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REVIEW 5 major objections 5 minor 34 references

The CTSkills App -- Measuring Problem Decomposition Skills of Students in Computational Thinking

T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The CTSkills app measures problem decomposition in grades 4–9 by scoring students' selections of objects and relations, and its pilot data show performance improving with grade and dipping in grade 9.

desk verdict Promising prototype for assessing decomposition is undermined by a scoring formula that is internally inconsistent, so the reported grade trends cannot be trusted as they stand. read the letter →

arxiv 2411.14945 v1 pith:ZWZ3REZE submitted 2024-11-22 cs.HC cs.CYcs.ET

Dorit Assaf , Giorgia Adorni , Elia Lutz , Lucio Negrini , Alberto Piatti , Francesco Mondada , Francesca Mangili , Luca Maria Gambardella This is my paper · ORCID
classification cs.HCcs.CYcs.ET
keywords computationalthinkingproblemdecompositionassessmenttoolK-12educationpilotstudysubstantiverelationalscoringmethodology
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that problem decomposition—a component of computational thinking that is often named but rarely assessed—can be measured directly with a browser-based app in K-12 classrooms. The app presents three game-like scenarios and asks students to drag the relevant objects and relations into a solution field; the score rewards correct selections and penalizes missed or irrelevant ones. The paper reports on a pilot with 75 students in grades 4–9, finding a general improvement with grade, a dip for grade 9, and no gender difference. If the app measures what it claims, it would give schools and researchers an automated way to collect decomposition-skill baselines across a wide age range, a step toward the baseline the field currently lacks.

What carries the argument

The machinery is a formal target/non-target scoring scheme. For each question and level the paper defines a set $X$ of target items or item pairs and a set $Y$ of non-target items or pairs; from the student's selected sets $S_X$ and $S_Y$ the score is $$score = |S_X| - (|X| - |S_X|) - |S_Y|,$$ which rewards correct picks, penalizes missed targets, and penalizes false positives. The raw score is rescaled to a 0–5 range using the achievable minimum, then averaged over questions and levels. This scheme operationalizes decomposition as boundary-drawing accuracy, and the three sceneries are designed so the same objects reappear in different contexts, letting pattern recognition contribute to later levels.

What would settle it

Re-analyze the Level 1, Q1 logs: count students who selected the tree while omitting an item the scoring rule counts as a target; if a substantial number of students who score high on Q2–Q4 did so, then the scoring rule penalizes a defensible decomposition rather than measuring the skill.

Watch

Extended reading notes

Core claim

The central claim is that substantive and relational decomposition—picking out the objects that matter in a problem scenario and identifying how those objects change or collide—can be assessed automatically through a structured drag-and-drop interface. Each of the three levels is followed by four questions: which objects are relevant, which are moving, which objects change into which, and which collide. The paper's target/non-target scoring formula treats decomposition as accuracy in drawing the boundary between what belongs to the problem and what does not. In the pilot data, the paper reports a consistent improvement in task performance across grades, a statistically significant grade-9 drop relative to grade 8, and no significant effect of gender, and it interprets these as evidence that the app can automate data collection for a future decomposition proficiency baseline.

Load-bearing premise

The scoring depends on the author-defined lists of which objects and relations count as correct; if a student's answer reflects a legitimate alternative decomposition, such as counting the tree as relevant or grouping apples with the basket, the score will misclassify their ability.

