Computational Thinking as an Emergent Learning Trajectory of Mathematics Pia Niemelä, Tiina Partanen, Maarit Harsu, Leo Leppänen, Petri Ihantola
Computational Thinking as anEmergent Learning Trajectory of
MathematicsPia Niemelä, Tiina Partanen, Maarit Harsu,
Leo Leppänen, Petri Ihantola
Computational Thinking added to Finnish National Curriculum in 2014
Y1-Y2 Y3-Y6 Y7-Y9
Digital
CompetenceUsing digital media
Noticing impacts of
computer science
Integrating
computer science
in other subjects
MathStep-by-step
instructions
Visual
programming
Algorithmic
thinking, problem
solving, good
coding conventions
CraftsRobots,
automation
Embedded
systems, own
artifacts
Code ABC MOOC
■ On-line course for in-service elementary school
teachers to learn computational thinking and
programming
■ Organized twice-a-year (2015-17)
■ Started/completed: 3649/1299
■ 2-3 credit points from Open University, University of
Helsinki
ScratchJr (Y1-2) Scratch (Y3-6)
Racket (Y7-9) Python (Y7-9)
Four tracks
Design targets
4
Visually interesting programming artifacts
Creativity
Programming integrated into math lessons
f(x)
Mathematics
Computing Exercises ready to be used in classroom
Racket track
Topic 1 Topic 2 Topic 3 Topic 7Topic 4 Topic 5 Topic 6
Variables,
expressions,
evaluation,
image
programming
Functions,
truth values,
comparisons,
predicates,
two-way
selection(if),
good coding
conventions
Logic, boolean
operators,
multi-way
selection
(cond),
handling of
mouse events,
animations
Recursion, I/O,
Design Recipe,
local variables,
helper
functions
Lists,
implementing
a quiz using
recursion and
lists, running
and sharing
code in
browser
Higher-order
functions and
Racket Turtle
images
Computational
thinking,
Finnish
curriculum,
different
approaches to
teaching
programming
Programmed artefact per topic Pedagogical essay
N=206
Model of computational thinking
Based on CT definitions from
Wing (2006) and
Cuny, Snyder and Wing (2010)
1. How do the teachers define computational thinking?
abstraction
automation
logic
analysiscreativity
Problem solving,
decomposition, functions
Algorithms, command
sequences, iterative
thinking
Debugging,
assessing results
“Algorithmic thinking produces such
routines that facilitate and speed up
our everyday actions.”
“Everybody benefits from decomposing
problems into subproblems and solving
them step-by-step. In computing, like in
math, problem-solving starts with
decomposing the problem into smaller
tasks, i.e., functions.”
Creative play vs. theoryClaim: “Computing should be taught by concentrating more on theory, concepts and design than creative hands-on experiments” (N=206)
“I think computing is not
creative at all! Not adhering
strictly to the rules will be
penalized. Creativity can
not be taught by
programming.
Teaching programming may
be reduced to merely
teaching the theory. ”
“It is crucial to learn the importance of
planning. It is important that a student
will be able to think about the program
and its functionality even without
knowing how to code. Thus, I consider
design as the most important skill.
Once the design is clear, it is easy to
implement the program.”
“I enjoy such tasks the most that
allow playing and experimenting.
When starting with a completely
new group, I would teach this
way, not so much going through
the pile of different concepts”
Inspired by creativity
Programming artifacts from topic 1
“Here is my owl. I wanted to include it
here, because while doing it I was
inspired like a child. The whole world
of coding, its opportunities and
creativity opened to me. I was capable
of doing this and the result was
unique!”
geometryalgebra
arithmetic
2. How do they integrate computing with math? Plane geometry
(drawing 2D shapes:
triangle, square,
circle), area, graphs,
solid geometry
(drawing 3D shapes:
cube, cylinder, cone),
volume, trigonometry,
symmetry,
transformations
coordinate system,
Pythagoras
Operations, order
of operations,
percentages
Functions, variables,
expressions/equations,
visualizing and analyzing function behavior
Logical thinking, Boolean values and operators, truth tables,
Creative exercises related mainly to geometry
3. What kind of a learning trajectory for CT can be constructed from the teachers’ essays?
Thank you!
AnalysisAbstraction
Automation Logic
Creativity
For more information: Computational Thinking as an Emergent Learning Trajectory of Mathematics in Proceedings of the 17th Koli Calling
International Conference on Computing Education Research