Cartesian Tuition

Cartesian Tuition: diagnostic-led online tuition from KS2 to GCSE

Cartesian Tuition is a family-run tutoring practice that teaches one-to-one online, covering Key Stage 2 through to GCSE. Its stated specialism is preparation for the 11+, specifically the Trafford Consortium and Clitheroe Royal tests. The practice presents itself as an alternative to two common models: software platforms that generate data without a teacher present, and agencies that supply a tutor without a diagnostic picture. Its proposition is to combine both, using an assessment to establish what a child needs and then teaching against that map.

Assessment before teaching

Every child begins with a diagnostic assessment, which the practice offers free of charge. The result is a written report showing where the child stands, and the family is free to use it for work at home whether or not tuition is booked. A sample report is published on the site.

The method is set out in four stages:

• Assess: a granular measurement against each strand of the Key Stage 2 curriculum, identifying which specific objectives are holding progress back rather than a general label such as weak at maths.
• Map: the assessment is converted into a pathway, an ordered sequence of skills to address, prioritised by what unlocks the most.
• Teach: sessions follow that pathway, each one aimed at a gap that has been measured.
• Re-measure: the practice reassesses as it goes, and objectives that become secure drop out of the plan.

The published examples show how this works in practice: a session on measures and conversion, and a re-assessment in which a strand moves from priority to secure while another remains in the plan.

11+ preparation and the FSCE change

The practice prepares pupils for the five Trafford Consortium schools — Altrincham Grammar (Boys), Altrincham Grammar (Girls), Sale Grammar, Stretford Grammar and Urmston Grammar — as well as Clitheroe Royal Grammar, which runs its own admissions. It notes that the consortium schools share one test and one score but each sets its own qualifying score and catchment rules, so a result that succeeds at one school may fall short at another.

A significant part of the site is devoted to the new FSCE 11+. FSCE stands for Future Stories Community Enterprise, a not-for-profit organisation that builds entrance tests for selective state schools; the Trafford Consortium appointed it as its new test provider in July 2026. According to the practice, the Trafford 11+ changes from September 2027, dropping verbal and non-verbal reasoning and moving onto the Key Stage 2 curriculum. Children currently in Year 5 sit the new test in September 2027 for entry in September 2028, and the test is drawn from Key Stage 2 English and maths up to the end of Year 5. From 2029 entry the test moves from September of Year 6 to the summer term of Year 5. The practice states it has mapped the new exam in detail and published a free breakdown covering both papers, the Key Stage 2 domains in scope and how the qualifying score is calculated.

Subjects and levels covered

For KS3 and GCSE, the practice lists maths and English Language as its first subjects, alongside sciences, geography and English Literature. The 11+ work is built on Key Stage 2 English and maths, with a published readiness map covering reading comprehension, grammar and punctuation, spelling and vocabulary, arithmetic and problem-solving, and written expression.

The teaching team

The practice describes itself as a family and states that the same small team teaches every session, with no pool of tutors and no subcontracting. Three tutors are named:

• Mohammad: Computer Science, University of Manchester; software engineer.
• Sara: MEng Chemical Engineering, University of Oxford; process engineer.
• Ahmad: Law, University of Kent; costs lawyer.

The site argues that continuity matters because observations from an assessment — a child who can do long division but cannot explain it, comprehension that collapses specifically on inference questions, an insecure grasp of equivalent fractions — would not survive a handover note. It also states that the practice deliberately stays small, preferring to work with fewer children properly than more children through a rota.

Parent feedback

The site quotes several parent reviews. One describes support with GCSE maths and English, another credits a tutor with improving a 14-year-old's maths, and a third refers to a daughter gaining entry to grammar school with a score of 387 and a second daughter sitting her entrance exam. The practice directs readers to Trustpilot for its full reviews.

Enquiries and assessment booking

Enquiries are handled by the tutors themselves rather than a call centre, by email or WhatsApp, or through a form asking for the parent's name, the child's name, email address, the child's current year (Year 3 to GCSE) and the question. The site states that these details are used only to reply and are not passed to anyone else.