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Mathematics Tutors of Burkina Faso | CEP, BEPC, BAC and Maths Support

Three students in school uniforms work through open books at a classroom table, with textbooks and stationery nearby and study notes on the whiteboard behind them.

Mathematics tutors in Burkina Faso work within a general school pathway of six primary years, four post-primary years and three upper-secondary years. The familiar class names are CP1, CP2, CE1, CE2, CM1 and CM2 in primary, followed by sixième, cinquième, quatrième and troisième in post-primary, then seconde, première and terminale in upper secondary. The three well-known academic examination stages are the CEP at primary completion, BEPC after the first secondary cycle and baccalauréat after upper secondary. Different technical and professional awards need their own preparation.

As of October 2026, an important date fact is that the Burkina Faso government’s 21 May 2026 examination briefing confirmed separate 2026 CEP, BEPC and baccalauréat schedules as well as BEP, CAP and professional certification arrangements. The 2026 baccalauréat written exams were scheduled from 23 June to 10 July, while the primary and post-primary programmes had earlier June assessment activity. Those dates describe a completed historical examination cycle, not an approved 2027 timetable. A tutor preparing a future candidate should obtain current ministry and school notices.

Continuity is also vital. UNICEF’s 2026 humanitarian education appeal reports that insecurity, displacement and school closures disrupt education in many areas, without defining the learning ability of individual children. A tutor may need to rebuild interrupted foundations or use safe offline materials before turning to a high-stakes paper. This article explains Burkina Faso’s Maths education and tutoring methods, original worked problems, family decisions and official sources; it is not a directory of inspected local teachers or a claim that eduKate operates in Burkina Faso.

Burkina Faso Mathematics tutors: immediate answers

What a parent or reader needsPractical answer
General school ladder6 years primary, 4 post-primary and 3 upper secondary.
Primary certificateCEP, Certificat d’études primaires, after CM2.
Lower-secondary completionBEPC, Brevet d’études du premier cycle, following troisième.
Upper secondaryBaccalauréat; check the student’s actual series and Mathematics programme.
Technical routesBEP, CAP and other vocational qualifications have separate assessment procedures.
2026 exam calendarGovernment briefing of 21 May 2026 distinguishes stages and schedules; do not reuse for 2027.
Languages and learning accessFrench and national-language contexts; interrupted schooling may need a readiness bridge.
Tutor successStudent independently explains and solves unfamiliar tasks after the relevant prerequisite is repaired.

Two government departments are relevant to the 2026 educational structure: the ministry responsible for basic education, literacy and national languages (MEBAPLN) and the ministry responsible for secondary education and vocational/technical training (MESFPT). The 29 May 2026 public examination briefing separated their candidate groups and professional certification processes. A private Mathematics tutor should similarly identify the pupil’s exact programme rather than market a single “Burkina Faso exam Maths” course for everyone.

1. The 6–4–3 school ladder and what the stages actually mean

The primary sequence CP1 through CM2 builds reading, numerical concepts, operations, measurement, geometry and elementary data reasoning. Post-primary, from sixième to troisième, usually adds more formal subject teaching including algebraic expressions, ratios, graphs and geometric explanation. The general upper-secondary stage from seconde to terminale can require more advanced mathematical work depending on subject series and school programme. A student moving from CM2 to sixième is not moving to the sixth primary year; the French class name denotes a new stage.

The education law sets a compulsory-schooling framework broadly associated with ages six to sixteen. Actual participation and continuity are affected by circumstances, including displacement and disrupted schools. Age does not establish attainment. A fourteen-year-old learner who missed several years of classroom Mathematics may need support with primary fractions while still being capable of learning more advanced reasoning later. The tutor should assess strengths respectfully rather than assume the same exercise level for every student of the same age.

An IFADEM overview of Burkina Faso’s education system explains the established six-four-three pattern and class labels. For current educational requirements, families should also seek the appropriate ministry and school materials. The broadly familiar French labels can help international readers, but a French national brevet or BAC paper is not automatically the same examination as the Burkinabè qualification.

The educational task can also differ between a school pupil preparing for the CEP and an older learner returning through an alternative route. A tutor must first identify whether the aim is to repair numeracy, follow current classwork, bridge to the next level, prepare for an official named examination or acquire reliable occupational mathematics. None of those aims is inherently superior for all learners.

