Original: Using Matchboxes to Teach the Basics of Machine Learning: an Analysis of (Possible) Misconceptions
Revised: Using Matchboxes to Teach the Basics of Machine Learning: an Analysis of (Possible) Misconceptions

Original: Anonymous Authors

Original: Abstract
Revised: Abstract

Original: The idea of chess-playing matchboxes, conceived by Martin Gardner as early as 1962, is becoming more and more relevant in learning materials in the area of AI and Machine Learning.
Revised: The idea of chess-playing matchboxes, conceived by Martin Gardner as early as 1962, is becoming more and more relevant in learning materials in the area of AI and Machine Learning.

Original: Thus, it can be found in a large number of workshops and papers as an innovative teaching method to convey the basic ideas of reinforcement learning.
Revised: Thus, it can be found in a large number of workshops and papers as an innovative teaching method to convey the basic ideas of reinforcement learning.

Original: In this paper the concept and its variations will be presented and the advantages of this analog approach will be shown.
Revised: In this paper the concept and its variations will be presented and the advantages of this analog approach will be shown.

Original: At the same time, however, the limitations of the approach are analyzed and the question of alternatives is raised.
Revised: At the same time, however, the limitations of the approach are analyzed and the question of alternatives is raised.

Original: 1. Introduction
Revised: 1. Introduction

Original: As Machine Learning (ML) has an increasing inﬂuence on many people’s everyday life, (Nayak & Dutta, 2017) there is a need for concepts to include ML in workshops and other learning scenarios.
Revised: As Machine Learning (ML) has an increasing inﬂuence on many people’s everyday life, (Nayak & Dutta, 2017) there is a need for concepts to include ML in workshops and other learning scenarios.

Original: Building these scenarios, so that beginners can gain insight into the underlying concepts, while avoiding oversimpliﬁcations and misconceptions can be very challenging, especially when talking about recent technological developments.
Revised: Building these scenarios, so that beginners can gain insight into the underlying concepts, while avoiding oversimpliﬁcations and misconceptions can be very challenging, especially when talking about recent technological developments.

Original: Unplugged materials like the
Revised: Unplugged materials like the

Original: Hexapawn game show a creative and motivating approach to the topic.
Revised: Hexapawn game show a creative and motivating approach to the topic.

Original: In this paper, we will take a look at these materials and discuss what misconceptions can occur, using this approach.
Revised: In this paper, we will take a look at these materials and discuss what misconceptions can occur, using this approach.

Original: 2. Misconceptions
Revised: 2. Misconceptions

Original: The study of misconceptions in computer science education and in education in general is a well-studied and still current research topic especially in computer science didactics (Sorva, 2012) (Ohrndorf, 2016)
Revised: The study of misconceptions in computer science education and in education in general is a well-studied and still current research topic especially in computer science didactics (Sorva, 2012) (Ohrndorf, 2016)

Original: (Qian & Lehman, 2017).
Revised: (Qian & Lehman, 2017).

Original: Misconceptions can be understood as entrenched systematic errors (Prediger & Wittmann, 2009).
Revised: Misconceptions can be understood as entrenched systematic errors (Prediger & Wittmann, 2009).

Original: However, Qian
Revised: However, Qian

Original: Lehmann also discuss other hard-to-deﬁne concepts such as difﬁculties, mistakes, and bugs, stating that there is no single deﬁnition (Qian & Lehman, 2017).
Revised: Lehmann also discuss other hard-to-deﬁne concepts such as difﬁculties, mistakes, and bugs, stating that there is no single deﬁnition (Qian & Lehman, 2017).

Original: As a deﬁnition for misconceptions in CS programming education (Sorva, 2012) states the following: “understandings that are deﬁcient or inadequate for many practical programming contexts”.
Revised: As a deﬁnition for misconceptions in CS programming education (Sorva, 2012) states the following: “understandings that are deﬁcient or inadequate for many practical programming contexts”.

Original: In reference to (Ohrndorf, 2016)
Revised: In reference to (Ohrndorf, 2016)

Original: we deﬁne misconceptions as cognitive representations of knowledge that contradict or deviate from the scientiﬁcally correct concepts.
Revised: we deﬁne misconceptions as cognitive representations of knowledge that contradict or deviate from the scientiﬁcally correct concepts.

