# The Impact of Tolerance for Ambiguity on Algorithmic Problem Solving in Computer Science Lessons

Lisa Zapp, Matthias Matzner, Claudia Hildebrandt

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Lisa Zapp, Matthias Matzner, Claudia Hildebrandt. The Impact of Tolerance for Ambiguity on Algorithmic Problem Solving in Computer Science Lessons. IFIP World Conference on Computers in Education (WCCE), Aug 2022, Hiroshima, Japan. pp.173-183, 10.1007/978-3-031-43393-1_17 hal-05533340

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# The Impact of Tolerance for Ambiguity on Algorithmic Problem Solving in Computer Science Lessons

Lisa Zapp<fnref n="1" /> ID, Matthias Matzner<fnref n="2" />(✉) ID, and Claudia Hildebrandt<fnref n="2" /> ID

matthias.matzner@uni-oldenburg.de, hildebrandt@ph-heidelberg.de

**Abstract.** Learners can perceive algorithmic problem solving to be ambiguous, especially in computer science lessons. Tolerance to this individually perceived ambiguity is an internal factor that can influence the absorption and processing of knowledge both positively and negatively. Thus, it was examined whether there is a connection between tolerance for ambiguity and the performance of students such a task for algorithmic problem solving in computer science lessons. The results show that there is a significant correlation between tolerance for ambiguity and the number of points achieved in the test for algorithmic problem solving.

**Keywords:** Tolerance for Ambiguity · Algorithmic Problem Solving ·

Quantitative Research · Computer Science Lessons · Upper Secondary Education

## 1 Introduction

Algorithmic problem solving is one of the central competencies that students should learn during computer science lessons. This skill helps students to acquire more knowledge about computer science and is applicable in a plethora of professions. The authors have observed often how some students would be stumped by ambiguous algorithmic problem-solving tasks. On inquiry the students replied that they were irritated by the diversity of possible solutions or by the openness of the task itself.

This phenomenon can also occur when learning a foreign language and is theoretically associated with the factor of tolerance for ambiguity [1]. It is assumed that students can accept and endure ambiguous situations to varying degrees [2, 3]. The aim of the study at hand is to answer the question “To what extent are tolerance for ambiguity and solving ambiguous algorithmic problem-solving tasks connected?”, which relates to the empirical findings in the field of foreign languages [4–6]. For this study, an ambiguous task for algorithmic problem solving was developed. Using a standardized test for tolerance for ambiguity [7] and the students’ solutions on the task, the relationship between tolerance of ambiguity and performance in algorithmic problem solving is investigated. The performance measures include the number of points achieved and the time required for the task.

<footnote n="1">¹ Studienseminar Leer Für das Lehramt an Gymnasien, Leer, Germany</footnote>

<footnote n="2">² University of Education Heidelberg, Heidelberg, Germany</footnote>
# 2 Theoretical Background

The first part of the study is comprised of definitions for tolerance for ambiguity and algorithmic problem solving. Since the factor of tolerance for ambiguity has not yet been investigated in the field of computer science education, related research about foreign language acquisition and mathematics education is processed. After that, the theoretical relationship between the variables is worked out, considering the definitions and categories according to Budner [8] and Norton [9].

## 2.1 Tolerance for Ambiguity

Tolerance for ambiguity describes how well or badly a person can deal with ambiguous situations and can influence the absorption and processing of knowledge and information [3]. Intolerance for ambiguity is a psychological factor which Budner (1962) defined as "[...] the tendency to perceive ambiguous situations as sources of threat" [[8], p. 29]. In reversal, the tolerance for ambiguity describes a tendency which either tolerates ambiguous situations or rejects their ambiguous nature.

Budner forgoes a determination of the valence of the factor of tolerance for ambiguity, although the wording of the definition seems to tend towards a negative valence of intolerance for ambiguity [8]. The more neutral definition of tolerance for ambiguity by Brown (2000) is chosen as the central definition for the study at hand: "The degree to which you are cognitively willing to tolerate ideas and propositions that run counter to your own belief system or structure of knowledge" [1, p. 118].

It should be noted that ambiguity is subjectively perceived – something may seem clear to one person and ambiguous to another. Also, ambiguity can arise in various situations and to varying degrees. Budner (1962) developed three categories to describe the varying degrees, while Norton (1975) added a fourth category. The four categories that a situation can be characterized as are:

1. In a completely new situation all the information is new and unknown [8].

2. In a complex situation a lot of information is available, but either the amount of information is too large or the information is too complex [8].

