1-on-1 Mastery-Based Geometry · Taipei

Geometry, from shapes to proof.

Geometry asks students to do something most earlier math doesn't. They have to justify every step. Lessons build from the visual reasoning students already have toward the proof-writing their class is now requiring.

Audience
Geometry and equivalent geometry content, international school students
Format
1-on-1, 1 to 1.5 hours per lesson
Duration
Typically 6 to 12 months per program
Begin
Complimentary consultation & assessment class

What Students Learn

Mastery-based Geometry at the level your child's school actually requires.

Geometry is for students who could handle algebra and arithmetic but are running into difficulty with the proof discipline geometry introduces. The program covers the core geometry content high school mathematics builds on. Working with definitions, postulates, and basic geometric constructions. Reasoning through angle relationships and parallel-line theorems. Writing two-column and paragraph proofs for triangle congruence. Working with quadrilaterals, polygons, and similarity. Applying right-triangle trigonometry to real-world problems. Reasoning through circle theorems and arc relationships. Connecting algebra to geometry through coordinate proofs and transformations. These are the topics every later high school math course assumes.

Different geometric content demands different approaches. A triangle congruence proof reads differently from a coordinate-geometry calculation, and a circle theorem works differently from a transformation problem. Students learn to recognize what kind of geometry problem they're working with and to apply the strategies that fit. By the end of Geometry, this distinction is what separates students who reason geometrically from students who only memorize theorems.

Lessons follow Harland's Geometry curriculum, which is built to bring students to mastery of Geometry content and matches international school expectations. The program is structured into five units that follow the natural flow of Geometry content. Each unit closes in a deliverable that measures whether the student has reached mastery of the content before moving on. Lessons calibrate to your child's individual gaps and the topics they're working through at school. If a student is working through triangle congruence proofs at school, the teacher works through it with the student, applying the unit's deductive structure to the kinds of proofs their class is currently writing. Harland's curriculum decides what gets taught. The student's school Geometry class is where the teaching happens.

Progress shows up in places parents can see. Your child stops freezing on proof problems. They start naming the postulates and theorems that justify each step. School feedback shifts from "needs work on showing reasoning" toward "writes clear, well-justified proofs."

How We Teach It

Geometry taught through what students are working on.

Harland's pedagogy is content-based learning. Geometric reasoning, deductive proof, and problem-solving develop through the topics, problem sets, and assignments your child is already working on at school. Assessments check whether the reasoning holds up when the student moves to new content alone.

That means lessons that work directly with school material. A student working through angle relationships and basic constructions works on it with their teacher, applying the unit's reasoning structure to the geometry their school is asking for. A student moving into triangle congruence and the start of formal proofs works on it with their teacher, applying the unit's deductive structure to the proof-writing their class is doing. A student working through coordinate geometry, circle theorems, and the introduction to transformations works on it with their teacher, building the synthesis skills the next courses in the sequence will assume.

Geometry is also a question of engagement. Some students arrive having handled algebra fluently and are unprepared for the proof-writing geometry now demands. The justification feels arbitrary, the steps feel slow, and what worked in earlier courses stops working. The 1-on-1 format gives teachers room to slow down where the proof structure is unfamiliar, and to push for careful justification without losing the student's interest. Skill and rigor develop together. Neither moves far in isolation.

The format also lets teachers calibrate within the program's structure. A student strong in algebraic manipulation but uncomfortable with proof structure gets work calibrated to build proof fluency before moving to harder geometry content. They aren't held to a generic remediation script. A student fluent with spatial reasoning but rushed in justification gets pushed toward the careful step-by-step work their school will eventually demand. What does this step prove. Why does this theorem apply here. What postulate or definition justifies this line.

Curriculum and Alignment

A structured curriculum that aligns with your child's school.

Geometry at Harland follows a structured curriculum keyed to the typical Geometry course content taught in international schools. A student who completes the program has demonstrated mastery of Geometry content.

Harland's curriculum runs five units. Most school Geometry courses spread across more. 1-on-1 lessons don't lose time to group pacing or mixed-ability instruction, so the same core content fits in fewer, more substantive units. The time saved goes into the proof-based reasoning Geometry rewards.

Lessons coordinate with whatever curriculum your child's school follows. The Geometry curriculum tracks against the Common Core State Standards for High School Geometry. Students from US-curriculum schools work through it as their school's Geometry course. Students at IB or Cambridge schools, where the geometry content sits within an integrated G9–10 mathematics syllabus, use the program for targeted geometry reinforcement calibrated to whatever their school is currently working on. Where a school uses its own internal curriculum, the Student Coordinator translates school expectations into lesson goals.

Standards
Harland's Geometry curriculum, with cross-references to Common Core State Standards for High School Geometry and school-specific expectations as relevant
Materials
Harland curriculum materials, with school texts, worksheets, and assignments integrated as ongoing input
Assessment
End-of-unit assessments, tracked against Geometry mastery and school-flagged skills
Reporting
Skill-level tracking against Harland's internal rubrics, matched to international school standards

Prerequisites and What Comes Next

Where Geometry fits in your child's learning.

