Pharmaceutical Calculations: 3 Reasons Why Students Get Questions Wrong

Do you struggle getting pharmaceutical calculations questions correct? In this blog, I'm going to show you three reasons why students get pharmaceutical calculation questions wrong.

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Pharmaceutical Calculations: 3 Reasons Why Students Get Questions Wrong

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If you are not getting pharmaceutical calculations questions consistently correct, then it's probably because of at least one of these reasons.

I'm going to start off by telling you upfront what those three reasons are, and then we'll take each one of them and look at them at a deeper level using an example.

The first reason why students get pharmaceutical calculations questions wrong, is due to a lack of proper understanding of the purpose or goal of the problem or the question.

The second reason is due to improper or incomplete assessment of the arithmetic process needed to reach the goal or the answer.

The third reason is due to poor implementation of the correct arithmetic manipulations.

Now, let's take each of these reasons and use an example to see how exactly students get questions wrong.

Reason #1:  A lack of proper understanding of the purpose or goal of the problem

So if we use this example, and the question here says the maximum recommended rate of infusion of dextrose solution is 0.1 g/kg/h. How many hours will it take to infuse 1,000 mL of D30W in a patient weighing 172 lbs?

So I've come across several instances where as soon as students finish reading the question, the first thing that they ask is, which numbers do I multiply? Which ones do I divide? Which ones do I add? Where do we subtract? Which numbers are important? And all of this has to do more with method manipulation than it is with actually understanding the question.

But the key thing to do is always to start off by preparing yourself to understand what the question is about, and what the purpose of the question is, and then you go ahead and develop the plan and then you solve the problem.

So if we take this question, how do you know that you really understand the goal of the problem? And there are a number of ways you could do it, but there are a series of questions one could ask to help elucidate or make it clear, but that you really understand the question.

So the first question you could actually ask yourself to find out whether you really understand the purpose of the question is, do you know the underlying mathematical concepts?

So the question that we just looked at is a type of pharmaceutical calculations questions. But there are several types of concepts that you would encounter in pharmaceutical calculations. You have million equivalence, osmolarity, flow rates, and so on.

The first thing is to take that question and place it in the proper context. This question is a flow rate question. The moment you're able to narrow down the topic to the precise concept you are dealing with in that moment, it helps you focus all your mental resources to be able to understand the question better.

In this example, the question we just looked at, that's a flow rate calculations type of question. That's the mathematical concept we're looking at.

The next thing you can ask yourself is, what a problem is it? When you talk about flow rates. But when you talk about flow rates, you are giving the patient a specified amount of drug, basically using the fluid, and you're giving this fluid in such a way that over a specified time, the patient will get enough of the drug.

So when you talk about flow rates in this example, you're either always going to be asked to calculate the rate of the infusion, the volume of the preparation, or the time that it takes. This question is talking about time, how many hours. So this problem is the type of flow rate calculation question where we are looking for duration or the time, the duration of flow or the time. So this helps us understand the real intent of the question.

The next thing we could ask is, what exactly is being asked? 

And specifically, this question is asking you how many hours, not how many minutes, how many days, how many seconds, it's how many hours. And that's important, especially when it comes to the third reason why you get questions wrong, to make sure that you're actually doing the arithmetic manipulation that answers the question.

So what is being asked here? How many hours? Not days, not seconds, not minutes.

The next question that you could ask to actually improve your understanding of the question is what do the terms mean? 

So the whole lot of terms in the question, for example, rate of infusion, do we actually know what it means? We may be familiar with the term, but do we understand what it means? Rate of infusion, how quickly are you giving the fluid? Is the volume administered per time?

The next thing that you could ask is the 0.1 g/kg/h. What exactly does that mean? It means you're given 0.1 g of dextrose every hour, but that is a mass rate and that has been normalized to the weight of the patient.

So that's why you have the per kilogram there. 

So once you understand that the per kilogram is a normalized dose or normalized to body weight, then you would understand the significance of the patient's weight being provided.

The other term that you may want to make sure that you really understand is the D30W, dextrose 30%. What does that exactly mean?

It means you have 30 grams of dextrose in 100 mL of preparation. Once you understand what that term actually means, 30 g of dextrose in 100 mL,

then it makes sense why you've been given the 1,000 mL quantity there, because you are going to use that volume together with the concentration that the D30W tells you to be able to solve the question.

Another question you could ask is, is there enough information to solve the problem, or do you need more information? So here we actually do have enough because we're starting off with a normalized dose, we know the patient's weight, we know the volume of the of the preparation, and so we could end up determining the hours. So we have enough information. 