3. In a contradictory situation different approaches or solutions to a problem are possible [8].

4. In an unstructured situation the necessary information, desired beginning and end states may be available, but lack any order which would promote problem solving [9].

## 2.2 Algorithmic problem solving

The PISA-consortium defines problem-solving as follows: "Problem solving begins with recognizing that a problem situation exists and establishing an understanding of the nature of the situation. It requires the solver to identify the specific problem(s) to be solved and to plan and carry out a solution, along with monitoring and evaluating progress throughout the activity" [10, p. 123]. In more abstract terms, problem solving are the activities that translate the beginning state to a desired end state [11, 12]. First, the beginning and the desired end state must be identified. Then, necessary transitional
states and transitional actions between the states must be determined. Finally, a definite sequence of clearly executable instructions must be formulated and implemented as an executable program that solves the given problem [13–15].

## 2.3 State of Research

The factor tolerance for ambiguity has been researched in foreign language acquisition since 1975, but the results in this area of research are quite controversial [7]. The controversy arises from disagreements between [1, 5] and [15] – among others – about whether tolerance for ambiguity has a positive or negative influence on the absorption and processing of knowledge. Brown [1] argues on a theoretical level that tolerance for ambiguity can be an advantage in foreign language acquisition, as students more tolerant towards ambiguity are better able to tolerate the irregularities in the foreign language. Intolerance can, however, also contribute to the fact that the students reject new knowledge, since this threatens the already existing knowledge [1]. Brown (2007) even argues that very high levels of intolerance could prevent language learning. Inversely, it could be concluded that a certain degree of tolerance for ambiguity can have a positive influence on students when learning a foreign language. However, a low tolerance for ambiguity can also have a positive effect, as this can protect the students’ existing knowledge from doubts that could arise from new knowledge [1]. However, it is unclear how much tolerance for ambiguity there must be for this positive effect to occur [16].

In addition to these theoretical arguments, empirical findings are available as well. For example, Stark, Gruber, Renkl and Mandl (1997) have studied the connection between tolerance for ambiguity and the acquisition of transferable knowledge. They examined 60 vocational commerce school students with the help of a computer simulation [17]. The research design is a 2x2 factor correlational study, where ambiguous situations were developed through different learning contexts (uniform vs. multiple) with varying levels of support (unguided vs. guided) [17]. A statistically significant link was identified between close transfer and tolerance for ambiguity. Even if the connection between tolerance for ambiguity and transfer of learning varied greatly between the groups, the authors nevertheless concluded that a higher tolerance generally tends to indicate better transfer of learning [17]. Furthermore, Stark et al. (1997) found that solving simple tasks worked better when there was no support from the teacher. In contrast, the learning process for more complex tasks was more likely to be improved if the teacher provided guidance. A different study suggests that more ambiguity-tolerant students benefit from a more complex learning environment [18]. Additionally, the study by Buela and Joaquin (2018) found that tolerance for ambiguity can be a positive predictor of mathematical problem solving [2]. Furthermore, they were able to determine moderate positive associations between the ability to solve problems and the tolerance for ambiguity [2]. Summarizing, it seems that students with higher tolerance for ambiguity are better able to cope with more complex tasks, can transfer knowledge better and have a higher ability to solve problems.

While performing cognitively demanding tasks, the available amount of cognitive resources people invest in performing a task are also important in this context. According to the classical Cognitive Load Theory (CLT) extraneous, germane, and intrinsic
cognitive load are three types of cognitive load which together make up total cognitive load [16, 17]. But this aspect is not part of investigation.

## 2.4 Tolerance for Ambiguity in Algorithmic Problem Solving

In the following section, we will illustrate the ambiguity of algorithmic problem-solving tasks through examples taken from recent computer science lessons. Imagine the following example task: implement a square with an edge length of 5 cm in the Scratch programming environment. This task defines the desired end state very clearly. The situation can still be classified as completely new [8] if the students have no prior knowledge of programming and the Scratch environment. For students that have prior knowledge, the task will have less or even no ambiguity at all. Imagine another example task: sort an uncertain quantity of numbers using a program. This task offers no information about the quantity of numbers that should be sorted, whether an application should be developed or found and used (such as currently available table calculation software) or which developing environment should be used for implementing an eventual application. This task can be classified as first, third and fourth category or completely new, contradictory and unstructured. The first category is applicable since the developing environment is unspecified. As no desired end state is specified, the students must determine it themselves which justifies numerous approaches and, thusly, the task can also be classified in the 3rd category [8]. As no structure for the solution is provided by the task description, the 4th category [9] applies here as well.