Original: (Heuer et al., 2021) examined machine learning tutorials for misconceptions and misleading explanations, identifying four main misconceptions: (H1) ML as adapting in response to new data and experiences to improve efﬁcacy over time; (H2) ML as automating and improving the learning process of computers based on their experiences without any human assistance; (H3) ML can discover hidden patterns that are invisible to humans; (H4) ML can be applied without special expertise.
Revised: (Heuer et al., 2021) examined machine learning tutorials for misconceptions and misleading explanations, identifying four main misconceptions: (H1) ML as adapting in response to new data and experiences to improve efﬁcacy over time; (H2) ML as automating and improving the learning process of computers based on their experiences without any human assistance; (H3) ML can discover hidden patterns that are invisible to humans; (H4) ML can be applied without special expertise.

Original: 3. The Game
Revised: 3. The Game

Original: The original game idea of (Gardner, 1962) is a chess variant called ”Hexapawn”.
Revised: The original game idea of (Gardner, 1962) is a chess variant called ”Hexapawn”.

Original: On a 3x3 chess board, three pawns of different colors face each other ( Figure 1 ).
Revised: On a 3x3 chess board, three pawns of different colors face each other ( Figure 1 ).

Original: The objective is either to move a pawn to the opponent’s baseline or to capture all of the opponent’s pawns.
Revised: The objective is either to move a pawn to the opponent’s baseline or to capture all of the opponent’s pawns.

Original: One can also win by achieving a position in which the enemy cannot move (Stalemate).
Revised: One can also win by achieving a position in which the enemy cannot move (Stalemate).

Original: The pawns move one step forward as in chess and capture diagonally forward.
Revised: The pawns move one step forward as in chess and capture diagonally forward.

Original: With these simple game rules it is possible to construct what
Revised: With these simple game rules it is possible to construct what

Original: Gardner described as a ”learning machine” or ”Hexapawn
Revised: Gardner described as a ”learning machine” or ”Hexapawn

Original: Educable Robot” (HER) 1 .
Revised: Educable Robot” (HER) 1 .

Original: The human player controls the white pieces, the AI the black ones.
Revised: The human player controls the white pieces, the AI the black ones.

Original: For each position that black might face, there is a corresponding matchbox.
Revised: For each position that black might face, there is a corresponding matchbox.

Original: It contains different colored beads, each of which is assigned to one particular move, that is possible in this position ( Figure 2 ).
Revised: It contains different colored beads, each of which is assigned to one particular move, that is possible in this position ( Figure 2 ).

Original: White begins to play and makes the ﬁrst move.
Revised: White begins to play and makes the ﬁrst move.

Original: When it is the AI’s turn, the move is determined by picking a beat (and, subsequently, a move) randomly from the matchbox, that corresponds to the current state of the game.
Revised: When it is the AI’s turn, the move is determined by picking a beat (and, subsequently, a move) randomly from the matchbox, that corresponds to the current state of the game.

Original: After that the human player makes the next move, changing the state of the game from which the next move of HER is derived.
Revised: After that the human player makes the next move, changing the state of the game from which the next move of HER is derived.

Original: The reason why Gardner’s idea is often used when teaching machine learning is that HER can learn.
Revised: The reason why Gardner’s idea is often used when teaching machine learning is that HER can learn.

Original: Everytime when
Revised: Every time when

Original: HER loses a game, the last drawn bead is removed from the box to make the corresponding losing move unable to happen again, which then makes it increasingly unlikely that HER loses in the following games.
Revised: HER loses a game, the last drawn bead is removed from the box to make the corresponding losing move unable to happen again, which then makes it increasingly unlikely that HER loses in the following games.

Original: After 10-15 games  HER is nearly unbeatable  (Gardner, 1962).
Revised: After 10-15 games against a skilled player HER is nearly unbeatable when faced with optimal play (Gardner, 1962).

Original: 4. Reception and Adaptions
Revised: 4. Reception and Adaptions

Original: Gardner’s idea can be construed as CS Unplugged activity, even though it did not appear on the original website 2 .
Revised: Gardner’s idea can be construed as CS Unplugged activity, even though it did not appear on the original website 2 .

