Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Generating Pedagogically Meaningful Visuals for Math Word Problems: A New Benchmark and Analysis of Text-to-Image Models

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read MATH2VISUAL claims that grade 1–3 math word problems are best turned into teaching visuals through a tree-structured Visual Language rendered with teacher-approved layouts, and that direct text-to-image models still fail to represent…

desk verdict A useful benchmark and deterministic pipeline for teacher-aligned math word problem visuals, but the 'pedagogically meaningful' claim outruns the evidence and the human evaluation needs more rigor. read the letter →

arxiv 2506.03735 v1 pith:XBAYRK2L submitted 2025-06-04 cs.CL cs.AIcs.HC

Junling Wang , Anna Rutkiewicz , April Yi Wang , Mrinmaya Sachan This is my paper
classification cs.CLcs.AIcs.HC
keywords mathwordproblemstext-to-imagegenerationpedagogicalvisualsvisuallanguagebenchmarkdataseteducationmultimodaltree-structuredrepresentation
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

The paper tries to establish that grade 1–3 math word problems can be turned automatically into teaching visuals by first translating the problem into a tree-structured Visual Language—entities inside containers joined by operations—and then rendering that tree with teacher-approved layouts and SVG icons. Such a pipeline matters because teachers currently hand-make these visuals, and text-to-image models, when asked directly, draw the objects but routinely misrepresent the mathematical relationships. The authors build MATH2VISUAL, annotate 1,903 rendered visuals from 94.4% of the grade 1–3 ASDiv problems, and show that fine-tuning text-to-image models on this dataset improves structural alignment and completeness. They also report that even after fine-tuning, relation errors persist at very high rates, so the framework is presented less as a final solution than as a benchmark and a proof that structured intermediate representations are the workable route.

What carries the argument

Visual Language (VL), a tree-structured representation whose nodes are entities, containers, and operations (addition, subtraction, multiplication, division, surplus, comparison, unit transformation), closely mirrors the solution expression tree. It carries the argument because it converts an ambiguous narrative into an unambiguous layout specification: containers become labeled rectangles, entities become SVG icons with quantity labels, operations set spatial arrangements, and a rendering program traverses the tree bottom-up to plan relative positions and top-down to draw the final SVG. The second component is the annotated dataset of 1,903 rendered visuals, which serves both as benchmark ground truth and as fine-tuning data.

What would settle it

A controlled classroom experiment with grade 1–3 students: same word problems, one group with MATH2VISUAL-style visuals and one with text only or with unrelated decoration, measuring solution accuracy and comprehension. If students do not solve more problems correctly or explain the math better with the visuals, the pedagogical-meaningfulness claim is refuted regardless of Likert scores.

Watch

Extended reading notes

Core claim

MATH2VISUAL's central claim is that a text-to-semantics-to-visual pipeline, rather than direct text-to-image generation, is what makes pedagogy-preserving visuals feasible for math word problems. The Visual Language sits between the problem text and the picture: an LLM maps the MWP to operations over containers that hold countable entities, and a deterministic renderer turns that tree into two co-designed visual styles—Formal, with math symbols, and Intuitive, with operation-specific arrangements such as crossed-out items for subtraction and a balance for comparison. On the authors' human-evaluated benchmark, this pipeline scores near the top of the scale on accuracy, completeness, clarity, and cognitive-load criteria, while direct text-to-image models score 2.6–3.6 and commit relation errors in 81–92% of generated images. The paper therefore establishes the intermediate tree representation, not better pixel generation, as the load-bearing idea for educational visual generation.

Load-bearing premise

The claim that the visuals are pedagogically meaningful rests on the alignment of the design with what five teachers rated 7/7 and on criteria those same teachers helped define; if teacher self-report does not track what grade 1–3 students actually learn, the educational contribution is unproven even if the pipeline generates clean visuals.

