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How do I assess a new online math tutoring student? (Or: what to do in the first 30 minutes before you know what to teach)

Running a math diagnostic online works when the surfaces you'd use to teach — the shared whiteboard, the virtual manipulatives, the math symbols palette, the cobrowser to a third-party site — all pull double duty as evaluation instruments. In practice that means the first 20 to 30 minutes with a new student is a purpose-built diagnostic session, not a first lesson: you're figuring out three things — how fluent the student is at computation, whether the concepts underneath are actually there or are just memorised procedures, and how they solve a problem they haven't seen before. On Koala Go, the same Number Rods, Number Lines, Fraction Bars, Math Symbols palette, PDF upload, and cobrowser that carry a normal math lesson also carry the diagnostic — you hand the student a rod and ask them to build 3 + 4, or hand them a fraction bar and ask them to make 3/4, or drop a Desmos or Khan Academy diagnostic in the cobrowser and watch how they navigate it. The rest of this page walks through what to assess, how to do it on each surface, and what to route the student into once you know what the gaps are.

Why math assessment online needs its own workflow

The instinct to skip the diagnostic and jump straight into teaching — the parent has said "she's struggling with fractions", so surely you can just start with fractions? — is the single most common failure mode of a new online math tutoring relationship. It goes wrong for three reasons that are worse online than in person.

  1. The parent's description of the gap is usually wrong. Parents (and often teachers) name the topic the student is currently failing at — "she can't do fractions" — but the actual break is almost always a prerequisite two or three levels back. The child who can't add fractions usually can't decompose a whole into equal parts. The child who can't do long division usually doesn't have fluent times-tables recall. If you start teaching the topic the parent named, you build on rubble.
  2. You can't watch over the student's shoulder. In person, the diagnostic is partly informal — you sit next to the student, watch which finger they use to count, whether their lips move on the times table, how many seconds pass before they answer. Online, none of that is visible unless you build a shared surface where the student's thinking happens in front of you. The whiteboard is that surface. If you ask "what's 7 × 8?" over a webcam and hear "56" a second later, you learned exactly one bit of information. If you ask the student to build 7 × 8 on the whiteboard with rods, you see whether they reached for arrays, skip-counting, or a chant — and how long each part took. Same question, ten times more information.
  3. The first-session engagement stakes are higher online. A young student who's just been dropped into a video call with a stranger already isn't sure this is going to work; a session that opens with "let me test you on math" is the fastest way to lose them. The diagnostic has to feel like an activity, not a test. That's a design constraint online, and it changes what tools you reach for — you're not handing them a paper diagnostic and watching them work, you're inviting them to build something on a shared canvas and observing what they build.

An online math diagnostic that works has an answer to each of these: it starts from the surfaces the student can act on directly (rods, lines, fraction bars, a shared page), it produces observable evidence (not just correct-or-incorrect answers), and it feels enough like an activity that a nervous seven-year-old wants to keep going. The rest of this page is that workflow.

What to assess: three domains, not one

The math-tutoring literature is fairly aligned that you're looking for three separate things when you assess a student, and they usually don't move together. A student can be fluent in the first and hollow in the other two; the gap that needs teaching is different in each case.

  1. Computational fluency. Can the student do the mechanical operation quickly and accurately — the times-table fact, the column addition, the long-division algorithm, the standard fraction addition? Fluency is what school assessments are usually calibrated to, so the parent's account of the gap usually names a fluency problem ("he can't do his 7s", "she gets long division wrong"). Necessary but not sufficient — fluency without the concept underneath is a memorised procedure that breaks the moment the problem shape changes.
  2. Conceptual understanding. Does the student know why the operation works? Can they show 3 × 4 as an array before writing it? Can they show 3/4 as a shaded region before symbolically manipulating it? A student who can produce "12" for "3 × 4" but can't build the array is memorising, not understanding — the fact will fade, and the next concept (division as the mirror of multiplication, distributive property, area model) will land on empty foundations. This is the domain school assessments miss most often.
  3. Problem-solving. Given a problem the student hasn't seen the exact shape of before — a word problem, a novel application, "here's a shape, find its area a different way" — can they choose an approach, run it, check it, and back out if it isn't working? This is the highest-stakes domain and the one most in-school assessments barely touch. In tutoring it matters because most of what a family pays for is a student who can eventually work independently on problems they haven't been walked through.

