Ask Better Questions

This week, the Providence Student Union ( published the results of an experiment they conducted. They gave fifty successful adults a math test that was based on the sample New England Common Assessment Program. Rhode Island uses the NECAP as a high-stakes test where students must achieve at least “Partially Proficient” to graduate high school.

Who can argue with making sure that students are at least “Partially Proficient” in math?

Except, apparently you don’t need to be considered partially proficient to be successful, as the results show:

The results were: Four of the 50 adults got a score that would have been “proficient with distinction,”  seven would have scored “proficient,” nine would have scored “partially proficient,” and 30 – or 60 percent – would have scored “substantially below proficient.” Students scoring in the last category are at risk of not graduating from high school. (

Now, some folks will say that the adults didn’t have the time to study for the test, but that isn’t the point. The point is that these successful adults were no longer proficient in the math skills on the test because they did not use them in their day-to-day lives. And yet, Rhode Island is going mandate “Partially Proficient” as a graduation requirement for students starting next year.


If we are to have mandatory graduation exams, let’s base them on the skills that adults need in their world. What would happen if we asked successful adults what the math they used day-to-day was? Do most people use the quadratic equation or do they need more math skills that allow them to create budgets for their business, calculate interest rates on their mortgages, understand polling data in the New York Times?

That doesn’t mean we shouldn’t teach skills beyond what may show up on a graduation exam. What it means is that we have to start asking better questions about what skills are necessary for a high school diploma. And we need to start asking better questions to our students too.

10 thoughts on “Ask Better Questions

  1. Agreed. We definitely need better questions. This week, our maintenance guy was working building a ramp. As he started drawing, I said, “Why don’t you give this whole project to the Year 9 students?” The maintenance worker would have done just fine, but those types of tasks are authentic assessments for students.

    This past year, a popular blog writer argued that not all students need algebra. While I see his points and I rarely use algebra in my daily life, I’m thankful for algebra and geometry proofs for forcing me to think logically and linearly. That type of thought process was not natural for me, but has helped me in mapping out policy options.

  2. Good points Chris. The ironies of the situation are (1) that the mathematical sophistication necssary for current graduates to pay for school wisely, plan for retirement, and manage their healthcare is only getting more complex, and (2) the skills necessary to address these issues are not stressed (and may not even be present) in a “college prep” curriculum. The Ss in RI (and everywhere) should see math as a ticket to a bright future!

    My memories of high school math were that it served as the perfect baby sitter: focusing on simple repetitive tasks without authentic context where a child’s compliance could be assessed and rewarded. Hopefully it has changed, but I doubt it.

    Once they are weaned off the pablum of 1-30 odd, I believe that more Ss would buy-in to math if they were given real world challenges that required research, creativity, analysis, and debate.

    Your descriptions of how Ss work at SLA keep me reading your blog! I agree that high stakes assessments should focus on things that Ss NEED to know to be successful citizens.

  3. I am not surprised in the least by the results. Heck, I work in a field that is regard as being very math heavy and I’d guess that the results of 50 randomly selected people that I work with would look pretty much like the results of the study in Rhode Island.

    For me it is a more of a sign of the overall mathematical illiteracy in the country than anything else.

    Interestingly, this is the second time this week that I’ve seen a blog discussing the results of the experiment in Rhode Island. I’ve done a quick google search to find the first article, but unfortunately can’t. The article quoted one of the adults who took the test and gave his reaction to a problem about two spinners. By strange coincidence, I’d just done an almost identical problem with my 9 year old a few days before:

    I don’t consider this to be particularly difficult math (I do consider it a good example for a 3rd grader . . . .), but, hey, there are lots and lots of successful people who aren’t going to see much math in their day to day lives, so they may very well indeed struggle with questions like this one.

    Oh wait, after a break, I found the article I was talking about:

    Anyway, I’d be happy to scrap any and all graduation exams, the SATs and any other standardized test. I think they are all silly, but that isn’t really my point.

    I don’t think math should be taught based on what people are going to use in their day to day life in the not-so-easy-to-define real world. There’s a practical side and a good, well-rounded education side to my point.

    Let’s hit the practical side first, and I’ll use the example of a mortgage. If you took 50 people you thought were successful adults – however you want to define it – how many of them do you think could correctly calculate the monthly principal and interest payments on a $200,000, 30 year amortizing mortgage with 5% interest? I’d guess not very many, but I’ll tell you a funny story – because I knew this math, I caught my bank cheating me out of about $30 / month about 5 years into my mortgage. Their computer program changed how they applied some payments. Surely it was totally accidental that the mistake accrued to their benefit (ha ha). This change was pure theft, but I’ll bet not 1 in 100 of the people they were stealing from in this way caught it.

