Who this is for
Polaris is not for the student who needs to be convinced that math matters. It is for the one who already suspects they are capable of more than their current results show, and willing to do the work if someone gives them the structure and the right people to do it with.
That student does not need remediation. They need a goal, a plan, and six peers who take it as seriously as they do.
Capable, motivated students who see room to grow and want a structured path to get there
Students preparing for honors tracks, competitive STEM programs, or accelerated high school placement
Students who want peers who take hard thinking seriously, not just a room to finish homework
Students who need foundational remediation or are not yet motivated to engage challenging work
What Polaris Is
For the student
Most math instruction is passive. Polaris is active. You work through problems with peers who are just as motivated, present your thinking out loud, and build the habit of figuring things out before reaching for help. The framework you develop here transfers to every hard problem you face, in math and beyond it.
For the parent
The peers around your child set the standard for what feels normal. Polaris curates that peer group intentionally: six students of similar ability and drive who take hard thinking seriously. Over twelve weeks, ambition becomes the default, not the exception. Reasoning through unfamiliar problems, presenting thinking out loud, returning to challenges that haven’t yielded yet: these habits travel far beyond any single math course.
Polaris is not remediation. It is not test prep. It is a thinking community built for students who are ready to go further than their school takes them.
Session Design
Every segment is designed. Every minute has a purpose.
One problem dropped in the chat. Students have 90 seconds to write their first instinct, simultaneously, so no one goes first alone. When answers are revealed, the differences between them become the session's first real question.
Your coach works through the cold open problem using FGS, without naming it. "What are we finding?" "What are we given?" "What routes do we have?" Students drive the answers. Multiple solution paths surface. The framework is absorbed, not assigned.
Students break into pairs. Each pair gets a different but related problem and a shared whiteboard. Twelve minutes to work it through together, then one student from each pair presents their thinking to the group. The thinking, not just the answer.
One problem above grade level. No student is expected to solve it. The frame is explicit: "I want to see how far you get." Students who make one step forward leave with a real win. Students who get stuck experience what it feels like to attempt something genuinely hard. That problem returns next week.
Each student says one sentence: what they figured out today, or what they are still thinking about. Then your coach names next week's arena challenge. Students leave with open loops, which is exactly what makes them want to come back.
The Framework
Every problem in Polaris is approached the same way. Not because students are required to, because it is modeled every single session, and students absorb it until it becomes their own instinct.
What is this problem actually asking?
Before a student touches a number, they define, in plain language, exactly what they are looking for. Not a vague sense of the answer. A precise statement of what solving it means.
What do I have, and what does it mean?
Students write out what they are given and, crucially, what each piece means in the context of what they are trying to find. This step surfaces misunderstanding before it becomes a wrong answer.
What route gets me there?
Once Find and Given are clear, Solve becomes a question of mapping a path rather than executing a memorized procedure. Different students find different routes. That is exactly the point.
Students who internalize FGS stop asking “what formula do I use?” They start asking “what am I actually trying to find?” That is the shift.
Why it works
Effect size of peer collaborative learning on math achievement
Students in structured peer learning environments outperformed control groups by more than half a standard deviation, equivalent to moving from the 50th to the 73rd percentile.
Capar & Tarim, 2015 meta-analysis
Metacognitive strategies produce higher standardized test scores than procedural instruction alone
Students taught to define what they are finding, organize what they are given, and plan their route before solving consistently outperform students who learned procedures without that structure.
College Board research
Rewards multi-step reasoning and problem setup, not recalled procedures
The redesigned SAT Math section tests whether students can set up and navigate unfamiliar problems, the exact skill FGS trains. Procedural fluency alone no longer predicts the score.
College Board (2024)
These findings describe what Polaris is designed to produce. The peer group raises achievement norms. The FGS framework trains the metacognitive habits that standardized tests reward. The Stretch builds the tolerance for difficulty that separates students who persist from students who stop.
The Parent Experience
Not enrichment for its own sake. Outcomes that change how a student approaches hard problems in math and beyond.
