaluation and Discussion
Diagram (for Matriculation Number 123 459)
1 2 3 4
−4
−3
−2
−1
1
2
3
4
t in s
i(t) in A
Personalized Engineering Tasks in L
ATEX 21
Motivation Implementation in L
ATEX Evaluation and Discussion
Create Randomized PGFPLOTS Diagrams
 documentclass { standalone }
 usepackage { pgfplots , s i u n i t x }
 begin { document }
% Set random number generator to m a t r i c u l a t i o n number
 pgfmathsetseed {123456}
% Current at time 1 s ( in A, can also s t i l l be zero , but should not be )
 pgfmathrandominteger {  stromeinsrandom }{ −4}{4}
% i f current i s zero , set to 1 A
 pgfmathsetmacro {  stromeins } { i f t h e n e l s e (  stromeinsrandom ==0 ,1 , stromeinsrandom ) }
% Current in the period from 1 s to 2 s ( in A, can also be zero )
 pgfmathrandominteger {  stromzwei }{ −4}{4}
% Current in the period from 2 s to 3 s ( in A, can also be zero )
 pgfmathrandominteger {  stromdreirandom }{ −4}{4}
% i f the current i s equal to the value from the previous period , i n v e r t the sign
 pgfmathsetmacro {  stromdrei } { i f t h e n e l s e (  stromzwei == stromdreirandom , − stromdreirandom ,  stromdreirandom ) }
% i f both currents are zero , set new current to 1 A
 pgfmathsetmacro {  stromdrei } { i f t h e n e l s e ( abs (  stromzwei )+abs (  stromdrei )==0 ,1 , stromdrei ) }
% Current in the period from 3 s to 4 s ( in A, can also be zero )
 pgfmathrandominteger {  stromvierrandom }{ −4}{4}
% i f both currents are zero , set new current to 1 A
 pgfmathsetmacro {  stromvier } { i f t h e n e l s e ( abs (  stromzwei )+abs (  stromvierrandom )==0 ,1 , stromvierrandom ) }
% i f both currents are zero , set new current to 1 A
 pgfmathsetmacro {  stromvier } { i f t h e n e l s e ( abs (  stromdrei )+abs (  stromvier )==0 ,1 , stromvier ) }
% i f the current i s equal to the value from the previous period , i n v e r t the sign
 pgfmathsetmacro {  stromvier } { i f t h e n e l s e (  stromdrei == stromvier , − stromvier ,  stromvier ) }
Personalized Engineering Tasks in L
ATEX 22
Motivation Implementation in L
ATEX Evaluation and Discussion
Create Randomized PGFPLOTS Diagrams
 begin { t i k z p i c t u r e }
 begin { axis } [
xlabel ={ $t$ in  s i {  second } } ,
ylabel ={ $i ( t ) $ in  s i {  ampere } } ,
xmin= −0.9 ,xmax=4.9 , ymin= −4.9 ,ymax=4.9 ,
x t i c k ={1 ,2 ,3 ,4} , y t i c k ={ −4 , −3 , −2 , −1 ,1 ,2 ,3 ,4} ,
x t i c k l a b e l s t y l e ={ below r i g h t } ,
y t i c k l a b e l s t y l e ={ below l e f t } ,
axis x l i n e =middle , axis y l i n e =center ,
xmajorgrids , ymajorgrids , ]
 addplot +[mark=none , l i n e width=1pt ] coordinates {
( −0.5 ,0)
(0 ,0)
( 1 ,  stromeins )
( 1 ,  stromzwei )
( 2 ,  stromzwei )
( 2 ,  stromdrei )
( 3 ,  stromdrei )
( 3 ,  stromvier )
( 4 ,  stromvier )
(4 ,0)
( 4 . 5 , 0 ) } ;
 end { axis }
 end { t i k z p i c t u r e }
 end { document }
Personalized Engineering Tasks in L
ATEX 23
Motivation Implementation in L
ATEX Evaluation and Discussion
1. Sample Solution (for Matriculation Number 123 456)
Sectionwise calculation:
0 ≤ t ≤ 1 s: Current in the 1. section (1 point):
i(t) = 1
A
s
· t
Charge in the 1. section (1 point):
Q(t) =
t
Z
0
1
A
s
t′
dt′
+ 0 = 1
A
s
·

t′2
2
t
0
= 0.5
A
s
t2
Charge at the end of the 1. section (1 point):
Q(1 s) = 0.5 A s
Personalized Engineering Tasks in L
ATEX 24
Motivation Implementation in L
ATEX Evaluation and Discussion
1. Sample Solution (for Matriculation Number 123 457)
Sectionwise calculation:
0 ≤ t ≤ 1 s: Current in the 1. section (1 point):
i(t) = −2
A
s
· t
Charge in the 1. section (1 point):
Q(t) =
t
Z
0
−2
A
s
t′
dt′
+ 0 = −2
A
s
·

t′2
2
t
0
= −1
A
s
t2
Charge at the end of the 1. section (1 point):
Q(1 s) = −1 A s
Personalized Engineering Tasks in L
ATEX 25
Motivation Implementation in L
ATEX Evaluation and Discussion
1. Sample Solution (for Matriculation Number 123 458)
Sectionwise calculation:
0 ≤ t ≤ 1 s: Current in the 1. section (1 point):
i(t) = 4
A
s
· t
Charge in the 1. section (1 point):
Q(t) =
t
Z
0
4
A
s
t′
dt′
+ 0 = 4
A
s
·

