Maria Knobelsdorf, University of Dortmund, Germany - Didaktik der ...

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While the factors A, B and C were regarded as independent variables, the dependent variable was the respondents’ evaluation of the importance of a specific process concept for a specific content concept. Ratings were given on a 6-point scale from 0 (“no importance”) to 5 (“great importance”). 6.2 Power analysis A power calculation of type II, N being a function of power (1–β), Δ, and α, was used to determine the necessary sample size for the 2•15×16 split-plot design (see [31]): With a power (1–β) of 0.99, only large effects (Δ = 0.80) on the dependent variable being considered significant, and a significance level of α = 0.05, a total sample of approximately N*= 30 ( n1* = 15 Baden-Württemberg teachers of computer science teachers, n 2* = 15 Bavarian teachers of computer science teachers), would be required, based on the power computations of Mueller and Barton [30] or Mueller et al. [31] for ε-corrected F tests. 6.3 Operational hypothesis Given the study design and the above specification of the independent and dependent variables, the operational hypothesis of the study can be formulated as follows: “CS teachers from BW differ from CS teachers from BY in their evaluations of the relations between central content concepts of computer science (CC, see section 2.1) and central process concepts of computer science (PC, see section 2.1), as operationalized by their rating on a sixpoint scale of the importance of a specific process concept for a specific content concept." 6.4 Sampling A total of 120 CS teachers in BW and 120 CS teachers in BY were contacted and invited to complete a questionnaire pertaining to computer science concepts. The questionnaire began with a short introduction, in which the 15 central content concepts and the 16 central process concepts were listed in tabular form in alphabetical order. Following this, the q = 15 content concepts and the r = 16 process concepts were presented in alphabetical order in a matrix, with the content concepts in the rows and the process concepts in the columns. Participants were asked to rate the following statement for each of the 15×16 = 240 cells of the matrix: Each cell represents a combination of a concept and a process and requires an integer from 0 (no importance) to 5 (great importance) indicating the relevance of the combination. Participants filled in each cell on a 6-point scale from 0 (“no importance”) to 5 (“great importance”). To maximize the return rate, we mailed both samples the questionnaires in sealed, personalized envelopes, enclosing a preaddressed return envelope franked with stamps showing flower designs (see [9] for recommendations on increasing return rates). The return rate for the BW teachers was 14.2% (n1 = 17 valid questionnaires), which can be considered reasonable for a postal survey (see [45]). The return rate for the BY teachers was 17.5% (n2 = 21 valid questionnaires). 6.5 Data Analysis The procedure used to analyze the experimental data was as follows: First, we performed a descriptive analysis (7.1-7.2), focusing on the content concepts. Second, we conducted a three-factor analysis of variance with repeated measures (7.3) in accordance with the SPF-2•15×16 split-plot design (see Winer [46], chapter 7). Third, we conducted a posteriori comparisons of means to test for significant effects of the A × B interaction (7.4) and the A × B × C interaction (7.5). The process concepts were included in analyses (2) to (4). 70 Data analyses were conducted using SPSS 17.0; the power analysis was computed with PASS 8.0.9. 7. RESULTS Fig. 6 in the appendix displays the original data of the mean ratings obtained from the BW teachers (a 1) and the BY teachers (a 2) for each of the 15 × 16 combinations of content concepts × process concepts (repeated measures factors B × C). 7.1 Means The four content concepts with the highest averages (see Appendix) are the same for the two groups of teachers: problem, information, model and algorithm. The concept with the lowest average is also the same, namely computer. Major differences in the assessment of content concepts between the two groups of teachers can be found for the content concepts information (2.79 vs. 3.11), model (2.62 vs. 3.30), system (1.90 vs. 2.44) and computer (1.62 vs. 2.04). 7.2 Process-related coverage To determine differences in the assessment of content and process concepts by the two groups of teachers, the process-related coverage can be used: A content concept has high process-related coverage if it is rated as highly important (> 2.50) for many of the process concepts; it has lower process-related coverage if it is rated as less important (≤ 2.50) for many of the process concepts. It is striking that the content concepts information, model and system are rated highly in relation to more process concepts by the BY teachers compared to the BW teachers. On the other hand, teachers from Bavaria rate more process concepts highly in combination with the content concepts information (14 vs. 11), model (15 vs. 12) and system (6 vs. 1) compared to the BW teachers, while the latter rate more process concepts highly in combination with computation (8 vs. 3) and program (8 vs. 5). 