When solving problem tasks the application of meta-cognitive strategies can improve process and product. Metacognition is often defined as “thinking about thinking” [12, p. 188]. More fittingly meta-cognitive strategies should be described as the “focus on the selection and control of problem-solving strategies”. Examples of meta-cognitive strategies are “planning how to approach a given learning task, evaluating progress, and monitoring comprehension” [12, p. 188]. With an effect size of d = 0.69, the meta-cognitive strategies factor is one of the most effective teaching interventions [12].

# 3 Research Method

A written two-part questionnaire was administered: the part was a tolerance for ambiguity test [7] and the second part was a test for algorithmic problem solving. The data of 23 German 12th and 13th grade students attending a computer science course in the school year of 2020/2021 were collected. The sample was split into students with high and low levels of tolerance for ambiguity and compared on their task performance using non-parametric procedures using SPSS.

## 3.1 Instrumentation

**Tolerance for Ambiguity Test.** The independent variable tolerance for ambiguity is assessed through the Multiple Stimulus Types Ambiguity Tolerance Scale-II, MSTAT-II [7]. The test does not use examples and is not tied to a specific context. Furthermore, McLain (2009) developed the questions in adherence to the definitions of tolerance
for ambiguity by Budner [8] and Norton [9]. Additional advantages of this test are its demonstrated reliability and validity [7].

In addition, the test by McLain (2009) consists of 13 statements, which are rated on a five-digit scale ("does not apply" – "does apply") and is therefore very short and compact, making it very suitable for a written survey [7]. The 13 statements were translated into German. The translation attempts to preserve the original intentions of McLain (2009). The test – therefore – remains complex due to its abstract level, repetition and similarity between statements and reversely coded statements.

In the MSTAT-II test, a maximum of 65 and a minimum of 13 points can be achieved, whereby higher scores indicate higher tolerance for ambiguity [9]. Reversely coded statements are 1 through 6, 9, 11 and 12 (Table 1). The internal consistency was determined good to very good [19] with a Cronbach's alpha of 0.83.

<table><caption>**Table 1.** Statements of the tolerance for ambiguity test according to McLain [7].</caption><thead><tr><td>Item</td><td>Reverse</td><td>Statement</td></tr></thead><tbody><tr><td>1</td><td>✓</td><td>I don't tolerate ambiguous situations well</td></tr><tr><td>2</td><td>✓</td><td>I would rather avoid solving a problem that must be viewed from several different perspectives</td></tr><tr><td>3</td><td>✓</td><td>I try to avoid situations that are ambiguous</td></tr><tr><td>4</td><td>✓</td><td>I prefer familiar situations to new ones</td></tr><tr><td>5</td><td>✓</td><td>Problems that cannot be considered from just one point of view are a little threatening</td></tr><tr><td>6</td><td>✓</td><td>I avoid situations that are too complicated for me to easily understand</td></tr><tr><td>7</td><td></td><td>I am tolerant of ambiguous situations</td></tr><tr><td>8</td><td></td><td>I enjoy tackling problems that are complex enough to be ambiguous</td></tr><tr><td>9</td><td>✓</td><td>I try to avoid problems that don't seem to have only one "best" solution</td></tr><tr><td>10</td><td></td><td>I generally prefer novelty over familiarity</td></tr><tr><td>11</td><td>✓</td><td>I dislike ambiguous situations</td></tr><tr><td>12</td><td>✓</td><td>I find it hard to make a choice when the outcome is uncertain</td></tr><tr><td>13</td><td></td><td>I prefer a situation in which there is some ambiguity</td></tr></tbody></table>

**Test Items for Algorithmic Problem Solving.** The students' algorithmic problem solving is assessed by an implementation task. The procedure for the survey is based on the research by Atef-Vahid et al. (2011) [4]. The performance of the students was reflected by two measures, namely the number of points earned and the processing time.