But once you've gone through the series of questions from A to D, it will begin to be very clear in your mind whether you need more information to solve the problem that has already been given in the actual question.

Finally, the next question you could ask is, what is known and what is unknown? 

In this example, we do know the mass rate. We know it is 0.1 g/kg/h. So the mass rate is grams per hour and it's been normalized to the patient's body weight. We do know the volume of the preparation that is going to be infused. So it's 1,000 mL of DW30 (dextrose 30%), and we know the weight of the patient.

The one thing we don't know in this question is the time it takes to infuse the 1,000 mL of the DW.

So I know it took some time to go through these questions, but typically, once you've done this a few times, you'd be asking these questions rather expeditiously, probably at the speed of thought. So it doesn't take as long as it did in this particular presentation.

But if you go through these series of questions at the minimum, you should have a better understanding of the goal of the question. And if it's not clear, you know that you need some clarity in terms of answering one of those specific questions to be able to see very clearly what the question is actually asking.

So we just looked at reason number one, why students typically get pharmaceutical calculations questions wrong, and that is due to a lack of proper understanding of the purpose or goal of the problem.

Reason #2: Improper or incomplete assessment of the arithmetic process needed to reach the goal

Now, let's take a look at reason number two. Reason number two is due to improper or incomplete assessment of the arithmetic process needed to reach the goal or your answer. So if reason number one is on that issue for you, that means you really understand the purpose of the question or the goal of the question completely.

Then the next thing you want to do is actually develop a plan to get to your answer. Now, instead of just going ahead and saying, Which numbers do I multiply, divide? You want to develop a plan, and that's the arithmetic process that this particular region is talking about

Because if your plan is faulty, then two things could happen. One, you may end up with the wrong answer, and that's a non-starter. Or two, you may actually end up with the right answer, but it will take you a really long time to get to the answer. And so in calculations or pharmaceutical calculations, it's always about speed and accuracy.

Now, let's take a look at the same example that we use for reason number one, and see how we could develop a plan that will help us arrive at the solution to the question in an expeditious way. Here again, the question says the maximum recommended rate of infusion of dextrose solution is 0.1 g/kg/h. How many hours will it take to infuse 1,000 mL of D30W in a patient weighing 172 lbs.

So sometimes when I ask students, how do you solve this problem? What typically the response should be is you take the 0.1, you multiply that by 172, and then you multiply that by 1,000. And that really is not the kind of plan I'm talking about.

The plan I'm talking about is you take the question and understand what the key steps are that would allow you to get to your solution, like the milestone moments that will let you get to your solution.

Here's a recommended approach for this question, and you can use a similar strategy for all types of questions that you come across. The first thing we could do is from the question, we could go ahead and determine the rate of infusion in grams per hour that is given to the patient.

And that is because when we looked at the first sentence, you were given the recommended rate of infusion. It was 0.1 g/kg/h. This rate is normalized to the patient's body weight. In the question, we have the patient's weight to be 172 pounds. So if we took the maximum recommended rate of infusion and we multiplied that by the patient's weight, of course, once the weight has been converted to kilograms, your units must be consistent, then that will give us the weight of infusion in grams per hour. But why are we doing that? That will lead us to the next strategic milestone step in our plan to get the solution.

Because the next thing we want to do is we've been given the volume of D30W to infuse, but we would like to know how much dextrose in grams is actually present in that 1,000 mL preparation.

And why, again, do we need those two pieces of information? Because if we divided the amount of dextrose in grams in a 1,000 mL preparation by the rate of infusion, which was given in g/h,

then automatically we end up determining the number of hours that is needed to infuse the 1,000 mL preparation of D30W.

So this is how you go about developing an arithmetic process, a plan for you to arrive at the solution. It's about the logic that you need to follow that will help you arrive at the solution. And once again, we went through this fairly slowly, but this is something that through practice and strategically employing this approach, you could do at the speed of thought, and so it will be much, much more quicker. So here we are, three steps in the plan that would allow you to get to your solution.

And so if we missed step B, then our plan will be incomplete. And typically, this happens to quite a lot of students where they know to determine the rate of infusion g/h, but miss the step in determining the amount of dextrose in grams in the 1,000 mL preparation.

And so you have step A completed, but there's no step B, and so there's a struggle in determining the hours. So we just looked at reason number two, why students tend to get pharmaceutical calculations questions wrong, and that has to do with improper or incomplete assessment of the arithmetic process needed to reach the goal.

Reason #3: Poor implementation of the correct arithmetic manipulations

Now, let's look at reason number three. Reason number three has to do with poor implementation of the correct arithmetic manipulations. So this is errors that are due to punching the wrong numbers in the calculator, setting up the actual solution incorrectly. And as simple as it may look, it's actually one of the biggest culprits as to why students get the questions wrong.