Original: These focus on the problem-solving nature of computer science and are popular around the world.
Revised: These focus on the problem-solving nature of computer science and are popular around the world.

Original: Unplugged material is characterized by the fact that computers are deliberately avoided and instead analog work materials and a playful approach are used to introduce the basic ideas of CS.(Nishida et al., 2009)
Revised: Unplugged material is characterized by the fact that computers are deliberately avoided and instead analog work materials and a playful approach are used to introduce the basic ideas of CS.(Nishida et al., 2009)

Original: Besides other versions (The Royal Institution, 2008)  (Demˇsar & Demˇsar, 2015), the ”Sweet Learning Computer” created by McOwan & Curzon as part of the cs4fn project is the most known version of Hexapawn created as teaching material.
Revised: Besides other versions (The Royal Institution, 2008) activities/ (Demˇsar & Demˇsar, 2015), the ”Sweet Learning Computer” created by McOwan & Curzon as part of the cs4fn project is the most known version of Hexapawn created as teaching material.

Original: The authors focus on the playful aspect of the idea, for example by replacing beads with sweets, which may then be eaten in the learning step.
Revised: The authors focus on the playful aspect of the idea, for example by replacing beads with sweets, which may then be eaten in the learning step.

Original: Within the material, the workings of the Matchbox computer are described, but not the basic ideas of ML (McOwan & Curzon).
Revised: Within the material, the workings of the Matchbox computer are described, but not the basic ideas of ML (McOwan & Curzon).

Original: Starting from this basic concept, several works can be found that convey individual aspects of ML or AI.
Revised: Starting from this basic concept, several works can be found that convey individual aspects of ML or AI.

Original: (The Royal Institution, 2008) for example, used Gardner’s example in its Christmas lecture, explaining how the machine learns.
Revised: (The Royal Institution, 2008) for example, used Gardner’s example in its Christmas lecture, explaining how the machine learns.

Original: Motivated by the example, it then gives an overview of how a real chess computer works.
Revised: Motivated by the example, it then gives an overview of how a real chess computer works.

Original: A deeper insight into ML is provided in the material of Lindner & Seegerer and Opel et.
Revised: A deeper insight into ML is provided in the material of Lindner & Seegerer and Opel et.

Original: al. ,
Revised: al. ,

Original: where
Revised: where

Original: Hexapawn is used directly to convey two principles form the ﬁeld of AI (Lindner & Seegerer, 2020).
Revised: Hexapawn is used directly to convey two principles form the ﬁeld of AI (Lindner & Seegerer, 2020).

Original: The original concept is used for reinforcement learning.
Revised: The original concept is used to teach reinforced learning.

Original: Here the students should learn that computers learn by ”reward” and ”punishment”, adapt their strategy accordingly and try to maximize their proﬁt.
Revised: Here the students should learn that computers learn by ”reward” and ”punishment”, adapt their strategy accordingly and try to maximize their proﬁt.

Original: For this purpose, the rules are slightly adapted by adding beads to winning moves.
Revised: For this purpose, the rules are slightly adapted by adding beads to winning moves.

Original: Second, Hexapawn is also used to explain expert systems and then compare the two methods.
Revised: Second, Hexapawn is also used to explain expert systems and then compare the two methods.

Original: (Opel et al., 2019) have created a larger set of materials 3 for an entire ML and AI module in which HER took the central role to explain and to reﬂect how ML works.
Revised: (Opel et al., 2019) have created a larger set of materials 3 for an entire ML and AI module in which HER took the central role to explain and to reﬂect how ML works.

Original: The material was developed for students from the age of 12 and has been adapted accordingly.
Revised: The material was developed for students from the age of 12 and has been adapted accordingly.

Original: First and foremost, a role system and a game ﬂow chart were created to make the learning process more understandable.
Revised: First and foremost, a role system and a game ﬂow chart were created to make the learning process more understandable.

Original: In addition, questions were designed to reﬂect the insights gained from the game afterwards.
Revised: In addition, questions were designed to reﬂect the insights gained from the game afterwards.