The rest of this workflow builds a diagnostic that produces evidence on all three, in one session, without turning into a two-hour formal test.

The four diagnostic surfaces on Koala Go

Koala Go's classroom ships four surfaces that do double duty as diagnostic instruments — you're not using a separate testing tool; the same whiteboard-and-tools that carry a lesson carry the diagnostic. Here's what each one tells you.

1. The open whiteboard: "show me how you'd solve this"

The single most useful diagnostic move online is: drop a problem in a text box on the whiteboard, hand the pen to the student, and ask them to show you how they'd solve it. That's it. What you're evaluating isn't whether they get the right answer — you're evaluating the strategy they reach for, the fluency of their execution, and the moment they hit the edge of what they can do.

A few examples of what you can learn from one problem:

  • A grade-3 student handed "8 × 7 = ?" and given the pen will either (a) write "56" immediately (fluent, likely from memorised chant), (b) skip-count in their head and then write "56" (fluent enough, but derived), (c) draw an array of eight rows of seven dots (conceptual — good sign), (d) count on their fingers (a red flag for grade 3 fluency), or (e) freeze and ask what the × means (a much larger gap than the parent named). Same problem, five different diagnostic outcomes.
  • A grade-5 student handed "3/4 + 1/2 = ?" and given the pen will either (a) write "5/6" or "4/6" (an "add across" error — you've found the misconception you need to address), (b) write "3/4 + 2/4 = 5/4 = 1 1/4" (fluent — the fraction is not the gap), (c) draw the bars or circles and count pieces (conceptual and fluent — the strongest signal), or (d) freeze (fraction addition isn't yet established — back up to equivalent fractions).
  • A grade-8 student handed "solve for x: 2x + 3 = 11" and given the pen will either (a) write "x = 4" (fluent), (b) show every step of the balance-scale reasoning (fluent and conceptual), (c) subtract 3 from the left side only and get "2x = 11" (a red flag for the do-the-same-to-both-sides rule), or (d) freeze (the equation-solving concept isn't yet established).

The whiteboard is the primary lesson surface across every tier of Koala Go, so this diagnostic move works on Free (with the base whiteboard tools) as well as Pro and up. The pen tool, the text tool, and the sticky-note tool are all on Free. The student can be on any device with a modern browser — no install, no signup, they open the invite link and land on the shared canvas.

2. Math manipulatives as diagnostic instruments

The Math Tools panel inside the Whiteboard Library (Pro and up) turns each of the built-in manipulatives into a diagnostic instrument. Rather than "here's how rods work, let's learn to add", you say "here are ten rods, one for each value 1 to 10 — can you build 3 + 4 for me?" What you learn from watching them reach for rods (or not) is qualitatively different from what you learn from a written problem.