Editorial extensions

If this is right

  • Text-to-image models can be steered toward correct math visuals by conditioning on a structured intermediate, not by prompt engineering alone.
  • The 1,903-visual dataset gives a reproducible benchmark for measuring accuracy, completeness, clarity, and cognitive load in educational image generation.
  • Fine-tuning a diffusion model on the dataset cuts structural misalignment and missing-item errors, so the benchmark doubles as training signal, not just evaluation.
  • Any remaining progress on direct TTI generation must solve relation errors—currently 0.81–0.92—which no tested model avoids.
  • Teachers can obtain first-pass Formal and Intuitive visuals for new word problems without hand-drawing, then verify and edit.

Reading between the lines

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

  • Beyond the paper: the same tree-to-renderer idea should transfer to other languages and to multi-equation problems by decomposing them into a sequence of intermediate visuals; the authors note the latter as future work.
  • Beyond the paper: the Visual Language could be reused as an input interface for question generation or explanation generation, giving educational NLP a visual scaffold rather than only text.
  • Beyond the paper: because pedagogical meaningfulness is currently inferred from five teachers' ratings rather than from student outcomes, the strongest test is a classroom study comparing comprehension with and without these visuals; the paper itself does not run one.
  • Beyond the paper: the high relation-error rate suggests a concrete evaluation target—models that can place quantities correctly but cannot show 'surplus' or 'comparison'—which future benchmarks should isolate.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper introduces Math2Visual, an automatic framework that converts grade 1–3 math word problems into a tree-structured Visual Language using LLMs and then renders this VL into two teacher-designed visual formats: 'Formal' (symbol-based) and 'Intuitive' (context-rich). The authors construct a dataset of 1,903 annotated visuals from ASDiv problems, benchmark text-to-image models against their design, and fine-tune LLMs and TTI models to improve visual generation. A five-teacher exploratory study is used to co-design the visual style and to report high Likert ratings. The paper's central claim is that Math2Visual generates 'pedagogically meaningful' visuals that help learners comprehend MWPs, and that the accompanying benchmark quantifies the limitations of current TTI models in representing mathematical relationships.

Significance. If the pedagogical claim is accepted, the paper makes a useful contribution: a reproducible, deterministic rendering pipeline (Algorithm 1), a public dataset and code release, and a clear benchmark showing that TTI models still fail at relational reasoning (relation error rates of 0.81–0.92 in Table 3). The VL design is well specified and its coverage of ASDiv Grade 1–3 problems (94.4%) is a concrete, falsifiable metric. However, the paper's headline claim of 'pedagogical meaningfulness' is not supported by the evidence presented, and the human evaluation foundation is thin. The benchmark's internal target (alignment with the authors' design) is legitimate, but the external-validity claim that these visuals help students understand MWPs requires direct student data or substantially reworded claims.