Original: Additionally background knowledge on ML, artiﬁcial neural networks and ”deep learning” was provided to help teachers answer possible queries from students.
Revised: Additionally background knowledge on ML, artiﬁcial neural networks and ”deep learning” was provided to help teachers answer possible queries from students.

Original: 5. Limitations and Possible Misconceptions
Revised: 5. Limitations and Possible Misconceptions

Original: In order to work out possible misconceptions, it is required to analyze how HER is structured.
Revised: In order to work out possible misconceptions, it is required to analyze how HER is structured.

Original: A fully trained HER formally consists of a handful of formal IF-THEN rules (if the game is in state a, then use move b).
Revised: A fully trained HER formally consists of a handful of formal IF-THEN rules (if the game is in state a, then use move b).

Original: HER is therefore a symbolic AI, or more precisely a rule-based expert system (Stuart, 1992, p. 3).
Revised: HER is therefore a symbolic AI, or more precisely a rule-based expert system (Stuart, 1992, p. 3).

Original: While these rule-based systems are very popular, they generally do not have the ability to expand their knowledge base through ML (Ogidan et al., 2018).
Revised: While these rule-based systems are very popular, they generally do not have the ability to expand their knowledge base through ML (Ogidan et al., 2018).

Original: Thus, the attempt to represent aspects of ML by Hexapawn faces the fundamental problem that Gardner’s model does not learn by common means of ML.
Revised: Thus, the attempt to represent aspects of ML by Hexapawn faces the fundamental problem that Gardner’s model does not learn by common means of ML.

Original: This inconsistency can lead to the following misconceptions:
Revised: The authors argue that this inconsistency can lead to the following misconceptions:

Original: M1)
Revised: M1)

Original: ML only produces results when the complete problem/data space is exhausted.
Revised: ML only produces results when the complete problem/data space is exhausted.

Original: M2)
Revised: M2)

Original: The way ML works is that undesirable behavior is trained out through negative examples.
Revised: The way ML works is that undesirable behavior is trained out through negative examples.

Original: M3)
Revised: M3)

Original: The way ML works in rule-based expert systems is that wrong rules are sorted out through negative examples.
Revised: The way ML works in rule-based expert systems is that wrong rules are sorted out through negative examples.

Original: M4)
Revised: M4)

Original: A decision tree is trained by training its nodes individually.
Revised: A decision tree is trained by training its nodes individually.

Original: The authors divide these misconceptions  into two areas.
Revised: These misconceptions are divided into two areas.

Original: The ﬁrst involves misconceptions about the ﬁeld of ML and its understanding.
Revised: The ﬁrst involves misconceptions about the ﬁeld of ML and its understanding.

Original: The second one contains misconceptions about individual models used in ML.
Revised: The second one contains misconceptions about individual models used in ML.

Original: 5.1. Misconceptions of ML
Revised: 5.1. Misconceptions of ML

Original: The following misconceptions arise from the structure and learning process of Gardner’s model.
Revised: The following misconceptions arise from the structure and learning process of Gardner’s model.

Original: Machine learning is the discipline of deriving actions or new insights from a (sufﬁciently large) collection of data.
Revised: Machine learning is the discipline of deriving actions or new insights from a (sufﬁciently large) collection of data.

Original: ML is used to derive an approximate solution that can be used to solve the problem for other unknown cases (Alpaydin, 2014, p. 1 ff.).
Revised: ML is used to derive an approximate solution that can be used to solve the problem for other unknown cases (Alpaydin, 2014, p. 1 ff.).

Original: The
Revised: The

Original: ML process roughly follows three steps.
Revised: ML process roughly follows three steps.

Original: The ﬁrst step is the data input step, in which data relevant to the problem is collected and processed.
Revised: The ﬁrst step is the data input step, in which data relevant to the problem is collected and processed.

Original: This data set is generally incomplete, as in practice the complete data space cannot be covered.
Revised: This data set is generally incomplete, as in practice the complete data space cannot be covered.

Original: This point is followed by step two, the abstraction .
Revised: This point is followed by step two, the abstraction .

Original: Here, the data is abstracted from its original form and passed to a model.
Revised: Here, the data is abstracted from its original form and passed to a model.