Tasks from the Society for Computer Science [20] were deemed too time intensive, while tasks from the Bebras Contest [21] would have to be altered too much to reflect an implementation task. Therefore, an ambiguous task of algorithmic problem-solving was designed by altering Lutz Kohl's (2009) telephone provider task dealing with the main concept of if-else statements and being solved with a block-based programming language
[14]. The alteration made consisted of converting telephone rates, originally presented in tabular form, into an unstructured text (cf. Test items for algorithmic problem solving).

Assignment: Marco made too many phone calls in the last month. His parents have now decided to allow him a fixed amount of money for phone calls. Marco wants to make optimal use of his allowance and has therefore selected the minute rates from four different providers and the associated telephone numbers. The new provider Telefonus with the number 01357 would cost Marco 0.03 euros per minute for landline calls and 0.38 euros for calls to the mobile network. In the off-peak times, calls are cheaper, as the landline network costs only EUR 0.02 and the mobile network EUR 0.30. Mobilus (02368) is a provider that has particularly low mobile network prices. In this case, it would cost Marco 0.25 euros to make calls during peak hours and 0.20 euros during off-peak times. However, the prices with this provider for the fixed network are more expensive compared to the other providers. Peak hours for fixed network at Mobilus cost 0.07 euros and off-peak time 0.05 euros. His girlfriend Anna recommended the provider Genialio (096573) to Marco, because it costs only 0.01 euros for the fixed network during off-peak times and 0.04 euros during peak hours. For the mobile network, Marco would pay 0.32 euros (peak hours) and 0.27 euros (offpeak time). The name says it all for the provider Cheapus (016783), because it costs 0.05 euros per minute in the fixed network during peak times and 0.03 euros per minute in off-peak times. The prices for the mobile network are 0.03 euros for the main time and 0.27 euros in the off-peak time. Marco now asks you whether you can implement an operation for him which always selects the best rate.

The task can be classified as 3rd category [8] due to the different approaches and solutions possible. The task is also classified in the 4th category since the information regarding the telephone provider is presented in an unstructured manner [9]. The ambiguity of the task is increased by having to solve the task on paper (i. e. programming on paper). Therefore, the structure and feedback provided by the interface of the block-based programming language is not available. The students noted the exact point of time before starting and after solving the task.

## 3.2 Participants

At the selected secondary school in Germany, a total of 27 students attended a computer science course at an increased level of difficulty in the school year of 2020/2021. Of these, 13 students attend a course in 12th grade and 14 students in 13th grade. A total of 23 students were interviewed as four students could not be interviewed due to quarantine. All students took computer science classes in 11th grade. During the course, the students implement programs with the block-based programming languages Snap! and Scratch. The students are used to record their syntax when programming on paper in exam situations. Furthermore, both courses are supervised by the same teacher and mainly dealt with implementation tasks for multi-dimensional lists in the lessons prior to the data collection. The students did not know the concept of algorithmic problem solving. The teacher explained in a preparatory meeting that all implementation tasks dealt with prior in the classroom relate to this task.
## 3.3 Data Collection and Processing

The 23 questionnaires were digitized and evaluated using Statistical Packages for the Social Sciences (SPSS). The sample was divided into two groups according to split-half method on their tolerance for ambiguity: rather low tolerance for ambiguity (TfA-low) and rather high tolerance for ambiguity (TfA-high). In the TfA-low and TfA-high group, were split at a value of higher than 47. Based on this classification, twelve of the students can be classified in the TfA-low group and eleven in TfA-high group.

The students' solutions to the implementation task were rated according to four different sample solutions. These sample solutions were prepared in advance by computer science and electrical engineering students. It should be noted that there are other solutions that solve the problem validly. The answers were rated with a minimum of zero to a maximum of 15 points. The Mann-Whitney U test was determined as most suitable to compare the score and the processing time of the two groups, since the sample is small, the groups are independent from one another, and normality of sample distribution is not required [22]. In addition, Spearman-Rho correlations were calculated for the independent variable tolerance for ambiguity and the dependent variables score and processing time. A correlation analysis according to Spearman-Rho is carried out, since this is a non-parametric statistic, which can reduce the influence of extreme values [22].

## 4 Results

For preliminary analyses, the composition of the sample was investigated including quitters and grade level. In total seven students quit the ambiguous task and did not record an end time. It was checked whether the quitters differed in their level of tolerance for ambiguity. A Mann-Test revealed no statistically significant difference in tolerance for ambiguity between the quitters and completers ($U = 32.0, p = 0.107$).