major comments (3)
  1. [Section 1, Section 3.6, Limitations (iii)] The paper defines 'pedagogically meaningful' visuals as those that 'help learners in accurately and clearly comprehending' the content, and this claim appears in the abstract, introduction, and conclusion. The only supporting evidence is a 5-teacher Likert survey (Section 3.6) where teachers awarded 7/7 for 'usefulness for teaching' and 6.8/7 for 'helpfulness for student understanding,' plus evaluations by the two researchers who constructed the dataset using criteria co-defined with those same teachers (Section 3.7). No student-level comprehension or learning outcome is measured anywhere in the paper. Section 3.6's conclusion that 'these ratings indicate that our design is pedagogically meaningful' is a leap from stated teacher preference to demonstrated efficacy, and Limitations (iii) overstates the evidence by claiming the controlled approach 'ensures the pedagogical validity of visuals.' This is load-bearing because the central contribution is framed as pedagogical, not merely as a teacher-approved visual style. The authors should either add a small randomized comprehension study with actual students (e.g., comparing MWP-solving or error rates with and without the visuals) or explicitly temper the claims to 'teacher-endorsed' visuals for the benchmark.
  2. [Section 5.1, Table 2, Table 3] The human evaluation that grounds the benchmark's quantitative comparisons is very thin. Each visual is rated by only two researchers, with no inter-rater agreement metric (e.g., Cohen's kappa), no per-item score distribution or variance, and no confidence intervals. The initial test sets are 24 visuals per condition, and the expanded evaluation is 72 visuals per condition. The 1–5 scale scores in Table 2 are reported to two decimal places as averages of two raters, which implies a resolution that cannot be supported by the sample. Table 3's error ratios (e.g., relation error rates of 0.81–0.92) are also derived from two researchers' coding of 576 visuals, again without agreement statistics. Without reliability evidence, the paper's claims about the ordering of models (e.g., fine-tuning improvements, o3-mini vs. Gemini differences) are not robust. The authors should report inter-rater agreement, per-item variance, and ideally increase the number of independent raters or provide a power analysis justifying the sample size.
  3. [Section 5.4, Table 2] The fine-tuned Llama-3.1-8B results in Table 2 are suspiciously uniform: all four criteria for the Intuitive condition are exactly 4.83, and the Formal condition scores are 4.79/4.83/4.83/4.83. Similarly, the expanded evaluation shows ft_llama scores of 4.92–4.99 across all criteria. This uniformity, combined with the fact that the two raters are likely the same researchers who built the dataset, raises the concern that the evaluation instrument is not discriminating between criteria or conditions, possibly due to ceiling effects or rater recognition of the fine-tuned outputs. The paper should show per-item distributions and rater-level data, and should address whether the raters were blind to the generation method. Without this, the claim that fine-tuning 'demonstrates improvements in educational visual generation' (abstract) is not fully supported.
minor comments (5)
  1. [Global] Typos and formatting: 'entit y_quantit y' in Figure 2, 'Paticipants' in Appendix C.3, 'prefered' in C.3, 'buble' in the prompts of Appendix F.2, and the reference 'svgrepoRepoFree' is inconsistently formatted. These should be corrected.
  2. [Section 4.2] The dataset composition is unclear: the paper reports 1,268 Formal visuals and 635 Intuitive visuals totaling 1,903, but it is not stated how many MWPs have both visual types versus only Formal or only Intuitive. Please clarify the mapping between MWPs and visuals and how the Intuitive subset was selected.
  3. [Section 5.3] The expanded evaluation is described as using 'the best-performing TTI model and MATH2VISUAL with the best LLM,' but the paper does not specify which LLM (o3-mini or Gemini-2-flash) was used for the Intuitive expanded set, even though the initial results show Gemini performing slightly better on Intuitive. This matters for reproducibility.
  4. [Section 5.5, Table 3] The qualitative error analysis is based on a thematic analysis where three of the initially identified eight error types occurred fewer than eight times and were consolidated. The paper does not report the frequency or resolution of disagreements in the close coding phase; please provide at least a brief description of how coding disagreements were resolved.
  5. [Section 7 and Appendix I] The paper does not disclose whether the two human evaluators were the authors themselves or independent annotators. If they were the authors, this should be stated and ideally augmented with independent ratings; if they were independent, their qualifications and instructions should be described. This is relevant to interpreting all human evaluation results.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the Math2Visual pipeline and benchmark are self-contained; the teacher-proxy validation is an external-validity gap, not a circular step.

full rationale

The technical derivation chain is not circular. The Visual Language is a fixed grammar defined in Section 3.3, the rendering is a deterministic algorithm (Algorithm 1) over a separately collected SVG dataset, and the benchmark evaluates independent TTI models against a held-out annotated dataset with standard train/test splits (Section 5). Fine-tuning results reflect genuine generalization to held-out instances, not a fit to the evaluation target. The teacher co-design study (Section 3.6) provides preference data that informed the design, but those Likert ratings are not inputs to the VL grammar or the renderer, and no number in Tables 1-3 is constructed from the evaluation criteria. The closest thing to a closed loop is the paper's inference from five teachers' ratings to 'our design is pedagogically meaningful' (Section 3.6), while its own definition of that term requires helping learners actually comprehend (Section 1). That is an external-validity gap: teacher approval is a proxy, not the defined outcome, and no student-level comprehension is measured. It does not make the generation claim equivalent to its inputs by construction. Limitations (iii) overstates that the controlled approach 'ensures the pedagogical validity of visuals'; that assertion is unsupported by student-outcome data, but it is a validity/correctness concern rather than a circularity in the derivation. Self-citations to prior work by the same group are contextual (e.g., container definition after Opedal et al.) and are not load-bearing for the central pipeline or benchmark results.

