Mathematics
Models, probability and statistical inference for complex questions.
COGNIPRAXIS ACADEMY · ZONE 4 OF 4
DesignersFrom learner to creator.
Ages 15–16 · UK Years 11–12 · Greek Lykeio 1–2
Young people plan, take initiative, manage complex projects and regulate their own learning with growing autonomy, with a sense of purpose, responsibility and readiness for what comes next.
1 : 4Two educators for up to 8 children, in every lesson.
29capabilities with clear milestones for this age, from the Developmental Map.
1independent inquiry, with their own question, method and criteria.
DESIGNERS 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
4 units × 8 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 PATHFINDERS
In Pathfinders, learners read their own path. Here they design it.
The horizon becomes more real: choices, larger projects, higher demands and decisions about what comes next create authentic settings in which learners organise, choose, adapt and take on more responsibility. Growth is not “complete” at 16; the aim is a more mature ownership of learning and action.
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
Critical reading, the essay and writing for a real audience, in the language of the Track.
Science
Complex systems, energy, biotechnology and the science behind public issues.
Alongside them, within the units: History & Social Sciences · Computing & Robotics.
The year in Designers.
4 units, two Developmental Profiles and three parent meetings.
SEPOCTNOVDECJANFEBMARAPRMAYJUN
1st Developmental Profile
2nd Developmental Profile
Getting to know you
01SCI + MATH
Report02MATH + LANG
Report03LANG + HIST
Report04SCI + COMP
ReportParent meeting
Parent meeting
Parent meeting
- SEPGetting to know you
- OCT–DECUnit 01 · SCI + MATH+ Unit Report
- NOVParent meeting
- DEC–FEBUnit 02 · MATH + LANG+ Unit Report
- FEB1st Developmental Profile
- FEBParent meeting
- FEB–APRUnit 03 · LANG + HIST+ Unit Report
- APR–JUNUnit 04 · SCI + COMP+ Unit Report
- MAYParent meeting
- JUN2nd Developmental Profile
Designers: 4 units × 8 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
GROWTH · THE MILESTONES OF THIS ZONE
What the child will be able to do in Designers.
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 memoryWhen there is a lot of information, organises it into smaller parts without losing the links between them.Within the task
- Inhibitory controlCompletes their checking steps to the end, even when they see others have already finished.Within the task
- Cognitive flexibilityExamines an issue from two perspectives and changes approach when one no longer explains the data.Within the task
- PlanningManages two strands of work that depend on each other, and adjusts both when one gets stuck.Within the task
Interpersonal, emotional, ethical
- Emotional awareness and self-awarenessRecognises which situations consistently wind them up, and says so before going into them.Bridge
- Empathy and respect for diversityWhen someone describes an experience they have not lived, tries first to understand it before comparing it with their own.Bridge
- Communication and collaborationExplains something complex to someone who does not know it, without oversimplifying it wrongly.Way of working
- Ethical thinking, integrity and responsibilityIn a group decision, voices a reasoned objection when they believe a principle is being breached, even if the majority disagrees.Bridge
Thinking and meaning-making
- Critical thinking, problem solving and decision-makingMakes a decision with incomplete information and states what would change their mind.Within the task
- Systems thinkingPredicts how a change in one part of a system creates at least one second consequence elsewhere.Within the task
- Creativity, imagination and innovationWhen a first idea fails, redesigns it substantially instead of making small fixes.Within the task
- Curiosity, inquiry and reflectionSets their own question for a long project, plans the inquiry and sees it through.Within the task
Future-ready, citizenship, care
- Health literacy and well-beingOrganises their routine to cope with a period of pressure, not just a single day.Bridge
- Global citizenship and environmental awarenessWeighs collective benefit against individual cost in a real issue, and takes a position.Bridge
- Digital and AI literacyUses AI output as one source, independently checks the critical points, and separates what they verified from what they accepted.Within the task
- Computational thinkingTurns a solution into a reusable process, and recognises when it stops working.Within the task
- Financial literacyAllocates time, money and effort between options according to how much each contributes to the goal.Within the task
- Initiative and entrepreneurial mindsetRecognises a need nobody has put into words, and designs a response.Way of working
Core functions
- Sense of purposeExplains which personal goal or value a long-term effort serves, and what would make them reconsider it.Way of working