A Mann-Test revealed statistically significant difference in score on the algorithmic problem-solving task between the 12th and 13th grade students ($U = 33.5, p = 0.050$). With 12th (mean rank = 14.4) graders outperforming the 13th graders (mean rank = 8.9). This difference prompted a further check whether grade level was connected to placement in either group with a $\chi^2$ - Test. The result shows no statistical connection between grade level and the group placement ($\chi^2 (1) = 0.03, p = 0.855$). Although this contradicts the expectation that higher grade is connected to higher performance, the grade level does not predict classification into tolerance for ambiguity groups. Grade level is therefore excluded from possible mitigating variables.
For the main analysis, the connection between the tolerance for ambiguity and the score on the algorithmic problem-solving task was investigated. Table 2 shows the mean ranks of the score on the algorithmic problem-solving task across the tolerance for ambiguity groups (TfA-low vs TfA-high). The statistical inference via Mann-Whitney U-test returns a statistically significant result. The direction of the difference can be determined by comparing the mean ranks of the groups, revealing the TfA-high group to have outperformed the TfA-low group. The effect size of group membership of .490 can be classified as medium according to Cohen (1992) [23], calculated via the formula [22]:

$$r = z \frac{z}{\sqrt{N}}$$

<table><caption>**Table 2.** Mann-Whitney results on the comparison of score and processing time on algorithmic problem-solving task between tolerance of ambiguity groups.</caption><thead><tr><th rowspan="2">TfA-groups</th><th colspan="3">Score</th><th colspan="3">Processing time</th></tr><tr><th>N</th><th>mean rank</th><th>rank sum</th><th>N</th><th>mean rank</th><th>rank sum</th></tr></thead><tbody><tr><td>Low</td><td>12</td><td>8.83</td><td>106</td><td>7</td><td>8.50</td><td>59.50</td></tr><tr><td>High</td><td>11</td><td>15.45</td><td>170</td><td>9</td><td>8.50</td><td>76.50</td></tr><tr><td>Total</td><td>23</td><td></td><td></td><td>16</td><td></td><td></td></tr><tr><td>Mann-Whitney</td><td></td><td>U = 28.0</td><td>p = 0.019</td><td></td><td>U = 31.5</td><td>p = 1.000</td></tr></tbody></table>

If no division into groups is made, a Spearman-Rho correlation returns similar results. Spearman-Rho correlation between tolerance for ambiguity and score on algorithmic problem solving was also found to be statistically significant (rho = 0.58; p = 0.004). The positive correlation coefficient indicates that higher levels of tolerance for ambiguity can be associated with a higher score on algorithmic problem solving. This correlation coefficient can be classified according to Cohen as a medium to strong correlation [23]. Spearman-Rho correlation between tolerance for ambiguity and processing time on algorithmic problem solving was found to be not statistically significant (rho = -0.06; p = 0.816).

# 5 Discussion and Conclusion

The research question of the paper at hand was based on previous research [4, 17]. The results presented above represent an extension of previous research. The question to what extent tolerance for ambiguity and solving ambiguous algorithmic problem-solving tasks are connected was investigated by group differences and correlations. The results clearly demonstrate that there is a positive relationship between level of tolerance for ambiguity or the sheer score on tolerance for ambiguity and the number of points achieved in ambiguous algorithmic problem-solving tasks. There was no connection
between tolerance for ambiguity and processing time, which may have been due to the considerable number of quitters of the task. The quitting behavior was not connected to the level of tolerance for ambiguity of the students, leading to speculations about a mitigating variable, such as self-efficacy.

Based on the present results, the research question can be answered to the effect that there is a positive connection between tolerance for ambiguity and the solving of ambiguous algorithmic problem-solving tasks. However, in this context it should not be disregarded that a small and specific sample was examined, so that the representativeness of these results is limited. Nevertheless, these results extend the results from the foreign language research [4, 5] and that for problem-solving and transfer [2, 17]. Further analyses investigated the possible connection between time spent on the ambiguous task and the score. Neither a group comparison, nor a bivariate correlation indicated a connection between the two. However, as not all students finished the ambiguous task, the processing time for these quitters could not be recorded truthfully. However, tolerance for ambiguity did not seem to be the explanation for whether the students finished the ambiguous task or not. As the students may have not been fully engaged with the task yet, low self-efficacy could have played a role in the decision to quit [24]. Self-efficacy is the trust in one's own skills to be able to master difficult situations. Either the quitters did not know how to solve the ambiguous task, or they did not persevere enough to activate the necessary knowledge. To further corroborate this speculation, data on self-efficacy and an objective measure for the general problem-solving skill would be needed.