2. CEP and primary Mathematics: teach number relationships first

CEP refers to the Certificat d’études primaires at the end of primary school. The 2026 official government briefing described the primary examinations and associated school-entry selection process. A future candidate needs their own examination-year instructions; the 2026 calendar should not be quoted as if it were an immutable 2027 schedule. Parents should obtain their child’s current school guide and actual intended assessment.

A good primary tutor tests place value before proposing a long revision course. If the pupil thinks 406 is smaller than 85 because four is smaller than eight, use hundreds, tens and ones to make the quantities visible. Four hundreds already exceed eighty-five. Give 503 and 79 as an independent variation, asking the learner to explain why the first is greater.

Teach multiplication as equal groups and division as the inverse operation. Six packets each containing seven objects have forty-two objects; forty-two divided into six equal groups gives seven. The pupil should be able to show an array and retell the relationship. Memorising multiplication facts helps fluency, but a changed grouping story can reveal whether meaning is secure.

Fractions often hide under a disappointing school score. A pupil might say one seventh is greater than one fourth because seven exceeds four. Use identical wholes and compare the size of one of four versus one of seven equal pieces. Then ask whether three quarters is greater than five eighths by expressing three quarters as six eighths. Visual comparison should lead into symbolic explanation, not stop at one drawing.

3. Post-primary BEPC: the challenge of algebra and geometry

BEPC is a qualification at the end of the post-primary first cycle. A pupil in sixième may be building the foundation for work that becomes more demanding through troisième, while a pupil nearing BEPC may benefit from actual year-specific paper familiarisation. The teacher should identify current lesson objectives and the child’s independent mathematical understanding before using timed practice.

One common transition difficulty is representing a situation as an equation. Four equal-priced items with a fixed delivery cost of 500 CFA francs total 4,500 in a fictional exercise. Writing 4x+500=4,500, subtracting the fixed charge and dividing by four gives x=1,000 CFA francs. A strong tutor shows four equal groups on a diagram, then removes the illustration for a fresh word problem.

Another issue is a false distribution: 3(x+4)=3x+4. Three complete groups each contain x and four, so the correct result is 3x+12. With x=2, the original expression gives eighteen, while the false result gives ten. This numerical contradiction helps the student see the meaning of brackets. A later unseen task such as 5(a−3)=5a−15 shows whether the relationship has been retained.

Geometry can demand the same careful diagnosis. A rectangle five metres by seven metres has area 35 m² but perimeter 24 metres. A pupil who gives 35 metres for fencing has misunderstood whether the task measures surface or boundary. Draw the figure and label units. Repeating multiplication without discussing the geometric meaning will not repair the error.

4. Baccalauréat Mathematics: use the correct series and year

General upper-secondary education leads towards a baccalauréat subject series, but not every student has identical Mathematics depth or the same assessment. Scientific, literary, technical and other programme categories can carry different mathematical requirements according to the actual authorised route. A teacher who says they prepare “all BAC Maths” should identify the specific series, applicable year and current paper.

Government communication about 2026 examinations distinguishes the BAC from BEPC and CEP, with its written assessments scheduled later in the session. See the 21 May 2026 Council of Ministers report. That timetable is a historical fact, not an exam timetable for 2027. For later preparation, ask the candidate’s school for the current syllabus, eligibility and exact subjects before designing an intensive study calendar.

Upper-secondary Mathematical study can involve algebra, functions, geometry, trigonometry, probability and statistics to an extent determined by the actual course. The safest teaching sequence begins with a diagnostic of fractions, indices and equation manipulation before moving into more complex topics. A pupil may have copied a quadratic-solving formula but still fail an unfamiliar modelling task because the meaning of a variable or domain is insecure.

Timed examination practice is useful after concepts are stable. Ask the learner to choose a method, explain why it applies, solve accurately and check the result’s sign and units. Past papers help students recognise legitimate examination demands; repeated identical papers are not a guarantee of transfer. School completion and higher-education admission remain separate institutional decisions.

5. Technical and vocational Mathematics are distinct routes

Burkina Faso provides technical and professional programmes whose certificates include BEP, CAP and other qualifications. The May 2026 government education briefing described different 2026 candidate groups for these awards as well as professional certification. They are not interchangeable with the BEPC or academic BAC simply because all concern a young person’s next educational stage.