Editorial extensions

If this is right

  • Classrooms could run the same decomposition assessment across grades 4–9 and compare performance year to year without manual coding analysis.
  • The automated scoring formula gives researchers a compact outcome measure for studying how decomposition skill develops with age.
  • The pilot's null gender difference suggests decomposition skill is distributed evenly across genders in this sample, supporting inclusive computational thinking education.
  • The grade-9 dip points to a transitional period where secondary-school task complexity may outpace students' decomposition strategies, a target for intervention.
  • The same scoring scheme can be extended to functional decomposition once the app adds tasks that require grouping objects into reusable classes or procedures.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The current target sets may be too narrow; a validity study comparing app scores with open-ended decomposition explanations could reveal that some 'incorrect' selections are legitimate alternative decompositions.
  • Because the interface asks students to select pre-listed objects, the test measures recognition of relevant objects rather than the ability to generate the decomposition from scratch; a generative-response version might measure a different facet of the skill.
  • The cross-sectional age trend conflates age with cohort and curriculum; longitudinal retesting of the same students would be needed to claim individual development.
  • The format could transfer to non-programming subjects: any scenario with objects and relations could be scored the same way, making decomposition assessment domain-general.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The manuscript presents CTSkills, a browser-based assessment app designed to measure students' problem decomposition skills as a component of computational thinking in K-12 education. Students play three levels of an interactive game and answer four questions per level about relevant objects, moving objects, state changes, and collisions. The authors define target and non-target sets for each question, compute per-question scores with a proposed rescaling, and average the scores across questions and levels. They report descriptive statistics, ANOVA, chi-square tests, Tukey post-hoc tests, and linear mixed-effect models on pilot data from 75 students in grades 4-9. The paper claims that the app effectively automates data collection (RQ1) and that the data show age-related improvement in decomposition skills, with a noted dip in Grade 9.

Significance. If the instrument were validated, this work could provide a scalable, classroom-ready tool for measuring a relatively under-explored CT skill, and the design is sensibly grounded in the decomposition framework of Rich et al. The usability testing with children and the attention to classroom data collection are strengths. However, the central measurement claim is not currently supported: the scoring formula in Section 3.3 is internally inconsistent and undefined for several question-level combinations, the author-defined target sets are not independently validated, and the grade-comparison conclusions rest on small and uneven samples. At this stage the contribution is best described as a feasibility prototype and data-collection pipeline, not a validated measure of problem decomposition.

major comments (5)
  1. [Section 3.3] The rescaling formula is undefined for several reported cells. With score = |S_X| - (|X|-|S_X|) - |S_Y| and min_score = -|X| + |Y|, the denominator |X| - min_score equals zero whenever |X|=2 and |Y|=4, which occurs for Q3-L1, Q4-L1, Q3-L3, and Q4-L3 according to Table 2. Yet Fig. 6 shows nontrivial score distributions for these cells. Either the paper does not report the scoring rule actually used, or the displayed scores cannot be produced by the described method. Because every aggregate and inferential result depends on these scores, the quantitative claims in Section 4 are not reproducible from the manuscript as written.