- EfficiencyAllocates effort across demands according to how much each contributes to the goal, not only according to preference.Way of working
- FlexibilityWhen circumstances change substantially, decides whether to change the plan, the goal or both, and explains why.Way of working
Psychological resources
- Overcoming adversityAfter a serious failure in something they cared about, makes it part of their journey and carries on with a revised plan.Way of working
- Resilience in everyday difficultiesIn a period of pressure, stays functionally engaged and adjusts pace, strategy or support before becoming exhausted.Way of working
- Emotion regulationUses their own technique to calm down before a demanding test, without being reminded.Way of working
- Attention regulationChooses working conditions that help them concentrate, and sticks to them.Way of working
- Generalised self-efficacyPersists with a difficult task and can show what makes them believe they can do it.Way of working
- Optimistic explanatory styleAfter a negative result, separates what was changeable from what they do not control, without generalising it to themselves.Way of working
- Success mindsetSeeks feedback that will show what did not go well, not reassurance.Way of working
- Contextual awarenessNEWIn a new context, identifies the key requirements and constraints before acting, and adapts their approach.Way of working
- Self-regulated learningCompares two of their own methods by their results, and keeps what worked better.Way of working
- Self-DeterminationDefines, together with the teacher, what counts as success for them.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 DESIGNERS
From the day’s knowledge to a human question.
Complex public issues. A reasoned objection, an article or a proposal for a real audience.
10–14 minutes before reflection. In the Bridge we assess how the child thinks, never what they believe.
- “Me or my mood?”Probability and cognitive biases · MATHEmotional awareness and self-awareness
- “The gap in the CV”Selection algorithms, base rate · MATH + LANGEmpathy and respect for diversity
- “Genes made to order?”Biotechnology · SCIEthical thinking, integrity and responsibility
- “Who paid for the study?”Statistical inference · MATHCritical thinking, problem solving and decision-making
- “After lignite”Energy and the economy · SCI + MATHSystems thinking
- “The open questions of science”The scientific method · SCICuriosity, inquiry and reflection
A LESSON IN DESIGNERS
One session in Designers, 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 4 OF 8 · MATHEMATICS + ENGLISH LANGUAGE & LITERATURE
“Would you trust an algorithm?”
Today: The algorithm that selects · 90′
KNOWLEDGE · LEARNING OBJECTIVES
- O1Builds a weighted scoring model in a spreadsheet and checks how sensitive it is to the weights.
- O2Calculates false positives and false negatives from a two-way table and interprets the base rate.
- O3Writes an argument paragraph with a position, evidence from their own data and a counter-argument.
GROWTH · OBSERVATION TARGETS
- Digital and AI literacyWithin the task
- Ethical thinking, integrity and responsibilityBridge
- EfficiencyWay of working
Executive functions Holistic competencies Mental toughness
BRIDGE · THE PERSON BEHIND THE NUMBER · CARE AND FAIRNESS
“The gap in the CV”
The model deducts points for “gaps”. Ellie was away for two years to look after her mother.
5′Welcome
10′Warm-up
28′Academic core
24′Application & creation
14′Bridge
9′Reflection
Designers · 15–16
“The algorithm that selects” · 90′ · 4 pages
Bridge: “The gap in the CV”
See the samples for the other zones on the Academy page →
THE LEARNING EXPERIENCE
How they learn in Designers.
Independent inquiry
Learners set a question, plan the inquiry, choose methods and judge the outcome against agreed criteria.
Case studies & structured dialogue
They analyse complex situations, bring opposing views together and defend choices with evidence.
Major projects with a real audience
At least one project connects with a real audience, need or recipient outside the classroom.
Deliberate learning & reflection
Study strategies, managing workload and reflecting on the data of their own learning become an explicit focus of work.
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 DESIGNERS
Learners take part in what is tracked, and why.
- SPARKSThe educators observe
- EXPLORERSThe child compares
- PATHFINDERSReads their own path
- DESIGNERSHelps decide what is tracked
In Designers learners decide with the educators which capabilities to focus on and what will count as evidence of progress, within the shared criteria of the CogniPraxis Developmental Evidence System.
The shared framework and criteria stay the same. What changes is that learners help shape their own goals.
AFTER EVERY LESSON
Lesson Report
4 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.