Applied Mathematics can be demanding: an electrical apprentice may need ratios, units and circuit relationships; a building student may calculate areas, angles and material quantities; a business student might work with percentages and records. The teaching examples should match an actual module or next task. A tutor who assigns advanced abstract algebra without addressing a learner’s missing unit conversion may be technically impressive but educationally inefficient.

A student seeking an authorised qualification or a place in a technical centre must consult its entry requirements, availability and location. Government educational reform proposals and new programmes may be introduced in phases. Do not assume a new course is offered by every school or that a private tutor can issue its certificate. The teacher can help improve the prerequisite mathematics and explain the path clearly.

For higher education, the CampusFaso platform and official institutional admissions information may be relevant to a student. Application eligibility, programmes and deadlines belong to the institution and current intake. A tutor should not claim that merely passing a particular BAC Mathematics paper guarantees the desired place or professional accreditation.

6. French, national languages and a child’s reasoning

French is an important formal language of instruction, but Burkina Faso is linguistically diverse, and national-language or bilingual education programmes also exist. A mathematical relationship can be understood through a spoken home language yet misread when it appears as a long French instruction. Tutors should ask the pupil to retell the quantities and draw them before deciding whether the problem is conceptual or linguistic.

Terms such as le double, la moitié, la différence, pourcentage, proportionnel and aire need precise mathematical meaning. Memorising them as single-operation triggers can be harmful when a story includes several linked steps. The child should identify the starting whole, transformation and requested result. Then symbolic notation can formalise the reasoning.

A learner who reads slowly is not automatically unable to reason mathematically. Ask the child to solve a numerical or diagram version of the same problem. If that works but the word problem fails, teach vocabulary, reading strategy and expression alongside the mathematics. If both fail at the same ratio relationship, rebuild the concept using concrete groups.

For students whose previous school instruction was interrupted, the language of a newly entered school may be unfamiliar as well. A tutor can preserve dignity by describing a specific missing skill rather than a child’s permanent ability. “Can add whole numbers but needs support comparing unlike fractions” is a useful observation; “bad at Maths” is not.

7. Continuity when schooling is interrupted: safety and realism

UNICEF’s 2026 humanitarian appeal describes substantial educational disruption associated with insecurity, displacement, school closures and overloaded host-community classrooms. Its figures are population-level evidence, not a reason to label individual Burkinabè children as deficient. Tutors should be attentive to gaps and stress while making no assumptions about a particular family’s situation.

A returning learner may have solid mental computation but little recent exposure to formal written algebra. Another may have studied equations yet forgotten fractions after a long break. Begin with varied independent questions to locate what remains secure. Repair the earliest missing connection, then reconnect to the present school topic. Restarting every pupil from the beginning can waste time and diminish motivation.

Offline materials can be practical. Number lines, fraction strips cut from paper, small sets of varied word problems and a dated progress notebook allow genuine teaching without daily video calls. A teacher should design work that can be completed safely and with available resources. No child should be asked to travel into unsafe conditions merely to maintain a private tutoring schedule.

A tutor must be honest about credentials. Informal learning can sustain mathematical knowledge, but a private attendance note is not an accredited CEP, BEPC or baccalauréat certificate. Students and families should ask the appropriate public authorities about recognised pathways, re-entry and examination registration rather than believe an unverified seller promising special access.

8. Original worked lesson: fictional CFA-franc market quantities

Imagine a fictitious market problem in which three metres of fabric cost 4,800 CFA francs. The unit price is 4,800÷3=1,600 francs per metre. Five metres at that constant price cost 5×1,600=8,000 francs. Add an invented fixed delivery fee of 500 francs, giving a total of 8,500 francs. These are classroom figures, not real prices in Burkina Faso.

For a primary student, draw three equal blocks totalling 4,800, then create five blocks of the same size. This model teaches proportional reasoning and the distinction between unit price and total price. A pupil who simply adds two francs rather than two metres’ worth of price has misunderstood the scale factor.

A secondary pupil can express the total as C(m)=1,600m+500 for m metres. The slope is 1,600 CFA francs per metre, while the fixed fee is the intercept at zero metres. If the budget is 10,100 francs, solve 1,600m+500≤10,100 to obtain m≤6. Under the simplified model, six metres exactly exhaust the budget.