  • Number Rods (Pro tier) as a K-2 number-sense diagnostic. Ten Cuisenaire-style rods, values 1 to 10, each a different colour, that the student can drag onto the canvas. Ask the student to build 3 + 4. A student with solid K-1 number sense will grab a 3-rod and a 4-rod, place them end to end against a 7-rod, and say "seven". A student who's still counting will grab a 1-rod and drag it four times, then grab another 1-rod, and so on. A student who reaches for the 10-rod and starts breaking off units is showing you a subtraction misconception. Then: "can you make 7 + 5?" — same rod set, and you're watching whether they subitize (grab 7 and 5 rods directly), decompose the 5 into "3 to make 10 and 2 more" (very strong sign), or count on. Ten minutes on rods, and you have a genuinely fine-grained read on where in the K-2 arc the student sits — a much finer read than "she can add up to 20". Sibling depth on the number-rod workflow lives in the number-sense spoke; we're using the same tool as a diagnostic here rather than as a teaching tool.
  • Number Lines (Pro tier) as a magnitude and skip-counting diagnostic. Preset lines for 0-10, 0-20, 0-30, 0-100 (by 5s or 10s), −10 to 0, −10 to 10, and blank. Place a 0-100 by 5 line and ask a grade-3 student to hop from 0 to 40 in fives. A student who has automatic skip-counting will place five hops. A student who has to count each five will do it slowly but correctly. A student who lands on 45 or 35 has a fluency gap on the fives. Place the -10 to 10 line for a grade-6 student and ask them to hop from -3 to 5 — a student who understands integers will count eight hops; a student who says "two" (subtracting the magnitudes) has an integer-arithmetic misconception you need to know about. The number-line workflow at teaching depth is in the number-sense spoke.
  • Fraction Bars and Fraction Circles (Platinum tier) as a fractions readiness diagnostic. Individual bar segments and pie-slices for denominators 1/2 through 1/12 (plus 1/16). Ask a grade-4 student to build 3/4. A student with solid fraction concept will place three quarter-bars or three quarter-slices side by side. A student who reaches for a half-bar and a quarter-bar and adds them is showing you they've noticed equivalence but haven't formalised it. A student who places three of any bar is showing you they don't yet see the denominator's role. Then: "can you show me a fraction equal to 3/4 but with a different denominator?" — you're diagnosing equivalent-fraction concept. This diagnostic surface is Platinum-only; on Pro the workaround is asking the student to draw the fraction pictures with the pen tool on the whiteboard, which loses some of the drag-and-arrange information but still surfaces the concept. Depth on the fractions workflow is in the fractions spoke.
  • Math Symbols palette (Pro covers the four operations and equals, the basic comparisons < and >, the fraction / ratio / percent group, √, °, and round brackets; Platinum adds ≠ ≈ ≤ ≥, the superscript powers ² ³ ⁿ, π ± ∞, the geometry markers ∠ △ ⊥ ∥, and square and curly brackets) as a notation-fluency diagnostic. Drop a text box and ask a grade-7 student to write "3/4 × 1/2 = 3/8". Worth knowing which symbols actually carry diagnostic signal: the palette's +, =, /, :, %, <, > and round brackets are the same characters the keyboard produces, so you can't see how they were entered. The ones you can read off the screen are × (a proper multiplication sign rather than the letter "x" or an asterisk), − (a minus sign rather than a hyphen), and everything in the Powers, Algebra, and advanced Compare sets. A student who writes "3/4 x 1/2" with a letter x is telling you the palette isn't yet in their toolkit — a small thing that snowballs into "why does my student's algebra look so messy" if not caught. For older students, ask them to write "x² + 3x − 4 = 0" — the palette's superscript ² (Platinum) is the tell for whether they know how to write exponents at all, and the standalone minus vs. hyphen catches a common typo. Palette entry points and the full six notation moves are in the math-notation spoke.
  • Stickies and Stamps for anything the built-in tools don't cover. Ten-frame tokens, dot cards, place-value counters (tens and ones), integer chips (positive and negative), coins for money work — anything a physical manipulative-drawer would hold can be dropped as a Sticky or Stamp on the canvas, and both you and the student can drag them. These are the same primitives the dyscalculia and dyslexia workflows rely on; for a diagnostic they let you extend beyond the built-in tools when the student's curriculum uses a specific manipulative you want to see them work with.

3. Cobrowser into a third-party diagnostic

A cobrowser is a shared browser window inside the classroom — the tutor opens a page, and both the tutor and the student can click, type, drag, and interact with the page live. Not screen sharing — actual shared control. For a math diagnostic, this pairs the open-ended whiteboard work with a standardised third-party diagnostic layer that a well-established site can carry better than a hand-run assessment. The tools tutors usually reach for:

  • Khan Academy's Mastery challenges and course diagnostics. Free to use, standard sequence across most US elementary and middle-school topics. A short Mastery challenge in a grade-appropriate unit gives you a percentage-based first read. Not a formal placement test but a widely-used baseline.
  • IXL's Real-Time Diagnostic (subscription). Adaptive diagnostic that estimates a student's level per strand (numbers and operations, algebra, geometry, measurement, data). Some tutoring families already have IXL through school; when they do, the diagnostic is a five-to-fifteen-minute session that produces a printable snapshot the tutor can walk through with the parent afterwards.
  • ALEKS's initial knowledge check (subscription, K-12 and college). Adaptive assessment that maps to a specific curriculum; slower than IXL but more granular for the students it fits.
  • Beast Academy's placement guide (or the equivalent for whatever curriculum the family is on). Curriculum-tied placement tests that map to specific programme entry points. Useful when the family has already picked a curriculum and wants to know where in it to start.