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

The paper introduces a representational notation (Visual Language with entity, container, operation) but no new physical or conceptual entity requiring independent evidence. The design choices are covered under free parameters and axioms.

free parameters (2)
  • quantity display threshold = 10
    Section 3.4 and Appendix C.4: entities are drawn individually only when entity_quantity <= 10; larger quantities are shown as a single icon with the number overlaid. This cutoff is a design convention, not a fitted quantity.
  • number of in-context VL examples = 30
    Section 4.2: 30 manually written VL examples were used to prompt LLMs. These examples encode the authors' interpretation of the visual language and are not reproduced in full; the mapping from MWP to VL depends on them.
assumptions (4)
  • domain assumption Five Prolific-recruited math teachers are a sufficient source for pedagogical validity of the visual design.
    Sections 3.6 and C.1 rely on interviews with five teachers to establish the design and the evaluation criteria; there is no broader sample or student-outcome validation.
  • domain assumption The solution expression tree is the correct semantic backbone for visualizing MWPs.
    Section 3.3 defines VL as a composition of the solution expression and operations, and the renderer follows that tree. This choice is not derived from data.
  • standard math Zhang-Shasha tree edit distance and logic match ratio are valid measures of VL quality.
    Section 5.1 uses these standard tree metrics to compare generated and ground-truth VLs; they are accepted algorithms.
  • domain assumption The manually validated LLM-generated VLs constitute reliable ground truth.
    Section 4.2: VLs were generated by o1-mini using 30 in-context examples, then validated by two researchers. Any systematic LLM error that passed validation becomes ground-truth error.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Generating Pedagogically Meaningful Visuals for Math Word Problems: A New Benchmark and Analysis of Text-to-Image Models." pith.science (2026). https://pith.science/paper/XBAYRK2L

@misc{pith2026250603735,
  author       = {Pith},
  title        = {Pith review of: Generating Pedagogically Meaningful Visuals for Math Word Problems: A New Benchmark and Analysis of Text-to-Image Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XBAYRK2L}},
  note         = {Machine review of arXiv:2506.03735}
}
read the original abstract

Visuals are valuable tools for teaching math word problems (MWPs), helping young learners interpret textual descriptions into mathematical expressions before solving them. However, creating such visuals is labor-intensive and there is a lack of automated methods to support this process. In this paper, we present Math2Visual, an automatic framework for generating pedagogically meaningful visuals from MWP text descriptions. Math2Visual leverages a pre-defined visual language and a design space grounded in interviews with math teachers, to illustrate the core mathematical relationships in MWPs. Using Math2Visual, we construct an annotated dataset of 1,903 visuals and evaluate Text-to-Image (TTI) models for their ability to generate visuals that align with our design. We further fine-tune several TTI models with our dataset, demonstrating improvements in educational visual generation. Our work establishes a new benchmark for automated generation of pedagogically meaningful visuals and offers insights into key challenges in producing multimodal educational content, such as the misrepresentation of mathematical relationships and the omission of essential visual elements.

Figures

Figures reproduced from arXiv: 2506.03735 by the authors.