Before starting

Geometry assumes Algebra I content fluency. Students should have completed Algebra I or equivalent algebra content before starting, including linear equations, manipulating expressions, and basic graphing. Students whose Algebra I has gaps in these areas typically work in Algebra I first or alongside Geometry, depending on how foundational the gaps are.

Some students at Geometry level still find that mathematical word problems and proof-reading run harder than the geometry itself, because the English vocabulary is doing more work than the geometry is. Where this is the case, Academic English (Grades 3–12) runs alongside as a parallel program. The Student Coordinator helps families judge whether the gap is in the geometry or in the language carrying the geometry.

The consultation and assessment class establishes whether Geometry is the right starting point and whether parallel work in another program would help. Some students arrive needing both Algebra I review and Geometry support, and the lesson plan covers what's most urgent first.

What comes after

Most students complete Geometry in 6 to 12 months, depending on starting position and lesson cadence. At completion, families have a clear decision point.

Many students continue with Algebra II in the standard high school mathematics sequence. Others step away from Harland once Geometry content is mastered, returning if later courses become difficult.

Students on AP tracks at higher grades progress to AP Calculus AB or BC and other AP mathematics offerings on our AP Program. Students at IB schools continue through to IB Diploma Mathematics: Analysis and Approaches, or Applications and Interpretation, at Standard or Higher Level on the IB Diploma Programme. Students preparing for SAT, SSAT, or ISEE may use Geometry work as foundation for Test Preparation.

The longer-term aim of Geometry is to make itself unnecessary. The program brings students to mastery of Geometry content. Some continue with Algebra II, others don't need Harland until later in the sequence. A parent who's no longer worried about their child's math is the point of all of it.

Common Questions

Common questions about Geometry at Harland.

Who is Geometry at Harland for? +
Geometry at Harland is for students who have completed Algebra I or equivalent algebra content and are now working through high school Geometry. Most of our students fall into one of three patterns. Some are at US-curriculum international schools where Geometry is the standard G9 or G10 course and they're falling behind their teacher's pace, particularly when proof-writing begins. Some are advanced students working through Geometry at G8 or earlier and want to deepen their mastery of proof and reasoning. Some are at IB or Cambridge schools where the geometry strand of their integrated mathematics syllabus needs targeted reinforcement.
My child can see the answer but can't write the proof. Is this the right program? +
Yes, in most cases. Proof-writing is one of the most common difficulty points in international school Geometry. Earlier math courses gave concrete answers and procedural steps. Geometry asks students to justify each step, naming the postulates and theorems that earn each line of reasoning. The program focuses on what makes that transition difficult. Reading geometric figures and identifying what's given. Naming the postulates and theorems that justify each step. Writing two-column and paragraph proofs that hold up to a teacher's marking. Building the rigor that proof-writing demands.
Can my child begin Harland over the summer? +
Yes. Summer enrollment is available across most Harland programs. The summer block is a 4 to 8 week 1-on-1 program scheduled between late June and early August, typically two to three sessions per week, calibrated to what your child's school will be teaching later in the school year. See Summer Enrollment for full details.
What does Geometry at Harland cover? +
Geometry at Harland covers the core geometry content typically taught in a high school Geometry course. Working with definitions, postulates, and basic geometric constructions. Reasoning through angle relationships and parallel-line theorems. Writing two-column and paragraph proofs for triangle congruence. Working with quadrilaterals, polygons, and the properties of special figures. Applying similarity and right-triangle trigonometry to real-world problems. Reasoning through circle theorems, inscribed angles, and arc relationships. Connecting algebra to geometry through coordinate proofs and transformations. Working with surface area and volume of three-dimensional figures. Lessons calibrate to whichever topics your child's school is emphasizing. If a teacher has flagged a specific skill, the lesson plan can focus on that skill rather than running through the whole program.
How long is each lesson and how often does my child attend? +
Lessons are 1-on-1 sessions of 1 to 1.5 hours, in person at our head office in Da'an or online. Most students attend one to three lessons per week. The Geometry program is structured around five units of work, each closing in a deliverable. At one or two lessons per week, the program typically takes a school year. At three lessons per week, a semester. The Student Coordinator helps you choose the cadence that fits.
How are lessons scheduled, and what if we need to reschedule? +
Lessons happen on a fixed weekly slot reserved with your child's primary teacher. This protects the teacher's time and keeps a consistent rhythm for your child. If you need to reschedule, give us at least 24 hours of notice and we'll find another time when your teacher is available. Many families add classes during summer or winter vacation, either to accelerate progress or to make up for a slower term. Once a unit has started, it should be completed within a defined window. The Student Coordinator walks through the details when you enroll.
How do you measure progress? +
Progress is measured through the curriculum's assessments. The Geometry program has five units, each closing in an assessment that measures conceptual understanding, proof-writing fluency, problem-solving, and mathematical reasoning across the unit's content. Parents receive updates after every lesson and formal progress reports when each unit ends. Skill-level tracking uses Harland's internal rubrics, which match international school standards. Where helpful, the Student Coordinator translates this into the expectations of your child's school.
How do we begin? +
Every Harland relationship begins with a consultation, followed by a 1-on-1 assessment class. The consultation is about your goals and your child's situation. The assessment class is about how your child works in the subject. Together they tell us where to start and what kind of teacher will fit best.

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