Let's go ahead and illustrate this reason using the same example. The question once again says the maximum recommended rate of infusion of dextrose solution is 0.1 g/kg/h. How many hours will it take to infuse 1,000 mL of D30W in a patient weighing 172 lbs?

So to illustrate this point, I'm actually going to go ahead and solve the question using the plan that we developed when we looked at reason number two, and then we could spotlight some of the areas where you are likely to make an error.

So step one, we needed to determine the rate of infusion in g/h that is given to the patient. So how do we do that? We take the rate that has been provided, the rate of infusion, which was 0.1 g/kg/h, we multiply that by the patient's weight, which is 172 lbs.

The goal is to cancel the kilograms in the denominator of the rate, but pounds and kilograms are not consistent units, so they can't cancel out, which means we need to convert the pounds to kilograms.

So we multiply that by the conversion factor, which says every 1 kg contains 2.2 lbs.

So now the kilograms can cancel out and the pounds can cancel out. And so your units are now g/h.

But we need to multiply all the numbers in the numerator and then divide that by the 2.2 in the denominator, and that would give us the 7.82 g/h.

So in looking at this step, one of the areas in which there could be an incorrect arithmetic manipulation would have to be the conversion factor. So if you didn't know the conversion factor that 1 kg contains 2.2 pounds and you put in the wrong conversion factor, it doesn't matter how accurately you punch those numbers in the calculator, your answer will still be wrong and that will be an incorrect arithmetic manipulation.

Or another likely thing that I've seen happen is instead of multiplying the 0.1 grams per kilogram per hour by the 172 pounds, you actually flip it and divide the 0.1 g/kg/h by the 172 and try to make the units one way or the other fit. If you don't know what you're doing, then you're just trying to multiply numbers and divide. But having a very good understanding of the question and actually knowing the plan to get the solution, you know how to set up your arithmetic manipulations correctly in this particular step.

We're done with step one. The next thing we want to do is look at step two. So for step two, we need to determine the amount of dextrose in grams in the 1,000 mL preparation.

So dextrose 30% implies you have 30 g of dextrose in 100 mL.

The goal is to figure out how much is in the 1,000 mL. So you can multiply that ratio by 1,000 mL.

The millileters will cancel out and then you can multiply the 30 grams by the 1,000 divided by 100 and that will give you 300 grams.

Now, one of the common areas or sources of error in this particular step, just to illustrate, would be the zeros. So there are a whole bunch of zeros in there, and sometimes there and sometimes there could be an omission of the actual number of zeros that is needed. So instead of 300, it's not unreasonable from time to time to see people put 30 or 3,000, depending on how they punch the numbers in the calculator.

So being particularly attentive to the numbers that you're working with, especially when you have lots of zeros, is important to make sure that your arithmetic manipulation is actually accurate.

So the other piece, which is also intertwined with reason number one is if you did not accurately interpret what D30W is. So instead of 30% being 30 g out of 100, your understanding of percentage concentrations wasn't all that good.

There could be instances where you actually end up putting 0.3 grams out of 100 mL. And that will put you at least two decimal places off in terms of the answer that you get.

Everything is connected together and that is where if you don't do the arithmetic manipulations correctly, you may end up with a different number and then your whole answer will be completely wrong.

Now, let's take a look at step number three. In this step, we are trying to determine the number of hours.

So the approach then would be to take the amount of dextrose in grams, which was the answer you got in step two, which would be 300 grams, and then divide that by the rate of infusion in g/h, which was 7.82 g/h.

The grams cancelled out and because it's grams per hour in the denominator, the hour will flip to the numerator and you end up having 38.36 h.

So here again, the likely thing that could happen is if one decided to divide the 7.82 g/h by the 300 instead of doing it the way it is presented. So you end up with a fraction or a decimal and your answer will be totally wrong.

So we just looked at reason number three, why students get pharmaceutical calculations questions wrong, and that is due to poor implementation of the correct arithmetic manipulation.

So if you want to consistently get pharmaceutical calculations questions correct, then you need to be aware of these three reasons and use some of the suggestions that have been provided to ensure that you don't make those mistakes.

Now, the three reasons, once again, one, the lack of proper understanding of the purpose or goal of the problem or question. Reason number two is the improper or incomplete assessment of the arithmetic process needed to reach the goal. Reason number three is poor implementation of the correct arithmetic manipulations.

So I hope you found this tutorial useful. Thank you so much, and I will see you in the next blog.

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