t′2
2
t
0
= 2
A
s
t2
Charge at the end of the 1. section (1 point):
Q(1 s) = 2 A s
Personalized Engineering Tasks in L
ATEX 26
Motivation Implementation in L
ATEX Evaluation and Discussion
1. Sample Solution (for Matriculation Number 123 459)
Sectionwise calculation:
0 ≤ t ≤ 1 s: Current in the 1. section (1 point):
i(t) = 1
A
s
· t
Charge in the 1. section (1 point):
Q(t) =
t
Z
0
1
A
s
t′
dt′
+ 0 = 1
A
s
·

t′2
2
t
0
= 0.5
A
s
t2
Charge at the end of the 1. section (1 point):
Q(1 s) = 0.5 A s
Personalized Engineering Tasks in L
ATEX 27
Motivation Implementation in L
ATEX Evaluation and Discussion
Algorithmic Generation of the Sample Solutions
% Truncate decimal places f o r an integer number
 pgfmathdeclarefunction { trimzero } { 1 } {  pgfmathparse { i f t h e n e l s e (#1==round (#1) , i n t ( # 1 ) , # 1 ) } }
% Convert current ( in A) to integers
 pgfmathsetmacro {  stromeins } { i n t (  stromeins ) }
% Charge at the end of the 1 st section ( in As)
 pgfmathsetmacro {  ladungeins } { trimzero (  stromeins / 2 ) }
% D i f f e r e n t i a l operator ( small upright d )
newcommand * {  d i f f } {  mathop { }  !  mathrm { d } }
Current in the 1. section (1 point ) :
 begin { equation }
i ( t ) =  SI {  stromeins } {  ampere  per  second }  cdot t
 end { equation }
Charge in the 1. section (1 point ) :
 begin { subequations }  begin { align }
Q( t ) =  i n t  l i m i t s _ 0 ^ t  SI {  stromeins } {  ampere  per  second } t ’  d i f f t ’ + 0  
=  SI {  stromeins } {  ampere  per  second }  cdot  l e f t [  frac { t ’ ^ 2 } { 2 }  r i g h t ] _0^ t  
=  SI {  ladungeins } {  ampere  per  second } t ^2
 end { align }  end { subequations }
Charge at the end of the 1. section (1 point ) :
 begin { equation }
Q(  SI { 1 } {  second } ) =  SI {  ladungeins } {  ampere  second }
 end { equation }
Personalized Engineering Tasks in L
ATEX 28
Motivation Implementation in L
ATEX Evaluation and Discussion
1. Sample Solution (for Matriculation Number 123 456)
Graphical representation:
0 0,5 1 1,5 2 2,5 3 3,5 4
0
2
4
6
Time, t in s
Charge,
Q(t)
in
A
s
Personalized Engineering Tasks in L
ATEX 29
Motivation Implementation in L
ATEX Evaluation and Discussion
1. Sample Solution (for Matriculation Number 123 457)
Graphical representation:
0 0,5 1 1,5 2 2,5 3 3,5 4
−1
−0,8
−0,6
−0,4
−0,2
0
Time, t in s
Charge,
Q(t)
in
A
s
Personalized Engineering Tasks in L
ATEX 30
Motivation Implementation in L
ATEX Evaluation and Discussion
1. Sample Solution (for Matriculation Number 123 458)
Graphical representation:
0 0,5 1 1,5 2 2,5 3 3,5 4
0
1
2
3
Time, t in s
Charge,
Q(t)
in
A
s
Personalized Engineering Tasks in L
ATEX 31
Motivation Implementation in L
ATEX Evaluation and Discussion
1. Sample Solution (for Matriculation Number 123 459)
Graphical representation:
0 0,5 1 1,5 2 2,5 3 3,5 4
−2
0
2
4
Time, t in s
Charge,
Q(t)
in
A
s
Personalized Engineering Tasks in L
ATEX 32
Motivation Implementation in L
ATEX Evaluation and Discussion
Survey
If you are also teaching, can you think of personalised/randomize tasks that
can also be used for your subject?
1. yes, immediately, many
2. yes, some
3. yes, but only after some thought
4. no, not likely
5. nohow, no way
Personalized Engineering Tasks in L
ATEX 33
Motivation Implementation in L
ATEX Evaluation and Discussion
2. Task (same for all)
Nodal analysis shall be used to calculate the three nodal voltages UKn1, UKn2 and
UKn3 between the respective node and the reference node.
a) Draw the three nodal voltages UKn1, UKn2 and UKn3 in the circuit diagram
(3 points).
b) Set up the system of equations to calculate the nodal voltages using nodal
analysis in matrix form (9 points).
c) Insert the values of the components into the system of equations (1 point).
d) Solve the system of equations and thus calculate the three nodal voltages
UKn1, UKn2 and UKn3 (3 points).
Personalized Engineering Tasks in L
ATEX 34
Motivation Implementation in L
ATEX Evaluation and Discussion
Circuit Diagram (for Matriculation Number 123 460)
Iq1
R1
Iq2
R2
Iq3
Iq4
R3
0
1 2
3
Personalized Engineering Tasks in L
ATEX 35
Motivation Implementation in L
ATEX Evaluation and Discussion
Circuit Diagram (for Matriculation Number 123 461)
Iq1 Iq2
R1
Iq3
R2
Iq4
R3
0
1 2
3
Personalized Engineering Tasks in L
ATEX 36
Motivation Implementation in L
ATEX Evaluation and Discussion
Circuit Diagram (for Matriculation Number 123 462)
R1
Iq1
Iq2
R2 R3
0
1 2
3
Personalized Engineering Tasks in L
ATEX 37
Motivation Implementation in L
ATEX Evaluation and Discussion
Circuit Diagram (for Matriculation Number 123 463)
Iq1
R1 R2
Iq2
Iq3
R3
0
1 2
3
Personalized Engineering Tasks in L
ATEX 38
Motivation Implementation in L
ATEX Evaluation and Discussion
Create Randomized CircuiTikZ Circuits
 documentclass { standalone }
 usepackage {amsmath}
newcommand {  ind } [ 1 ] {  mathrm {#1}}
 usepackage [ european ] { c i r c u i t i k z }
 begin { document }
 begin { t i k z p i c t u r e } [ scale =1.3]
 draw (2 ,0) to [ short ] ( 0 , 0 ) ;
 draw (0 ,0) to [ I , i ^=$I_ {  ind { q }1} $ ] ( 0 , 2 ) ;
 draw (0 ,0) to [ short , * −] ( −2 ,0) to [R, l =$R_{1} $ ] ( −2 ,2) to [ short , −*] ( 0 , 2 ) ;
 draw (2 ,0) to [ short ] ( 4 , 0 ) ;
 draw (4 ,0) to [ I , i_ =$I_ {  ind { q }2} $ ] ( 4 , 2 ) ;
 draw (2 ,0) to [R, l ^=$R_{2} $ ] ( 2 , 2 ) ;
 draw (0 ,2) to [ short ] ( 0 , 4 ) ;
 draw (0 ,4) to [ I , i ^=$I_ {  ind { q }3} $ ] ( 4 , 4 ) ;
 draw (4 ,4) to [ short ] ( 4 , 2 ) ;
 draw (0 ,2) to [ I , i ^=$I_ {  ind { q }4} $ ] ( 2 , 2 ) ;
 draw (4 ,2) to [R, l_=$R_{3} $ ] ( 2 , 2 ) ;
 node [ c i r c ] at (2 ,0) { } ;  node [ below ] at (2 ,0) { 0 } ;
 node [ c i r c ] at (0 ,2) { } ;  node [ above l e f t ] at (0 ,2) { 1 } ;
 node [ c i r c ] at (4 ,2) { } ;  node [ above r i g h t ] at (4 ,2) { 2 } ;
 node [ c i r c ] at (2 ,2) { } ;  node [ above ] at (2 ,2) { 3 } ;
 end { t i k z p i c t u r e }
 end { document }
Personalized Engineering Tasks in L
ATEX 39
Motivation Implementation in L
ATEX Evaluation and Discussion
2. Sample Solution (for Matriculation Number 123 460)
Set up the system of equations to calculate the network:


