I was reading the powerpoints that came with a textbook, you know, in the instructor’s packet, and I was already thinking this book was a little more focused on computation over comprehension for my liking when I came to the following learning objective:
“Compute an Analysis of Variance by hand.”
Are you fucking kidding me? I have given this a lot of thought and I have come to the conclusion, “Just, no”.
You know why? Because this is the year 2013 and we have computers. Now, I’m not saying you cannot compute an ANOVA by hand if that makes you happy. I’m also not saying you should be like my friend from graduate school who answered the question on her comps
“What is the multiple R-squared and how do you get it?”
“The multiple R-squared is the square of the multiple R and the computer gives it to you.”
I can tease her about this now because she passed her exams the second time around and earned tenure over a decade ago. Contrary to what you think at moments like that, not only WILL you live it down, you will go on to laugh about it.
There will be those who say, “What if your computer doesn’t work?” In that case, I think I’d have more pressing issues on my mind, like getting my computer to work. For one thing, I’m going to assume that you are not just finding sums of squares due to your complete absence of a social life but rather are part of some organization that has an interest in sums of squares, and also probably has more than one piece of hardware. In my case, if one computer doesn’t work, I have two more in my office and four more upstairs. Of course, one each is currently occupied by The Spoiled One and The Invisible Developer, but I’m pretty certain if it came right down to it, I could wrestle a computer away from almost anyone in this group and that includes the dog. (She’s a Dogo Argentino, in case you wondered.)
Take tonight, for example. I am very, very annoyed because my class is using the SAS Web Editor and for some unknown reason the site has been down for the past 10 hours. Apparently, SAS has concluded that no one would ever do homework late at night or on weekends so there is no point in having the On-Demand for Academics available.
I do have SAS on my desktop, but that would involve switching over to boot camp. I also have SPSS but again, that would require restarting in Windows which I don’t feel like doing because I’m in the middle of writing a lecture. I installed Office 2010 on my laptop, was dismayed to find that there is no longer a data analysis tool pack for the Mac – yes, I do know it quit shipping with VBA at 2008 – and the third-part stat pack doesn’t do much.
So, what is the conclusion? Well, I guess I’ll see if the SAS Web Editor is up tomorrow. If not, I’ll finish the class that ends this month and go on to finally learn R. I thought the Web Editor was a great idea but you can’t run a program in the cloud that goes down for 14 hours and no one in your organization seems to notice. One of the reasons I have stuck with SAS is that they do have really cool statistical procedures, their model selection procedures are a neat idea and there is generally an enormous legacy of good stuff. I thought perhaps by moving to a web-based model SAS could recover some of the market share it has been losing, maybe even have both something students could use while in school and a product they could use once they graduated by paying a monthly use fee like Adobe has for its Creative Suite.
Contrast this with pair.com which we use for things like email, our MySQL databases, running our PHP scripts. I love pair. They have 24/7 support and not by some person reading out of a manual, but a person who can actually help you. Downtime on pair over the last several years (that we’ve noticed), hasn’t been more than two hours, total, and when we called them, they were already aware of it and able to fix it in under 30 minutes.
In fact, we’re already migrating away from SAS and for small clients that can’t afford a SAS license and require basic statistics, writing their applications in PHP and MySQL.
There are two points here.
First, nowhere in this situation did I think,
“You know what I need to do? I need to start computing statistics by hand, using a pencil and a piece of paper, like I did when I was in graduation school in 1978.”
Second, using SAS is becoming as laborious as computing statistics by hand. Yes, it’s great if you have it installed on your desktop (and that is often a whole kettle of fish in itself), but that is often thousands of dollars per seat. The Web Editor is a great idea but if it isn’t available, it’s not so great.
Here are your choices – using something that’s thousands of dollars, use something that’s free but doesn’t always work when you need it or use something that’s free and you can download on your desktop. I don’t know that I’m ready to give up on SAS completely let but I have to admit that I see why so many universities have gone to R.
It’s that time of year again when we hear complaints about how terrible the U.S. is doing in math. This article by The Atlantic with the title American Schools vs. the World: Expensive, Unequal, Bad at Math is just one of many, many reports that showed up in my twitter stream.
The first question anyone who has had more than a week of statistics should ask is about the sampling. Didn’t anyone notice that the top “country” is not a country at all but a city. The article goes on to say “parts of China, Japan, Korea and Liechtenstein topped the ratings… ”
Wait, what? PARTS of China?
