Word problems are among the most challenging tasks in mathematics lessons. Children have to understand a text, distinguish relevant from irrelevant information, create a mathematical model, and finally perform the calculation. Many fail not because of the mathematics itself, but because of text comprehension or modeling (Reusser 1997). "Real-Question Word Problems" is an app that uses AI to guide children in grades 1 through at least 6 through precisely these steps: not by giving them the answers, but by providing structured prompts based on proven problem-solving strategies.

Strategy-based work

Acquiring explicit problem-solving strategies is significantly more effective for solving word problems than repeatedly practicing individual problems (Rasch 2001). Word problems offer seven ways to work with mathematical situations:

1. Read text – Reading aloud, word explanations and visually supported reading as an introduction to the task for children who need support in this area (e.g. also German as a Second Language, …).
2. ask questions Children formulate their own questions about the situation and clarify any gaps in their understanding before they do the calculations.
3. Understanding the text – The app helps to create an information network: Which figures are relevant, what is the question, what is superfluous?
4. Developing solutions – Step-by-step guidance through the problem-solving process with tiered support.
5. Check solution – Metacognitive suggestions for evaluating the result: Is the result correct? Does it fit the situation?
6. Fault Detective – Analysis of deliberately flawed, predetermined solution paths. Examining others' errors allows for objective discussion without personal threat and strengthens mathematical argumentation.
7. Making assumptions – For estimation and Fermi problems: Children learn to deal with missing information and to formulate reasoned assumptions.

Task types

Many children reflexively calculate every number they encounter without truly considering the situation. "Captain's problems"—unsolvable problems where this very realization is the goal—make this pattern visible and encourage children to pause before calculating. Fermi problems pose open-ended questions that have no single, definitive answer but require reasoned estimation and argumentation. Both types of problems are integrated into the app, are carefully considered, and promote a deeper understanding of mathematical modeling. When generating modeling problems in the app, these problem types can be deliberately selected, or keywords such as "overdetermined" or "underdetermined" can be entered as a starting point.

Scaffolding and adaptivity

The support process follows Polya's four-phase model (understand, plan, implement, review) and utilizes the fading principle: Support begins with open-ended prompts and becomes more specific only as needed, progressing through strategic guidance and targeted assistance to step-by-step instructions. This allows children to work as close as possible to their zone of proximal development. The app adapts language, complexity, and intensity of support to the selected age group (grades 1 to 6).

Accessibility and reading support

In a classroom, native German speakers sit next to children with German as a second language, strong readers next to children with reading difficulties. Those who don't understand the text can't grasp the underlying mathematics. Therefore, "Math Stories" offers a read-aloud function with adjustable speed, syllable division, and picture words based on ARASAAC pictograms, which visually support reading comprehension. This isn't about simplifying the task, but rather providing a fair approach to mathematics.

Use in the classroom

Math Stories is particularly well-suited for teaching settings where children work independently: during free work time, weekly plans, remedial lessons, or as homework support – especially for children who don't receive academic support at home. While this support doesn't replace teacher guidance, it can effectively complement it in the micro-didactic realm, specifically during task completion when children lack support and might become discouraged. The app can be easily introduced on the interactive whiteboard to demonstrate its use and emphasize that it doesn't provide the answer but rather guides the thinking process. Tasks can be entered via text, photo, or QR code and shared between devices, facilitating integration into existing lesson plans. Any test question can therefore be completed with the app., of course also in combination with paper and pencil.

Additional functions

A problem generator creates word problems categorized by topic, operation, and difficulty level. Additionally, there is a collection of real-world scenarios for each grade level and difficulty level that can be used.

Children can create sketches on a drawing surface to illustrate the task and visualize their ideas about the situation.

For completed tasks, certificates of competence can be issued that acknowledge the process of working on the task – not the correctness of the solution. These certificates provide teachers with valuable insights into the quality of the task completion and the children's skill development.

Availability

Math Stories is available as a web app at math stories.urff.app It's freely accessible and works on all devices with a modern browser. However, a separate API key for AI is required to use the app's AI functions.
An app is available in the App Store for iPad and iPhone, where the purchase price also covers the AI costs, and therefore no API key with extra costs is necessary.

---

literature

• Franke, M., Ruwisch, S., & Padberg, F. (2010). Didactics of word problems in primary school (2nd ed.). Heidelberg: Spektrum Akademischer Verlag.
• Rasch, R. (2001). Working with challenging word problems in primary school mathematics lessons: A study of primary school children's approaches to demanding word problems and conclusions for lesson design that promotes corresponding problem-solving skills. Hildesheim: Franzbecker.
• Reusser, K. (1997). Acquisition of mathematical skills: Literature review. In F.E. Weinert & A. Helmke (Eds.), Development in primary school age (pp. 141–155). Weinheim: Beltz PsychologieVerlagsUnion (PVU).
• PIKAS (DZLM). Factual situations – sizes and measurements. pikas.dzlm.de.