Furthermore, Atef-Vahid et al. [4] found that students less tolerant for ambiguity took longer to process the ambiguous task than the more tolerant students. However, the processing time was clearly limited by the school's given time, so that not all students had the opportunity to complete the task at their own pace. A connection between tolerance for ambiguity and processing time could have been found if the students had had unlimited time. It is therefore advisable to allow more time for processing when repeating such a test. When examining the processing time, it was also found that seven students abandoned the task. Of these seven, five came from the group AT-rather low and two from the group AT-rather high. The task abandonment could be due to low tolerance for ambiguity as Budner [8] stated that a low tolerance can lead to people being overwhelmed by ambiguity and thereby refusing the situation. The research at hand could nonetheless not confirm this suspicion.

When interpreting these results, however, it should be considered that the relationship between tolerance for ambiguity and performance on an ambiguous task was only demonstrated for the present sample [22]. The scores on the ambiguous task represent the performance of the students on the day of the survey under the given circumstances only, so the performance of the students could differ between days, under different circumstances and on different tasks. The research at hand does not take such variations into account. Stark et al [17] created various situations of ambiguity in problem solving and compared the results. With such an approach, it could also be checked whether students more tolerant for ambiguity perform better in algorithmic problem solving if they work in groups compared to working alone or depending on the amount of information they receive.
The small sample limits the meaningfulness of the presented results as it cannot be assumed that the results of this sample represent the entirety of all computer science students [22]. Due to the small sample, the students were divided into two equally sized groups. However, the value of tolerance for ambiguity of six of the students are very close to the cutoff between the two groups. The same question with any cut-off arises whether a point difference in the tolerance for ambiguity value can really be decisive for whether a person can be viewed as more intolerant or more tolerant. The research at hand corroborated the group comparison with a correlation.

Regarding the sample composition, possibly mitigating variables could be ruled out by preliminary analyses. Therein, the students' grade level did not seem to matter for the placement into either of the tolerance for ambiguity groups. However, it was discovered that the 12th graders outperformed the 13th graders on the algorithmic problem-solving task. Intuitively, one could expect that this should be reversed, and the 13th graders should have outperformed the 12th graders. The 12th graders may have had related subject matter more recently than the 13th graders and therefore an advantage on the algorithmic problem-solving task. Additionally, the 13th graders are closer to their final examinations and may therefore be less focused on such a research related task. The study at hand has neither the data nor the scope to explain this finding in depth.

The results of this investigation indicate that there is a positive connection between tolerance for ambiguity and the solving of ambiguous algorithmic problem-solving tasks. Ambiguity in tasks may reduce performance of some students and therefore skew results. Consequently, it is necessary to develop students' tolerance for ambiguity if a reduction of ambiguity is not desirable. Open-ended tasks seem promising in achieving this by defining a general goal without specifying a solution. Such a general goal could be formulated as developing an algorithm that automatically sorts a set of elements, for instance sorting by size. Different algorithms can be used to sort a set of elements.

Ambiguity may be used to adapt task difficulty. There are students whose performance is hampered by the ambiguity of the task. Offering additional material (pertaining to the content or the solution approach) could reduce the degree of ambiguity and mitigate its negative effect on these students. It could be reasonably considered devising "learning-to-learn" programs for such situations as the targeted strategies would be highly associated with the subject matter to be learnt [12]. Computer science concerns the acquisition and application of various solution strategies. Additionally, algorithmic problem solving has to be communicated as a skill that requires mental flexibility. Nonetheless, it must be clear to the students that some solutions can be less optimal than other or plainly wrong – especially when not achieving the set goal.

Furthermore, the study at hand hints at new avenues of research, such as the understanding of the subjectivity of the perception of ambiguity and the reasons for abandoning algorithmic problem-solving tasks. Investigating these routes could help to improve lesson material and methods in computer science and possibly other subjects as well.