For independent transfer, change the unit price to 1,800 francs and delivery to 400. Five metres cost 9,000+400=9,400 francs. The student should rebuild the function C(m)=1,800m+400 rather than copying 8,500 from the original problem.

9. Worked lesson: an imaginary water-tank percentage

A fictional community water tank holds 600 litres when full. Suppose thirty per cent is used during an invented exercise. The volume used is 0.30×600=180 litres; the remainder is 420 litres. The scenario is not a claim about local household water consumption or water access.

For a younger learner, thirty per cent is three tenths. Each tenth of 600 litres is sixty litres, so three tenths total 180. This visual decomposition reveals the fraction relationship. The student can estimate first that more than half should remain because less than half was removed.

An algebra student can let x be the initial volume. Remaining water after thirty per cent use is 0.7x. Given a remainder of 420 litres, solving 0.7x=420 yields x=600. The inverse check is useful: thirty per cent of 600 is 180 and 600−180=420.

Change usage to twenty-five per cent. The remaining volume is three quarters of 600, or 450 litres. A pupil should predict that the remainder rises relative to the thirty-per-cent-use case before computing. That expected direction matters in practical Mathematics.

10. Worked lesson: geometry of a bordered rectangular plot

A completely fictional rectangular plot is 22 metres long and 14 metres wide, giving outer area 308 m². A one-metre-wide path runs inside all four edges. The remaining growing rectangle is 20 by 12 metres, with area 240 m². The path occupies 68 m².

A student who calculates 21×13 has removed the one-metre path on only one side of each dimension. The border exists at both opposite ends, so each outside dimension loses two metres. A drawing is more useful than another series of unexplained multiplication exercises.

For a more advanced learner, express inner area as A(w)=(22−2w)(14−2w)=308−72w+4w². Its meaningful domain is 0≤w≤7 when both interior dimensions are nonnegative. A value above seven would create a negative shorter dimension and cease to describe an actual plot.

At a path width of two metres, the inner dimensions are 18 by 10, area 180 m², while the path covers 128 m². Ask the pupil to predict that the useful area decreases when the path widens. Correct direction, units and diagram interpretation matter together.

11. Worked lesson: an invented solar-energy model

Suppose a fictional school solar panel array generates an average 1.8 kilowatts over four idealised productive hours. The energy produced is 1.8×4=7.2 kilowatt-hours. This simplified classroom model is not a performance claim about real Burkina Faso panels or sunlight. Power in kilowatts and energy in kilowatt-hours are different quantities.

If an invented electrical device uses 0.6 kW for three hours, it consumes 0.6×3=1.8 kWh. After this use, the simplified available energy is 7.2−1.8=5.4 kWh, ignoring real storage losses and other physical constraints. A student should distinguish energy and instantaneous power, rather than subtract 0.6 directly from 7.2.

Let P be mean power and t time. Energy E=Pt, so t=E/P when P is nonzero. If a 1.2-kW device needs 4.8 kWh, it would run for four hours under the idealised model. The tutor should explain the units and the simplifying assumption of constant power.

A transfer question changes production power to 2.0 kW for the same four hours. New energy is 8.0 kWh. The learner should predict an increase before calculation and say why. Maths in technical education must include interpretation as well as correct numerical multiplication.

12. Worked lesson: mean, median and study-time distributions

Five fictional Mathematics practice times are 10, 15, 20, 25 and 50 minutes. Their total is 120, so mean is 24 minutes. The median is twenty. The high final value pulls the mean above the middle observation. A tutor should ask what the two measures tell us, not merely dictate calculation rules.

Replace fifty with thirty. The total becomes one hundred, so mean and median both equal 20 minutes. One observation fell by twenty and the average of five observations fell by four. A pupil who understands the mean can predict that change without recomputing everything.

The original range is 50−10=40 minutes; the changed range is 30−10=20. A simple dot plot shows that the second set is less spread out. It would be misleading to infer national pupil study habits from five imaginary values. Sampling limitations belong to honest statistical reasoning.

For a fresh six-value set, use 6, 8, 10, 12, 14 and 22. Their total is seventy-two, giving mean twelve; median is (10+12)/2=11. If a pupil picks one middle observation instead of averaging two, the error is a precisely teachable misconception.