G1 0 0
0 G3 −G3
0 −G3 G2 + G3

 ·


UKn1
UKn2
UKn3

 =


Iq1 + Iq3 + Iq4
Iq2 − Iq3
−Iq4


Insert the values of the components into the system of equations:


9 S 0 0
0 7 S −7 S
0 −7 S 13 S

 ·


UKn1
UKn2
UKn3

 =


11 A
−3 A
−5 A


Personalized Engineering Tasks in L
ATEX 40
Motivation Implementation in L
ATEX Evaluation and Discussion
2. Sample Solution (for Matriculation Number 123 461)
Set up the system of equations to calculate the network:


G2 −G2 0
−G2 G2 + G3 −G3
0 −G3 G1 + G3

 ·


UKn1
UKn2
UKn3

 =


−Iq1 + Iq3 + Iq4
−Iq2 − Iq3
−Iq4


Insert the values of the components into the system of equations:


8 S −8 S 0
−8 S 16 S −8 S
0 −8 S 14 S

 ·


UKn1
UKn2
UKn3

 =


4 A
−15 A
−8 A


Personalized Engineering Tasks in L
ATEX 41
Motivation Implementation in L
ATEX Evaluation and Discussion
2. Sample Solution (for Matriculation Number 123 462)
Set up the system of equations to calculate the network:


G1 + G2 0 −G2
0 G3 −G3
−G2 −G3 G2 + G3

 ·


UKn1
UKn2
UKn3

 =


−Iq2
Iq1 + Iq2
0


Insert the values of the components into the system of equations:


7 S 0 −4 S
0 1 S −1 S
−4 S −1 S 5 S

 ·


UKn1
UKn2
UKn3

 =


−1 A
2 A
0


Personalized Engineering Tasks in L
ATEX 42
Motivation Implementation in L
ATEX Evaluation and Discussion
2. Sample Solution (for Matriculation Number 123 463)
Set up the system of equations to calculate the network:


G1 0 0
0 G2 + G3 −G3
0 −G3 G3

 ·


UKn1
UKn2
UKn3

 =


−Iq1 − Iq3
0
Iq2 + Iq3


Insert the values of the components into the system of equations:


7 S 0 0
0 6 S −3 S
0 −3 S 3 S

 ·


UKn1
UKn2
UKn3

 =


−6 A
0
10 A


Personalized Engineering Tasks in L
ATEX 43
Motivation Implementation in L
ATEX Evaluation and Discussion
Create Randomized Systems of Equations
 begin { equation * }
 begin { bmatrix }
G_{1}  0  0  
0  G_{3}  −G_{3}  
0  −G_{3}  G_{2} + G_{3}
 end { bmatrix }  cdot  begin { bmatrix }
U_ {  ind {Kn}1}  
U_ {  ind {Kn}2}  
U_ {  ind {Kn}3}
 end { bmatrix } =  begin { bmatrix }
I_ {  ind { q }1} + I_ {  ind { q }3} + I_ {  ind { q }4}  
I_ {  ind { q }2} − I_ {  ind { q }3}  
− I_ {  ind { q }4}
 end { bmatrix }
 end { equation * }
Personalized Engineering Tasks in L
ATEX 44
What has come out of it?
Motivation Implementation in L
ATEX Evaluation and Discussion
Evaluation of a Typical Cycle
Bare numbers:
▶ Tasks sent to about 200 students
▶ Solutions submitted by about 150 students
▶ Review carried out by about 140 students
Personalized Engineering Tasks in L
ATEX 46
Motivation Implementation in L
ATEX Evaluation and Discussion
Evaluation of a Typical Cycle
Bare numbers:
▶ Tasks sent to about 200 students
▶ Solutions submitted by about 150 students
▶ Review carried out by about 140 students
Advantage:
▶ excellent activation
▶ good exam preparation without „teaching to the test“
Personalized Engineering Tasks in L
ATEX 46
Motivation Implementation in L
ATEX Evaluation and Discussion
Typical Distribution of the Points
0–2 2–4 4–6 6–8 8–10 10–12 12–14 14–16
0
20
40
60
Number of points (maximum 16)
Absolute
frequency
Personalized Engineering Tasks in L
ATEX 47
Motivation Implementation in L
ATEX Evaluation and Discussion
Typical Distribution of the Point Deviation
0–1 1–2 2–3 3–4 4–5
0
20
40
60
Absolute deviation between reviewer 1 and 2
Absolute
frequency
Personalized Engineering Tasks in L
ATEX 48
Motivation Implementation in L
ATEX Evaluation and Discussion
When Do Students Submit?
0 1 2 3 4 5 6 7 8 9 1011121314151617181920212223
0
50
100
150
200
Time of day in h
Absolute
frequency
(2377
in
total)
Personalized Engineering Tasks in L
ATEX 49
Motivation Implementation in L
ATEX Evaluation and Discussion
Survey
What questions come to your mind regarding the evaluation?
▶ . . .
Personalized Engineering Tasks in L
ATEX 50
Motivation Implementation in L
ATEX Evaluation and Discussion
Fun Facts
Personalized Engineering Tasks in L
ATEX 51
Motivation Implementation in L
ATEX Evaluation and Discussion
Fun Facts
Personalized Engineering Tasks in L
ATEX 51
Motivation Implementation in L
ATEX Evaluation and Discussion
Fun Facts
Personalized Engineering Tasks in L
ATEX 51
Motivation Implementation in L
ATEX Evaluation and Discussion
Survey
Do you use a learning management system and if so, which one?
1. Moodle
2. ILIAS
3. OLAT/OPAL
4. Blackboard
5. something else
6. none
Personalized Engineering Tasks in L
ATEX 52
Motivation Implementation in L
ATEX Evaluation and Discussion
Further Information
Achievements to date:
▶ 13 different task types developed so far
▶ 36 runs in 8 semesters so far
▶ 6400 personalized tasks sent out
▶ 3000 student solutions submitted
▶ 5720 student peer reviews accomplished
Links (in German):
Lightning Talk: https://youtu.be/LDw_Ifmg2WM
Twitter: #PersonalisierteAufgaben
Article: Die TEXnische Komödie 4/2019
FAQ: SlideShare
Personalized Engineering Tasks in L
ATEX 53
Motivation Implementation in L
ATEX Evaluation and Discussion
Thank you very much for your attention!
Are there any questions?
Personalized Engineering Tasks in L
ATEX 54

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How to Generate Personalized Tasks and Sample Solutions for Anonymous Peer Review in Electrical Engineering using LATEX, PGFPLOTS and CircuiTikZ