## References

1. Brown, H.D.: Principles of Language Learning and Teaching. Pearson Longman, Harlow (2007)
2. Buela, M., Beltran-Joaquin, N.: Student ambiguity tolerance as predictor of problem-solving ability in mathematics. In: The Asian Conference on Education 2018: Official Conference Proceedings (2018)

3. Liu, C.: Relevant researches on tolerance of ambiguity. Theor. Pract. Lang. Stud. 5(9), 1874–1882 (2015)

4. Atef-Vahid, S., Alireza Fard Kashani, A.F., Haddadi, M.: The relationship between level of ambiguity tolerance and cloze test performance of Iranian EFL learners. Linguist. Literary Broad Res. Innov. 2(2), 149–169 (2011)

5. Ely, C.M.: Tolerance of ambiguity and use of second language learning strategies. Foreign Lang. Ann. 22(5), 437–445 (1989)

6. Husch, B.: Software-Entwicklung im Unterricht. Informatik als Schlüssel zur Qualifikation: GI-Fachtagung, „Informatik und Schule 1993 “Koblenz, 11.–13. Oktober 1993, 101 (2013)

7. McLain, D.L.: Evidence of the properties of an ambiguity tolerance measure: the multiple stimulus types ambiguity tolerance scale-II (MSTAT-II). Psychol. Rep. 105(3), 975–988 (2009)

8. Budner, S.: Intolerance of ambiguity as a personality variable. J. Pers. 30(1), 29–50 (1962)

9. Norton, R.W.: Measurement of ambiguity tolerance. J. Pers. 39(6), 607–619 (1975)

10. OECD: PISA 2012. Assessment and Analytical Framework: Mathematics, Reading, Science, Problem Solving and Financial Literacy. OECD, Paris, France (2013)

11. Betsch, T., Funke, J., Plessner, H.: Problemlösen: Denken – Urteilen, Entscheiden, Problemlösen. Springer, Berlin, Heidelberg (2011)

12. Hattie, J.A.C.: Visible Learning: A synthesis of Over 800 Meta-analyses Relating to Achievement. Routledge, Oxon (2009)

13. Barnes, D. J., Fincher, S., Thompson, S.: Introductory problem solving in computer science. In: Daughton, G., Magee, P. (eds.) 5th Annual Conference on the Teaching of Computing, pp. 36–39. Centre for Teaching Computing, Dublin City University, Dublin, Ireland (1997)

14. Kohl, L.: Kompetenzorientierter Informatikunterricht in der Sekundarstufe I unter Verwendung der visuellen Programmiersprache Puck. Friedrich-Schiller-Universität Jena, Jena (2009)

15. Erten, İH., Topkaya, E.Z.: Understanding tolerance of ambiguity of EFL learners in reading classes at tertiary level. Novatis-Royal 3(1), 29–44 (2009)

16. Sweller, J., van Merriënboer, J.J.G., Paas, F.G.: Cognitive architecture and instructional design. Educ. Psychol. Rev. 10(3), 251–296 (1998)

17. Stark, R., Gruber, H.H., Renkl, A., Mandl, H.: Wenn um mich herum alles drunter und drüber geht, fühle ich mich so richtig wohl – Ambiguitätstoleranz und Transfererfolg. Psychol. Erziehung. Unterr. 44(3), 204–215 (1997)

18. Leiserson, C.E., Rivest, R.L., Stein, C.: Algorithmen – Eine Einführung. Oldenbourg Verlag, München (2010)

19. Grunwald, G., Hempelmann, B.: Angewandte Marktforschung: Eine praxisorientierte Einführung. Oldenbourg Wissenschaftsverlag GmbH, München (2012)

20. Gesellschaft für Informatik: Grundsätze und Standards für die Informatik in der Schule. Bildungsstandards Informatik für die Sekundarstufe I. LOG IN 28, 150/151 (January 2008), Beilage, (2008)

21. Bundesweite Informatikwettbewerbe. Downloads 2019. https://bwinf.de/biber/downloads/ (2019). Retrieved 4 May 2021

22. Field, A.: Discovering Statistics Using IBM SPSS Statistics. Sage, Los Angeles (2018)

23. Cohen, J.: A power primer. Psychol. Bull. 112(1), 155–159 (1992)

24. Albert Bandura, A.: Toward a psychology of human agency. Perspect. Psychol. Sci. 1(2), 164–180 (2006)