The cobrowser makes these usable inside the diagnostic session rather than as homework. On Koala Free, the cobrowser is capped at 10 minutes per session with a 20-minute cool-down — enough for one Khan Mastery challenge in the diagnostic, but you'll want to sequence carefully. On Pro and up, the cobrowser is unlimited, which matters if you're running a longer IXL or ALEKS diagnostic. The mechanic itself, and how it differs from screen sharing, is in the cobrowser explainer. Two things to name honestly: adaptive diagnostics like IXL and ALEKS are calibrated for independent student work, so your presence during a cobrowsered diagnostic changes the signal a little — the student may work harder knowing you're watching, or freeze knowing you're watching, and either way the result is a rougher estimate than if they'd taken it alone. Use it as one data point among several, not the definitive placement.

4. PDF upload for a paper-based diagnostic or a past paper

Some diagnostics live on paper — a school's own placement test, a curriculum-specific worksheet the family has been given, a past exam paper the older student was supposed to work through. On Koala Pro and up, you upload the PDF (or a PowerPoint slide deck) to the whiteboard and both of you can annotate on top of it in real time. That collapses the "here's a diagnostic PDF, work through it and send it back to me" workflow — which loses observation completely — into a live session where you see every hesitation, every erased attempt, every wrong turn.

Two ways to use it:

  • Live-annotated diagnostic worksheet. Family shares (via email or the classroom's activity upload) the school's placement worksheet or an end-of-unit assessment. Open it as a PDF on the whiteboard, hand the student the pen, and watch them work through it live. Same information as the open-whiteboard move but with the added benefit that you're working in the exact document the school uses.
  • Past-paper diagnostic for older students. A grade-10 student prepping for a specific exam (GCSE, IGCSE, A-level, IB, SAT, ACT) has past papers accessible. Upload one, hand it to the student, and use the first fifteen minutes as the diagnostic — you're evaluating exam technique alongside subject knowledge. This is the diagnostic move for the exam-prep flow described at depth in how do I teach exam prep online?

Uploaded material stays on the whiteboard between sessions, so the diagnostic worksheet is still there next week — useful for "here's what we saw last week; today let's tackle the parts you got stuck on."

A first-session diagnostic script by age band

Different age bands lean on different surfaces. A rough script for each, calibrated to fit a 25- to 40-minute first session (the diagnostic is roughly the first two-thirds; the last third is a short teaching move plus the parent debrief). These are typical US grade placements and adjust to the curriculum and the student in front of you.

K–2 (ages 5–7): rods and lines first, notation later

  1. Warm-up (5 min): "Hi! Let's play with some rods." Open the Whiteboard Library and place the ten Number Rods on the canvas one at a time, in a jumbled heap rather than in order. Ask the student to line them up from shortest to longest. What you're watching: do they immediately see the pattern, or do they need to compare each pair? (Platinum's "Add all" button drops all ten in a single click, but as a ready-made staircase — which does the sorting for the student, so place them individually for this particular move.)
  2. Number sense (10 min): "Can you build me a 3 and a 4? Now put them together — how long is that?" Repeat with 5 + 2, then 7 + 3, then 4 + 6. You're watching for: subitising (grab-and-place vs. count-each-unit), decomposition (does 8 + 5 become "8 + 2 + 3"?), and complements-to-ten strategies.
  3. Number line (5 min): Place a 0-20 line. "Can you hop from 0 to 12?" Then: "Now hop back from 12 to 4." Watching for: one-to-one correspondence on hopping, whether they need to count each tick or can jump multiple.
  4. Written notation (5 min): "Can you write 5 + 3 = 8 in a box for me?" Watching for: number formation, confident use of the + and = signs, whether the equation reads left-to-right cleanly.
  5. Reward and close (5 min): A short Playground visit or a Gems handout — see the gamified virtual classroom answer for the engagement layer. For a first-lesson K-2 student, this closing engagement moment is what makes them want to come back.