Figure 1
Figure 1. Surplus operation example in Intuitive design [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. MATH2VISUAL Framework: Our approach first converts the MWP text description into a Visual Language (VL) expression using an LLM. The VL is then passed to a rendering program that generates the corresponding visual. The presented visual is in “Formal” design. the conversion. The full procedure is detailed in Section 4.2. (1) Entity is the smallest unit in VL and repre￾sents an element to be visualized. For instance, … view at source ↗
Figure 3
Figure 3. Example of addition operation in Formal design (Intuitive version [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (19 more)
Figure 4
Figure 4. Figure 4: Example of subtraction operation in Formal [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: Example of multiplication operation in Formal [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 8
Figure 8. Figure 8: Example of division operation in Formal de [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
Figure 6
Figure 6. Figure 6: Example of area operation (a special type [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 9
Figure 9. Figure 9: Example of comparison operation in Formal [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 7
Figure 7. Figure 7: Example of division operation in Formal design (Intuitive version [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 10
Figure 10. Figure 10: Example of unit transformation operation [PITH_FULL_IMAGE:figures/full_fig_p016_10.png]
Figure 13
Figure 13. Figure 13: Example of subtraction operation in Intu [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]
Figure 14
Figure 14. Figure 14: Example of multiplication operation in Intu [PITH_FULL_IMAGE:figures/full_fig_p016_14.png]
Figure 15
Figure 15. Figure 15: Example of area operation (a special type [PITH_FULL_IMAGE:figures/full_fig_p017_15.png]
Figure 16
Figure 16. Figure 16: Example of division operation in Intuitive [PITH_FULL_IMAGE:figures/full_fig_p017_16.png]
Figure 19
Figure 19. Figure 19: Example of comparison operation in Intu [PITH_FULL_IMAGE:figures/full_fig_p018_19.png]
Figure 17
Figure 17. Figure 17: Example of division operation in Intuitive [PITH_FULL_IMAGE:figures/full_fig_p018_17.png]
Figure 18
Figure 18. Figure 18: Example of surplus operation in Intuitive [PITH_FULL_IMAGE:figures/full_fig_p018_18.png]
Figure 21
Figure 21. Figure 21: Example of multiple steps operation in Intu [PITH_FULL_IMAGE:figures/full_fig_p019_21.png]
Figure 23
Figure 23. Figure 23: Example visual with relation error. Corre [PITH_FULL_IMAGE:figures/full_fig_p019_23.png]
Figure 22
Figure 22. Figure 22: Example visual with quantity error. Corre [PITH_FULL_IMAGE:figures/full_fig_p019_22.png]
Figure 25
Figure 25. Figure 25: Example visual with missing visual item error. Corresponding MWP: Charles found 6 pennies on his way to school. He also had 3 nickels already at home. How much money does he now have in all? This example is generated by zero-shot Flux.1-dev with solution expression, t…
Figure 26
Figure 26. Figure 26: Example visual with missing contextual cues [PITH_FULL_IMAGE:figures/full_fig_p020_26.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. "GenAI Defaults to Bias!" Gamify AI Literacy Through Reflections on Prompts

    cs.HC 2025-09 conditional novelty 5.0 of 10

    Playing ImaginAItion, a prompt-minimization party game, helped 30 adults recognize GenAI default biases and adjust their prompting strategies, according to pre-post survey coding.

Reference graph

Works this paper leans on

32 extracted references · 30 canonical work pages · cited by 1 Pith paper

  1. [2]

    Intuitive

    How Operations Are Visualized: • Formal: Mathematical operations are represented using standard symbols (e.g., +, -, ×, ÷). • Intuitive: Operations are visualized us- ing specific arrangements for each opera- Figure 16: Example of division operation in Intuitive design (Formal version: Figure 8). It represents visuals of a division operation in an MWP, as...

    work page 2025

  2. [3]

    Operation Symbol: Between each two rectangles, include an operation symbol that varies depending on the problem

    work page

  3. [4]

    decoupled weight decay regularization

    Parsing algebraic word problems into equa- tions.Transactions of the Association for Computa- tional Linguistics, 3:585–597. Rik Koncel-Kedziorski, Subhro Roy, Aida Amini, Nate Kushman, and Hannaneh Hajishirzi. 2016. MAWPS: A math word problem repository. InProceedings of the 2016 Conference of the North American Chapter of the Association for Computation...