13. Worked lesson: comparing fictional transport rate plans

A school problem invents two transport charge models with no relationship to actual Burkina Faso services. Plan A costs 500 CFA francs fixed plus 100 francs per kilometre; Plan B costs 1,100 francs fixed plus 60 francs per kilometre. Let distance be x kilometres. A(x)=500+100x and B(x)=1,100+60x.

For a five-kilometre trip, A costs 1,000 and B costs 1,400 francs. Plan A is cheaper for the short distance. For twenty kilometres, A costs 2,500 and B 2,300, so the second becomes cheaper as its lower variable rate takes effect. The tutor should ask the student to explain this direction before solving for the crossing.

Set 500+100x=1,100+60x. This gives 40x=600, so x=15 km. At that point, both plans charge 2,000 CFA francs. The fixed charge is the intercept on a cost graph; the variable rate is the slope.

As an independent variation, make Plan B’s fixed cost 1,300 francs. Then equality occurs when 40x=800, or x=20 km. A student who predicts the crossing moves farther before calculating has demonstrated understanding of the fixed-versus-variable cost relationship.

14. Worked lesson: a quadratic area optimisation problem

A fictional enclosure has 36 metres of fencing for a rectangle. Let one side be x metres; the other is 18−x metres. Area A(x)=x(18−x)=18x−x². Completing the square gives 81−(x−9)², so the maximum possible area in this model is 81 m² at a 9-by-9 square.

Compare rectangles measuring seven by eleven, eight by ten and nine by nine. All have perimeter thirty-six; their areas are 77, 80 and 81 square metres. The examples help pupils see the trend, but the completed-square expression proves that the square maximises area across positive side lengths.

The domain is 0

Now change the perimeter to forty metres. The sides sum to twenty and the maximum occurs at a ten-by-ten square, producing 100 m². Ask the student to derive the new relationship independently; this changed context shows genuine transfer.

15. Worked lesson: probability with and without replacement

A fictional bag contains four yellow beads, three blue beads and two green beads, nine total. In a fair random draw the chance of blue is 3/9=1/3, and the chance of not green is 7/9. Pupils can begin by counting the equally likely objects and describing possible outcomes.

If a blue bead is returned and the bag remixed, the probability of blue twice is (3/9)×(3/9)=1/9. Without replacement, it is (3/9)×(2/8)=1/12. The result changes because after drawing blue, the bag has two blue beads among eight.

A tutor can draw a tree diagram and ask why the denominator of the second fraction changed. Blind multiplication of identical probabilities may show that the pupil overlooked the “without replacement” condition. The correction belongs to reading and modelling, not necessarily multiplication.

For independent transfer use five red and five blue beads. The chance of drawing blue twice without replacement is (5/10)×(4/9)=2/9. A pupil who reconstructs the expression and explains both factors has understood the conditional structure.

16. What the first Mathematics tutoring meeting should accomplish

Bring the pupil’s current class book, a correct worked question and two incorrect ones with full working. Also obtain the school’s next assessment and the actual CEP, BEPC, BAC or vocational route if relevant. Ask the tutor to give a new short prerequisite task. Watch the first unsupported move before the teacher speaks. That is a better diagnostic than a broad promise of top examination grades.

The pupil may misunderstand a quantity, fail to connect a diagram with a calculation, read French mathematical language incorrectly or make a procedural slip. Those are different causes of the same wrong final mark. A teacher should name the cause, choose a suitable visual or symbolic explanation, and then allow the student to attempt a fresh problem without hints.

The instructional sequence should move from a concrete or visible idea to an equation, a guided example and then independent application. The tutor should not complete every first line. After a short delay or next lesson, revisit the idea with unfamiliar numbers. If the student succeeds only immediately after seeing the worked solution, the learning needs consolidation.

A small group can work when each child receives different tasks for the same mathematical concept. One learner may need fraction strips, a second proportional tables and a third a rate problem. This is a teaching principle illustrated by eduKate’s actual Singapore three-pupil approach, not evidence that eduKate operates in Ouagadougou or another Burkina Faso location.

17. Four weeks of measurable learning rather than indefinite tuition

WeekTeaching stepParent-visible result
1Confirm educational access, class and examination; diagnose independent skills.A precise baseline and first prerequisite to repair.
2Use diagrams, explanations and scaffolded-to-independent practice.Pupil solves a changed-number task without a teacher starting it.
3Connect repaired concept to current class or exam work, with delayed retrieval.Retention after time and transfer to an unfamiliar story.
4Use parallel new problems and review the pupil’s confidence and working.Evidence of accuracy, method selection and a continue/change/stop decision.