    Take another example – pension and post retirement obligations. This is a multi trillion dollar issue in the US and one way or another the lives of millions of people are going to be impacted by how local governments deal with this issue. Hardly anyone understands the math or the accounting, though. Take this article here, for example, which is plenty objectionable but don’t get caught up in the politics – I want to only focus on one paragraph:

    The paragraph of interest is this one:

    “Few Californians in the private sector have $1 million in savings, but that’s effectively the retirement account they guarantee to public employees who opt to retire at age 55 and are entitled to a monthly, inflation-protected check of $3,000 for the rest of their lives.”

    So, not a policy question, or a political question, but purely a math question – what is the expected value today of a $3,000 per month, inflation protected check that will go to a 55 year old for the rest of their lives?

    It is a good question to work through. Again, though, I doubt that 1 in 100 adults would be able to do it correctly.

    Now back to the pure, well-rounded educational side. I’ll start with the quadratic formula. The Greeks understood how to solve some quadratic equations, and if my memory is right, the quadratic formula was pretty well understood when Fibonacci published Liber Abaci in the early 1200s. We wouldn’t be satisfied, I hope anyway, with teaching music, or literature, or history, or, well anything only up to the 1200s and I hope we don’t stop at the year 1200 with math. There are so many beautiful results since then. Those results led to remarkable discoveries in classical physics as Newton began to understand the world using calculus. The other incredible mathematical results in geometry and group theory helped people develop relativity and quantum mechanics. Set theory and, in particular, Cantor’s work on infinities in the late 1800s is one of the most beautiful intellectual achievements ever (read “The Mystery of Aleph” to get this story). There was amazing work done by Alan Turing in WWII, which, unfortunately, is a terrible story, but a good lesson nonetheless.

    I wouldn’t argue that kids should master this stuff in high school, but I would argue that they should be aware of it, or at least some of it. I learned a hint of it from a book of essays called “Bridges to Infinity” when I was a sophomore in high school. That book, along with “The History of Pi” and “Goedel, Escher , Bach” opened my eyes to the beautiful world of advanced mathematics. I wish all kids could learn some of this material – it would change the way people think about math for sure.

    In the mean time, though, I hope the fact that many nice adults in Rhode Island seem to be able to get along just fine without knowing much math doesn’t lead us to conclude that most math should be dropped from high school curriculums.

    • Tross – I don’t want to see most math dropped from the curriculum, although, I would like to see far more statistics taught than what we teach now. To me, it is simply this… what do we *require* kids to know before we say they can graduate, and its corollary – what are we judging schools on?

      Schools are becoming high-stakes testing factories to the detriment of learning. Let’s stop that.

      And while I can’t prove this, I think if we changed what we viewed as necessary for all students to master before graduating, we might actually find that more kids are excited to learn math without the threats currently associated with the test.

      • I really think all of the testing is a complete waste of time.

        Sometime in the late 90s I remember hearing that the University of California schools were going to drop the SAT/ACT requirements. Don’t know if that happened or not, but it seemed like a great idea to me.

        I probably don’t come close to understanding all of the various testing that goes on now and the associated pressure that puts on various kids. The fact alone that all the wealthy kids have access to tutors/programs/and other stuff to get ahead on every single one of these tests from K through 12 is enough of a reason for me to eliminate every single one of these tests.

  4. Pingback: Ask Better Questions | For Parents: On Learning and Education |


    Things always get better with time! The teaching profession has always suffered in the areas of recognition and compensation. As educators, we are driven by the results of our instruction. When we see a child succeed, we often say it’s enough. However, due to the overcrowding of classrooms and lack of resources, our jobs are becoming even more challenging. A slight increase in salary will motivate teachers to stay the course. Balance must be present for all parties involved in the educational process to benefit. We must speak to a larger audience. This is the only way to promote change.

  6. Chris,
    The Answer Sheet had a very neat piece, in which a parent wrote in that his son shouldn’t have to take chemistry and a chemist wrote back saying he should. It’s pretty good: Part one ( and the Response (

    I have some problems with the rhetoric. I think talk of “using this later in life” plays right into the “the only purpose of education is to get a job” nonsense. I never *thought* I would use geometry in High school, until I bought a house. I never thought I would care about biology until I started brewing beer. A goal of education is to introduce students to things they might not have encountered otherwise, and to only focus on strengths of students would be to do them a massive disservice.

    I don’t think you disagree with this, I think the point here is larger. But it always gets me worried when kids talk about “how will I use this later in life?”.

    • I don’t disagree with that at all. The caveat I’d say is that a good Geometry teacher would integrate architecture (like Caitlin does at SLA, actually) so that kids can see how what we teach relates to their world. Not everything has to be applicable for the rest of our lives, but I do believe we have an obligation to answer the question, “Why do we have to learn this?” with something better than, “It’ll be on the test,” or “You might need it some day.”

      There’s a world of knowledge and information out there. More than we can ever teach. We have an obligation to make sure that what we’re teaching in school has some relevance to the lives we lead, especially given everything we don’t teach.