As a statistician, I am intensely interested in just how representative these parts of China might be. So, I track this down in another article, since many of those in the U.S. didn’t bother to investigate, I tracked this information on the demographics of the sample down from an article written for The Guardian by a correspondent in Beijing,
Its population is less than 2% of the country’s total, and its per capita GDP is more than twice the national average. According to Tom Loveless, an expert on education policy at Harvard University, 84% of its high school graduates enroll in college, compared with 24% nationwide.
I’m not saying that U.S. education could not use improvement. (Although the more I work with the Common Core Standards for mathematics, the more I’m convinced they have been over-hyped. ) What I am saying is that calls for improvement should be based on well-reasoned arguments that have some understanding of science – random sampling being a good start. It is also worth noting that the same article in The Guardian mentioned that 12 provinces in China had students take the test but only the results for one CITY were released.
There were also several articles that discussed Finland “slipping”, math scores 7 points, from 548 to 541. A lot of potential explanations and remedies were given in this Washington Post blog, sadly, none of which mentioned regression towards the mean, sampling error or the nature of the test itself. Also, there is the question of how much in absolute terms that difference really means. Children don’t answer 600 questions. They’ll answer a test with 50 or 60 questions which will then be normed to, say, a mean of 500 with a standard deviation of 100. That drop may well represent that the average child answered 43.7 questions correctly last year and 43.2 questions correctly this year.
Then, there are the host of articles that went on about how the sky is falling because countries that have low PISA scores are also those who do poorly economically and therefore China is going to eat our lunch. Don’t even get me started on correlation and causation.
All of this has led me to conclude that the PISA data are unclear on whether or not American (and Finnish) children are really doing that terribly in math, but have led to the firm conclusion that most journalists’ articles that I read could certainly use a refresher in statistics. (See how I did not generalize to all journalists in the entire world? Take note.)
In fairness, the very same Washington Post had another blog on how public opinion is being manipulated using the PISA findings. Is it or is it not an outlier? Discuss.
One of the questions I get asked a lot is
“How do you get so much done?”
I sometimes think that growing up without advantages can be an advantage.
For example, when I was a kid, I never had my own room. I always shared it with my sister, or sometimes my sister and my youngest brother. It never occurred to anyone to be quiet so I could get some sleep or study. In fact, I’m certain that if I had suggested such a thing at least two of my brothers would have been louder just on general principle.
I never had a desk growing up. I did my homework wherever I could find a spot to sit and be out of the way. Sometimes it was the dining room table, but just as often on my bed, sitting outside, or even in the attic. Since no one told me I was supposed to have a spot to study, quiet and a lack of interruptions, I was never bothered in the least by any of this.
For all of my life, I have been able to work anywhere and sleep anywhere. Darling Daughter Number 3 was in two Olympics. This meant that I spent an inordinate amount of my time for years sitting in bleachers while she practiced. Almost all of that time was spent grading papers, like tonight, or writing grants or doing data analysis. I spend countless hours in planes and airports every month. When the plane is taking off, I pull out articles I printed out to read for the latest proposal or publication I’m working on. When the plane hits 10,000 feet, I go right to writing or programming and can usually get four solid hours of work done while flying cross-country.
This isn’t the same as multi-tasking, really. I think the whole multi-tasking idea is a myth. I try having a conversation with someone while programming and it is usually a failure. I either miss what they are saying or delete a line I wanted to leave in – it’s not a good idea.
No, the secret to being productive isn’t always doing two things at once, it’s never doing nothing.
Waiting at the DMV, the Social Security office or on hold for some humorously named “customer service” representative, I can easily whip out 30 minutes of work.
Sure there is work, like a game design or coding that is best done in blocks of uninterrupted time. Guess how you get those blocks? By doing all of the 5- and 10-minute tasks, like answering that email or grading that paper while you’re waiting for your child to be done at practice.
This month, I’m teaching biostatistics for National University, and so far I am really enjoying it. There is just a really minor problem, though. While I received a copy of the textbook, I did not receive a copy of the instructor’s manual with answers to the homework problems. Since I am going to grade 20 people based on whatever I get, I need to be 100% correct in everything and it is taking up my time to computer Cumulative Incidence for the population, cumulative incidence for people with hypertension, population attributable risk - and I am busy.
So, check this out, and all of you epidemiologists, I am sure this is old hat to you …. I had a table that gave me the number of people who were and were not hypertensive and whether or not they had a stroke in the five years they were followed. I wanted cumulative incidence for those with hypertension, those without and the population attributable risk.