  • 1. How to Generate Personalized Tasks and Sample Solutions for Anonymous Peer Review in Electrical Engineering using L A TEX, PGFPLOTS and CircuiTikZ Doctoral Student Meeting 2021 IEEE German EMC Chapter Mathias Magdowski Chair for Electromagnetic Compatibility, Institute for Medical Engineering Otto von Guericke University, Magdeburg, Germany November 9, 2021 License: cb CC BY 4.0 (Attribution, ShareAlike)
  • 2. Motivation Implementation in L ATEX Evaluation and Discussion Organizational Matters Slides: yes Personalized Engineering Tasks in L ATEX 2
  • 3. Motivation Implementation in L ATEX Evaluation and Discussion Organizational Matters Slides: yes Recording: no Personalized Engineering Tasks in L ATEX 2
  • 4. Motivation Implementation in L ATEX Evaluation and Discussion Organizational Matters Slides: yes Recording: no Questions: with pleasure Personalized Engineering Tasks in L ATEX 2
  • 5. Motivation Implementation in L ATEX Evaluation and Discussion Overview Why all this? How are the tasks generated in L A TEX? Topic „Charge and Current“ Topic „Nodal Analysis“ What has come out of it? Personalized Engineering Tasks in L ATEX 3
  • 7. Motivation Implementation in L ATEX Evaluation and Discussion Traditional Performance Assessments Source: https://pixabay.com/de/photos/taschenrechner-notizblock-1687962/ Personalized Engineering Tasks in L ATEX 5
  • 8. Motivation Implementation in L ATEX Evaluation and Discussion Demands in the Working World Source: https://pixabay.com/de/arbeitsplatz-team-gesch%C3%A4ftstreffen-1245776/ Personalized Engineering Tasks in L ATEX 6
  • 9. Motivation Implementation in L ATEX Evaluation and Discussion Classical E-Learning Tasks Personalized Engineering Tasks in L ATEX 7
  • 10. Motivation Implementation in L ATEX Evaluation and Discussion Free Handwritten Solution Personalized Engineering Tasks in L ATEX 8
  • 11. Motivation Implementation in L ATEX Evaluation and Discussion Free Handwritten Solution Personalized Engineering Tasks in L ATEX 9
  • 12. Motivation Implementation in L ATEX Evaluation and Discussion Examples of Student Misconceptions Specification of Fourier coefficients in V and V ◦ : also see: https://twitter.com/LehrstuhlEMV/status/1257605076308426753 Personalized Engineering Tasks in L ATEX 10
  • 13. Motivation Implementation in L ATEX Evaluation and Discussion Examples of Student Misconceptions Complex impedance converted to time function: € #ß = 2.42Mt 8,411J -- ZAB = 81751 " Sin Iwtt 73,95 ) I 8,751 . ewtt 73,95 - also see: https://twitter.com/LehrstuhlEMV/status/1264294433027174401 Personalized Engineering Tasks in L ATEX 11
  • 14. Motivation Implementation in L ATEX Evaluation and Discussion Idea Personalizable tasks for handwritten solution: ▶ handwritten −→ authentic, low-threshold for formulas, schematics, diagrams, misconceptions become visible ▶ personalized −→ no plagiarism possible ▶ peer review −→ no correction effort −→ good ready-made personalized sample solution ▶ via Moodle and e-mail −→ scalable, no „red tape“ Personalized Engineering Tasks in L ATEX 12
  • 15. Motivation Implementation in L ATEX Evaluation and Discussion Creation and Sending of the Tasks Registration MAT- LAB LaTeX Matriculation No. PDF Task Sample Solution Folder Personalized Engineering Tasks in L ATEX 13
  • 16. Motivation Implementation in L ATEX Evaluation and Discussion Submission and Distribution of the Solutions ZIP File MAT- LAB Folder Sample Solution Form Personalized Engineering Tasks in L ATEX 14
  • 17. Motivation Implementation in L ATEX Evaluation and Discussion Mutual Correction and Completion 2 Reviews Sample Sol. Folder ZIP File Score List MAT- LAB Sample Solution Personalized Engineering Tasks in L ATEX 15
  • 18. How are the tasks generated in L A TEX?
  • 19. Motivation Implementation in L ATEX Evaluation and Discussion 1. Task (same for all) The displayed time curve shows the current i as a function of time t. The charge Q(t) is searched for the four sections 1. 0 s ≤ t ≤ 1 s, 2. 1 s < t ≤ 2 s, 3. 2 s < t ≤ 3 s and 4. 3 s < t ≤ 4 s. The initial charge is Q(t = 0) = 0. Calculate the charge Q(t) for each section as a formula by integrating the current over time and draw the corresponding time curve. Personalized Engineering Tasks in L ATEX 17
  • 20. Motivation Implementation in L ATEX Evaluation and Discussion Diagram (for Matriculation Number 123 456) 1 2 3 4 −4 −3 −2 −1 1 2 3 4 t in s i(t) in A Personalized Engineering Tasks in L ATEX 18
  • 21. Motivation Implementation in L ATEX Evaluation and Discussion Diagram (for Matriculation Number 123 457) 1 2 3 4 −4 −3 −2 −1 1 2 3 4 t in s i(t) in A Personalized Engineering Tasks in L ATEX 19
  • 22. Motivation Implementation in L ATEX Evaluation and Discussion Diagram (for Matriculation Number 123 458) 1 2 3 4 −4 −3 −2 −1 1 2 3 4 t in s i(t) in A Personalized Engineering Tasks in L ATEX 20
  • 23. Motivation Implementation in L ATEX Evaluation and Discussion Diagram (for Matriculation Number 123 459) 1 2 3 4 −4 −3 −2 −1 1 2 3 4 t in s i(t) in A Personalized Engineering Tasks in L ATEX 21
