Monday, February 29, 2016

The Wrong Way to Target Math (Part II)

Andrew Hacker: Which graph wore it better? 

Now that we've summarized the Hacker philosophy of math education, let's get back to my issues with the most recent Andrew Hacker OpEd regarding his insults to AP Statistics. This is where I start to get angry.

Hold up, did you read Part I yet? If not: The Wrong Way to Target Math (Part I)

In the recent NY Times OpEd Andrew Hacker writes: "Calculus and higher math have a place, of course, but it’s not in most people’s everyday lives. What citizens do need is to be comfortable reading graphs and charts and adept at calculating simple figures in their heads." Let me start off by saying that I don't disagree with Andrew Hacker's concern with the general public's lack of numeracy and statistical literacy skills. I fully support the idea of people being able to read a graph, do some mental math, and having a good grasp of arithmetic. You can find no argument from me there. But, actually, most people do use Calculus daily, they just don't know it or think about it explicitly. [You step on the gas pedal, guess what happens? Just guess.] Where he loses me completely, though, is with the argument that people don't need to learn beyond his daft definition of everyday mathematics.

Hacker goes on to discuss what kind of math he thinks these everyday type people should learn. I start to get excited because I know what's coming, he's about to talk about statistics. Alright, maybe he can redeem himself a bit. Nope, the buzz kill that follows is his trashing of the AP Statistics curriculum. "The A.P. syllabus is practically a research seminar for dissertation candidates." Pump the brakes, you think these kids are ready to do dissertations? Awww, well maybe in your academic field they are.

Now, wait for it cuz it gets even sillier, his criticism comes from sitting in on a few AP Stats classes. Guys, that's the extent of his research it seems. Some anecdotal evidence, no meta-analysis, not even a lit review. Weak. Anyway, he's not happy at all because AP Stats is not about the 'citizen statistics' like he'd wanted. Nah kid, let's ignore the curriculum developed by real statistics educators (including my own statistics professor, by the way) with real statistics degrees and go with the retired PoliSci professor's plan. Because he thinks it's just too hard. Okay.

Here's where it gets really fun: "What’s needed is a facility for sensing symptoms of bias, questionable samples and dubious sources of data." Yes, Andrew Hacker, that's the kind of stuff we do in AP Statistics. He goes on to give a bit of an explanation about what he would teach instead, giving an example of his numeracy class (to be used with the chart above):
"One exercise focuses on visualizing data. I have the class prepare a report on how many households in the United States have telephones, land and cell. After studying census data, they focus on two: Connecticut and Arkansas, with respective ownerships of 98.9 percent and 94.6 percent. They are told they have to choose one of the following charts to represent the numbers, and defend their choice. 
The first chart suggests a much bigger difference, but is misleading because the bars are arbitrarily scaled to exaggerate that difference."
And that's it? Really? He's going to end the conversation there? I mean, I like that he uses accurate data here. (I checked; it's accurate.*) Spoiler alert: there might be more to this story! A skeptical, but fun person might comment about that Choice B graph: "I see that Connecticut has a higher percentage of households with phones than in Arkansas, but it doesn't look like a big difference. Is that a significant enough difference?" In that case, Andrew Hacker is the biggest stats tease there ever was if that's where he wants to end it. [To my students reading this, I promise you'll get to learn how to finish that story if you're skeptical.]

Oh, Andrew Hacker, that's great. (No really, I think that's a great activity. I like the use of real data. Crappy graph scales are a personal pet peeve of mine. I did essentially that very lesson last year on Day 1 of my AP Statistics class... because making appropriate graphs is part of the AP Stats curriculum, duh.) But AP Statistics ≠ AP Graph Reading. I know, I know. We'd like it to all be easy-peasy, but apparently Andrew Hacker missed the part where AP stands for Advanced Placement, not Stuff Kids Should Have Learned in Elementary School.

Real course evaluation question from my AP Statistics class last year. Notice the appropriate scale!

You see, statistics is about measuring variability, learning how to plan studies appropriately so that we can make solid conclusions from them, making decisions from data, and so much more. That's no easy feat. And this big kid stuff we do in AP Stats is challenging, sure. I'd be willing to bet that all the students in my AP Stats class would tell you they've been challenged by the material. That doesn't mean it's not a worthy challenge, however.

Hacker ends with this thought: "The assumption that all this math will make us more numerically adept is flawed... Perhaps this is because in the real world, we constantly settle for estimates, whereas mathematics — see the SAT — demands that you get the answer precisely right." Ok, so that moment there is how I know for sure that Andrew Hacker has no real grasp of statistics. (For how his understanding of math is lacking, refer to Part I of this rant.) You see, this is precisely how statisticians and mathematicians differ. In statistics, we do a lot of that estimation to which he refers. We don't mind if we're not super precise. In fact, we know that our estimates are likely wrong. We don't lose sleep over it. We don't because we can quantify the errors that we make. No one can be perfect, so we try to at least minimize those errors with regard to desired outcomes.

And, here's the thing... I am in disbelief with the argument that Andrew Hacker makes about this introductory level of college statistics not being useful or necessary for everyday people. I just don't buy it and, thankfully, neither do my students. I don't ever get the question, "Ms. Hogan, when am I ever going to need this?" Like ever. My students often come back to tell me how useful the course was for them. The use of the term 'real-world application' is on broken record in their open-ended course evaluations, even the whiners and ones who found the course to be really challenging. Many of my former students talk about how applicable the AP Stats class was for their college learning. By the way, not all are Math or Statistics majors. Some of them are majoring in less challenging things like Political Science.