And here we go …..
DATA stroke ;
INPUT Event_E Count_E Event_NE Count_NE;
18 252 46 998
proc stdrate data=stroke
population event=Event_E total=Count_E;
reference event=Event_NE total=Count_NE;
All I need to do is create a data set where I give the number of people who were exposed, (in this case, who had hypertension) who had the event, a stroke, in my example, and the total number of exposed people. Then, the number not exposed (that is, not hypertensive) who had the event, and the total number not exposed.
I just invoke the PROC STDRATE giving it the name of my dataset and specifying that I wanted risk as the statistics.
In my POPULATION statement, I specify that for the population of interest, people with hypertension, the number who had the event was found in the variable Event_E and the total number was in Count_E .
In my REFERENCE statement, I give the number who had the event and the total number for people who were not exposed to the risk factor.
A lot of start-ups we know are not as fortunate as we are and they are looking for developers and having trouble finding them. Some have even tried to poach The Invisible Developer away from me, but they have found it impossible to compete with my offer of paying him six figures, letting him work at home in his underwear and having sex with him. (Every time I say this, The Spoiled One puts her fingers in her ears and chants, “La la la, I can’t hear you!” )
If you are looking for a software developer of your very own, here are a few suggestions from me and additions from The I.D. Stop thinking about what YOU need and start thinking what you might offer. Yes, you might be able to go on some random website and find someone willing to code for minimum wage. I guarantee you that the best people (isn’t that who you want by your side to change the world?) are not there. They already are working on other projects.
1. Pay decent money: I don’t care WHAT stupid article you read that said technical people are motivated by more than salary. Yes, there are is a threshold. If you came in and offered us each a million dollars to work for you today doing something like creating a replacement for SQL or a new operating system, neither of us would be interested. The key point is, though, we are already making enough money to live by the beach and shop at Bloomingdales with The Spoiled One. If people can’t pay their bills on what you are paying they will either:
- Quit your project for one that does pay enough that they can afford housing, food, clothes and Chardonnay, or
- Take another job to pay the bills and work on yours in their spare time, which will be very limited.
2. Have interesting work: The definition of ‘interesting’ is a personal one but anyone who is really good got that way because they were continually learning. In selling your potential developers, talk about how they will have the opportunity to choose the language, IDE, libraries, hardware, etc. they use to develop. Talk about the new things they could learn. Certainly, there will be some limits. At the moment we don’t develop for Linux, although we’d love to, because it’s not compatible with Unity. Both the I.D. and I have left six-figure jobs for other jobs because they weren’t fun. Note that I did not say we left to work for free. Fun only matters after the rent and kids’ tuition are paid (see #1).
3. Have perks: Like interesting, this is a personal definition. For some people, it is having flexible hours so they can spend time with their children. For others, it might be telecommuting. At The Julia Group, we know we can’t match Microsoft or Google in salaries and other financial incentives. We can offer you the flexibility to set your own hours, work from home, maybe buy you the exact hardware and software to your specifications.
4. Address a need the developer is passionate about: It seems most start-ups looking for a developer start here but I don’t know a lot of developers who do. This isn’t to say that I don’t know some great people who would like to have an impact on the world, but they first would like to pay the rent (Maslow’s hierarchy, anyone?). I know developers who are passionate about climate change, education, inequality – but really not all that many. I mean, they do care about those things but they aren’t any more likely to quit their day jobs and devote their lives to them than the guy who runs the car lot down the street from me. Your mileage may vary. I’m sure people I know personally are not a representative, random sample.
The Invisible Developer added this:
5. Hang out where the developers hang out: If you are looking for someone to create iphone apps, there are iphone developer forums. Lurk there and see who is asking beginner questions and who is answering them. In many forums, people will post if they are available and looking for work. If you’ve read a number of their posts, you might have an idea if you want to contact them or not.
6. Learn to code or at least a little bit about coding: I’m not saying you need to create your own operating system from scratch, but you ought to know the difference between a jpeg file and a website design, have some idea about how long it should take to code a web form (not very) versus a really good 3-D adventure game (the rest of your natural life – just kidding, sort of).
I was wrong.
