but with identity, purpose, and an understanding of how they contribute to the guild.
In Frostfall, survival depends on more than strength.
think carefully
adapt under pressure
communicate clearly
notice patterns
solve problems creatively
and persist when situations become difficult
The Mathematical Thinking Laboratory is built around the idea that students grow stronger through challenge, collaboration, and reflection. Your character is not simply a fictional avatar. Your character is a representation of the ways you learn, think, struggle, adapt, and contribute.
As the expedition continues, your adventurer will grow alongside your mathematical abilities.
Rowan Vale
Tundra
Flint Mercer
Echo
Sable North
Mira Ash
Orion Pike
The Quartermaster
Polaris
Wren
practical
mysterious
scientific
historical
adventurous
humorous
or connected to nature and survival
real names
nicknames
callsigns
or fully fictional identities
Research on identity and learning suggests that students engage more deeply when they feel agency, autonomy, and personal investment in the learning environment.
Guild Backgrounds
Every adventurer enters the guild with different experiences.
Backgrounds help explain:
how an adventurer approaches problems
what strengths they developed before joining the expedition
and how they contribute to the group
Guild backgrounds are not about combat.
They are about habits, experiences, and ways of thinking.
Example Guild Backgrounds
Surveyor
You grew up mapping difficult terrain and identifying safe routes through dangerous environments.
Strengths:
noticing patterns
spatial reasoning
observation
precision
Mechanic
You spent years repairing machines, generators, sleds, tools, or field equipment.
Strengths:
debugging
systems thinking
persistence
logical troubleshooting
Courier
You carried messages and supplies between distant settlements.
Strengths:
adaptability
time management
resilience
strategic planning
Research Apprentice
You worked beside archivists, scientists, engineers, or navigators studying the changing world.
Strengths:
curiosity
documentation
questioning
information analysis
Salvager
You learned to recover useful materials from ruins, wreckage, and abandoned sites.
Strengths:
creativity
flexible thinking
resourcefulness
unconventional strategies
Trail Cook
You managed food, fuel, and supply systems during long expeditions.
Strengths:
organization
ratios and measurement
planning
teamwork
Students may also create custom backgrounds with approval from the Guide.
Starting Traits
Traits represent how an adventurer tends to approach problems and challenges.
Traits are not fixed talents.
They are starting points.
Throughout the expedition, traits can strengthen through:
practice
reflection
collaboration
and experience
The six core traits of the Mathematical Thinking Laboratory are:
Trait
Description
Grit
Persistence during challenge
Logic
Reasoning and problem-solving
Focus
Attention and task management
Ingenuity
Flexible and creative thinking
Communication
Explaining and discussing ideas
Awareness
Pattern recognition and error detection
Students will explore these traits more deeply in Chapter 2.
At the start of the expedition, adventurers should reflect honestly:
Which traits feel strongest?
Which traits are hardest?
Which traits are growing?
The goal is not to create a “perfect” character.
The goal is self-awareness and growth.
Character Journals
Every adventurer keeps a field journal.
In Frostfall, journals are essential survival tools.
They contain:
maps
calculations
sketches
observations
supply records
strategies
reflections
and expedition logs
Inside the Mathematical Thinking Laboratory, the Adventurer’s Log serves as:
a portfolio
a reflection tool
a progress tracker
and a record of mathematical growth
Students are expected to document:
revisions
discoveries
failed attempts
successful strategies
and evidence of learning
Research on metacognition and mathematical reasoning consistently shows that reflection strengthens learning and improves transfer to new situations.
The journal is not about producing perfect notes.
It is about making thinking visible.
Starting Equipment
Every guild member begins with a small collection of expedition tools.
These tools represent:
preparation
strategic support
and ways of interacting with mathematical challenges
Starting equipment may include:
graph paper
pencils
ruler
compass
whiteboard marker
sticky notes
calculator
colored pencils
reference cards
manipulatives
dice
or expedition maps
Some equipment exists physically.
Some exists symbolically inside the campaign system.
Equipment may provide:
hints
retries
strategy boosts
organizational support
or collaborative advantages
The purpose of equipment is not to avoid thinking.
The purpose is to support productive thinking.
Research on executive functioning and cognitive load suggests that external tools and supports can significantly improve student persistence and problem-solving capacity.
Strong adventurers are not the ones who never need tools.
Strong adventurers are the ones who learn how to use tools strategically.
Preparing for the Expedition
The frozen frontier of Frostfall is unpredictable.
No adventurer succeeds alone.
As you prepare your character, remember:
Your role is not to be perfect.
Your role is to:
think
adapt
collaborate
persist
and continue growing
Every experienced adventurer was once a beginner.
Every expert was once confused.
Every strong mathematician was once stuck.
The expedition begins with preparation.
But growth begins when the real challenges arrive.