computational thinking as an emergent learning trajectory of mathematics

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Computational Thinking as an Emergent Learning Trajectory of Mathematics Pia Niemelä, Tiina Partanen, Maarit Harsu, Leo Leppänen, Petri Ihantola

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Page 1: Computational Thinking as an Emergent Learning Trajectory of Mathematics

Computational Thinking as anEmergent Learning Trajectory of

MathematicsPia Niemelä, Tiina Partanen, Maarit Harsu,

Leo Leppänen, Petri Ihantola

Page 2: Computational Thinking as an Emergent Learning Trajectory of Mathematics

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

Page 3: Computational Thinking as an Emergent Learning Trajectory of Mathematics

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

Page 4: Computational Thinking as an Emergent Learning Trajectory of Mathematics

Design targets

4

Visually interesting programming artifacts

Creativity

Programming integrated into math lessons

f(x)

Mathematics

Computing Exercises ready to be used in classroom

Page 5: Computational Thinking as an Emergent Learning Trajectory of Mathematics

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

Page 6: Computational Thinking as an Emergent Learning Trajectory of Mathematics

Model of computational thinking

Based on CT definitions from

Wing (2006) and

Cuny, Snyder and Wing (2010)

Page 7: Computational Thinking as an Emergent Learning Trajectory of Mathematics

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.”

Page 8: Computational Thinking as an Emergent Learning Trajectory of Mathematics

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”

Page 9: Computational Thinking as an Emergent Learning Trajectory of Mathematics

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!”

Page 10: Computational Thinking as an Emergent Learning Trajectory of Mathematics

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

Page 11: Computational Thinking as an Emergent Learning Trajectory of Mathematics

3. What kind of a learning trajectory for CT can be constructed from the teachers’ essays?

Page 12: Computational Thinking as an Emergent Learning Trajectory of Mathematics

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