Original: The model is formed by appropriate procedures (e.g. training of the model) in such a way that it corresponds to the input data.
Revised: The model is formed by appropriate procedures (e.g. training of the model) in such a way that it corresponds to the input data.

Original: In the last step the generalization takes place.
Revised: In the last step the generalization takes place.

Original: The model should now be able to make decisions about an unknown data set (test data set).
Revised: The model should now be able to make decisions about an unknown data set (test data set).

Original: This is the reason why in general a predeﬁned rule set is not sufﬁcient.
Revised: This is the reason why in general a predeﬁned rule set is not sufﬁcient.

Original: Instead, a heuristic approach is chosen, according to which the solution is approximated (Chandramouli & Dutt, 2018).
Revised: Instead, a heuristic approach is chosen, according to which the solution is approximated (Chandramouli & Dutt, 2018).

Original: There are multiple ways to implement ML, the most common being supervised, unsupervised and reinforcement learning.
Revised: There are multiple ways to implement ML, the most common being supervised, unsupervised and reinforcement learning.

Original: Common models used in ML include artiﬁcial neural networks or decision trees (Alpaydin, 2014).
Revised: Common models used in ML include artiﬁcial neural networks or decision trees (Alpaydin, 2014).

Original: 5.1.1. ML VIA B RUTE F ORCE
Revised: 5.1.1. ML VIA B RUTE F ORCE

Original: Now let us look at how HER generates its rules.
Revised: Now let us look at how HER generates its rules.

Original: The rules to move a piece in a given position are ”learned” by testing all possible states of the game and eliminating moves if the result is undesirable.
Revised: The rules to move a piece in a given position are ”learned” by testing all possible states of the game and eliminating moves if the result is undesirable.

Original: However, this brute force approach contradicts the general approach of ML, in that information is derived from a ﬁnite data set to lead to generalized behavior.
Revised: However, this brute force approach contradicts the general approach of ML, in that information is derived from a ﬁnite data set to lead to generalized behavior.

Original: This brute force method is also why Hexapawn does not scale well to more complex scenarios (4x4 or 8x8 squares) when the amount of needed matchboxes becomes impracticable.
Revised: This brute force method is also why Hexapawn does not scale well to more complex scenarios (4x4 or 8x8 squares) when the amount of needed matchboxes becomes impracticable.

Original: HER thereby illustrates well, why we need ML for these kinds of problems, but represents it poorly itself.
Revised: HER thereby illustrates well, why we need ML for these kinds of problems, but represents it poorly itself.

Original: It can also contribute to the misconception H2 of (Heuer et al., 2021).
Revised: It can also contribute to the misconception H2 of (Heuer et al., 2021).

Original: Thus, one of the central problems of ML, data preparation, is downplayed by portraying the process as the collection of all possible data.
Revised: Thus, one of the central problems of ML, data preparation, is downplayed by portraying the process as the collection of all possible data.

Original: 5.1.2. T RAINING WITH NEGATIVE EXAMPLES
Revised: 5.1.2. T RAINING WITH NEGATIVE EXAMPLES

Original: The second misconception arises from the learning process and in particular the type of data HER receives.
Revised: The second misconception arises from the learning process and in particular the type of data HER receives.

Original: The learning process of removing beads characterizes both reinforced learning and ML deﬁcient.
Revised: The learning process of removing beads characterizes both reinforced learning and ML deﬁcient.

Original: In practice reinforced learning also relies on reinforcement of behavior.
Revised: In practice reinforced learning also relies on reinforcement of behavior.

Original: However, by removing beads in the original idea, only punishment is addressed (which is also less used in practice).
Revised: However, by removing beads in the original idea, only punishment is addressed (which is also less used in practice).

Original: While
Revised: While

Original: HER uses negative examples to remove unwanted behavior, in classical ML tasks behavior is trained using positive examples.
Revised: HER uses negative examples to remove unwanted behavior, in classical ML tasks behavior is trained using positive examples.

Original: Thus, while the learning procedure of HER is not categorically wrong, the student may get the wrong impression, which is that knowledge or behavior is built by removing undesirable behavior through negative examples rather than generalizing behaviour through example data in a ground-up process.
Revised: Thus, while the learning procedure of HER is not categorically wrong, the student may get the wrong impression, which is that knowledge or behavior is built by removing undesirable behavior through negative examples rather than generalizing behaviour through example data in a ground-up process.

