Tricky Numerical Concepts

Hi Everyone,

I found the following post on another list and would love to get your thoughts as adult educators. Specifically, could you please share with us some examples of challenging mathematical concepts that your students are faced with? It would also be great to get your ideas on how to teach these concepts!

Thanks for your help! Health literacy advocates and health educators are working hard to train health care providers and public health spokespeople to present numerical information in a way that is easier to understand. Your expertise as teachers could be very helpful to this effort!

Best, Julie

Numeracy is an important subset of both literacy and health literacy. We would like to see a comprehensive list of terms and concepts used commonly in health conversations which require the patient to understand a mathematical or numerical concept. Once we have this list, we can begin to build ways of describing the term or the concept so that a person with low numeracy skills can access the information in a real way.

Example: Usual presentation of concept: “The surgery that I am proposing carries a 15% risk of complication. This risk increases to 25% if the patient smokes or is overweight.”

Numeracy skills required to access and understand what the doctor said:  What does percent mean? What does risk mean? What does increase in risk mean?

Real information and concept that the doctor wants and needs the patient to understand:  “We do this surgery enough to know how well it turns out for most patients. Most patients do well, and the surgery goes as planned, and nothing happens afterwards that we do not want to happen, like bleeding or infection. But some patients do have things happen that are not good, like bleeding and infection. Out of every one hundred patients that has this type of surgery does have one of these problems afterwards. If a person smokes or is overweight, he is more likely to have bleeding or infection after this surgery than a person who does not smoke or have too much body weight.”

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Second example: Usual presentation of concept: “Your baby is in the 39th percentile for head circumference, the 45th percentile for length, and 89th percentile for weight.

Numeracy skills required:  What is percentile? How could my baby be in three different groups? What do these measurements mean in terms of how my baby is doing? Is my baby failing on all counts? What is my baby being compared to?

Real information the patient needs to understand: “ We measure three things every time you bring the baby in, to see how she is growing. We measure the size of her head from her forehead around to the back of her head. We measure the length of the baby from top of head to her heels when she is lying down. And we measure her weight. The number give us a general idea of whether she is growing pretty normally or whether any part of her growth is way too much or way too little. These numbers are a comparison of your baby to all the other babies out there. Each number tells us how many babies are bigger or heavier than your baby, as well as how many babies are smaller or lighter than your baby. Today, your baby is heavier than most babies, but certainly not the heaviest baby out there. Your baby is right in the middle of all babies in terms of how long she is, so half the babies out there are longer than she is, and half of them are shorter than she is. Her head is not on the larger side, but is well within the normal size for her age.

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Third example:  Usual presentation of concept: “Decrease the dose by 2mg every day until you reach 10 mg a day, then decrease it by half and keep doing that for one more week.”

Numeracy skills required: What is the concept of so many mg per pill or tablet? What is the difference between decrease by 2 and cut it in half?

Real information the patient needs to understand: “ You are now taking a total of 25 milligrams of medicine every day. In the morning you are taking one tablet with 10 milligrams in it, and in the evening you take a tablet with 15 milligrams in it. You need to take a bit less of this medicine every day, in specific steps. Your schedule will look like this:  Tomorrow take 23 milligrams all together, so take 10 milligrams in the morning and 13 milligrams in the evening. 13 milligrams means one ten milligram tablet plus three tablets of one milligram each.  The day after tomorrow, or Thursday, you will take 21 milligrams all together…”

I would love to solicit examples of common things we say to patients that require comprehension of mathematical or numeric concepts. Please send me as many as you can.

 

Comments

Hi, Julie -

Your second example highlights the issue of what percentile means.  This is something that I think still confuses many adults, across a spectrum of education levels. Add to that a comparison of percentile and percentage, and it becomes even more confusing for some.  Just for review sake, let's  say that 100 people are given a questionnaire on 50 different healthy behaviors.  If I meet the requirements for 40 of these healthy behaviors, then I'm at an 80%  of the 50 healthy behaviors.  However, I don't know my percentile until I know the percentages of the other 99 people who answered the questionnaire.  If all 99 of the other people only get 60% (or fewer) of the items correct, then with my 80%, I scored better than all other 99 people.  I am in the 99th percentile. 

