Illustrations play a major role in helping students understand probability and statistics, yet there are limited studies examining how textbook illustrations evolve alongside technology. This paper compares illustrations from two editions of the same probability and statistics textbook published 34 years apart. Because the author and target audience remained the same, we were able to isolate how illustration practices changed. We analyzed 103 illustrations across three chapters using thematic analysis. We aimed to answer two questions: how did the use of illustrations change between the two editions, and how do illustration types differ depending on the topic? We found that, over time, illustrations shifted away from showing step-by-step procedures and instead focused on final results. The newer edition uses color to highlight answers, includes computer software output, and places more detailed images closer to the text. However, when comparing different topics, we found that specific topics rely on distinct types of illustrations. ... Read more

In this paper, illustrations in both computation-based calculus and proof-based analysis textbooks are analysed, with particular attention to differences in their roles. Using a thematic analysis approach, we examine how visualisations of continuity, differentiability, and integration function within a corpus of three textbooks.

Our analysis identifies the juxtaposition of rigor and intuition as a central theme. The coded illustrations reveal differences that support this distinction and are divided into three subthemes: definitions, examples, and proofs. For definitions, analysis textbooks appear to use illustrations related to more formal definitions, whereas calculus textbooks more frequently use illustrations tied to informal definitions and introductions to definitions. Examples show a similar distinction between analysis and calculus textbooks: counterexamples and examples that build intuition versus exercises and confirming examples. For proofs, this study shows how illustrations are adapted such that the same illustration serves a different role depending on the textbook: either as a substitute for the proof or as a general outline of the proof. ... Read more

Illustrations are widely used in propositional logic education, yet little is known about their role in contemporary textbooks. This study investigates the pedagogical and communicative functions of illustrations in three contemporary propositional logic textbooks through qualitative thematic analysis. A hybrid deductive--inductive coding scheme was developed to classify illustration types, instructional contexts, and communicative roles.

Two recurring themes were identified. First, illustrations function as representational translations and definitional tools, re-expressing symbolic expressions through more inspectable visual forms such as truth tables, parse trees, and logic circuits. Second, illustration choices are systematically associated with different forms of logical activity, including computation, structural analysis, and formal proof. The findings suggest that illustrations are integrated components of propositional logic exposition rather than standalone explanatory devices. This study provides an exploratory qualitative analysis of illustration practices in contemporary propositional logic textbooks and highlights the communicative and pedagogical functions of visual representations in logic education. ... Read more

Students often struggle to abandon geometric intuition when transitioning to formal abstraction in linear algebra. Prior textbook analyses documented a decline in visual support alongside this transition, but the communicative function of the remaining illustrations has not been examined in detail. This qualitative study investigates the role of textbook illustrations across treatments of Euclidean spaces (R²-R³), general Rⁿ, and abstract vector spaces. A thematic analysis was conducted through open coding of four undergraduate textbooks, informed by established typologies. The analysis reveals three shifts in function. First, illustrations systematically shed spatial characteristics to distance readers from geometric intuition. Second, the way illustrations coordinate different mathematical representations shifts from literal geometric mapping in R²-R³ to metaphorical proxies in abstract spaces. Third, illustrations shift from introducing new concepts to reinforcing established theory through repeated examples. These findings emphasize limitations of relying on geometric models for abstraction. ... Read more

Tree-based illustrations are widely used in Algorithms and Data Structures (ADS) textbooks to communicate hierarchical relationships. This study investigates how tree-based illustrations are used and what communicative functions they serve across different topics and textbooks.

A comparative qualitative thematic analysis was conducted on three ADS textbooks. Illustrations of general trees, binary trees, binary search trees, AVL trees and heaps were analysed using a coding framework derived from Levin's functional taxonomy of illustrations, Mayer's multimedia learning theory and Duval's theory of semiotic representation. The analysis focused on signalling and register shift.

The results revealed two main patterns. First, signalling techniques such as highlighted paths, arrows and geometric shapes were frequently used to communicate algorithmic behaviour that is not directly visible in tree structures. These techniques often accompanied register shifts between visual and verbal representations. Second, the textbooks differ substantially in their visual conventions, reflecting different approaches to communicating information through illustrations.

The study concludes that tree-based illustrations function as communicative tools that support both structural and procedural understanding, while shaping how readers connect visual and verbal representations. ... Read more