  2. [Section 3.3] The stated min_score is not the minimum achievable score. Since S_X is a subset of X and S_Y is a subset of Y, the lowest possible value of score is -|X|-|Y| (select no targets and all non-targets), not -|X|+|Y|. For some configurations the stated min_score even exceeds the maximum score |X|, so the rescaling can produce negative or inverted values. The claim that scores are standardised to a 0-5 range is therefore not correct for the stated formula, and all comparisons involving rescaled scores are affected.
  3. [Appendix A.2, Table 2] Table 2 is internally inconsistent with the scoring model. For Q4-L1 the table lists three target pairs (including the optional Apple spoiled red and Grass pair) but reports |X|=2; for Q4-L3 it lists five target pairs but reports |X|=2. The optional-pair bonus of 0.5 mentioned in the table is absent from the score formula in Section 3.3, so a student selecting an optional pair receives no credit under the stated formula, or the target counts used in the formula are wrong. Either way, the scoring rule does not match the described items.
  4. [Sections 3.2 and 5.1] The central construct-validity question is unaddressed. The target and non-target sets are defined by the authors, and the paper itself acknowledges in Section 3.2 that the tree could reasonably be considered relevant in Q1 and admits in Section 5.1 that creative solutions such as grouping apples with baskets are difficult to quantify. No expert panel, inter-rater reliability check, item-level analysis, or comparison with an external decomposition measure is provided. Until such evidence is supplied, the score is best interpreted as agreement with the authors' answer key rather than as a validated measure of problem decomposition skill.
  5. [Section 4 and Table 1] The conclusion of a 'consistent improvement in task performance as students progress through grades' is not consistent with the reported results. The post-hoc test shows Grade 9 scoring significantly lower than Grade 8 (MD = -0.6500, p = 0.0175), and the sample sizes are highly uneven: Grade 7 has only 4 students while Grade 9 has 24. The LMM also attributes only modest variance to grade (Variance = 0.061, SD = 0.247). The discussion should temper the developmental-claim language and address the small and unbalanced grade samples explicitly.
minor comments (5)
  1. [Section 4, Fig. 6 paragraph] The text contains a duplicated phrase: 'potentially potentially indicating different difficulty levels.'
  2. [Section 4, Fig. 5 discussion] The text refers to 'grade 8 to 11' when describing selection rates, but the study only covers grades 4-9; this appears to be a typo and should be corrected.
  3. [Section 3.3] The value of max_scaled is never stated; the paper should specify that it is 5 (or whatever value was used) so the rescaling is reproducible.
  4. [Fig. 6] The caption and surrounding text describe the axes inconsistently: the text says difficulty levels are on the x-axis and score categories on the y-axis, but the figure layout appears to show score categories on the y-axis and levels on the x-axis. Please align the caption with the actual figure.
  5. [Section 5, RQ1] The statement that 'the app proved effective in automating data collection' is presented as a finding, but the paper reports no usability or completion metrics (e.g., task completion rates, time-on-task, or error logs) to support this claim; 'feasible' would be a more accurate descriptor for the pilot evidence.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the rubric is an a priori key, not a fit; the scoring-formula defects are correctness issues, not circularity.