  • 24. Motivation Implementation in L ATEX Evaluation and Discussion Create Randomized PGFPLOTS Diagrams documentclass { standalone } usepackage { pgfplots , s i u n i t x } begin { document } % Set random number generator to m a t r i c u l a t i o n number pgfmathsetseed {123456} % Current at time 1 s ( in A, can also s t i l l be zero , but should not be ) pgfmathrandominteger { stromeinsrandom }{ −4}{4} % i f current i s zero , set to 1 A pgfmathsetmacro { stromeins } { i f t h e n e l s e ( stromeinsrandom ==0 ,1 , stromeinsrandom ) } % Current in the period from 1 s to 2 s ( in A, can also be zero ) pgfmathrandominteger { stromzwei }{ −4}{4} % Current in the period from 2 s to 3 s ( in A, can also be zero ) pgfmathrandominteger { stromdreirandom }{ −4}{4} % i f the current i s equal to the value from the previous period , i n v e r t the sign pgfmathsetmacro { stromdrei } { i f t h e n e l s e ( stromzwei == stromdreirandom , − stromdreirandom , stromdreirandom ) } % i f both currents are zero , set new current to 1 A pgfmathsetmacro { stromdrei } { i f t h e n e l s e ( abs ( stromzwei )+abs ( stromdrei )==0 ,1 , stromdrei ) } % Current in the period from 3 s to 4 s ( in A, can also be zero ) pgfmathrandominteger { stromvierrandom }{ −4}{4} % i f both currents are zero , set new current to 1 A pgfmathsetmacro { stromvier } { i f t h e n e l s e ( abs ( stromzwei )+abs ( stromvierrandom )==0 ,1 , stromvierrandom ) } % i f both currents are zero , set new current to 1 A pgfmathsetmacro { stromvier } { i f t h e n e l s e ( abs ( stromdrei )+abs ( stromvier )==0 ,1 , stromvier ) } % i f the current i s equal to the value from the previous period , i n v e r t the sign pgfmathsetmacro { stromvier } { i f t h e n e l s e ( stromdrei == stromvier , − stromvier , stromvier ) } Personalized Engineering Tasks in L ATEX 22
  • 25. Motivation Implementation in L ATEX Evaluation and Discussion Create Randomized PGFPLOTS Diagrams begin { t i k z p i c t u r e } begin { axis } [ xlabel ={ $t$ in s i { second } } , ylabel ={ $i ( t ) $ in s i { ampere } } , xmin= −0.9 ,xmax=4.9 , ymin= −4.9 ,ymax=4.9 , x t i c k ={1 ,2 ,3 ,4} , y t i c k ={ −4 , −3 , −2 , −1 ,1 ,2 ,3 ,4} , x t i c k l a b e l s t y l e ={ below r i g h t } , y t i c k l a b e l s t y l e ={ below l e f t } , axis x l i n e =middle , axis y l i n e =center , xmajorgrids , ymajorgrids , ] addplot +[mark=none , l i n e width=1pt ] coordinates { ( −0.5 ,0) (0 ,0) ( 1 , stromeins ) ( 1 , stromzwei ) ( 2 , stromzwei ) ( 2 , stromdrei ) ( 3 , stromdrei ) ( 3 , stromvier ) ( 4 , stromvier ) (4 ,0) ( 4 . 5 , 0 ) } ; end { axis } end { t i k z p i c t u r e } end { document } Personalized Engineering Tasks in L ATEX 23
  • 26. Motivation Implementation in L ATEX Evaluation and Discussion 1. Sample Solution (for Matriculation Number 123 456) Sectionwise calculation: 0 ≤ t ≤ 1 s: Current in the 1. section (1 point): i(t) = 1 A s · t Charge in the 1. section (1 point): Q(t) = t Z 0 1 A s t′ dt′ + 0 = 1 A s · t′2 2 t 0 = 0.5 A s t2 Charge at the end of the 1. section (1 point): Q(1 s) = 0.5 A s Personalized Engineering Tasks in L ATEX 24
  • 27. Motivation Implementation in L ATEX Evaluation and Discussion 1. Sample Solution (for Matriculation Number 123 457) Sectionwise calculation: 0 ≤ t ≤ 1 s: Current in the 1. section (1 point): i(t) = −2 A s · t Charge in the 1. section (1 point): Q(t) = t Z 0 −2 A s t′ dt′ + 0 = −2 A s · t′2 2 t 0 = −1 A s t2 Charge at the end of the 1. section (1 point): Q(1 s) = −1 A s Personalized Engineering Tasks in L ATEX 25
  • 28. Motivation Implementation in L ATEX Evaluation and Discussion 1. Sample Solution (for Matriculation Number 123 458) Sectionwise calculation: 0 ≤ t ≤ 1 s: Current in the 1. section (1 point): i(t) = 4 A s · t Charge in the 1. section (1 point): Q(t) = t Z 0 4 A s t′ dt′ + 0 = 4 A s · t′2 2 t 0 = 2 A s t2 Charge at the end of the 1. section (1 point): Q(1 s) = 2 A s Personalized Engineering Tasks in L ATEX 26
  • 29. Motivation Implementation in L ATEX Evaluation and Discussion 1. Sample Solution (for Matriculation Number 123 459) Sectionwise calculation: 0 ≤ t ≤ 1 s: Current in the 1. section (1 point): i(t) = 1 A s · t Charge in the 1. section (1 point): Q(t) = t Z 0 1 A s t′ dt′ + 0 = 1 A s · t′2 2 t 0 = 0.5 A s t2 Charge at the end of the 1. section (1 point): Q(1 s) = 0.5 A s Personalized Engineering Tasks in L ATEX 27
