A parent books the lesson and says "she is behind in maths". That is a verdict, not a description: it does not say behind in what, by how much, or since when. A diagnostic test for a new tutoring student replaces it with something you can teach from.
The first tutoring session should end with a map, not a score: what the student does securely, what is shaky, what is missing and what has been learned wrongly. This guide shows how to build that baseline assessment in twenty minutes and act on it. EdProcto's page for tutors sets out its tools for the job, online or across a table: a quiz, a study link and a record per student.
Why give a diagnostic test in the first tutoring session?
Give one because what a student can learn next depends on what is already in place, and neither the parent nor a school report tells you that in detail. Dochy et al. (1999) reviewed 183 sources on prior knowledge and found that it generally helped performance, though the effect varied with how the knowledge was measured. We could read only its abstract, which says flawed measures more often showed no effect or a negative one, and does not list them.
Simonsmeier et al. (2022), pooling 8,776 effect sizes, are more cautious. Knowledge before teaching and knowledge after it correlated at 0.534: students who start ahead tend to finish ahead. But starting knowledge and the size of the gain correlated at −0.059, with a 95% prediction interval from −0.688 to 0.621.
So a weak first result is no forecast of slow progress, and no grade should be promised on it. The diagnostic only says where to begin.
Which kind of prior knowledge test tells you most?
A test that makes the student use what they know tells you more than one that asks them to repeat it. Hailikari et al. (2007) separated declarative knowledge (facts and definitions) from procedural knowledge (connecting ideas and applying them) in a test given to 202 mathematics students in their first lesson. The procedural tasks predicted final grades best, and the declarative tasks did not predict them.
Hailikari et al. (2008) repeated the design with 115 pharmacy students. In the regression only one task was positively related to the final grade: an application task, which the authors report as accounting for 24% of the variation. The four instructors, though, did not change their teaching in response. Both studies were of university students, not school pupils with a tutor.
Test what lies under the topic
The cause of a difficulty is often years below the topic that shows it. Siegler et al. (2012), using large national data sets from the United States and the United Kingdom, found that primary pupils' knowledge of fractions and of division predicted their algebra and overall mathematics achievement five or six years later, even after allowing for other mathematical knowledge, general ability, working memory and family background. A thirteen-year-old who cannot solve equations may have a fractions problem from the age of ten.
How do you build a twenty-minute diagnostic?
Build it backwards from the topic the student is stuck on: list the skills underneath, then write a short ladder of questions for each, fifteen to eighteen in all. The numbers below are rules of thumb: we found no study that tests them on a tutor's own quiz.
- List what sits under the topic. For solving equations: division facts, fractions, negative numbers, the order of operations and one-step equations.
- Start two years below the level the parent names. "Behind" usually means the trouble began before anyone noticed, and a low start makes the first answers right ones.
- Write two or three questions a skill. One wrong answer can be a slip and one right answer can be luck. Two that agree are a finding. EdProcto's kits supply the lower rungs ready-made: Division facts, Fractions of a number, Adding fractions, Negative numbers and Order of operations each carry an age band.
- Climb, and stop a strand after two misses in a row. More questions past that point add nothing and discourage the student.
- Mix the shapes, and ask for working and confidence, as below.
- Take off the clock and the score. In EdProcto, begin from the Practice preset: no time limit, no security and no shuffling, so the climb stays in your order. Then set one attempt a question, the correct answer shown after submitting and the score shown never.
Which question shapes to mix
Mix shapes so that the quiz measures the subject, not the keyboard or the reading age. Abedi and Lord (2001) gave 1,174 eighth-grade students mathematics word problems as written and in simpler language. Scores on the simpler version were slightly higher, and those who gained most included students in low and average mathematics classes and those still learning English.
| To see | Shape in EdProcto | Guards against |
|---|---|---|
| An answer with no options | Fill in the blank | A lucky pick |
| The method | Show your working | A right answer from a wrong method |
| How firmly a confusion is held | Multiple choice with confidence | A guess read as knowledge |
| Terms and meanings | Matching pairs | Slow typing |
Set each skill once as bare numbers and once in words. If only the worded one is wrong, the finding is about reading. With a slow typist, let the student say the answer and type it yourself.