7.3 Analysis of Variance To examine whether the BW teachers differed from the BY teachers in their evaluations of the relationships between the content concepts and the process concepts, we formulated three statistical hypotheses, which were tested at the significance level of α = 0.05. The three null hypotheses were chosen as follows: i) The means of the content concepts µ1 under factor level a1 (BW teachers) and µ2 under factor level a2 (BY teachers) are equal, such that: H 0: µ 1 = µ 2. ii) The means of the content concepts µ1�1, µ1�2, ..., µ2�15 under the 2 � 15 levels of the factor combinations A × B are equal, such that: H0: µ1�1 = µ1�2 = ... = µ2�15. iii) The means of the content concepts µ1�1×1, µ1�1×2, ..., µ2�15×16 under the 2 � 15 ×16 levels of the factor combinations A × B × C are equal, such that: H0: µ1�1×1 = µ1�1×2 = ... = µ2�15×16. For an analysis of variance of a split-plot design, the data must satisfy the condition of sphericity. This assumption was tested using Mauchly’s W test for sphericity, with the test statistic W being compared to a chi-square distribution to assess the adequacy of the sphericity assumption.
The assumption of sphericity was not met for either the content concepts (W = 0.003, χ 2 104 = 178.35, p < 0.001) or the process concepts (W < 0.001, χ 2 119 = 248.60, p < 0.001) at the α level of 0.05. In the further analyses, we therefore applied the ε correction of degrees of freedom proposed by [23], as presented in table 1. Table 1. Results of the ANOVA with Huynh–Feldt ε correction of degrees of freedom The main effect A (BW vs. BY teachers) was not significant at the α level of 0.05 (F1, 36 = 0.24, p < 0.63). The corresponding H0 was therefore not rejected: The teachers from BW respectively BY did not differ in their global evaluations of the content concepts. The interaction effect A × B (group × content concept) was significant at the α level of 0.05 (F10, 360 = 2.26, p < 0.02). The corresponding H0 was therefore rejected: The teachers from BW respectively BY differed significantly in their evaluations of individual content concepts. The interaction effect A × B × C (group × content concept × process concept) was not significant at the α level of 0.05 (F78, 2809 = 1.09, p < 0.29). The corresponding H0 was therefore not rejected: The teachers from BW respectively BY did not differ in their evaluations of the relationships between individual content concepts and individual process concepts. 7.4 Individual Comparisons for the A × B Interactions The global test of the A × B interaction revealed a significant overall effect of group × content concept. Therefore we evaluated, which concepts were rated differently by comparing the mean values, applying t-tests in order to test simple AB effects for p•q×r split-plot designs (see [46], pp. 535–536), concerning the ε correction of the degrees of freedom (see section 7.3). Fig. 4 visualizes the means of the A × B interaction. As the figure shows, the content concept model was rated significantly different by the two groups of teachers (a1, a2) at the α level of 0.05 (t396 = 2.23, p < 0.027). The differences for system, computer, and information are remarkable, but not significant. 7.5 Individual Comparisons for the A × B × C Interaction The global test of the A × B × C interaction did not reveal a significant overall effect of group × content concept × process concept. Taking into account the significant difference regarding the content concept model (see section 7.4), it makes sense to compare only this concept with respect to the process concepts a posteriori. Fig. 5 displays the comparisons of the means on the concept model regarding the different process concepts. 71 These were calculated by applying 16 t-tests to analyze simple AC effects for SPF-p•q×r experimental designs ([46] pp. 535- 536); An ε correction of degrees of freedom was taken into account again (see above). The t-tests were calculated at an adjusted α level of 0.05/16 = 0.0031. It turned out that the ratings from BW teachers (a 1) respectively from BY teachers (a 2) differed significantly regarding the content concept model related to the following process concepts: classifying, finding relationships, generalizing, comparing, questioning, and ordering. Content concepts b1 = problem b2 = information b3 = model b4 = algorithm b5 = data b6 = structure b7 = system b8 = computation b9 = process b10 = software b11 = program b12 = test b13 = communication b14 = language b15 = computer 0.0 1.75 Rating 2.0 2.25 2.5 2.75 3.0 3.25 3.5 Groups a1= BW teachers of computer science a2= BY teachers of computer science a1 a2 __ simple AB effects 0.85- 0.63-0.84 0.53-0.62 0.31-0.52 0.16-0.30 0.00-0.15 Figure 4. Comparisons for the factor level combinations A × B Rating 4.0 4.5 4.25 3.75 2.0 2.25 2.5 2.75 3.0 3.25 3.5 1.75 c1 = analyzing c2 = classifying c3 = problem solving and posing c4 = categorizing c6 = finding relationships c5 = investigating c7 = generalizing c8 = creating and inventing c9 = comparing c10 = finding cause-and-effect r. c11 = questioning c12 = transferring c13 = communicating c14 = presenting c15 = collaborating c16 = ordering p < .0006 p < .003 p < .006 1.05- 0.91-1.04 0.67-0.90 0.45-0.66 0.23-0.44 0.00-0.22 p < .01 p < .05 p < .10 Figure 5. Comparisons for the content concept model 8. DISCUSSION The results of the performed evaluations support the research hypothesis that computer science teachers from Baden- Württemberg differ from computer science teachers from Bavaria in the assessment of key content concepts of computer science related to central process concepts of computer science. Already from the descriptive evaluation, it has become clear that there are differences in the assessment of content concepts by the two groups of computer science teachers. There were differences for the concepts of content model, system, computer, and information. The analysis of variance and the individual comparisons showed that the two groups rated the individual process concepts classifying, finding relationships, generalizing, comparing, questioning, and ordering differently with respect to the content concept model. As the regular teacher education programs in the German states are standardized by the KMK (see section 5), it is not likely that those differences would be caused by the courses of lessons in CS that the teachers had attended at their universities. Therefore, the
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Fakultät für Mathematik, Informat
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Program Committee Michal Armoni Wei
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Challenge and Creativity: Students
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Challenges in Computer Science Educ
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These echo a 2008 report from the N
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examples, and in practice teachers
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Figure 3: A trace of bubble sort fr
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either their own program or another
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ital system used a variety of inter
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Page 31 and 32: Altogether 830 participants visited
Page 33 and 34: 7. ACKNOWLEDGMENTS The initial equi
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Page 51 and 52: 8. REFERENCES [1] Bell, T. et al. 2
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Page 91 and 92: (Some) Grand Challenges of Computer
Page 93 and 94: ecoming more student-centered. Inde
Page 95 and 96: [13] OECD. (2006). Are students rea
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Page 111 and 112: ABSTRACT Bringing Contexts into the
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Page 115 and 116: Real-world context Views of Computi
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number P-156 in Lecture Notes in In
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1. Context-based education in compu
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Figure 1. Network traffic for authe
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A weak point of the Vigenère algor
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We have learnt that we can both loo
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Comparing CSTA K-12 Computer Scienc
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grade 4, 5, 6 or 8, depending on ch
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Table 1. Scoring Scale for the Impl
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the highest rate of implementation
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Information Theory on Czech Grammar
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of information in a message M, repr
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Data modeling and database systems
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the knowledge about ICT and CS (see
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The Mindstorm Effect: A Gender Anal
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Exploring the processing of formatt
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Teachersʼ Perceptions Of The Value
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Technocamps: Bringing Computer Scie
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Abenteuer Informatik - Hands-on exh
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Gaming and Mathematics: A Cross Cur
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Turi: Chatbot software for schools
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ABSTRACT Learning Fields in Vocatio
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ABSTRACT This study examines the po
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