More on that in the next installment of "Who Needs Political Science? Not Everybody" – The Wrong Way to Target Math (Part III)

* For the Stats people who want to play with the data, here's the actual Census data regarding the percentage of phones in U.S. households cited in the Hacker OpEd: Telephones: 1960-2000. At least it's accurate.

(Graphic from Hacker, A. (Feb. 28, 2016). "The Wrong Way to Teach Math." New York Times Opinion; accessed:; Jennifer Lawrence thumbs up gif from


  1. For all that I appreciate reading these -- and yes, it's both useful and cathartic to rebut such silliness -- I could do without the constant dismissal of other disciplines. One political scientist being a jerk doesn't mean anything about political science.

    1. I am not dismissing these other disciplines at all. That's kind of my point. Don't you find it even remotely a bit odd that a person with such a prestigious education and as many degrees as Andrew has, that he would somehow believe that the things we teach in AP Stats is dissertation material?

    2. I think what Ms. Hogan is implying is exactly what you are alluding to. If I were to walk up to the English professor in a class and say, "I hope you'll work with me because I have English anxiety. I always made straight A's in reading, but when we got to literature, I had a bad teacher so I just don't understand it," I would be laughed out to the classroom. It has become fashionable to denigrate and belittle the importance of mathematics to society as a whole with comments that would be outright insulting when said about another discipline. To say that a political science major needs only "basic citizen mathematics" classes is equivalent to saying an engineer needs only "basic citizen civics" classes that teach how to read a ballot and how to know which politician they like best. It's a ludicrous argument, but one that's accepted because people are proud to be "bad at math". (If you think I'm being dramatic using "proud", I think about the number of times you've heard people say "I can't do math" vs "I can't read".)

    3. This is EXACTLY the point. Why does math curriculum alienate so many people, so much more than other subjects? Why do so many students fail? Why do high school math classes leave so many people discouraged? The sheer number of students that either can't pass or painfully scrape by high school math requirements should be a red flag that perhaps standards are too high. Otherwise, who do we blame for high failure and dropout rates? Students? Teachers? Holding the attitude--as Ms. Hogan seems to--that students who struggle with math are just not as smart as you, is pretentious and ignorant.

    4. I never said students who struggle are not smart. Ever.

  2. No, but a meme that depicts shopping as opposed to doing something hard surely points in that direction, Ms. Hogan. Do I sound emotional? I am. I have a child that struggles every day to keep up with an advanced math curriculum in his high school while at the same time is unable to calculate a basic percentage off an item he would like to purchase. Why not get him the help to reinforce his basic math knowledge? Not possible if he wants to graduate from high school. No basic math classes count toward graduation in our state so every high school simply doesn't offer them anymore. It is sink, swim, or fake it if you want a high school diploma. No opportunity to reinforce basic skills that would perhaps allow him to master higher level math at some point. No opportunity to slow down and try to learn these concepts at different pace. How does that help our kids? No one is arguing for eliminating higher level math...I think most well-informed people understand that we need graduates with those skills. And in fact, I have other children that have benefited greatly from advanced math curriculums. But can we at least talk about options to help kids that struggle? Can we at least acknowledge that not every student will fit into the very, very tiny box that we have created in the US Educational system in terms of math curriculum? It is difficult to read posts such as this without feeling as if professional turf wars have become a higher priority than figuring out ways to best educate our young people. While we banter about credentials, educational expertise, and academic elitism, many of our kids are struggling and missing out. I know....I see it lived out every single day.

    1. Math Mom, I agree with your sentiment. The meme in my previous post is alluding to the fact that Andrew Hacker's comments suggest that people in female-dominated occupations don't need math. I guess you didn't get the parody there. You are saying your son is unable to calculate a basic percentage? For us in New York, that standard happens in middle school. So it's not directly relevant to what we're discussing as standards for HS math.

      When you say, "not every student will fit into the very, very tiny box that we have created in the US Educational system in terms of math curriculum?" Yes, most of us math teachers would absolutely agree with you on that. That's precisely why it's so important for this conversation not to be in the hands of someone like Andrew Hacker. It should be with math education professionals who have worked with students just like your son and understand how to best education young people. The need to help kids who struggle is exactly why we need to have a real conversation about the standards and expectations of students. I would like to point out, students who have difficulties in a certain subject still can benefit from learning it.

    2. And yes, I am aware that my sample size (n=1) is too small to matter much in statistics. He just happens to matter to me a great deal.

  3. Then what would be your suggestion? If Mr. Hacker is so off base, what would the real math professionals do to fix it? I am aware that basic math percentages are usually covered in the MS curriculum....that is exactly my point. What about the students who didn't keep up? What are the options for them? I am not advocating that he shouldn't learn math. Obviously, if we all learned only what we enjoyed, we would regularly shortchange the educational process. I guess I am just not hearing the real conversation that you say you are advocating toward. I am hearing a lot of name calling, a lot of picky criticisms while ignoring the main point, a lot of academic mumbo-jumbo that makes parents very skeptical of the "professionals" in the first place. Real dialogue, real conversations, real solutions would be a huge step forward.

    1. I agree with you! We teachers often feel weighed down by that very mumbo-jumbo that's been rammed down our throats. That stuff is enacted via public policies and federal/state mandates. Those mandates are too influenced by non-educators, people who are not teachers, people who are so far removed from a classroom. I would love a system with flexibility so that students and parents and teachers had more choice, especially in how we are assessing our students. Imagine my surprise when I had to fight to get a project instead of a test, for example, as a final assessment in my own classroom.

      There are no clear answers. But that very conversation amongst teachers is happening, all around the country. Parents can support teachers in this conversation. Our opinions are often disregarded or, worse, used against us in retaliation. Start by asking your son's school how you can help.