Mathematics
Algebra, functions, statistics and modelling real situations.
COGNIPRAXIS ACADEMY · ZONE 3 OF 4
PathfindersThe years of identity and meaning.
Ages 12–14 · UK Years 8–10 · Greek Gymnasio 1–3
Young people deepen their critical and ethical thinking, understand themselves and others better and learn to work with greater steadiness amid more complex demands and uncertainty.
1 : 4Two educators for up to 8 children, in every lesson.
28capabilities with clear milestones for this age, from the Developmental Map.
1+project a year with a real audience outside the group.
PATHFINDERS AT A GLANCE
The practical details, in six lines.
Session
1 × 90′ a week
Six stages in every lesson, with the Bridge before the close
Year
5 units × 6–7 weeks
September–June · joining at the start of each unit
Group
Up to 8 children
With two educators in every lesson
Language
Greek or English Track
The whole learning experience in the language you choose
Levels
Junior and Senior
We choose the level together, after we get to know each other
Fees
Announced when enrolment opens
Those who have registered interest hear first · 10 monthly instalments, September–June
WHAT CHANGES FROM EXPLORERS
The same capabilities, now in more complex conditions.
In Explorers, learners learn to plan, check and revise their work. In Pathfinders the same capabilities have to work in more demanding conditions: under time pressure, when the group disagrees, when the project has a real audience or when a first attempt does not succeed. We never create artificial pressure; we use the authentic demands of learning.
KNOWLEDGE · WHAT THEY LEARN
Substantial knowledge, at the depth this age allows.
Three core subjects in every zone. Each unit opens with a question worth investigating and closes with a project or a presentation.
Language & Literature
Literature, rhetoric and evidence-based writing, in the language of the Track.
Science
Physics, Chemistry and Biology; data, correlation and causation.
Alongside them, within the units: History & Social Sciences · Computing & Robotics · Arts & Drama.
The year in Pathfinders.
5 units, two Developmental Profiles and three parent meetings.
SEPOCTNOVDECJANFEBMARAPRMAYJUN
1st Developmental Profile
2nd Developmental Profile
Getting to know you
01MATH + LANG
Report02SCI + MATH
Report03LANG + HIST
Report04SCI + COMP
Report05MATH + ARTS
ReportParent meeting
Parent meeting
Parent meeting
- SEPGetting to know you
- OCT–NOVUnit 01 · MATH + LANG+ Unit Report
- NOVParent meeting
- NOV–JANUnit 02 · SCI + MATH+ Unit Report
- JAN–MARUnit 03 · LANG + HIST+ Unit Report
- FEB1st Developmental Profile
- FEBParent meeting
- MAR–MAYUnit 04 · SCI + COMP+ Unit Report
- MAY–JUNUnit 05 · MATH + ARTS+ Unit Report
- MAYParent meeting
- JUN2nd Developmental Profile
Pathfinders: 5 units × 6–7 weeks · 90′ a week · Indicative schedule. the unit of the sample lesson
MATH Mathematics · LANG Language & Literature · SCI Science · alongside them: HIST History & Social Sciences · COMP Computing & Robotics · ARTS Arts & Drama
GROWTH · THE MILESTONES OF THIS ZONE
What the child will be able to do in Pathfinders.
The Developmental Map milestones for this zone, with the main route through which each capability is cultivated. Each milestone is one way for a capability to show, not the only one. “NEW” marks what appears for the first time in this zone.
- Working memoryKeeps track of a discussion and responds to what was actually said.Within the task
- Inhibitory controlWhen others give a different answer, checks the evidence before changing their own.Within the task
- Cognitive flexibilityChanges approach when new information appears, and shows what changed their thinking.Within the task
- PlanningBreaks a multi-week project into milestones and adjusts the schedule before it is at risk.Within the task
Interpersonal, emotional, ethical
- Emotional awareness and self-awarenessRecognises how their mood affects their judgement, and takes it into account.Bridge
- Empathy and respect for diversityRecognises when a disagreement is about values rather than facts.Bridge
- Communication and collaborationKeeps the discussion on topic when the group drifts. Presents to an audience outside their group, and handles a question they did not expect.Way of working
- Ethical thinking, integrity and responsibilityDistinguishes “it is legal” from “it is right”, and explains the difference.Bridge
Thinking and meaning-making
- Critical thinking, problem solving and decision-makingRecognises whose interest a position serves, without rejecting it for that reason alone.Within the task
- Systems thinkingSpots when an “obvious” solution moves the problem instead of solving it.Within the task
- Creativity, imagination and innovationProduces more than one genuinely different solution, and chooses which is worth testing.Within the task
- Curiosity, inquiry and reflectionFrames a question without a ready answer, and plans how to investigate it.Within the task
Future-ready, citizenship, care
- Health literacy and well-beingConnects screen time with how they perform the next day, and makes one change.Bridge
- Global citizenship and environmental awarenessRecognises that a rule they take for granted does not apply everywhere, and asks why.Bridge
- Digital and AI literacyChecks what an AI tool gave them, instead of using it as it came.Within the task
- Computational thinkingDescribes the process of a solution clearly enough for someone else to follow it.Within the task
- Financial literacyWorks out what a choice really costs, including what is given up.Within the task
- Initiative and entrepreneurial mindsetProposes a project with a real recipient outside the classroom, and sees it through.Way of working
Core functions
- Sense of purposeConnects what they do today with something they want in two years’ time.Way of working
- EfficiencyNEWDistinguishes where effort is worth putting in and where it is not, and justifies it.Way of working
- FlexibilityAdapts to a change they did not choose, without losing their direction.Way of working
Psychological resources
- Overcoming adversityAfter a period that went badly, asks for help and makes a plan, instead of treating it as closed.Way of working
- Resilience in everyday difficultiesKeeps going after a poor result, and comes back to the work the next time.Way of working
- Emotion regulationRecovers after an interruption that upset them, not merely one that interrupted them.Way of working
- Attention regulationSustains concentration on a demanding task for longer than is comfortable.Way of working
- Generalised self-efficacyRefers to a previous success of theirs when taking on something difficult.Way of working
- Optimistic explanatory styleExplains a poor result as specific and temporary, not as general and permanent.Way of working
- Success mindsetAsks for the harder version of a task when given a choice.Way of working
- Self-regulated learningReads their own progress data, and sets the next goal.Way of working
- Self-DeterminationChooses a project that expresses something they genuinely care about, and explains why.Way of working
FOR PARENTS AND EDUCATORS · PDF
The full Developmental Map 6–16
All four zones, so you can see where each capability starts and where it leads.