Original: A solution described by (Opel et al., 2019) and (Lindner & Seegerer, 2020) is already possible in Gardner’s model by adding beads for winning moves.
Revised: A solution described by (Opel et al., 2019) and (Lindner & Seegerer, 2020) is already possible in Gardner’s model by adding beads for winning moves.

Original: 5.2. Misconceptions of Models in ML
Revised: 5.2. Misconceptions of Models in ML

Original: The second type of possible misconceptions arises from the context in which HER is used.
Revised: The second type of possible misconceptions arises from the context in which HER is used.

Original: As analyzed in the reception and adaptions section, HER is mostly used as a simple example of ML processes.
Revised: As analyzed in the reception and adaptions section, HER is mostly used as a simple example of ML processes.

Original: Following on from this, speciﬁc models of ML are introduced.
Revised: Following on from this, speciﬁc models of ML are introduced.

Original: Since learners are mostly ML novices and the structure of HER is usually not analyzed in detail, there is a chance that students intuitively interpret
Revised: Since learners are mostly ML novices and the structure of HER is usually not analyzed in detail, there is a chance that students intuitively interpret

Original: Hexapawn as one of the speciﬁed models.
Revised: Hexapawn as one of the speciﬁed models.

Original: However, due to the fact that Hexapawn does not adequately represent these, misconceptions about individual models of ML may be formed.
Revised: However, due to the fact that Hexapawn does not adequately represent these, misconceptions about individual models of ML may be formed.

Original: 5.2.1. ML IN EXPERT SYSTEMS
Revised: 5.2.1. ML IN EXPERT SYSTEMS

Original: As already analyzed, HER is a rule-based expert system.
Revised: As already analyzed, HER is a rule-based expert system.

Original: These, however, are generally not based on methods that conform to the classical idea of ML (which is supposed to be transported with HER), because they lack the possibility to learn from input Data and to adapt their fact base (Ogidan et al., 2018).
Revised: These, however, are generally not based on methods that conform to the classical idea of ML (which is supposed to be transported with HER), because they lack the possibility to learn from input Data and to adapt their fact base (Ogidan et al., 2018).

Original: There are rarely approaches in which either a hybrid method is used to train a ML model and then postprocess the result by an expert system (Villena-Rom´an et al., 2011), or the rule base is derived inductively from facts (Weiss & Indurkhya, 1995).
Revised: There are rarely approaches in which either a hybrid method is used to train a ML model and then post-process the result by an expert system (Villena-Rom´an et al., 2011), or the rule base is derived inductively from facts (Weiss & Indurkhya, 1995).

Original: Not only are these approaches exceptions, but also is neither of them presented by HER.
Revised: Not only are these approaches exceptions, but also is neither of them presented by HER.

Original: Therefore, HER is suitable for the representation of a rulebased expert system, but not in combination with ML.
Revised: Therefore, HER is suitable for the representation of a rule-based expert system, but not in combination with ML.

Original: In addition, the misconception (M3) may arise, that ML on rule based expert systems is the systematic removal of false facts by negative examples.
Revised: In addition, the misconception (M3) may arise, that ML on rule based expert systems is the systematic removal of false facts by negative examples which builds on the general misconception ( M2 ).

Original: (Lindner & Seegerer, 2020) use
Revised: (Lindner & Seegerer, 2020) use

Original: Hexapawn elsewhere in their material as an example of an expert system.
Revised: Hexapawn elsewhere in their material as an example of an expert system.

Original: Here the use is justiﬁed and a good example with suitable didactic reduction.
Revised: Here the use is justiﬁed and a good example with suitable didactic reduction.

Original: 5.2.2. ML CHESS ENGINES AND DECISION TREES
Revised: 5.2.2. ML CHESS ENGINES AND DECISION TREES

Original: The use of a ”brute-force” method and the presentation of the game provide further opportunities for the formation of misconceptions.
Revised: The use of a ”brute-force” method and the presentation of the game provide further opportunities for the formation of misconceptions.