full rationale

The derivation chain is not circular. The construct of decomposition skill is operationalized by fixed target/non-target sets (Table 2) and the score formula in Section 3.3, with no parameter fitted to the pilot data and no post-hoc calibration of the key from student responses; the reported grade trends are therefore descriptive outcomes of an a priori criterion-referenced rubric, not predictions that reduce to their inputs. The framework of Rich et al. [23] is external to the author team, and the self-citations to the authors' prior algorithmic-thinking app ([1,2,4,20]) are methodological precedents, not load-bearing justifications for the decomposition key. The serious defects noted in Section 3.3 - the stated min_score is not the true minimum, the rescaling denominator is zero for |X|=2, |Y|=4 cells, and the optional-pair bonus of 0.5 has no term in the formula - invalidate the reported rescaled scores as a correctness matter, but they are not circular steps. The limitations acknowledged in Section 5.1 (pre-abstraction in the menu, difficulty quantifying creative solutions such as grouping apples and baskets) are construct-validity threats, not evidence that the measurement is equivalent to its inputs by construction.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The instrument's validity rests on author-defined target sets that have not been externally benchmarked. The numerical scoring involves a fixed upper bound (5) and a bonus (0.5) chosen by hand, and the construct interpretation depends on unverified domain assumptions.

free parameters (2)
  • Optional pair bonus = 0.5
    In Table 2, optional target pairs marked with a star add a bonus of 0.5 to the score if selected, but the main scoring formula in Section 3.3 does not include this bonus, so the effective scoring rule is partially undefined.
  • Rescaling upper bound (max_scaled) = 5
    The rescaled score range is fixed to 0-5. This is a convenient display scale chosen by the authors, not derived from measurement theory.
assumptions (4)
  • domain assumption The substantive, relational, and functional decomposition categories of Rich et al. (2019) are a valid theoretical model of decomposition skill.
    Section 3.1 adopts this framework to design the instrument, but the paper does not test whether the categories are exhaustive or whether the tasks actually instantiate them.
  • domain assumption Students' selections of target objects and pairs in a simplified game scenario accurately reflect their decomposition ability.
    Section 3.3 scores selections as correct or incorrect; no evidence, such as correlation with other decomposition measures or think-aloud data, links selections to the cognitive construct.
  • domain assumption The four questions Q1-Q4 and three levels are ordered by difficulty and contribute equally to the aggregate score.
    Section 3.3 averages scores across questions and levels without item analysis; Figure 6 shows large differences in difficulty, so equal weighting is an unexamined assumption.
  • standard math Standard statistical assumptions for ANOVA, chi-square tests, and LMMs hold, including independence and normality.
    Section 4 applies these tests; the clustered sample of students nested in classes may violate independence, though LMMs partially address clustering.

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Pith. "Pith review of The CTSkills App -- Measuring Problem Decomposition Skills of Students in Computational Thinking." pith.science (2026). https://pith.science/paper/ZWZ3REZE

@misc{pith2026241114945,
  author       = {Pith},
  title        = {Pith review of: The CTSkills App -- Measuring Problem Decomposition Skills of Students in Computational Thinking},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZWZ3REZE}},
  note         = {Machine review of arXiv:2411.14945}
}
read the original abstract

This paper addresses the incorporation of problem decomposition skills as an important component of computational thinking (CT) in K-12 computer science (CS) education. Despite the growing integration of CS in schools, there is a lack of consensus on the precise definition of CT in general and decomposition in particular. While decomposition is commonly referred to as the starting point of (computational) problem-solving, algorithmic solution formulation often receives more attention in the classroom, while decomposition remains rather unexplored. This study presents "CTSKills", a web-based skill assessment tool developed to measure students' problem decomposition skills. With the data collected from 75 students in grades 4-9, this research aims to contribute to a baseline of students' decomposition proficiency in compulsory education. Furthermore, a thorough understanding of a given problem is becoming increasingly important with the advancement of generative artificial intelligence (AI) tools that can effectively support the process of formulating algorithms. This study highlights the importance of problem decomposition as a key skill in K-12 CS education to foster more adept problem solvers.

Figures

Figures reproduced from arXiv: 2411.14945 by the authors.

Figure 1
Figure 1. Screenshots from Level 1, Level 2, and Level 3 of the CTSkills app. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Screenshots from Question 1 (Q1) to Question 4 (Q4) of Level 1 of the CTSKills app. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Pattern recognition, abstraction and generalisation to make code reusable. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Percentage of Times Each Item Was Selected as Relevant for Question 1 - Level 1. This chart illustrates the percentage [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Percentage of Times Each Item Was Selected as Relevant for Question Q1 across School Grades. This chart illustrates [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Percentage Distribution of Student Scores by Question and Level. This graph illustrates the percentage distribution [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Average Score across School Grades for Questions Q1-Q4 on Levels 1-3. [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Substantive decomposition and abstraction. [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Assigning properties to objects. (a) Level 1, Q3 (b) Level 2, Q3 (c) Level 3, Q3 [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Relational decomposition. A.2 Assessment Let 𝑋 represent the set of target items or pairs and 𝑌 the set of non-target items or pairs [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: Pattern recognition, abstraction and generalisation to make code reusable. [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: Percentage of Times Each Item Was Selected as Relevant for Question 1 - Level 1. This chart illustrates the percentage [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]
Figure 13
Figure 13. Figure 13: Percentage of Times Each Item Was Selected as Relevant for Question 1 - Level 2. This chart illustrates the percentage [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]
Figure 14
Figure 14. Figure 14: Percentage of Times Each Item Was Selected as Relevant for Question 1 - Level 3. This chart illustrates the percentage [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]
Figure 15
Figure 15. Figure 15: Visualisation of the Random Effects. Each point represents the variable deviation from the average score, with blue [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]

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Reviewed August 12, 2026 · model on record in the stance chip above.