THE BRIDGE IN PATHFINDERS
From the day’s knowledge to a human question.
Dilemmas, fairness and identity. A line of positions, reasoning with data and values, a principle for a real request.
10–14 minutes before reflection. In the Bridge we assess how the child thinks, never what they believe.
- “The teenage brain”Nervous system · SCIEmotional awareness and self-awareness
- “The voice missing from the survey”Sampling and statistics · MATHEmpathy and respect for diversity
- “Whitewash, plane trees and the delivery rider”Urban heat island · SCI + MATHEthical thinking, integrity and responsibility
- “The story shared 10,000 times”Percentages and exponential spread · MATHCritical thinking, problem solving and decision-making
- “Santorini in August”Water, energy, waste · SCI + MATHSystems thinking
- “The Antikythera Mechanism”Gears and ratios · MATH + SCICuriosity, inquiry and reflection
A LESSON IN PATHFINDERS
One session in Pathfinders, from the inside.
A sample lesson from this zone: the learning objectives, the growth targets with their routes, the Bridge and the flow. The full lesson plan opens alongside.
UNIT 02 · LESSON 2 OF 6 · SCIENCE + MATHEMATICS
“Can a city survive a heatwave?”
Today: Urban heat island: what the data show · 90′
KNOWLEDGE · LEARNING OBJECTIVES
- O1Uses the absorption–reflection model to explain why dark surfaces heat up more.
- O2Models temperature–greenery data with a straight line and interprets the gradient.
- O3Distinguishes correlation from causation by naming a possible confounding factor.
GROWTH · OBSERVATION TARGETS
- Cognitive flexibilityWithin the task
- Systems thinkingWithin the task
- Ethical thinking, integrity and responsibilityBridge
Executive functions Holistic competencies Mental toughness
BRIDGE · CULTURAL KNOWLEDGE · FAIRNESS IN A HEATWAVE
“Whitewash, plane trees and the delivery rider”
What did the old builders know about keeping cool? And who pays for the heat today?
5′Welcome
10′Warm-up
28′Academic core
24′Application & creation
14′Bridge
9′Reflection
Pathfinders · 12–14
“Urban heat island: what the data show” · 90′ · 4 pages
Bridge: “Whitewash, plane trees and the delivery rider”
See the samples for the other zones on the Academy page →
THE LEARNING EXPERIENCE
How they learn in Pathfinders.
Inquiry & case study
More complex problems, with no single obvious answer.
Structured debate & dialogue
Learners defend a position, hear a counter-argument and revise when the evidence calls for it.
A project with a real audience
At least one unit a year connects with a community, an organisation or a real audience outside the group.
AI as an object of critique
Learners check, question and cross-check what an AI tool produces.
As much support as they need. As much autonomy as they can take.
The emphasis in this zone. Support adapts to the child and the task, not just their age.
- Targeted Supportmodelling · guidance · scaffolding
- Active Participationeffort · exploration · feedback
- Gradual Responsibilityorganisation · choices · reflection
- Growing Autonomyself-regulation · initiative · persistence
- Independent Application & Transferat school · in new contexts · in life
MORE SUPPORTMORE AUTONOMY
PROGRESS IN PATHFINDERS
Learners read their own path.
- SPARKSThe educators observe
- EXPLORERSThe child compares
- PATHFINDERSReads their own path
- DESIGNERSHelps decide what is tracked
In Pathfinders the Developmental Profile becomes a tool for learners themselves: they read their path, compare it with the educators’ observations and take part in setting the next goal.
Mental Toughness becomes an explicit area of reflection. Structured self-reports become material for discussion alongside the year’s observations, never a score or a diagnosis.
AFTER EVERY LESSON
Lesson Report
5 TIMES A YEAR
Unit Report
TWICE A YEAR
Developmental Profile
THREE TIMES A YEAR
Parent meeting
Measurable progress on every objective. No comparison with other children.See sample reports on the Academy page →
THE STARTING POINT
First, we get to know the family. Then, the right start.
Meeting the parents
We talk about your expectations, our approach and how the Academy and the family work together.
A Developmental Introduction with the child
We get to know the child and where they are starting from. It is not a test; there is no pass or fail.
A shared decision on the start
Together we agree the zone, the level (Junior or Senior) and the support the child needs.
Junior and Senior. Every zone has two levels, Junior and Senior: the same architecture, a different degree of challenge and autonomy. We choose the level together, after we get to know each other.