The Case for Not Teaching Estimation – or Why Your Grandmother Got Too Much Medication

Dave and I have discussed our 2e daughter, H, before, and her diagnosis of dyscalculia. There are actually several forms of math LD; hers appears to be a combination of many forms at once. She is more comfortable home-schooling math, where she can work on the computer instead of a worksheet, repeat the information as often as she needs to, and take tests that are not timed. Despite all of this, she struggles to make a “B” in her online class (and as you know from prior posts, we could care less about grades as long as she is working at it.)

We have had to accept, though, that she will not learn some math in her life. Dave and I don’t think it’s realistic for her to learn every math function, and we’ll be ecstatic if she’s  able to make it through algebra. To an outsider, and even to some 2e parents and kids, this comment might seem mean, or defeatist. We have not “given up” on her, and would never stop her from tackling a subject if she wanted to try. We are, however, realistic about the fact that there is only so much time in life, and spending it struggling on every math concept – when she could be spending that time on utilizing tools to help her in the long run (digital watches, calculators, MS Excel spreadsheets) – doesn’t make sense. So, with this in mind, we treat every math unit as a trial. Is this something she will need to know and use in life? Great – let’s teach it. However, if we’ve tried for weeks (or years) and she still doesn’t “get it”, let’s then switch to teaching her to use tools that can help her achieve the same outcome, and skip through this unit. Focusing on what she’ll truly need to function in life shapes our lesson planning from week-to-week.

A few weeks ago, she started the “estimating and rounding” unit of her math class. She has tried to learn this many times before. What has been explained to us is that subitization, or the ability to recognize that, say, three dots on a page equals the number “3”, or that four dots is more than three dots, in an inborn ability. People with dyscalculia just don’t have this inborn ability. Therefore, they do not estimate as well as others, even into adulthood, and have a difficult time retaining some concepts as a result.

So, as we started the unit, we asked ourselves the question: will she need this to function in life? Neither Dave or I could pinpoint a single time recently that we had used estimation, and, more specifically, any time in the past decade. There’s a reason for that; we’re just now wrapping up the first decade of the smartphone era. Prior to 2002, this concept of not teaching estimation would have earned us an incredulous, wide-eyed response – namely, ‘what are you going to do? Carry a pocket calculator everywhere?’ Since then, smartphone ownership has exploded, to the point where more of us own one than not, a trend that appears to be here to stay. In just a decade, we’ve gone from phone-as-phone to phone-as-PDA. The parallel trend in usage of the free Google Docs platform has resulted in similar use of spreadsheets as a society. When (Google Docs precursor) VisiCalc launched in 1980, it cost an amount in 1980 dollars roughly equal to an entire copy of Microsoft Office today, and could do much less. Today, you can have a spreadsheet for nothing more than a few minutes of time registering a Google Docs account. We’ve arrived at a new state of expectations in mathematical precision; one in which we can really be as precise as we’d like to be, at any point during our day.  Numbers are now of two kinds: the kind we can precisely know, or the kind that frankly matter so little it’s not even worth pulling a phone from my pocket. The theory is that we need estimation to figure out whether the answer is in the “ballpark”; to me, that’s why you double-check calculations, or enter them into a spreadsheet to see the logic structure.

In fact, by this point in my career, I actively try NOT to use any mental math or estimation in my practice – and here’s an example of why.

I’m an internist in a geriatric practice. One of the things that happens as patients get older is that their kidney function declines, some more quickly than others. We use a blood test, called creatinine, to calculate whether each patient has a normal kidney function, and thus decide whether we can use certain medications or not, and at what dose. The formula involves four factors: the patient’s creatinine, age, weight, and gender. There are actually even more accurate (and invasive) ways to measure the kidney filtration rate, but given the ease of getting the data, we use this one in internal medicine as an acceptable benchmark.

Until we had electronic medical records (again, within the last 10 years), many physicians would estimate what the kidney function was. Generally, on rounds, physicians were not calculating (even with a calculator available) the actual kidney function for each individual patient. They were estimating based on the creatinine result alone (which would be listed by the lab as “normal”) whether the kidney function was within range. Trouble is, they were wrong more than not, because the creatinine would not be abnormal until the patient had lost 50-60% of their kidney function. Studies showed that physicians routinely overestimated the kidney function of older adults, and thus often gave them medication doses that were too high. Nowadays, we use an electronic medical record in my practice where I can simply type in an automated phrase –  “.gfrc” – and it will pull the information from the patient’s record and enter that data into the formula to calculate the kidney function. Then, when I order medications, it will help me pick the correct dose for their calculated kidney function. If I need to, I can quickly look up the formula on the web, or my iphone, and calculate it myself.