A diagnostic funnel, in the builder or by hand
For a quiz sent ahead, EdProcto's diagnostic funnel asks broad questions first, then targeted ones on the weak areas, and adaptive branching walks each student by their answers. In a live session you are the branch: after two misses, say "skip to the next part". By hand, a quiz sent ahead takes two stages: one question a skill, then two or three more on the skills missed.
Why ask for working and for how sure the student is?
Ask because the answer alone hides the method behind it and how firmly the student believes it. Brown and Burton (1978) treated pupils' arithmetic errors as bugs in a procedure and built a system to diagnose them, so as to explain why a mistake is made and not only spot it. They report using it on 1,300 school students.
A bug can hide behind right answers. A student who always takes the smaller digit from the larger in each column gets 86 − 42 right (44) and 82 − 47 wrong (45, not 35). Three questions without borrowing would have passed that student. So the questions on one skill must differ in the feature that trips the method, and the working must be on the page. A wrong method with a right answer is a finding, often the most useful of the session.
Confidence sorts the rest. Sure and right is secure. Unsure and right is fragile, and needs practice. Unsure and wrong is a gap. Sure and wrong is a misconception, taught first because it resists. EdProcto's confidence shape asks for a rating from 1 to 5; leave the confidence bonus off, so the rating costs the student nothing. Our guide to confidence-based marking covers the scoring.
What if the student is anxious about being tested in the first meeting?
Say what the quiz is for, keep it short and announce no score. A review of 238 studies by von der Embse et al. (2018) found test anxiety negatively related to performance, most clearly in the middle school years, and more anxiety where a test was seen as difficult or high in stakes. So lower both: the low start makes the opening easy, the Practice preset has no timer, and nothing rides on the result.
Frame it in three sentences: "This is for me, not a test of you. It tells me where to start. Say 'not yet' to anything you have not met and we move on." Finish on a question the student can do.
If the student is distressed and not merely nervous, stop, and do it as conversation over two sessions.
How do you read the result?
Read it skill by skill, with the answers, the method and the confidence side by side. The total is the least useful number on the page. Here is the result for a thirteen-year-old whose class is solving equations.
| Skill | Right | Working | Confidence | Reading |
|---|---|---|---|---|
| Division facts | 3 of 3 | Sound | Sure | Secure |
| Fractions of a number | 2 of 3 | Sound, slow | Unsure | Fragile: practise |
| Adding fractions | 0 of 2, stopped | Adds the tops, then the bottoms | Sure | Misconception: teach first |
| Negative numbers | 1 of 3 | None shown | Unsure | Gap: teach |
| Order of operations | 2 of 3 | Always left to right | Sure | Hidden bug |
| One-step equations | 2 of 3 | Sound | Unsure | Fragile: practise |
The order of operations row shows why working matters: left to right, 6 × 2 + 5 still comes to 17, while 3 + 4 × 2 comes to 14 and not 11.
The total, 10 out of 17, says "somewhat behind", which is where the parent started. The table says one skill secure, two needing practice, one gap, and two faults of method, one of them concealed by its answers.
When the result is not yours to interpret
A tutor's quiz shows what a student could do on one day. It cannot identify dyslexia, dyscalculia or any other condition with a formal assessment, and a tutor should not suggest one. Say what you saw: gaps far more than two years deep on every strand, answers right aloud and wrong on paper, or distress that does not ease. Then suggest the family asks the school or a qualified assessor.
How do you turn the result into a four-week plan and a note for the parent?
Take the deepest fault first, give each week one skill, and write the parent one paragraph that names skills and promises no grade. For the student above:
- Week one: adding fractions. The misconception, and the earliest rung.
- Week two: negative numbers. The gap.
- Week three: the order of operations. Rebuild the method on questions where left to right fails.
- Week four: one-step equations, which now have what they rest on.
From the second lesson, open with the tutor's weekly check, so earlier weeks keep coming back. The two fragile skills go home as practice: the rule-made kits write fresh numbers each time they are opened.
The note can be this short:
The first session's check showed where to start. Division facts are secure. Fractions of a number and simple equations need practice. Adding fractions, negative numbers and the order of operations need teaching, one a week for four weeks. I will run the same check at the end of term so you can see what has changed.