Grades 3–5 (ages 8–10): fluency + fractions + strategies

  1. Warm-up (3 min): "Tell me about a math thing you're good at and a math thing that's tricky." Cheap information from the student's own account; parents don't always relay this accurately.
  2. Times-table fluency (7 min): Drop a text box: "6 × 7 = ?" Ask them to type the answer. Then "8 × 4?" "9 × 6?" "7 × 8?" You're watching timing (do they answer inside two seconds, or is there a long pause?) and error pattern (near-misses vs. wild guesses). If you have Platinum, place a Number Roller set to 1-12 and roll five random pairs — the roller removes tutor-invented bias in the fluency check.
  3. Fractions conceptual check (7 min): If Platinum, place a Fraction Bars set and ask "Can you build 3/4? Now build 1/2. Which is bigger?" On Pro, ask them to draw the fractions with the pen and shade — a rougher version of the same diagnostic. Then: "Can you build 1/2 in a different way?" Watching for: equivalent-fraction concept, comfort with denominators up to 8, whether they can see a half as 2/4 or 3/6 or 4/8.
  4. Word problem (5 min): Drop a text box: "There are 24 pencils in a box. If you share them equally among 6 kids, how many does each kid get?" Hand the student the pen. Watching for: strategy choice (skip-count, division, drawing), setup vs. computation, whether they check their answer.
  5. Notation snapshot (3 min): "Can you write 3 × 4 = 12 in a box, using the math symbols palette for the signs?" See whether they use × (proper multiplication sign) or "*" or "x" from the keyboard.
  6. Reward and close (5 min): Gems for effort on the harder parts; a short Playground moment if age-appropriate. Homework ask: one specific practice thing that came out of the diagnostic (see the homework answer for the between-lesson practice framing).

Middle school (ages 11–13): notation, fractions, integers, and a word problem

  1. Warm-up (3 min): Student's own account of what's going well and what isn't. This age band self-reports more accurately than younger.
  2. Fractions and decimals (7 min): Drop "3/4 + 1/2 = ?" as a text box. Then "0.3 × 0.2 = ?" Then "What's 40% of 60?" You're diagnosing the fluency of the rational-number arithmetic that pre-algebra depends on. Errors here explain a great deal of the trouble that surfaces in algebra later.
  3. Integer arithmetic (5 min): Place the −10 to 10 number line. "Can you hop from -3 to 5?" (Eight steps.) "From 4 to -2?" (Six steps.) Then in a text box: "−7 + 4 = ?" and "−3 × −5 = ?". Signed-number arithmetic is a common gap in this age band and a common cause of "my kid understands algebra when we walk through it, but can't do it alone" — because the arithmetic underneath breaks.
  4. A pre-algebra word problem (7 min): "A pencil costs $2. A notebook costs $5. Sam buys some pencils and 3 notebooks. He spends $23 in total. How many pencils did he buy?" Hand the student the pen. Watching for: whether they write an equation, whether they solve it or guess-and-check, whether they name the unknown as "x" or as "the number of pencils". This is the pre-algebra transition — many middle-schoolers can solve it by guess-and-check but not by algebra.
  5. Notation snapshot (3 min): "Can you type x² + 3x − 4 = 0, using the palette for the symbols?" Watching for: comfort with the superscript (Platinum), whether they know the − is not the same as the hyphen, whether they use the palette's × or "x" for multiplication.
  6. Debrief (5 min): Summarise what you saw, ask them what they thought of the session, and outline a week 1 plan. Send a short note to the parent inside 24 hours (parent-comms cadence in the progress-updates answer).