I believe that it is critical to teach learners percentage and percentile together.  Percentage is the more simple, numerical concept, and is the easier of the two concepts to understand.  However, without extending the lesson to include percentile, I think many learners never get to, or fully understand, percentiles, and how they are different from percentages.  What are others' experiences of teaching these two, often misunderstood, numeric concepts?  Do you find that learners understand them better in relation to one another, or as separate lessons?

Mike

   I tutor students in courses that teach about one or the other... so I'm not making the 'teaching' decision.  

    I think this is one of those "but will it be on the test?" situations that interferes with really learning and understanding things, because in our pre-algebra course, it's percentages, thank you... in stats it's percentiles.   I'd love to see more emphasis on discerning between the two (and would love pulling up some news articles where school board people have talked about standardized tests and confused the concepts and made decisions based on the confusion). 

     I know that students tend to simply assume "if it's a score, it's the percent."   So, when my happy student came down after working with Modumath for a week and a half, having placed into Trigonometry or Math 160, she saw the scores on her sheet of 90, 62 and 20 (at the three increasing levels) and assumed that she got that percentage of the questions right (and not scores based on some algorithm in the placement test program that simply decides whether they get to move up or not).   

Hi Mike,

It seems to make sense to teach them together because they can so easily be confused with each other. But whether you teach them together or separately, I would think it would be key to teach them in the context of some real-life meaning, like the baby measurements in the example above. If they can attach meaning to it that relates to their everyday life, it will make more sense.

Susan, you noted that students are motivated by what will be "on the test". Are they equally motivated, do you think, by what's on the "test of life"? This is not rhetorical--it may be that they are not, but I am curious to hear from your and others' experience!

Julie

   I am pretty sure that if the questions & examples they were given were more like those examples, they would be *much* more invested in understanding them *and* getting the right answers.   I know that there's a lot more engagement in our "math literacy" course which makes better connections between situations they might actually encounter and algebra & stats.  

Thanks! I wonder how often teachers check with students to get their input on what kinds of relevant topics they would like to use as a context for whatever skills they are learning in class.

 

I have thought about a way to get this across. Here's one that may work for some adults.

Every student who gets admitted to Harvard is (today) a straight A student at their high school.

Now there are 100 students in a Harvard freshman English class. Let's say everyone gets 91% to 100% correct on the first test. And lets say that there is an even distribution of scores (10 students at 91%, 10 at 92%, etc.). Based on percents, they would all get an A.

BUT...

If you look at percentiles - the students who scored 91% are in the 0to10 percentile, the students who scored 92% are in the 10to20 percentile.

I think if you can put both percent and percentile into the same example, people might have a better grasp of the difference. I think this is important, since politicians have been heard to say "It is unacceptable that half of our students are below the 50th-percentile." Such people obviously do not understand that half the students will always be below that 50th-percentile, even if they are all earning an A on the test.

Dorothea Steinke

Greetings!  The recent Wisconsin Health Literacy Conference has presenters' PowerPoints available on their website.  One Plenary Speaker, Brian Zikmund-Fisher, PhD, presented on numeracy:  "I Know My Number but What Does It Mean?"  The PowerPoint has several examples and is available on this webpage, just below Jackie Taylor's presentation on the health implications of the PIAAC data (Go, Jackie!).  There are several other PPTs you may want to look at.

http://wisconsinliteracy.org/health-literacy/training-conferences/powerpoint-presentations.html

And a second PowerPoint with a slightly different take from the Legacy Health Literacy Conference.  Look down the list of documents to another presentation by Brian Zikmund-Fisher titled, "The Challenge of Numeracy."

http://www.legacyhealth.org/our-legacy/legacy-values/health-literacy/health-literacy-conference.aspx

Cynthia