    work page 2016

  4. [5]

    For surplus, similar as division, only difference is you should visualize the surplus container at the last and place the purple circle at the right bottom side of surplus container rectangle

    work page

  5. [6]

    Visualize entities on the left and right side of the scale separately

    For comparison, use a balance scale to weigh different containers. Visualize entities on the left and right side of the scale separately

    work page

  6. [7]

    For unit transformation, use a purple buble with the converted value in it on the top of each item to represent the unit value of the current item

    work page

  7. [8]

    InProceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 11931–11944, Singa- pore

    Enhancing textbooks with visuals from the web for improved learning. InProceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 11931–11944, Singa- pore. Association for Computational Linguistics. Marian Small and Amy Lin. 2025.Eyes on math: A visual approach to teaching math concepts. Teachers College Press. Elsbeth S...

    arXiv 2023

  8. [9]

    Jake picked up three ap- ples in the morning

    Navigating text-to-image customization: From lycoris fine-tuning to model evaluation. InThe Twelfth International Conference on Learning Repre- sentations. Umut Hope YILDIRIM. 2023. umuthopeyildirim/svgen-500k · Datasets at Hugging Face — huggingface.co. https://huggingface. co/datasets/umuthopeyildirim/svgen-500k. [Accessed 13-02-2025]. Kaizhong Zhang an...

    work page 2023

Show all 32 references
  1. [12]

    Inside each rectangle, display the entities of this container (e.g., apples, balls, etc.)

    Container: We use rectangular sections to represent different containers or group of entities. Inside each rectangle, display the entities of this container (e.g., apples, balls, etc.)

  2. [13]

    Container Name: Above each rectangle, place a container icon (e.g., an orange basket, jar , or other container type) and label it with the container's name (e.g.,'basket,' 'jar, etc)

  3. [15]

    Lucy" and

    Outcome Section: To the right, place an'=' symbol followed by a'?'to symbolize the unknown solution. Example: For problem: Lucy has five oranges and Jake has two oranges. How many oranges do they have together? Solution expression: 5+2=7 The visual consists of two containers, ...

  4. [16]

    +" symbol indicates the addition of their strawberries . To the right of this, an

    For comparison problem, please use a balance scale to weigh different entities. For problem'Lucy has 4 strawberries. Jake gave her 5 more. She needs 10 strawberries to make a cake. Does she have enough to make a cake?'We draw a balance scale. On the left side of the scale, two...

  5. [17]

    on his way

    For unit transformation problem, please use a purple buble with the converted value in it on the top of each item to represent the unit value of the current item. For example, a problem like'Charles found 6 pennies on his way to school. He also had 3 nickels already at home. H...

  6. [18]

    For surplus problem, please use text remainder with a new question mark after previous question mark

  7. [19]

    +" symbol between the two entities indicates the addition operation, and an

    If any container have item quantity higher than 10, please visualize only one item inside this container rectangle to be bigger and put the quantity number to cover the item. For example, if the problem is'Lucy has 15 apples and Jake has 3 apples. How many apples do they have ...

  8. [20]

    Inside each rectangle, display the items of this container (e.g., apples, balls , etc.)

    Container: We use rectangular sections to represent different containers or group of items. Inside each rectangle, display the items of this container (e.g., apples, balls , etc.)