The point is that we, as doctors, received a healthy dose of estimation math in the 1970 and 1980s, and we went on to take a full slate of mathematics, through calculus. We did all of it, all of the estimation worksheets and gumballs-in-a-jar word problems, and much, much more in the way of traditional mathematics. We are the outflow vector of everything mathematics teachers ever hoped for in teaching estimation, and we suck at it. Moreover, we suck at it in an environment that can be truly life or death. So, doctors have moved to the next step:  using tools to help us be more accurate, safer, better. Are there really situations anymore in which a phone-less, laptop-less engineer is put on the spot to calculate the load-bearing stress on that bridge right now?

I have begun to wonder, based on working with our 2e daughter, why we don’t have these conversations for all of education. What process do we use to decide what is obsolete, to actively stop teaching what we don’t need in favor of new skills that are much more important?

We, in my opinion, have generally moved beyond the need to estimate, and even moved to a point where relying on estimation can be harmful. What about, instead, teaching the value of a precise calculation – using the correct tools, and rechecking your work? We might thank ourselves when it’s our turn to be grandparents.

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11 responses to this post.

  1. I wrote about subitization last year and I confess that estimation as a negative had never occurred to me. Great post.

    Reply

  2. I hate that my sons ever learned estimation, that the public schooled 3rd grader gets points marked off for just answering the question. I’m in the same boat: what do I teach my 2e homeschooled son because he needs to know it vs what could be passed over because it’s not really necessary. It’s driving me crazy.

    Reply

    • Jen, we really do take H’s math a section at a time, and we continuously ask ourselves, ‘what’s she doing in this area when she’s 30?’ There are things adults need to know how to do to function in society, and there’s things they don’t, and we try and make sure H is getting what she needs to get by. The best yardstick for us, as two busy adults, is our own lives – do we really sit down with a calculator to convert liters to quarts, or do I google LITER QUART CONVERSION CALCULATOR? Do I spend a great deal of my day wrestling with improper fractions? (No.) The realities of dyscalculia, in our case, are such that we need to prepare H for a life without a full complement of math skills – so thank God we live in an age where every crap prepaid phone (let alone smartphone) has a calculator, and Google Docs IS free. Add in a digital watch, or the clock on her phone, and I think she’s going to have the tools she needs to compensate.

      Reply

  3. I hated estimation. It felt like they were making me answer the question wrong. I sometimes wrote the correct answer somewhere on the paper so I didn’t feel weird.

    Reply

    • Posted by Kathy on October 15, 2012 at 6:48 pm

      Hi Katie-thanks for your comments! I also did what you describe-I would calculate the exact answer first. Estimation didn’t make sense to me then, either, so it makes it hard to teach.

      Reply

  4. Posted by mbl on October 15, 2012 at 6:19 pm

    Love your blog!! I didn’t see a contact email, so I’ll post here even though I’m not an external grammar nazi, except with my husband and daughter. When I saw “and as you know from prior posts, we could care less about grades as long as she is working at it” I cringed a little bit, but chalked it up to either a typo or an endearing quirk. However, when I saw your Khopitar post I just knew I had to act. (I can’t spell worth a damn, so sorry about that.)
    Regarding your post, my daughter is 2e, but I haven’t really looked into dyscalcula since she is ahead in math concepts. But she’s average on the rote portions so who knows. I can see the value of your post to those dealing with dyscacula and how it can apply to other hard to surmount weaknesses. That said, I can’t image not being able to estimate. I do it all the time from calculating shopping tallies and counting coins to baking and divvying up portions.
    I found the information about subitization intriguing so I’ll probably blow a couple of hours going down that rabbit hole. So thanks ever-so-much for that. “inserteyerollemoticon” 😀

    Again, love your blog. I was led here by someone on a listserve posting a link regarding your response to the NY Times charmer.

    Reply

    • Posted by Kathy on October 15, 2012 at 6:45 pm

      Thanks for your comments! The posts are actually written by two different people, myself (Kathy) and my husband, Dave. You’ll notice that my posts are not typically grammatically correct – I leave that to Dave. He has a great post he’s writing as a follow up to “Estimation” – addressing the issues you and others have brought up – so I’ll let you look in on his reply when he posts it!

      Reply

      • Posted by mbl on October 15, 2012 at 7:11 pm

        LOL, I just realized the error of my ways and was coming back to retreat, retreat, retreat. Mea culpa.
        It was funny because I read a couple of posts assuming a female writer and then got a comment in one of Dave’s posts with the word “Dad” and felt guilty of gender bias for assuming the blog was written by a female. When I got the comment about using estimation in the spa project I was thoroughly confused and went to the “about” page for clarification.
        Thanks for not making feel like a cad with my very first comment!

      • Posted by Kathy on October 15, 2012 at 7:21 pm

        No worries at all! It is a bit confusing that we switch back and forth. Glad you like our blog! It’s been a great way to connect with like-minded people.

  5. […] that’s mostly harmless, as Douglas Adams would say; and sometimes, as Kathy pointed out in her post, it’s potentially deadly. I suppose my question is this: what sort of mathematical questions […]

    Reply

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