Started PhD project to the subject of "E-Feedback to overcome Misconceptions

1. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 1
Felix Johlke
Projekt EoM
E-Feedback to overcome Misconceptions
The goal of the project
… is to generate feedback
elements to overcome
misconceptions in the field of
functional relationships by using
computer-based automatic
feedback.
The goal of the project
… is to generate feedback
elements to overcome
misconceptions in the field of
functional relationships by using
computer-based automatic
feedback.

2. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 2
1. Misconceptions
Features of misconceptions (cf. Nitsch, 2015; Vosniadou, 2008)
• repeatable
• explicit
• strongly held
• based on stable cognitive structures
► Conceptual-Change-Theory► Conceptual-Change-Theory

3. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 3
2. Project EoM
Connection to other projects
independent online diagnostic tools
analysis of mathematical errors and misconceptions
Digital Diagnostic
TAsk
COnceptual DIfficulties
In the field of
functional relationships
• tasks with adaptive elements
(Feldt-Caesar, Bruder, 2014;Kallweit et al., 2017)
• automatic feedback restricted to
the “knowledge of correct result”
(Jacobs, 2002; Kulhavy & Stock, 1989)
• systematic errors / error patterns
• are relatively stable
• result from misconceptions
(Nitsch & Bruder, 2014 ; Nitsch, 2015)
• nine misconceptions at >10%

4. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 4
2. Project EoM
Overview
• implementation in DDTA
• immediate / delayed
feedback
EE FeedbackFeedback
multimedia design individual type of learning
activating Conceptual-Change-process
automatic generation
performance expectation
individual misconception

5. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 5
3. Item example
The task
In the following picture a skier is skiing down the hill.
Decide which of the given graphs describes the
situation best.
The function value v(t) gives the velocity at the time t.
Nitsch, 2015

6. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 6
3. Item example
Right answer
In the following picture a skier is skiing down the hill.
Decide which of the given graphs describes the
situation best.
The function value v(t) gives the velocity at the time t.
✓ Nitsch, 2015
66.1 %
n = 569

7. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 7
3. Item example
GAP-misconception
In the following picture a skier is skiing down the hill.
Decide which of the given graphs describes the
situation best.
The function value v(t) gives the velocity at the time t.
Graph-as-picture misconception
16.0 %
Nitsch, 2015
Nitsch & Johlke, 2016
43.4 %
n = 569 n = 100
• perceptions from everyday life are very stable

8. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 8
4. Activation of Conceptual-Change
Example: Dissatisfaction
Possible intervention approach (cf. Posner et al., 1982; Vosniadou, 2008)
(1) cause dissatisfaction with an existing concept and explain a given
problem in an intelligible manner
(2) support the election of a proper fruitful concept for a given situation
EE FeedbackFeedback
multimedia design individual type of learning
activating Conceptual-Change-process
automatic generation
performance expectation
individual misconception

9. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 9
5. Video example
Video tutorial with causing dissatisfaction
Understanding functional
relationships and plotting it
• Aim: To overcome the graph-as-
picture misconception.
• Task description: A graph of a
function should be represented with
the velocities a car goes to a random
time on that route.
• Method: Multimedia (here: in vision + sound) (Mayer & Moreno (2002)
Neufeld, 2016

10. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 10
5. Video example
Video tutorial with causing dissatisfaction
Velocity
in km/h
Time in seconds

11. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 11
6. Project EoM
Overview
EE FeedbackFeedback
multimedia design individual type of learning
activating Conceptual-Change-process
automatic generation
performance expectation
individual misconception

12. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 12
6. Project EOM
Feedback-individualization
Three characteristics of feedback
(1) What kind of incorrect knowledge causes the misconception?
▪ Knowledge of what to do and
▪ Knowledge of how to do that
▪ Motivation
(Campbell, 1990)

13. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 13
6. Project EOM
Feedback-individualization
Three characteristics of feedback
(1) What kind of incorrect knowledge causes the misconception?
(2) Which way of learning does the student prefer?
(Gregory, 2005)
Beach BallBeach Ball
ClipboardClipboardMicroscopeMicroscope
PuppyPuppy

14. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 14
6. Project EOM
Feedback-individualization
Three characteristics of feedback
(1) What kind of incorrect knowledge causes the misconception?
(2) Which way of learning does the student prefer?
(Gregory, 2005)
MicroscopeMicroscope
PuppyPuppy

15. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 15
6. Project EOM
Feedback-individualization
Three characteristics of feedback
(1) What kind of incorrect knowledge causes the misconception?
(2) Which way of learning does the student prefer?
MicroscopeMicroscope PuppyPuppy
logical /
mathematical
logical /
mathematical
professional
information
professional
information
alone &
success /
appreciation
alone &
success /
appreciation
objective, computerbased
delayed, facilitative
specific, goal-directed
verbal /
linguistic
verbal /
linguistic
intuitively
accessible/
personalized
intuitively
accessible/
personalized
success /
appreciation
success /
appreciation
personalized, units
direct, corrective
note areas of strength
(Bangert-
Drowns et
al., 1991;
Hattie &
Timperley,
2007;
Shute,
2008)

16. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 16
6. Project EOM
Feedback-design
Three characteristics of feedback
(1) What kind of incorrect knowledge causes the misconception?
(2) Which way of learning does the student prefer?
(3) Which learning targets are necessary to be reached?
► goal-orientation► goal-orientation

17. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 17
7. Project EOM
Next steps
Interviews
learning characteristics
⇔ types of multimedia
realization Autonomous tool
EE FeedbackFeedback
multimedia design individual type of learning
activating Conceptual-Change-process
automatic generation
performance expectation
individual misconception

18. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 18
7. Project EOM
Open questions
Are there differences
between the effects
on learning?
Is it possible to
identify some
characteristics
of a student‘s
learning
behaviour?
Is it possible to activate
Conceptual Change processes?
What about measurement?
How is it possible
to integrate it in
moodle?
Thank you for your attention
And I am looking forward to your comments
Thank you for your attention
And I am looking forward to your comments
johlke@mathematik.tu-darmstadt.de
EE FeedbackFeedback
multimedia design individual type of learning
activating Conceptual-Change-process
automatic generation
performance expectation
individual misconception

19. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 19
References I
J. P. Campbell, “Modeling the performance prediction problem in industrial an organizational psychology,” in
vol. 1, Handbook of industrial and organizational psychology, M. D. Dunnette and L. M. Hough, Eds., 2nd
ed., California, US: Consulting Psychologists Press, pp. 687–732.
R. L. Bangert-Drowns, C.-L. C. Kulik, J. A. Kulik, and M. Morgan, “The Instructional Effect of Feedback in
Test-like Events,” Review of Educational Research, vol. 61, no. 2, p. 213, 1991.
N. Feldt-Caesar and R. Bruder, “Assessing Mathematical Basic Knowledge by means of Adaptive Testing
Elements,” in vol. 6, Proceedings of the 38th conference of the International Group for the Psychology of
Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of
Mathematics Education, S. Oesterle, C. Nicol, P. Liljedahl, and D. Allan, Eds., Vancouver, Canada: PME,
2014, p. 68.
G. Gregory, Differentiating instruction with style: Aligning teacher and learner intelligences for maximum
achievement. Thousand Oaks, Calif.: Corwin Press, 2005.
M. Kallweit et al., “Digitale Diagnostische Testaufgaben - Theoretisches Design und interaktives Beispiel,”
in Beiträge zum Mathematikunterricht 2017, Münster: WTM-Verlag, 2017.
Dr. Bernhard Jacobs, Aufgaben stellen und Feedback geben. Url: http://psydok.psycharchives.de/jspui/
bitstream/20.500.11780/1024/1/feedback.pdf. Accessed on: Jun. 15 2017.

20. 7/6/2017 | Department of Mathematics | TU-Darmstadt | WG-Didactics | Felix Johlke | 20
References II
R. Nitsch, Diagnose von Lernschwierigkeiten im Bereich funktionaler Zusammenhänge: Eine Studie zu
typischen Fehlermustern bei Darstellungswechseln. Wiesbaden: Springer Spektrum, 2015.
R. Nitsch and R. Bruder, “Diagnosis of Students' Learning Difficulties in the field of functional relationships,”
in vol. 6, Proceedings of the 38th conference of the International Group for the Psychology of Mathematics
Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics
Education, S. Oesterle, C. Nicol, P. Liljedahl, and D. Allan, Eds., Vancouver, Canada: PME, 2014, p. 373.
R. Nitsch and F. Johlke, “Stabilität von Fehlermustern bei funktionalen Zusammenhängen,” in Beiträge zum
Mathematikunterricht 2016: Vorträge auf der 50. Tagung für Didaktik der Mathematik vom 07.03.2016 bis
11.03.2016 in Heidelberg, Münster: WTM Verlag für wissenschaftliche Texte und Medien, 2016.
G. J. Posner, K. A. Strike, P. W. Hewson, and W. A. Gertzog, “Accommodation of a scientific conception:
Toward a theory of conceptual change,” Sci. Ed., vol. 66, no. 2, pp. 211–227, 1982.
V. J. Shute, “Focus on Formative Feedback,” Review of Educational Research, vol. 78, no. 1, pp. 153–189,
2008.
S. Vosniadou, X. Vamvakoussi, and I. Skopeliti, “The Framework Theory Apprioach to the Problem of
Conceptual Change,” in Educational psychology handbook series, International handbook of research on
conceptual change, S. Vosniadou, Ed., New York: Routledge, 2008, pp. 3–34.