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arxiv: 2604.25082 · v1 · submitted 2026-04-28 · 💻 cs.CY

Does This Even Matter in the Real World? Real World Problems in Foundational Theory Courses

Anna Kuznetsova This is my paper

Pith reviewed 2026-05-07 15:06 UTC · model grok-4.3

classification 💻 cs.CY
keywords real-world applicationsdiscrete mathematicsprobability theorystudent attitudesfoundational courseshomework designsurvey studycomputer science education
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The pith

Adding real-world homework problems to discrete math and probability courses leaves student views on relevance largely unchanged, with under 7 percent seeing the material as irrelevant both before and after the term.

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

The paper tests whether homework questions drawn from concrete applications can address instructors' worries that discrete mathematics and probability theory feel too abstract for computer science students. Researchers added problems based on court cases, code correctness checks, and machine learning ethics, then measured attitudes with surveys at the start and end of the term. The results show that only a small minority of students expected the content to be irrelevant to their futures, and that share stayed about the same after the term. Students also reported enjoying the new problems and asked for them to continue in future versions of the courses. This suggests the problems can be added without disrupting existing positive perceptions while still providing a welcome practical connection.

Core claim

The central claim is that introducing real-world application homework questions throughout introductory discrete mathematics and probability theory courses produces stable student attitudes, with fewer than 7 percent expecting the material to be irrelevant to them both at the beginning and at the end of the term, while qualitative responses indicate enjoyment of the problems and a desire for their continued use.

What carries the argument

Real-world homework problems grounded in applications such as court cases, verifying code correctness, and machine learning ethics; these problems supply the concrete links between abstract theory and computer science practice that the study tracks for effects on relevance perceptions.

If this is right

  • Instructors can incorporate real-world application problems into foundational theory courses without risking an increase in students viewing the material as disconnected from practice.
  • Student enjoyment and requests for continuation indicate that such problems can improve course experience even when baseline relevance perceptions are already positive.
  • The low and stable percentage of students seeing the material as irrelevant suggests that abstract foundational content may already align better with student expectations than instructors assume.
  • The approach provides a low-risk way to add concrete examples while preserving the core theoretical focus of the courses.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If most students already see relevance, then the value of these problems may lie more in deepening understanding or motivation than in shifting broad attitudes, which could be tested by comparing exam performance with and without the problems.
  • The specific applications chosen, such as machine learning ethics, could be adapted to other CS courses to address emerging topics like AI safety without requiring major curriculum changes.
  • Extending the method to larger or more diverse student populations might reveal whether the low irrelevance rates hold across different institutions or backgrounds.

Load-bearing premise

That pre- and post-term survey responses accurately capture genuine student attitudes toward relevance and that stability in those attitudes can be attributed to the real-world homework problems rather than other course elements or response biases.

What would settle it

A replication study that replaces the surveys with anonymous in-depth interviews or measures of actual homework engagement and finds substantially higher rates of perceived irrelevance after the real-world problems are added.

Figures

Figures reproduced from arXiv: 2604.25082 by Anna Kuznetsova.

Figure 5.1
Figure 5.1. Figure 5.1: Student responses to Likert Scale questions. The bars show Strongly Disagree view at source ↗
read the original abstract

Discrete mathematics and probability theory contain foundational material for computer scientists. Despite their importance, instructors often worry that students will find these courses to be too abstract and seemingly disconnected from their future careers. For this research project, we introduced homework questions throughout our introductory theory courses based on real world applications of the course content. Areas of application included a court case, code correctness, and machine learning ethics. We surveyed students at the beginning and end of the term on their attitudes toward the relevance of the course material. Our results, surprisingly, indicate that a small minority of students (less than 7%) expected the material to be irrelevant to them at the start of the term, and a similarly small number believed that at the end of the term. Our surveys and qualitative feedback also indicate students enjoyed having the problems and wanted them to continue being offered in future iterations of the courses.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper describes an intervention adding real-world application homework problems (e.g., court cases, code correctness, machine learning ethics) to introductory discrete mathematics and probability theory courses. Pre- and post-term student surveys indicated that fewer than 7% of students viewed the material as irrelevant at both time points, with qualitative feedback showing enjoyment of the problems and support for continuing them.

Significance. If the empirical results hold after fuller reporting, the work would demonstrate that most CS students already perceive foundational theory courses as relevant and that real-world examples can increase enjoyment. This provides useful data for CS education practitioners seeking to improve engagement in abstract courses without assuming widespread student disinterest.

major comments (2)
  1. The central claim that fewer than 7% of students found the material irrelevant at the start and end of the term rests on survey responses, but the manuscript provides no details on sample size, response rate, exact question wording, or statistical methods used to derive the percentage. This information is required to evaluate the reliability of the reported figure.
  2. The study design includes no control condition, such as parallel sections without the real-world problems or historical data from prior terms. Consequently, observed attitude stability and positive feedback cannot be attributed specifically to the intervention rather than other course components or pre-existing factors.
minor comments (2)
  1. The abstract and results section should clarify whether the <7% figure reflects the same cohort of students across pre- and post-surveys or aggregate percentages, and whether any individual attitude shifts occurred.
  2. A dedicated limitations paragraph would strengthen the paper by addressing potential social-desirability bias in self-reported relevance once students are aware of the instructor's focus on real-world applications.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: The central claim that fewer than 7% of students found the material irrelevant at the start and end of the term rests on survey responses, but the manuscript provides no details on sample size, response rate, exact question wording, or statistical methods used to derive the percentage. This information is required to evaluate the reliability of the reported figure.

    Authors: We agree that these methodological details are essential. The initial submission omitted them for space, but the data were collected. In the revision we will add a dedicated survey methods subsection reporting the number of enrolled students and respondents, the pre- and post-term response rates, the exact wording of the relevance item(s), and the straightforward descriptive calculation used to obtain the less-than-7% figure. No inferential statistics were performed. revision: yes

  2. Referee: The study design includes no control condition, such as parallel sections without the real-world problems or historical data from prior terms. Consequently, observed attitude stability and positive feedback cannot be attributed specifically to the intervention rather than other course components or pre-existing factors.

    Authors: This is a fair critique of causal attribution. Institutional constraints (single sections per term and no prior comparable surveys) made a controlled design infeasible. We will revise the limitations and discussion sections to state this explicitly, framing the results as descriptive evidence that the real-world problems coincided with stable low perceptions of irrelevance and positive qualitative feedback, without claiming the intervention caused the stability. We believe the findings remain useful for instructors considering similar additions. revision: partial

Circularity Check

0 steps flagged

No circularity: empirical survey study with no derivations or self-referential constructs

full rationale

The paper is a straightforward empirical survey study reporting pre- and post-term student responses on perceived relevance of discrete math and probability material after adding real-world homework examples. It contains no equations, fitted parameters, mathematical derivations, or load-bearing self-citations. Claims rest directly on tabulated survey percentages and qualitative comments rather than any self-defined or constructed quantities. The design therefore has no derivation chain that could reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the assumption that self-reported survey data reliably measures changes (or lack of changes) in perceived relevance caused by the homework intervention.

axioms (1)
  • domain assumption Student survey responses accurately reflect their true attitudes toward course relevance.
    The <7% irrelevance finding and enjoyment claims rest entirely on self-reported pre- and post-term survey data.

pith-pipeline@v0.9.0 · 5442 in / 1284 out tokens · 46881 ms · 2026-05-07T15:06:38.770121+00:00 · methodology

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