Original: A classical chess engine generally consists of a heuristic function and a search tree optimization.
Revised: A classical chess engine generally consists of a heuristic function and a search tree optimization.

Original: While the search tree optimization is a classical optimization task, a ML approach can be used for the heuristics.
Revised: While the search tree optimization is a classical optimization task, a ML approach can be used for the heuristics.

Original: The trained model receives the current position as input and outputs an evaluation of the position.
Revised: The trained model receives the current position as input and outputs an evaluation of the position.

Original: Thus, the mode of operation is fundamentally different from HER and cannot be derived from it (M1)(M2) .
Revised: Thus, the mode of operation is fundamentally different from HER and cannot be derived from it (M1)(M2) .

Original: This would at the same time reinforce the misconception (H4) formulated by Heuer et al , since the complexity of chess engine engineering is disregarded.
Revised: This would at the same time reinforce the misconception (H4) formulated by Heuer et al , since the complexity of chess engine engineering is disregarded.

Original: It is true that the learning outcome of HER is critically dependent on the strength of the player.
Revised: It is true that the learning outcome of HER is critically dependent on the strength of the player.

Original: However, this does not sufﬁciently simulate the extent to which AI engineers are necessary for ML success, in that they are especially involved in modeling and data preparation rather than in the active learning process (H2) .
Revised: However, this does not sufﬁciently simulate the extent to which AI engineers are necessary for ML success, in that they are especially involved in modeling and data preparation rather than in the active learning process (H2) .

Original: (The Royal Institution, 2008) try to make the leap from HER to chess by addressing the game tree that results over several moves in a game of Hexapawn, referring to it as a decision tree.
Revised: (The Royal Institution, 2008) try to make the leap from HER to chess by addressing the game tree that results over several moves in a game of Hexapawn, referring to it as a decision tree.

Original: This is problematic in several ways.
Revised: This is problematic in several ways.

Original: A decision tree is a common model in ML but is not to be confused with the game tree of a chess game.
Revised: A decision tree is a common model in ML but is not to be confused with the game tree of a chess game.

Original: Furthermore, HER does not adequately represent either a game tree (the white moves are missing) or a decision tree nor does HER use a decision tree to evaluate a position.
Revised: Furthermore, HER does not adequately represent either a game tree (the white moves are missing) or a decision tree nor does HER use a decision tree to evaluate a position.

Original: In fact, each position is considered independently of its successors.
Revised: In fact, each position is considered independently of its successors.

Original: Therefore, HER is not suited to represent a decision tree, which in turn enables the formation of a misconception (M4) regarding decision trees.
Revised: Therefore, HER is not suited to represent a decision tree, which in turn enables the formation of a misconception (M4) regarding decision trees.

Original: (Lindner &
Revised: (Lindner &

Original: Seegerer, 2020) take a different approach by replacing the pawns with crocodiles and monkeys.
Revised: Seegerer, 2020) take a different approach by replacing the pawns with crocodiles and monkeys.

Original: This weakens the similarity to chess and tries to avoid listed misconceptions.
Revised: This weakens the similarity to chess and tries to avoid listed misconceptions.

Original: 5.2.3. ML AND NEURAL NETWORKS
Revised: 5.2.3. ML AND NEURAL NETWORKS

Original: Lastly, it should be noted that in the investigated material artiﬁcial neural networks (ANN) are also often mentioned.
Revised: Lastly, it should be noted that in the investigated material artiﬁcial neural networks (ANN) are also often mentioned.

Original: At this point it is important to point out that HER is not a good model for these networks either, since neither neurons, layers, edges, weights nor activation functions are represented by the model.
Revised: At this point it is important to point out that HER is not a good model for these networks either, since none of its components are represented by the model.

Original: Nevertheless, especially inexperienced students (for whom the material is designed) can make a connection from HER to ANN, since, on the one hand, ML is used almost synonymously with ANN in public media and, on the other hand, similarities from box to neuron and bead to weight can be made unconsciously.
Revised: Nevertheless, especially inexperienced students (for whom the material is designed) can make a connection from HER to ANN, since, on the one hand, ML is used almost synonymously with ANN in public media and. On the other hand, due to the structure of interconnected items (matchboxes) and the weighting of the game paths (beads), there is a possibility that students will make a connection to the neurons and weights of ANN.

