Teaching algorithms in upper secondary education: a study of teachers’ pedagogical content knowledge

Figures & data

Table 1. Teaching experience of teachers participating in the study.

Teacher	Teaching experience (years)	Teacher education
1	16–20	CODI
2	6–10	CS Education (BSc)
3	6–10	CS Education (student)
4	6–10	CS Education (MSc)
5	6–10	CS Education (MSc)
6	16–20	CODI
7	1–5	CS Education (MSc)

Table 2. Interview questions used in this study.

	Questions
1.	What do you see your students doing during lessons on algorithms and algorithmic thinking?
2.	What do you do during these lessons?
3.	What do you intend for your students to learn?
4.	Why is it important for students to learn this?
5.	What elements do your students enjoy or find interesting about this topic?
6.	What elements do your students think of as easy about this topic? How do you recognize this?
7.	What elements do your students think of as difficult about this topic? How do you recognize this?
8.	Do you notice during lessons whether students fully comprehend what is taught? How can you tell?
9.	Do differences in the prior knowledge of students play a role when teaching this topic? How do you deal with that?
10.	For this topic, how do you handle the different interests of the students?
11.	Are there other differences between students that you observe and take into account in your lessons? How do you do that?

Figure 1. Definition of algorithmic thinking.

Table 3. Coding scheme for PCK.

Categories	Codes
Goals	Goals for teaching algorithms
	• learning to analyze algorithmic problems (e.g. decomposition)
	• learning to solve algorithmic problems
	• learning to code an algorithm
	• learning to analyze quality aspects of algorithms
	• being able to apply problem-solving skills outside CS
	• learning transversal skills while solving algorithmic problems
	Motivations for objectives
	• preparing for a role in society
	• working with computers as tools
Students’ understanding	Variation in student approaches to learning because of:
	• different abilities
	• different interests
	• other reasons (e.g. different levels, motivation, gender)
	Prior knowledge and skills with respect to:
	• programming experience
	• mathematical knowledge
	• analytical skills
	Activities that are difficult or easy to learn
	• difficult: how to start solving problems
	• difficult: abstract problems, generalizing
	• difficult: analyzing and optimizing an algorithm
	• difficult: describing the analysis of algorithms, asymptotic notation
	• easy: concrete problems, puzzles
	Elements students get (dis)engaged by
	• engaged by satisfaction, gratification of finding a solution
	• engaged by solving puzzles, “unplugged”
	• engaged by understanding “how it works”
	• disengaged by specifying algorithm (e.g. flowchart)
Instructional strategies	Representations for algorithms
	• describe algorithm in different languages (natural or programming)
	• express algorithms in schematic diagrams (e.g. flowchart)
	• use illustrations, examples (e.g. puzzles)
	Teacher activities to help students comprehend specific concepts
	• coaching or scaffolding
	• discussing solutions with the class
	• lecturing or instructing a class
	Class activities to help a class comprehend specific concepts
	• where students are active in practical work
	• where students think, reflect, evaluate
	• where students cooperate
Assessment	Aspects of students’ learning that are important to assess
	• developing an algorithm
	• implementation of an algorithm
	Specific instruments of assessment
	• observing students during class
	• asking questions to students
	• giving students a test or a practical assignment
Interconnections	Connection GO–SU
	• focus regarding goals is related to the appreciation of prior programming experience
	•
	• students like to find the solution of an algorithmic problem
	• students are interested in relevant algorithmic problems
	Connection SU–IS
	• adapting instructional strategies to meet student differences
	• scaffolding for topics that are difficult to learn
	Connection GO–IS
	• specific instructional strategies for reaching certain goals
	• use of representations that are dependent on goals
	Connection GO–AS
	• specific types of assessment for tracking certain goals

Figure 2. Interconnection between PCK components (Adapted from Bayram-Jacobs et al., 2019).

Figure 3. Two foci in teachers’ PCK for teaching algorithms.

Bayram-Jacobs, D., Henze, I., Evagorou, M., Shwartz, Y., Aschim, E. L., Alcaraz-Dominguez, S., Barajas, M., & Dagan, E. (2019). Science teachers’ pedagogical content knowledge development during enactment of socioscientific curriculum materials. Journal of Research in Science Teaching, 56(9), 1207–1233. https://doi.org/10.1002/tea.21550

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