  9. [21]

    Handle different operations:

    Container Name: Above each rectangle, place a container icon (e.g., an orange basket, jar , or other container type) and label it with the container's name (e.g.,'basket,' 'jar, etc). Handle different operations:

  10. [22]

    And place a purple circle with question mark inside at the right bottom side of the big rectangle

    For addition, use a big rectangle to cover all container rectangles need to be added together. And place a purple circle with question mark inside at the right bottom side of the big rectangle

  11. [23]

    Place a purple circle with question mark inside at the right bottom side of the minuend container rectangle

    For subtraction, first visualize minuend container then cross out item that has been subtracted. Place a purple circle with question mark inside at the right bottom side of the minuend container rectangle

  12. [24]

    Use a big rectangle to cover all container

    For multiplication, repeatedly visualize the multiplicand container. Use a big rectangle to cover all container. Place purple circle with question mark similar as addition

  13. [25]

    If asking about quantity in single container, place purple circle at the right bottom of the last container rectangle

    For division, visualize it as the state after division, with many container rectangles represent different groups. If asking about quantity in single container, place purple circle at the right bottom of the last container rectangle. If asking about number of container, place ...

  14. [29]

    Lucy" and

    For problem involving multiple addition and subtraction, use the same visualization rule and combine dynamically. Example: For problem: Lucy has five oranges and Jake has two oranges. How many oranges do they have together? Solution expression: 5+2=7 The visual consists of two...

    2024

  15. [30]

    Multiple Visuals: Each visual represents one sentence of the MWP

  16. [31]

    Please indicate your preference between these two approaches

    Single Visual: One visual represents the en- tire MWP. Please indicate your preference between these two approaches. Session Two – Design Variation Evaluation: You will review six design variations for visual- izing MWPs. These variations differ based on:

  17. [32]

    • Hybrid: A single item is visualized with a label at the bottom-right corner indicat- ing its quantity

    How Quantities Are Visualized: • Abstract: Quantities are represented as text from the MWP. • Hybrid: A single item is visualized with a label at the bottom-right corner indicat- ing its quantity. • Visual: Items are directly drawn in quan- tities matching their number

  18. [33]

    Intuitive

    How Operations Are Visualized: • Formal: Mathematical operations are represented using standard symbols (e.g., +, -, ×, ÷). • Intuitive: Operations are visualized us- ing specific arrangements for each opera- tion. For each design variation, please complete a ques- tionnaire r...

  19. [2003]

    Shen-yun Miao, Chao-Chun Liang, and Keh-Yih Su

    College student web use, perceptions of infor- mation credibility, and verification behavior.Com- puters & Education, 41(3):271–290. Shen-yun Miao, Chao-Chun Liang, and Keh-Yih Su

  20. [2015]

    International journal of Stem education, 2:1–13

    The role of visual representations in scien- tific practices: from conceptual understanding and knowledge generation to ‘seeing’how science works. International journal of Stem education, 2:1–13. Gerald Goldin and Nina Shteingold. 2001. Systems of representations and the devel...

    2001

  21. [2020]

    InProceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 975–984, Online

    A diverse corpus for evaluating and developing English math word problem solvers. InProceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 975–984, Online. Association for Computational Linguistics. Mistral. 2024. mistralai/Mistral-7B-v0...

    2024

  22. [2022]

    InProceedings of the 2022 Conference on Empirical Methods in Nat- ural Language Processing, pages 4136–4149, Abu Dhabi, United Arab Emirates

    Automatic generation of socratic subquestions for teaching math word problems. InProceedings of the 2022 Conference on Empirical Methods in Nat- ural Language Processing, pages 4136–4149, Abu Dhabi, United Arab Emirates. Association for Com- putational Linguistics. Anjali Sing...

    2022

  23. [2023]

    Jonas Belouadi, Simone Paolo Ponzetto, and Steffen Eger

    Automatikz: Text-guided synthesis of sci- entific vector graphics with tikz.arXiv preprint arXiv:2310.00367. Jonas Belouadi, Simone Paolo Ponzetto, and Steffen Eger. 2024. DeTikZify: Synthesizing graphics pro- grams for scientific figures and sketches with TikZ. InThe Thirty-e...

    2024 arXiv

  24. [2024]

    InForty-first Interna- tional Conference on Machine Learning

    Scaling rectified flow transformers for high- resolution image synthesis. InForty-first Interna- tional Conference on Machine Learning. Maria Evagorou, Sibel Erduran, and Terhi Mäntylä

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.