Getting the pages in the game to all look alike was one of those tasks I put off until later, and maybe we would just hire someone to do it. Well, guess what, later has arrived. So, I spent a day reading Stylin’ with CSS (which rocks, by the way) . The main motivating factor was that I had to do some test questions for our game that match up to the type of items on the new computerized exams testing the Common Core curriculum. This means that I needed things draggable and droppable – no problem with jquery – but I also needed them laid out very specifically on a number line. I could have done this with the canvas tag, but really, css proved the perfect solution.
Not only was I able to use margins, relative positioning and float to get my objects on the page to show up exactly how I wanted them, but I was also able to do it so that I am pretty sure it will look the same in most browsers on most computers and not just my lovely cinema display using Firefox.
On top of this, I learned about the acronym tag which I could not believe I did not know existed before now. (Yes, I know it is an HTML tag but it was in a book on CSS I happened to be reading.)
In short, you do this
<acronym title="What you want to show up when you hover">The thing you hover over</acronym>
In our games, we use many words from the students’ tribal language. For example, for the game we are going to be piloting on the Turtle Mountain reservation this spring,
Nookomis says …
How was it possible I did not know this? Because I had the stupid idea that CSS was a woman thing and if you want to make money in life and be taken seriously you hire someone at a low salary to do the things that women do and you concentrate in other areas.
I was wrong about CSS and that was the second thing involving stereotypes about women that I was completely wrong about this week. The other one was a book on women in fitness. You can read about that here.
I’ve written about the challenges of finding a mentor previously, Why the cool kids won’t hang out with you.
Let’s be frank, if you are old and pumping gas, not too many people are interested in you as a mentor, but the last few years have been good here at The Julia Group, and the dozen years before that didn’t suck either. I’ve gotten millions in grants funded, started a couple of companies. Just this year, I have a new game out to teach kids math, published a book on martial arts and another chapter in a book on Real Talk from Real Women, was listed in Forbes as one of the 40 women to watch over 40 – and that’s nowhere near everything. It’s been wild.
The more successes I have, and the older I get, the more I am asked to serve either formally or informally as a mentor to younger people. This could be anything from hiring someone for their first job to looking over a grant proposal. Regardless, there are far more requests than I could possibly ever manage to meet.
I try to do as much as I can, in part because I did benefit from some wonderful mentors when I was younger. I also try to do as much as I can because I am well aware that I did not get nearly as much mentoring as people who came from more advantaged circumstances, and that I could have done more in my career, and sooner, if I’d had the benefits of more mentoring. (I can already hear my sister saying, “Christ! You have a Ph.D., company president, founded a start-up and won a world championships, what more do you want? President of Harvard? Secretary of State?” Maybe. That’s not the point.)
Reflecting on this, it occurred to me that there are characteristics that probably make it hard to find a mentor.
1. If you are the opposite gender of the majority of the senior people in your field, it’s harder.
When a younger person of the opposite sex shows an interest in someone they may be uncomfortable for several reasons:
- They find this person attractive and that is uncomfortable in general. Most people in their fifties really don’t want to be involved with someone 20 years younger.
- They are afraid this person finds them attractive and have the sense to realize it is only due to their position, and they are not interested anyway.
- They are worried that their colleagues will misinterpret the relationship and they care about their reputation.
- They are worried that their spouse/ significant other will misinterpret the relationship and want to keep the peace at home.
- The younger person subconsciously or deliberately flirts and tries to use their youth/ attractiveness to appeal to a mentor.
Sex is a part of life and railing about how it is unfair isn’t going to get you anywhere. The unfortunate fact is that it’s usually impossible to tell whether your failure to connect with a potential mentor is due to one of those factors or that they are just plain too busy. The only one you can do anything personally about is the last one. I’ve seen people get some mentoring that way, usually attractive women, but sometimes men in female-dominated fields. Even if it works to get you some attention from a mentor or two, though, don’t fool yourself that it won’t be noticed by your peers that you are almost literally kissing up to older men. There will also be potential mentors who are very put off by that behavior.
I don’t know if for some young people that is just the only experience they have of interacting with the opposite sex other than their immediate family. Here is my suggestion, when you meet a potential mentor, treat that person like the mother or father of a good friend. If you went home for spring break with your college roommate, you didn’t call their mom or dad “Honey”, you didn’t invite them out for a drink, you didn’t touch them other than to shake their hand and you probably didn’t wear anything your Grandma would not have approved of.
The other thing you can do to address points 2-4 is to get an introduction. If you call someone up and say your Uncle Bob or your advisor from graduate school, Dr. Schmoe recommended you talk with someone, they are a lot more likely to accurately interpret your interest and they are more likely to make time for you out of respect for Uncle Bob/ Dr. Schmoe.