  • 30. Motivation Implementation in L ATEX Evaluation and Discussion Algorithmic Generation of the Sample Solutions % Truncate decimal places f o r an integer number pgfmathdeclarefunction { trimzero } { 1 } { pgfmathparse { i f t h e n e l s e (#1==round (#1) , i n t ( # 1 ) , # 1 ) } } % Convert current ( in A) to integers pgfmathsetmacro { stromeins } { i n t ( stromeins ) } % Charge at the end of the 1 st section ( in As) pgfmathsetmacro { ladungeins } { trimzero ( stromeins / 2 ) } % D i f f e r e n t i a l operator ( small upright d ) newcommand * { d i f f } { mathop { } ! mathrm { d } } Current in the 1. section (1 point ) : begin { equation } i ( t ) = SI { stromeins } { ampere per second } cdot t end { equation } Charge in the 1. section (1 point ) : begin { subequations } begin { align } Q( t ) = i n t l i m i t s _ 0 ^ t SI { stromeins } { ampere per second } t ’ d i f f t ’ + 0 = SI { stromeins } { ampere per second } cdot l e f t [ frac { t ’ ^ 2 } { 2 } r i g h t ] _0^ t = SI { ladungeins } { ampere per second } t ^2 end { align } end { subequations } Charge at the end of the 1. section (1 point ) : begin { equation } Q( SI { 1 } { second } ) = SI { ladungeins } { ampere second } end { equation } Personalized Engineering Tasks in L ATEX 28
  • 31. Motivation Implementation in L ATEX Evaluation and Discussion 1. Sample Solution (for Matriculation Number 123 456) Graphical representation: 0 0,5 1 1,5 2 2,5 3 3,5 4 0 2 4 6 Time, t in s Charge, Q(t) in A s Personalized Engineering Tasks in L ATEX 29
  • 32. Motivation Implementation in L ATEX Evaluation and Discussion 1. Sample Solution (for Matriculation Number 123 457) Graphical representation: 0 0,5 1 1,5 2 2,5 3 3,5 4 −1 −0,8 −0,6 −0,4 −0,2 0 Time, t in s Charge, Q(t) in A s Personalized Engineering Tasks in L ATEX 30
  • 33. Motivation Implementation in L ATEX Evaluation and Discussion 1. Sample Solution (for Matriculation Number 123 458) Graphical representation: 0 0,5 1 1,5 2 2,5 3 3,5 4 0 1 2 3 Time, t in s Charge, Q(t) in A s Personalized Engineering Tasks in L ATEX 31
  • 34. Motivation Implementation in L ATEX Evaluation and Discussion 1. Sample Solution (for Matriculation Number 123 459) Graphical representation: 0 0,5 1 1,5 2 2,5 3 3,5 4 −2 0 2 4 Time, t in s Charge, Q(t) in A s Personalized Engineering Tasks in L ATEX 32
  • 35. Motivation Implementation in L ATEX Evaluation and Discussion Survey If you are also teaching, can you think of personalised/randomize tasks that can also be used for your subject? 1. yes, immediately, many 2. yes, some 3. yes, but only after some thought 4. no, not likely 5. nohow, no way Personalized Engineering Tasks in L ATEX 33
  • 36. Motivation Implementation in L ATEX Evaluation and Discussion 2. Task (same for all) Nodal analysis shall be used to calculate the three nodal voltages UKn1, UKn2 and UKn3 between the respective node and the reference node. a) Draw the three nodal voltages UKn1, UKn2 and UKn3 in the circuit diagram (3 points). b) Set up the system of equations to calculate the nodal voltages using nodal analysis in matrix form (9 points). c) Insert the values of the components into the system of equations (1 point). d) Solve the system of equations and thus calculate the three nodal voltages UKn1, UKn2 and UKn3 (3 points). Personalized Engineering Tasks in L ATEX 34
  • 37. Motivation Implementation in L ATEX Evaluation and Discussion Circuit Diagram (for Matriculation Number 123 460) Iq1 R1 Iq2 R2 Iq3 Iq4 R3 0 1 2 3 Personalized Engineering Tasks in L ATEX 35
  • 38. Motivation Implementation in L ATEX Evaluation and Discussion Circuit Diagram (for Matriculation Number 123 461) Iq1 Iq2 R1 Iq3 R2 Iq4 R3 0 1 2 3 Personalized Engineering Tasks in L ATEX 36
  • 39. Motivation Implementation in L ATEX Evaluation and Discussion Circuit Diagram (for Matriculation Number 123 462) R1 Iq1 Iq2 R2 R3 0 1 2 3 Personalized Engineering Tasks in L ATEX 37
  • 40. Motivation Implementation in L ATEX Evaluation and Discussion Circuit Diagram (for Matriculation Number 123 463) Iq1 R1 R2 Iq2 Iq3 R3 0 1 2 3 Personalized Engineering Tasks in L ATEX 38
  • 41. Motivation Implementation in L ATEX Evaluation and Discussion Create Randomized CircuiTikZ Circuits documentclass { standalone } usepackage {amsmath} newcommand { ind } [ 1 ] { mathrm {#1}} usepackage [ european ] { c i r c u i t i k z } begin { document } begin { t i k z p i c t u r e } [ scale =1.3] draw (2 ,0) to [ short ] ( 0 , 0 ) ; draw (0 ,0) to [ I , i ^=$I_ { ind { q }1} $ ] ( 0 , 2 ) ; draw (0 ,0) to [ short , * −] ( −2 ,0) to [R, l =$R_{1} $ ] ( −2 ,2) to [ short , −*] ( 0 , 2 ) ; draw (2 ,0) to [ short ] ( 4 , 0 ) ; draw (4 ,0) to [ I , i_ =$I_ { ind { q }2} $ ] ( 4 , 2 ) ; draw (2 ,0) to [R, l ^=$R_{2} $ ] ( 2 , 2 ) ; draw (0 ,2) to [ short ] ( 0 , 4 ) ; draw (0 ,4) to [ I , i ^=$I_ { ind { q }3} $ ] ( 4 , 4 ) ; draw (4 ,4) to [ short ] ( 4 , 2 ) ; draw (0 ,2) to [ I , i ^=$I_ { ind { q }4} $ ] ( 2 , 2 ) ; draw (4 ,2) to [R, l_=$R_{3} $ ] ( 2 , 2 ) ; node [ c i r c ] at (2 ,0) { } ; node [ below ] at (2 ,0) { 0 } ; node [ c i r c ] at (0 ,2) { } ; node [ above l e f t ] at (0 ,2) { 1 } ; node [ c i r c ] at (4 ,2) { } ; node [ above r i g h t ] at (4 ,2) { 2 } ; node [ c i r c ] at (2 ,2) { } ; node [ above ] at (2 ,2) { 3 } ; end { t i k z p i c t u r e } end { document } Personalized Engineering Tasks in L ATEX 39
  • 42. Motivation Implementation in L ATEX Evaluation and Discussion 2. Sample Solution (for Matriculation Number 123 460) Set up the system of equations to calculate the network:   G1 0 0 0 G3 −G3 0 −G3 G2 + G3   ·   UKn1 UKn2 UKn3   =   Iq1 + Iq3 + Iq4 Iq2 − Iq3 −Iq4   Insert the values of the components into the system of equations:   9 S 0 0 0 7 S −7 S 0 −7 S 13 S   ·   UKn1 UKn2 UKn3   =   11 A −3 A −5 A   Personalized Engineering Tasks in L ATEX 40