A transferable problem-solving framework
FGS (Find, Given, Solve) is not a math trick. It is a structured way to approach any unfamiliar problem: define what you need, define what you have, map the solution from the two points. Students who internalize it apply it across subjects, standardized tests, and decisions long after the cohort ends.
Confidence with hard, unfamiliar problems
Every session includes a Stretch problem students are not expected to solve. That deliberate, structured exposure to difficulty without stakes builds the tolerance for challenge that separates students who persist from students who shut down when something is unfamiliar.
Stronger academic positioning
Students in honors tracks, competitive programs, or preparing for selective high schools need more than correct answers. They need to explain their reasoning, defend an approach, and adapt when a method fails. Polaris develops exactly that. Students who complete a cohort are better positioned for honors placements, selective high school admissions, and competitive STEM programs.
A community that makes ambition feel normal
Most middle schoolers aiming for honors tracks, competitive STEM programs, or accelerated courses don't know many peers who want the same thing. Polaris changes that. The cohort is curated by ability and drive. Between sessions, students stay connected. Over time, the peer group becomes the environment that makes big goals feel achievable rather than unusual.
Weekly post-session parent recap
After each session, parents receive a short written note: what the cohort worked on, who drove a key insight, and what the next challenge is. You stay informed without needing to be in the room.
In their words
These are students Joshua has worked with. Polaris applies the same FGS framework in a peer group format.
Our philosophy→Outcomes
Standard 7th grade placement → Honors mathematics through accelerated mastery and above-grade-level work
8th grader prepared for rigorous private high school geometry through a focused summer intensive
Students solving problems 2 grade levels ahead within targeted concept areas
The track record
“I enjoyed his push to challenge me which helped me enhance my study habits and overall get me more ready for middle school. I learned about reciprocals ahead of time to help me when I needed it at school.”
Parent
“He made learning math fun. Super patient. Super professional.”
“I like how Joshua makes fun challenges, and if I got a math problem wrong he would not be mad. Joshua taught me how to do long division 100%.”
Parent
“Joshua does a great job of balancing the student learning needs and challenging them with new material.”
Cohort Structure
Twelve weeks. Six students. One fixed point to aim toward.
Founding Cohort rate
$250/month
Cohort 3 pricing
$300/month
Spots per cohort
6 students
Every student begins with the Northbound Skills Audit: a diagnostic that maps current mathematical thinking, identifies specific gaps, and informs cohort placement. You receive a written report and a 30-minute live review call. This step determines cohort fit, not just grade level.
Four 60-minute sessions per month via Zoom. Each follows the Cold Open, Breakdown, Arena, Stretch, and Send-Off structure. Cameras on. Shared whiteboards during pair work. Peer presentations every session.
Between sessions, one problem is sent to the cohort. No pressure, no grade. Just a question worth thinking about. Over twelve weeks, the students who engage with it (and eventually all of them do) are voluntarily working on mathematics outside of school.
After each session, parents receive a short written note: what the cohort worked on, who drove a key insight, and what next week's challenge is. Parents who know what happened in session ask better questions.
Between sessions, your cohort has a shared space on Discord. The coach drops one problem per week — no grade, no pressure — just a question worth thinking about. Students who engage build the habit of working on mathematics voluntarily. Over twelve weeks, all of them eventually do.
Get Started
Cohorts are small by design. Placement is reviewed individually.
Complete the brief application. Describe your child's current math course and what you are hoping Polaris does for them.
Your child completes a 20-minute diagnostic. Joshua reviews the results and schedules a 30-minute live call with you and your child — starting with what you're hoping Polaris does for them, then into exactly where they are. This determines cohort placement, and it is useful on its own.
If the fit is right, you'll receive your cohort's start date and a confirmation. One week before the first session, parents join a 30-minute onboarding call — we go through expectations, the session structure, and how to read the weekly recaps. Students join the cohort's Discord channel that same week. By session one, nobody walks in cold.
Questions
The ones parents ask before they send the intake form.
Still have a question? Email us at hello@northboundtutoring.com.