High school (ages 14–17): past paper first, algebra depth, cobrowser to Desmos

  1. Warm-up (3 min): The high-school student's own read on what they need help with. At this age band they've usually named the specific exam, unit, or topic accurately.
  2. Past paper or worksheet (15 min): Upload the PDF of the most recent piece of graded work the family shared, or a past-paper question at grade level. Hand the student the pen. Watching for: setup, algebraic manipulation, calculator use, notation habit, checking. Fifteen minutes of live-annotated past-paper work produces more diagnostic signal than any other move at this age.
  3. Graphing diagnostic (5 min): Open the cobrowser to Desmos, plot y = 2x + 3. Ask the student to change the slope, then the intercept, then to make a line perpendicular to it. Watching for: comfort with slope-intercept form, whether they see the geometric meaning of slope, whether they can predict the effect before pressing enter. This is the diagnostic move that pairs well with the algebra spoke walkthrough at how do I teach algebra online?
  4. Exam-technique check (5 min): If the student is prepping for a specific exam, ask them to answer one exam-style question with the palette's proper notation (√ and ° are on Pro; ∠, ≤, and π need Platinum). Watching for: mark-earning notation habits, whether they're leaving working out visible, whether they know the difference between an approximate and an exact answer. Exam-focused workflow at depth in how do I teach exam prep online?
  5. Debrief (5 min): With this age band the student is usually in the room for the parent debrief too, or is themselves the primary decision-maker. Give an honest read of what you saw and what you'd suggest as a week 1 focus.

Reading the results: which spoke to route the student into

A diagnostic without a downstream plan is a diagnostic that wastes the family's money. Once you've run the session and know where the gaps live, the math cluster is set up so each common gap has a specific follow-up spoke you can teach from. The rough mapping:

  • K-2 number-sense gap (student can't reliably compose to ten, can't skip-count on a line, isn't yet subitising): route into the workflow described in how do I teach number sense online with virtual manipulatives? The rods and lines are your primary tools for the coming weeks.
  • Times-tables fluency gap (grade 3+ student stalling on any single-digit multiplication, can't handle skip-counting on the 6s / 7s / 8s / 9s): route into how do I teach multiplication and times tables online? — arrays, skip-counting, derived facts, and Number Roller drill on Platinum.
  • Fractions concept gap (student adds "across", can't produce equivalent fractions, can't compare 3/4 and 2/3): route into how do I teach fractions online? — the fraction bars and circles workflow.
  • Math notation habit gap (student typing "1/2" instead of using the slash-fraction, using "x" for multiplication, hyphens for minus signs): route through how do I write math equations and notation on an online whiteboard? — the palette entry points and six notation moves. This tends to be a quick fix; the notation vocabulary catches up fast once demonstrated.
  • Pre-algebra / algebra gap (middle- or high-school student stalling on solving equations, expanding, factoring, working with variables): route into how do I teach algebra online? — the balance-scale, area-model, and cobrowser-to-Desmos workflow.
  • Geometry gap (student can't identify shape properties, area/perimeter formulas don't stick, coordinate geometry is opaque): route into how do I teach geometry online? — the 2D/3D shape library, shape labels, and GeoGebra cobrowser pairing pattern.
  • SEN pattern surfaced (persistent pattern that suggests a math learning difference — magnitude confusion that doesn't respond to concrete work, fact retrieval that stays laboured after weeks of drill, sequencing difficulty that's out of proportion to age): the diagnostic is not a diagnosis, and it isn't our job to hand out one. Read how do I tutor a student with dyscalculia online? for how to adapt the workflow, and — separately — recommend the family talk to an educational psychologist or their school's SEN coordinator for actual assessment. A tutor's diagnostic surfaces patterns; a qualified specialist diagnoses.

What NOT to do in a first-session math diagnostic

Six specific mistakes we've seen new online math tutors make when the first-session diagnostic goes wrong:

  • Don't skip the diagnostic because "the parent already told me the gap". The parent's account of the gap is a starting hypothesis, not a placement. More often than not, the actual break is one to three levels below what the parent named. Run the diagnostic anyway.
  • Don't turn the session into a formal test. A young student who feels they're being tested will freeze, shut down, or perform below their real level. Frame it as "let's play with some math and see what you know" for younger students; frame it as "let me get a read on where you are so I can plan our sessions" for older students. Both framings are honest and both preserve engagement.
  • Don't collect too much data in one session. The temptation is to run every diagnostic on the list because the surfaces make it possible. Stop at "enough to know where to teach next week" — usually 20 to 30 minutes of diagnostic, then a short teaching move and a close. Save the deeper diagnostics for weeks 2 and 3 as new gaps become visible.
  • Don't run adaptive third-party diagnostics (IXL, ALEKS) as if they're definitive placements. They're calibrated for independent student work; your presence changes the result. Use them as one data point among several, and read the printable snapshot with the parent as a rough baseline, not a final ranking.
  • Don't over-share the diagnostic result with the parent as a list of deficits. A three-minute parent debrief is "here's what your child does well, here's the one thing we'll focus on first, and here's why". Not a comprehensive audit of every gap you found. The full picture goes into your own planning notes, not the parent update. Cadence in how do I share progress updates with parents?
  • Don't skip the "one small win" close. A diagnostic session that ends with the student having successfully done something — built a fraction with bars, hopped a number line correctly, factored one small expression — leaves them wanting to come back. A diagnostic that ends with the student stuck on the last problem leaves them thinking they're bad at math. The last problem you drop should be one they can do; save the harder unknowns for week 2.