  • 43. Motivation Implementation in L ATEX Evaluation and Discussion 2. Sample Solution (for Matriculation Number 123 461) Set up the system of equations to calculate the network:   G2 −G2 0 −G2 G2 + G3 −G3 0 −G3 G1 + G3   ·   UKn1 UKn2 UKn3   =   −Iq1 + Iq3 + Iq4 −Iq2 − Iq3 −Iq4   Insert the values of the components into the system of equations:   8 S −8 S 0 −8 S 16 S −8 S 0 −8 S 14 S   ·   UKn1 UKn2 UKn3   =   4 A −15 A −8 A   Personalized Engineering Tasks in L ATEX 41
  • 44. Motivation Implementation in L ATEX Evaluation and Discussion 2. Sample Solution (for Matriculation Number 123 462) Set up the system of equations to calculate the network:   G1 + G2 0 −G2 0 G3 −G3 −G2 −G3 G2 + G3   ·   UKn1 UKn2 UKn3   =   −Iq2 Iq1 + Iq2 0   Insert the values of the components into the system of equations:   7 S 0 −4 S 0 1 S −1 S −4 S −1 S 5 S   ·   UKn1 UKn2 UKn3   =   −1 A 2 A 0   Personalized Engineering Tasks in L ATEX 42
  • 45. Motivation Implementation in L ATEX Evaluation and Discussion 2. Sample Solution (for Matriculation Number 123 463) Set up the system of equations to calculate the network:   G1 0 0 0 G2 + G3 −G3 0 −G3 G3   ·   UKn1 UKn2 UKn3   =   −Iq1 − Iq3 0 Iq2 + Iq3   Insert the values of the components into the system of equations:   7 S 0 0 0 6 S −3 S 0 −3 S 3 S   ·   UKn1 UKn2 UKn3   =   −6 A 0 10 A   Personalized Engineering Tasks in L ATEX 43
  • 46. Motivation Implementation in L ATEX Evaluation and Discussion Create Randomized Systems of Equations begin { equation * } begin { bmatrix } G_{1} 0 0 0 G_{3} −G_{3} 0 −G_{3} G_{2} + G_{3} end { bmatrix } cdot begin { bmatrix } U_ { ind {Kn}1} U_ { ind {Kn}2} U_ { ind {Kn}3} end { bmatrix } = begin { bmatrix } I_ { ind { q }1} + I_ { ind { q }3} + I_ { ind { q }4} I_ { ind { q }2} − I_ { ind { q }3} − I_ { ind { q }4} end { bmatrix } end { equation * } Personalized Engineering Tasks in L ATEX 44
  • 47. What has come out of it?
  • 48. Motivation Implementation in L ATEX Evaluation and Discussion Evaluation of a Typical Cycle Bare numbers: ▶ Tasks sent to about 200 students ▶ Solutions submitted by about 150 students ▶ Review carried out by about 140 students Personalized Engineering Tasks in L ATEX 46
  • 49. Motivation Implementation in L ATEX Evaluation and Discussion Evaluation of a Typical Cycle Bare numbers: ▶ Tasks sent to about 200 students ▶ Solutions submitted by about 150 students ▶ Review carried out by about 140 students Advantage: ▶ excellent activation ▶ good exam preparation without „teaching to the test“ Personalized Engineering Tasks in L ATEX 46
  • 50. Motivation Implementation in L ATEX Evaluation and Discussion Typical Distribution of the Points 0–2 2–4 4–6 6–8 8–10 10–12 12–14 14–16 0 20 40 60 Number of points (maximum 16) Absolute frequency Personalized Engineering Tasks in L ATEX 47
  • 51. Motivation Implementation in L ATEX Evaluation and Discussion Typical Distribution of the Point Deviation 0–1 1–2 2–3 3–4 4–5 0 20 40 60 Absolute deviation between reviewer 1 and 2 Absolute frequency Personalized Engineering Tasks in L ATEX 48
  • 52. Motivation Implementation in L ATEX Evaluation and Discussion When Do Students Submit? 0 1 2 3 4 5 6 7 8 9 1011121314151617181920212223 0 50 100 150 200 Time of day in h Absolute frequency (2377 in total) Personalized Engineering Tasks in L ATEX 49
  • 53. Motivation Implementation in L ATEX Evaluation and Discussion Survey What questions come to your mind regarding the evaluation? ▶ . . . Personalized Engineering Tasks in L ATEX 50
  • 54. Motivation Implementation in L ATEX Evaluation and Discussion Fun Facts Personalized Engineering Tasks in L ATEX 51
  • 55. Motivation Implementation in L ATEX Evaluation and Discussion Fun Facts Personalized Engineering Tasks in L ATEX 51
  • 56. Motivation Implementation in L ATEX Evaluation and Discussion Fun Facts Personalized Engineering Tasks in L ATEX 51
  • 57. Motivation Implementation in L ATEX Evaluation and Discussion Survey Do you use a learning management system and if so, which one? 1. Moodle 2. ILIAS 3. OLAT/OPAL 4. Blackboard 5. something else 6. none Personalized Engineering Tasks in L ATEX 52
  • 58. Motivation Implementation in L ATEX Evaluation and Discussion Further Information Achievements to date: ▶ 13 different task types developed so far ▶ 36 runs in 8 semesters so far ▶ 6400 personalized tasks sent out ▶ 3000 student solutions submitted ▶ 5720 student peer reviews accomplished Links (in German): Lightning Talk: https://youtu.be/LDw_Ifmg2WM Twitter: #PersonalisierteAufgaben Article: Die TEXnische Komödie 4/2019 FAQ: SlideShare Personalized Engineering Tasks in L ATEX 53
  • 59. Motivation Implementation in L ATEX Evaluation and Discussion Thank you very much for your attention! Are there any questions? Personalized Engineering Tasks in L ATEX 54