2. If you grew up poor or in a minority community, it’s harder
There are two reasons for this. One is that you don’t have the family and community connections that will get you an introduction. You don’t have an Uncle Bob or a Dr. Schmoe who lives next door. The second is that your potential mentors are busy, and they are more likely to make time for people they hit it off with. Yes, I believe you are awesome, interesting, smart and hard-working. However, another fact of life is that we all have people will feel more or less comfortable around.
I have a daughter who just made a couple of movies and she is around a lot of what I call “Hollywood people”. They all talk about stuff that I know nothing about and could care less, who they were on this movie with – I almost never watch movies and I never know who any of these people are. They have had “work done” so they don’t have the same wrinkles, grey hair and scarred knees that I have. They ask me things like, “Oh, is that dress a Donna Karan?” and I answer, “No, it’s black.”
My point is that if I could pick any of those people to hang out with or you, I pick you. And there are some smart, hard-working, interesting people in that crowd, I am sure. They are just not the type of people I want to hang out with.
I will give you three recommendations for what you can do. First, try to fit in somewhat. I actually do own some things made by Armani, Steve Madden, Calvin Klein, Ann Taylor and Ralph Lauren that I try to remember to wear instead of my jeans from The Gap when I know I’m going somewhere to meet with people like that. There are more cutting edge, high-end designers but that’s as far as I’m willing to go. I’ve given up on the name-dropping thing. Upon being introduced, I just say, “Sorry, if you’re mega-famous and I’ve never heard of you. I’m a statistician.” That is usually all the explanation they need. Second, do get an introduction – from your faculty members, from friends of a friend. I have hired several people over the years because they knew one of my children.
Third – Ask! You are going to have to be more proactive. The people you want to mentor you are busy and they have lots of people asking for their help and advice. They are not going to seek you out. Ask for introductions. I work on two American Indian reservations. Over the years, I have hired or worked with people because a parent, aunt or uncle called me up and recommended them. Ask your family members, your teachers if they know anyone who is looking for an intern/ can give you advice on college/ career advice, etc. Ask for help. I get far more requests to co-author papers, review grants , hire entry-level employees and even meet for coffee than I could ever do – but I notice that the people who have the fewest mentors in their lives seem to ask for it the least, perhaps because they don’t realize that they should.
It’s past two a.m. so that’s it.
I’m looking forward to teaching my first masters level course in a lo-o-ng time next week. Since this may be the first course students take in their masters program, the question I’m faced with is,
“What would you tell someone at the very beginning of learning about statistics?”
I’m starting with this:
Bias = bad
Bias is to statisticians as sin is to preachers. We’re against it.
Bias is SYSTEMATIC error. While it is generally impossible to avoid error, in an unbiased study, error will be random.
Random = good
If error is random, we would be equally likely to err in one direction as the other, and so, on the average, would get the correct result. For example, if I was evaluating fighters to decide if they really did have brain damage as a result of being hit in the head too many times, in some borderline cases I might incorrectly decide the fighter was fine when, in fact, there was some minimal brain damage. In other cases, I might decide the person had damage, when he or she was just somewhat on the low side of the bell curve in terms of functioning brain cells. On the average, though, those errors should balance out and I should get the correct conclusion.
Random assignment is good because it means that people are equally likely to be assigned to one group versus another, so it is likely to control for confounding variables. What are confounding variables? Those are factors that may have complex relationships that distort the relationships found between your predictors/ risk factors and outcome variables. For example, people residing in nursing homes (my predictor) may be more likely to die (my outcome) but that might be because they are older or in poorer health (confounding variables).
Random selection is good because it means that everyone in the population has an equal chance to be selected, which means that, if you have a large enough sample, your sample is likely to be representative.
What’s a sample? What’s a population? What’s representative?
Well, we’ll get into that shortly.
But, speaking of random, I thought the most important thing to begin with was not how to find a mean or standard deviation but that bias is bad, because if you have bias, you are worse off after you found the mean than before you knew how to compute it. Before you didn’t have any information, you didn’t know the mean and you knew you didn’t know it.
With bias, you still don’t know the mean, but you think you do. You’ve actually gone backwards.
Think about it.
I am old. I remember punched cards, COBOL, dumb terminals and having to walk over to the computer center and load tapes on to the drive if I wanted to use large data sets – large back then meaning 100,000 records or more with a few hundred variables. We thought that was pretty big data.