Honest limits

Two limits worth naming plainly rather than papering over:

  • This is a tutoring diagnostic, not a formal educational assessment. Instruments like the Woodcock-Johnson, KeyMath, TEMA, or a curriculum-specific standardised placement test are administered by qualified educational psychologists or assessors, take longer, and produce results that stand up in school placement conversations. A tutor's first-session diagnostic is fit for purpose (planning the next few weeks of tutoring) but not a substitute for those instruments where they're needed. If the family needs a formal placement or the school is asking for one, point them to a qualified assessor.
  • Platinum unlocks help but Pro is enough for most first-session diagnostics. The Fraction Bars, Fraction Circles, Number Roller, "make your own" number line, and full Math Symbols set are Platinum-tier features (Koala Platinum is $49.99/mo monthly, $39.99/mo annual; Pro is $25.99/mo monthly, $21.99/mo annual). Pro (which covers Number Rods, all eight preset Number Lines, PDF upload, core shape library, and the base Math Symbols set — the four operations and equals, the basic comparisons < and >, /, :, %, √, °, and round brackets) is sufficient to run a good first-session diagnostic through most age bands; the Platinum tools sharpen the fractions and fluency-drill diagnostic specifically, and matter most if you have a fractions-heavy or drill-heavy caseload. Enterprise / B2B tutors are provisioned at the Pro feature level, and the Platinum tools are hidden from their panel rather than shown locked — so an enterprise tutor runs the diagnostic on the Pro set. On Free, the diagnostic runs on the whiteboard and the capped cobrowser (10 minutes per session, 20-minute cool-down) — enough to try a single 30-minute diagnostic, tight for anything longer.

Two implementation notes: (a) if you'd like to record the diagnostic session for your own notes or to share a short clip with the family (a parent seeing the child successfully build a fraction bar is worth a thousand words), see how do I record online tutoring lessons? — including the family-permission step; (b) if the student is in mainland China, the whiteboard and Math Tools all work through our Hong Kong proxy, but cobrowser reliability into US-hosted diagnostic sites can vary — see the China-specific answer for the workaround pattern.

Where the diagnostic fits inside the broader first-lesson workflow

The math diagnostic is one specific move inside a broader first-week onboarding. Three neighbouring pages that describe the rest of the shape:

  • How do I onboard a new online tutoring student? — the pre-lesson checklist, parent-invite mechanics, and first-week parent conversation. Subject-agnostic; this page is the math-specific diagnostic sub-step that lives inside it.
  • How do I run a free trial lesson that converts? — when the diagnostic doubles as a trial (typical for a new indie tutor still building their first ten paid students). A well-run diagnostic-trial answers two questions at once: is this tutor a good fit for my child, and what would we work on if we hired them.
  • How do I structure a 1-on-1 online lesson? — the per-lesson shape (opening, activities, close, homework) that applies to every ongoing lesson after the diagnostic session.

Related answers (and the math cluster we're building out)

This page sits inside a wider math-tutoring cluster. The neighbouring pages that cover an adjacent question:

If you'd like a walk-through of the diagnostic surfaces for a specific age band or subject mix you're planning, open Koala Go at classroom.teachwithkoala.com, or write to koala@teachwithkoala.com with a sentence about the shape of your math practice and we'll give you our honest read on the fit — including the parts where a specialist assessor or a curriculum-specific placement instrument would carry more of the load than a tutor's first-session diagnostic.

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