math_ladder

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the full burden of disclosing side effects, safety, and return behavior. It reveals a dependency on stored formulas and a pedagogical approach (concreteness fading) but does not state whether the tool reads or writes memory, what output it produces, or any potential side effects. The metaphor obscures operational certainty.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is a single sentence and not overly long, but it is dense with a metaphor and a parenthetical citation that add little operational value. While compact, it lacks the clear, front-loaded structure expected for an API description; the citation could be omitted without loss of usage-relevant information.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given no output schema, no annotations, and a sparse input schema, the description should clearly state what the tool does, how to invoke it, and what to expect. It does none of these adequately: parameters are unexplained, output is not mentioned, and the tool's behavior is buried in metaphor. For a simple 2-parameter tool, this is incomplete.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, and the description does not mention 'problem' or 'top_k' at all. The tool has only two parameters, but the description provides zero insight into what values they accept or how they influence the ladder process. This is a complete failure to compensate for the schema's lack of documentation.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description indicates a distinct math-focused approach ('Climb the math abstraction ladder') and mentions a specific method (concrete -> symbolic -> general rule), which differentiates it from siblings. However, the verb 'climb' is metaphorical and does not clearly state the tool's operation (e.g., generate, explain, transform), leaving the actual functionality vague.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

No explicit guidance is provided regarding when to use this tool versus alternatives. The phrase 'using formulas already stored in memory' implies a prerequisite (formulas must be in memory), but there is no mention of scenarios, exclusions, or comparisons to sibling tools like numeric_reasoning or practice_report.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.