So …. when I went to the Western Users of SAS Software conference this year, I was struck by the fact that I seemed to be about the median age. There were A LOT of people older than me. Most of the younger people were the student scholarship winners and junior professional award winners.
This does not bode well for SAS, and it made me a bit sad, because as I said in a prior post, the model selection procedures were cool, from a statistical perspective, there is a lot of good stuff from SAS.
I used to go to the user group meetings and they would give you a book (yes, on paper, children) that had macros written by SAS users. I think that was the first time I saw the parallel analysis criterion code for factor analysis – a macro I used in my dissertation and in one of the first articles I published.
Tonight, I was looking for a way to do power analysis for a repeated measures ANCOVA and I could not find it for SAS, neither using PROC POWER, PROC GLMPOWER nor any user-written macros. It may exist – I looked several other places as well, found a paper on how to do it using SPSS syntax (although that code did not work!) and someone else wrote a procedure in R that I didn’t try.
SAS used to be the place for the cutting edge. What happened?
One reason is that everyone used to use either SAS or SPSS at universities and that isn’t the case any more. A second is that SAS is really expensive, so universities who do not have a license aren’t inclined to get one.
This all sounds like the death knell is tolling for SAS and it is just a matter of time until it follows COBOL and Blackberry as one of those things that people ask, “Why are you using that?”
I think there is still some possibility for SAS to turn things around – although whether they will or not remains to be seen.
The smartest thing SAS has done in years is to come out with SAS On-Demand for Academics. This makes SAS free for university students and professors. It’s perfect for on-line courses because you can upload your data to the class website and all of your students can access it.
Now the next thing SAS needs to do is start making that available at a reasonable cost once students graduate. Instead of charging them thousands of dollars a year for a license, they can charge $50 a month like Adobe does for its design package or Google does for its apps. (Yes, Google apps for business are cheaper than $50 a month but they don’t do all that much.)
New graduates aren’t going to pay several thousand dollars for a license because they don’t have that kind of money. They might shell out $50 plus occasional extra charges to access some high performance computing capabilities.
SAS already has millions of lines of code and tens of thousands of pages of good documentation. It’s some good stuff.
Think about this – years ago, the Mac was considered a better computer than Windows but over-priced. Many people thought Apple would go under. Instead, they came out with the iPhone and the iPad and they are wildly successful.
The Web Editor and other cloud products could become the SAS version of the iPad.
Here’s to hoping they don’t fuck it up.
I was looking at one of the problems from the new common core assessment for mathematics at the fourth-grade level. To keep from being sued, I will change the numbers, but it looked like this:
1, 35_ -
The student is to fill in the blanks. I *suppose* that the question is designed to get at the student’s understanding of number concepts, that if you have 7 minus something equals 9 then that something must be 8.
Remember that part in Freaky Friday where the mom exchanges bodies with her teenage daughter? The Algebra II teacher is telling her that she will need this information when she is an adult and the mom-in-the-daughter’s body says,
I can guarantee you that I will not need this.
As someone who uses math every single day of her life, I can guarantee you that I will never need to solve a problem like the one above, unless maybe I decide to play Sudoku. I’ve never actually played Sudoku, so maybe it doesn’t help with that, either.
A few minutes ago, out of idle curiosity, I wanted to solve a problem that was (.01* 2**42)/(1E5)
It took me about 10 seconds. I used Excel.
This isn’t to say that all of the common core test questions are bad – they aren’t, nor that the the underlying idea of teaching fewer concepts with deeper understanding of each one is a bad idea – it certainly isn’t. It also isn’t to say that you can judge a test just by how good the questions look on the face of them (you can’t). It is to say that perhaps common core has been over-hyped as teaching real-world math and critical thinking skills.
Another example of this over-hype is the lauding the new tests for not having any multiple choice questions. Here is another, again modified to keep me from being sued for copyright infringement.
Drag the results less than 1 to Box A. Drag the results greater than 1 to Box B
| A |
| B |
Then you have a bunch of items like:
1 x 3/4
4 x 1/8
2 x 3/4
and so on.
Please explain to me how this is really different from:
1 x 3/4 is greater than 1
It might be a better question in that young children might be more amused by dragging and dropping the answers into a box and thus more likely to pay attention, but as far as revealing a greater depth of understanding of mathematics, I just don’t see it.