Original: HER, thus, should explicitly be differentiated from ANN.
Revised: HER, thus, should explicitly be differentiated from ANN.

Original: 6. Conclusion
Revised: 6. Conclusion

Original: HER is very motivating especially for young students due to its simple rules, illustrative learning process and playful character.
Revised: HER is very motivating especially for young students due to its simple rules, illustrative learning process and playful character.

Original: Therefore, it is a suitable tool to convey the idea of ML (in that a computer can learn and adapt its behavior through new information) or teaching the concept of reinforced learning.
Revised: Therefore, it is a suitable tool to convey the idea of ML (in that a computer can learn and adapt its behavior through new information) or teaching the concept of reinforced learning.

Original: Nonetheless, based on the previous analysis students may develop misconceptions about the general working of ML or important models used in ML with Hexapawn.
Revised: Nonetheless, based on the previous analysis students may develop misconceptions about the general working of ML or important models used in ML with Hexapawn.

Original: Further investigations are necessary to determine whether and to what extent the described misconceptions are developed when playing Hexapawn and which adaptions have to be made to the material to circumvent these.
Revised: Further investigations are necessary to determine whether and to what extent the described misconceptions are developed when playing Hexapawn and which adaptions have to be made to the material to circumvent these.

Original: Additionally with the aforementioned considerations in mind, the question must be raised whether individual aspects of ML can be better conveyed through other unplugged materials avoiding listed misconceptions, as there are already materials which clearly convey the basic concepts of
Revised: Additionally with the aforementioned considerations in mind, the question must be raised whether individual aspects of ML can be better conveyed through other unplugged materials avoiding listed misconceptions, as there are already materials which clearly convey the basic concepts of

Original: ML without sacriﬁcing formal accuracy.
Revised: ML without sacriﬁcing formal accuracy.

Original: With the material ”Train a Neuron” by cs4fn 4 , for example, a similar game feeling can be created with a game board and coins, but with the advantage that both the structure, functioning and learning procedures of an ANN are taught.
Revised: With the material ”Train a Neuron” by cs4fn 4 , for example, a similar haptic feeling can be created with a game board and coins, but with the advantage that both the structure, functioning and learning procedures of a Neuron are taught.

Original: With the material of Blum & Girschick it iseven possible to teach (un)supervised learning with pen and paper only 5 .
Revised: With the material of Blum & Girschick it is possible to teach (un)supervised learning with pen and paper only 5 .

Original: If one wants to focus on reinforcement learning, Blum developed a learning activity for this as well 6 .
Revised: If one wants to focus on reinforcement learning, Blum developed a learning activity for this as well 6 .

Original: If, on the other hand, one does not want to forego the approach via a game, ”Brain in a Bag”, also by cs4fn 7 , is a another choice.
Revised: If, on the other hand, one does not want to forego the approach via a game, ”Brain in a Bag”, also by cs4fn 7 , is a another choice.

Original: With this material, the game
Revised: With this material, the game

Original: Snap or, with slight adaptations, games such as Nods and
Revised: Snap or, with slight adaptations, games such as Nods and

Original: Crosses can be addressed.
Revised: Crosses can be addressed.

Original: This way it is also possible to simulate a classic game AI, by having the network evaluate the current board state.
Revised: This way it is also possible to simulate a classic game AI.

Original: This approach is also conceivable for Hexapawn.

Original: Finally, it should be pointed out that HER is also suitable for teaching a classical AI method: the rulebased expert system (as described by (Lindner &Seegerer, 2020)).
Revised: Finally, it should be pointed out that HER is also suitable for teaching a classical AI method: the rule-based expert system (as described by (Lindner &

Original: 4 https://cs4fndownloads.wordpress.com/ train-a [Table] neuron/ 5 https://explore.iteratec.com/blog/ [Table]
Revised: Seegerer, 2020)).

Original: teil-1 (german)https://explore.iteratec.com/blog/ [Table] teil-2 (german) 7 http://www.cs4fn.org/teachers/ activities/braininabag/braininabag.pdf
Revised: train