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# How many primary teachers are there per 28 students

estimation Market sizing
New answer on Jun 06, 2024
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Hello everyone,

I was solving a case from casecoach (which are always weird and uneasy for me) about finding how many primary school teachers should we hire next year. When calculating how many teachers are there, I was taking into consideration the number of subjects every teacher can teach and how many hours do they work, so more or less delving into the details. However the solution was baffling to me, simply at any time, there is only 1 teacher per 28 students(class size), so the number of teachers is number of students divided by 28. My question is how can I get better at using such simplifications and how accurate is this solution.

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Yes, the question is odd. But your answer is not correct. You are not considering a few things - and it's the ability to consider those things that is being tested here.

Assuming this is about Primary School teachers. Not all classes have the same number of students. To be honest, I don't which country this is referring to, but 28 is more likely to be the max class size than being the average class size. As such, using 28 students average may be simple but most likely inaccurate.

I would rather consider a max of 28, and consider that the average class is 25 (and 90% of classes would be between 22 and 28). Or 24 if you want to consider the low end tail of smaller class sizes in rural areas.

On top of that, you have multiple subjects. If you have a different teacher for physical education, arts, music, etc. than you will have a ratio of teachers per class that is higher. Let's say you have 2 auxiliary teachers, and each of them supports has 4 classes. That is 2 (teachers) / 4 (classes) = 0.5 additional teachers per class.

As such, you would have 28 / 25 * (1+ 0.5) teachers per 28 students. That is 1.68 teachers per 28 students.

If this is not about the Primary School teachers, then what you have to consider is the how many hours do the teachers have on average vs. average hours of classes that students have. For example, if the average student has 30 hours of classes, but the average teacher has 15 hours of classes, this means that you have a 1.5 to 1 ratio of teachers per class…

Hi,

Thanks for sharing. Without knowing additional details that were provided as part of initial prompt, it is tough to provide a solution for specific problem.

However, assuming this was your only prompt and if this were a real interview, the interviewer is evaluating you on how you structure the problem, ask the right questions and brainstorm to get to the solution. He/she is evaluating your thought process.

In this case, your structure could comprise of  demand and supply side framework:

1. Demand: factors that could drive the student teacher ratio some of which you have stated yourself (total # of subjects, # of subjects taught every day vs intermittenl, # of subjects taughetr per teacher, # of days of school/week, duration of classes, average student teacher ratio for school/district) and the list goes on

2. Supply - constriants the school has like budget, teacher availability, contraint on student teacher ratio (So even if demand is high, there could be a limit on student teacher ratio)

Once you have your structure, your interviewer may ask you to hone in on where you want to start or give you pointers.

The goal is to not make your structure too complicated so you can work through it in the limied time but still have the most important points to have a interactive, intelligent and focused discussion towards a solution.

Hope this helps.

Hi there,

I think you would get the best results if you posted the full question as well as your full approach. Then we can give more tailored feedback.

As regards the question, estimation questions can always be answered with different levels of granularity and that is something that has to be worked out with the interviewer in a live setting.

Looking at the number of students per teacher is a quick way to solve it. This could be your starting point. From there, however, in a real interview, your interview would be interested to go deeper to see how you come up with assumptions.

For instance, you could first size the number of students in the country, then segment them based on tiers (e.g., elementary school, high school, etc), clarifying in the beginning what types of students we are looking for.

Cheers,

Florian

The approach you took is more detailed and evolved - and most likely it will give you a more mature answer. Your limited description of your approach is making valid sense.

The Teacher:Student ratio concept in the case solution is not the best approach. The ratio is usually used by authorities / administrators to assess if a school has sufficient number of teachers or not.

While schools conduct teacher hiring based on a ratio that they determine (or is administered by the government) - it is not an input that you can blindly take for a market sizing question. Different countries/cities can have different ratio requirements.

The key is making sure that you first come up with the logic of the calculation and then you discuss it with the interviewer.

Even if your logic is not perfect, you can integrate the feedback of the interviewer and find the right path. That will then enable you to do the rest perfectly.

Don't assume that you can solve all problems or that you will ever get to the point where you can ‘crack’ any calculation approach.

Instead, seek to expose yourself to more problem types to develop your pattern recognition, and then work on the technique necessary to minimise the damage in case you can't figure out the approach from the beginning.

Best,
Cristian

Hi there,

I would be happy to share my thoughts on your question:

• First of all, as you correctly pointed out, CaseCoach case studies are typically a bit weird (and not realistic for an actual case study in an interview), which is why I would highly advise you to reconsider working with them. While it is certainly advisable to cover the full breadth and depth of case studies, working with just plain weird and unrealistic case studies is not helpful to your preparation and expectation management.
• Moreover, I would advise you to discuss your approach to estimating market size with the interviewer first before going into detail. Since you seem to have done the case study on your own, this is unfortunately not possible.

If you would like a more detailed discussion on how to best prepare for your upcoming interviews, please don't hesitate to contact me directly.

Best,

Hagen

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