Four weeks are a review period, not a claim that an entire baccalauréat Mathematics curriculum can be mastered in a month. A learner returning from interrupted schooling may need a longer, carefully sequenced programme, while another with one misconception may not need four whole weeks of paid tuition. The child’s evidence, safety and practical circumstances should guide the duration rather than a fixed sales package.

A productive progress record might state: “Can now solve a ratio with a table and verify it, but still confuses percentage decrease with remaining percentage in stories.” That leads to a specific next lesson. “Weak in Maths” gives parents little information. The ideal endpoint is increased independence, with fewer prompts and the ability to catch unreasonable answers.

18. Safety, pricing, qualifications and the actual choice of tutor

Relevant Mathematics qualifications and teaching experience matter, but a teacher’s personal high exam grade is not sufficient proof of explaining fractions effectively to a younger child. Ask for a short diagnostic demonstration using a real school problem and an unfamiliar variant. The tutor should also understand the learner’s actual examination stream and avoid claiming expertise in every technical certificate without checking the course.

There is no reliable single national tuition hourly price covering all Burkina Faso providers, schools, cities and delivery formats from the cited sources. The 2026 government issued private-school fee regulations, but those should not automatically be described as one universal cap on independent private tutors. Ask the actual provider for fees, lesson length, cancellation, marking, learning materials, travel and progress reporting.

For minors, guardians must know who teaches, where the lesson occurs, how communication is managed and whether photographs or recordings are used. In disrupted contexts, personal and physical safety must take precedence over travel to a private tuition session. A tutor should collect only necessary information and never demand unsafe attendance or promise accreditation they cannot verify.

Students may need accessible formats, national-language explanation, more processing time or school coordination. Such adaptation can make genuine Maths learning possible without changing the conceptual objective. Formal exam accommodations, qualification recognition or admission decisions must be confirmed with the competent institution.

19. Seven questions to ask before choosing a Burkina Faso Maths tutor

  • Which exact CP1–CM2, sixième–troisième or seconde–terminale programme is the student following?
  • Is the goal CEP, BEPC, a named BAC series, a technical qualification or rebuilding interrupted learning?
  • Can you show the actual examination-year syllabus rather than repeating 2026 dates for a future student?
  • How will you distinguish French-language comprehension from a mathematical misconception?
  • Will the learner solve a fresh independent question after a delay, and how is progress reported?
  • What are the full fees, references, safety arrangements, class size and cancellation terms?
  • When would you recommend fewer lessons, another specialist or no further paid tutoring?

20. Frequently asked questions

What is Burkina Faso’s general school ladder?

Six primary years, four years of post-primary and three years of upper secondary, with important alternatives in technical and vocational education.

Are CEP, BEPC and BAC the same examination?

No. They refer to different school levels and have distinct subject and qualification requirements. Technical awards such as BEP and CAP also have their own rules.

Can we reuse the 2026 examination calendar for 2027?

No. The government’s May 2026 briefing documents the 2026 cycle. Schools and the relevant authorities must confirm the next examination timetable and requirements.

Should a learner with interrupted schooling start every subject from the beginning?

Not automatically. Diagnose what has been retained and the earliest missing prerequisite, then reconnect with the appropriate next-level topic.

Does every school pupil learn Mathematics in identical French-language materials?

No. French is important, but school programmes, resources and national-language or bilingual provision may vary. Ask for the actual materials and assessment language.

Can paid tutoring guarantee a technical certificate or university place?

No. Tutors can teach and help a student prepare, but only authorised institutions can award official qualifications or decide admission.

Official 2026 sources and related eduKate Maths country articles

The most reliable Burkina Faso Mathematics tutor knows the student’s true education stage, language, learning continuity and current qualification requirements. They diagnose one concrete misconception, rebuild the mathematical relationship and later check a changed problem with no hints. This approach respects learners with interrupted schooling, avoids false examination guarantees and helps a family decide whether more paid support is genuinely useful.

Other Mathematics Tutors country guides in this batch

Explore how the countries in this four-article series compare in school Mathematics, formal assessments, tutor teaching and independent learning decisions.