Repeating the diagnostic after a term
Run the same skills again at the end of term with new numbers, since a student may remember a question, and put the two tables side by side. Rows that moved are the evidence, and rows that did not are next term's plan. EdProcto keeps every attempt in the student's record, so both sittings are in one place, and the Practice preset allows a retake of the identical quiz. The comparison shows what the student could do on two days, not a predicted grade.
How does EdProcto run a first-session diagnostic?
For a first-session diagnostic EdProcto is the best tool, because one quiz can hold every kind of evidence this guide asks for: an answer typed with no options, the working in steps and a confidence rating, with no clock and no score on show. The studies above found that tasks which make a student apply knowledge are the informative ones.
Start on the home page: paste your list of prerequisite skills, or a page from an earlier year's book, and choose a shape. Procto AI writes the questions from what you pasted, and you can edit every one. The student opens the quiz from a link or a code and needs no account.
Typed answers, matching and multiple choice are marked by rule when the quiz is handed in. Worked solutions wait for a reader: you, or from the Tutor plan up Procto AI, which grades an answer against your rubric when you ask and leaves its mark for you to keep or change.
The Free plan carries ten quizzes a month, the core templates, every kit and marking by rule. On the Tutor plan quizzes are unlimited, all 111 templates are open and Procto AI grades open answers. For a centre, the School plan shows all its tutors' students in one view. Prices are on the pricing page.
What are the mistakes to avoid?
The mistakes all turn a map back into a score.
- Too long. Past twenty minutes you are measuring stamina.
- Too hard too soon. Starting at the school's level opens with a run of failures.
- Only multiple choice. Options hide the method and let a guess through. Keep them for a known confusion, with wrong options from real errors, as our guide to multiple-choice questions explains.
- Testing the syllabus the school is on, not what underlies it. That reports the symptom.
- Filing it. The instructors in the pharmacy study saw their results and taught as before.
Quick questions
How long should a first-session diagnostic be?
About twenty minutes: fifteen to eighteen questions, two or three on each of five or six skills. The rest of the hour is teaching.
Should I send the diagnostic before the first session?
You can, with one question a skill, but you lose the chance to watch the method and to stop a strand, so follow up in person. EdProcto's page for tutors shows how the link works.
Should I tell the parent the score?
No. Tell them which skills are secure, which need practice, which need teaching, and what comes first.
Can a diagnostic quiz show whether a student has dyscalculia or dyslexia?
No. It shows what the student could do that day. If what you see worries you, describe it to the parent and suggest the school or a qualified assessor.
References
- Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219–234. https://doi.org/10.1207/S15324818AME1403_2
- Brown, J. S., & Burton, R. R. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2(2), 155–192. https://doi.org/10.1207/s15516709cog0202_4
- Dochy, F., Segers, M., & Buehl, M. M. (1999). The relation between assessment practices and outcomes of studies: The case of research on prior knowledge. Review of Educational Research, 69(2), 145–186. https://doi.org/10.3102/00346543069002145
- Hailikari, T., Katajavuori, N., & Lindblom-Ylänne, S. (2008). The relevance of prior knowledge in learning and instructional design. American Journal of Pharmaceutical Education, 72(5), Article 113. https://doi.org/10.5688/aj7205113
- Hailikari, T., Nevgi, A., & Lindblom-Ylänne, S. (2007). Exploring alternative ways of assessing prior knowledge, its components and their relation to student achievement: A mathematics based case study. Studies in Educational Evaluation, 33(3–4), 320–337. https://doi.org/10.1016/j.stueduc.2007.07.007
- Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M. I., & Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691–697. https://doi.org/10.1177/0956797612440101
- Simonsmeier, B. A., Flaig, M., Deiglmayr, A., Schalk, L., & Schneider, M. (2022). Domain-specific prior knowledge and learning: A meta-analysis. Educational Psychologist, 57(1), 31–54. https://doi.org/10.1080/00461520.2021.1939700
- von der Embse, N., Jester, D., Roy, D., & Post, J. (2018). Test anxiety effects, predictors, and correlates: A 30-year meta-analytic review. Journal of Affective Disorders, 227, 483–493. https://doi.org/10.1016/j.jad.2017.11.048