Posts tagged ‘math education’

Programming Is Not Math

Fun and interesting blog addressing the belief that mathematics is necessary for programming, a misconception that Nathan Ensmenger claims has reduced the percentage of women in computing.  Sarah Mei goes into some depth addressing (and dispensing with) each of the three claims below

Specifically, learning to program is more like learning a new language than it is like doing math problems. And the experience of programming today, in industry, is more about language than it is about math.And my next thought, of course, was why doesn’t anyone else think this? Why do we still have this idea that math skills indicate programming potential, while language skills mean you should go into poli sci?Well, when I feel out of my depth, I usually start by looking for “official” opinions. So I looked for relevant academic research.

I found absolutely none, which is pretty flabbergasting. I found a lot of opinions, both from computer science educators, and from people in industry. Perhaps within academia, the link between math and programming is considered such an obvious truth that it isn’t worth confirming with research.It seems more likely, though, that this research exists, but not under the search terms I tried. Please let me know if you are aware of relevant papers.In the meantime, if we can’t have data, we can at least examine the conversations people have on this topic. Here are some things people often say when asserting that people must be good at math to be good developers.Generally, they fall into three categories:

1. “You need to know math to be a good programmer.”

2. “You need to learn math to get the skills you need for programming.”

3. “Plenty of programming is still math!”

via Sarah Mei » Programming Is Not Math.

October 4, 2014 at 8:36 am 9 comments

Teach Real Algebra with Code: The Interdisciplinary Program Bootstrap #CSEdWeek

I got a chance to learn more about Bootstrap when Kathi Fisler visited us here at Georgia Tech recently.  This article doesn’t do a good job of selling the program.  Bootstrap is important for showing how programming can be used to teach something else that we agree is important.

“When you hear, ‘This is so amazing! These apps teach kids to program!’ That’s snake oil. Every minute your students spend on empty engagement while they’re failing algebra, you’re assuring that they’re not going to college. Studies show that the grade kids get in Algebra I is the most significant grade to predict future income.”

via GoLocalProv | News | Julia Steiny: Teach Real Algebra Instead of Wasting Time with Apps.

December 10, 2013 at 1:56 am 25 comments

More women pass AP CS than AP Calculus

Barbara Ericson has generated her 2012 Advanced Placement Computer Science report. has all of her reports. has her more detailed analysis just of 2012. Since one of our concerns with GaComputes and ECEP is on pass rates, not just test-takers, she dug deeper into pass rates.  For a point of comparison, she looked up AP Calculus pass rates.  What she found is somewhat surprising — below is quoted from her page.

Comparison of AP CS A to AP Calculus AB in 2012

  • The number of students that take the exam per teacher is much higher for AP Calculus AB at 21 students per teacher versus 11 for Computer Science A

  • The number of schools that teach Calculus is 11,694 versus 2,103

  • AP CS A had a higher pass rate than Calculus – 63% versus 59%

  • AP CS A had a higher female pass rate than Calculus – 56% versus 55%

  • AP CS A had a higher Hispanic pass rate than Calculus – 39.8% versus 38.4%

  • AP Calculus had a higher black pass rate than CS – 28.7% versus 27.3%

  • Calculus had a much higher percentage of women take the exam than CS – 48.3% versus 18.7%

  • Calculus had a higher percentage of black students take the exam than CS – 5.4% versus 4.0%

  • Calculus had a higher percentage of Hispanic/Latino students take the exam than CS – 11.5% versus 7.7%

July 26, 2013 at 1:39 am 1 comment

Attacks on mathematics education reform: If it’s on the Internet, it must be true

I recommend reading the whole sordid story below, of mathematics faculty decrying mathematics education reform efforts because they believe that it’s not rigorous enough.  The story is a familiar one to many who have tried to change education to be more engaging or improve retention.  I’ve certainly heard similar claims made about Media Computation (e.g., “If students are now passing MediaComp when they used to fail CS, then he must be lowering standards!  How else could he be getting students to stay?”).

A thread I found particularly intriguing in this story is the assumption by the critics that peer-review and publication are meaningless.  The only source for critique of the math ed reform in question is this one, never-published essay available on a Stanford FTP site.  One of the essay’s authors insists that it was peer-reviewed, just never published, because he never found time to make the corrections that he was required to make by the human research board.  In other words, it was peer-reviewed, found wanting, and he chose not to revise-and-resubmit.  In response to the quote below: Yes, if they couldn’t get it published, that fact does undermine its worth.

This is a rejection of academic standards — by academics!

Ze’ev Wurman, a supporter of Milgram and Bishop, and one who has posted the link to their article elsewhere, said he wasn’t bothered by its never having been published. “She is basically using the fact that it was not published to undermine its worth rather than argue the specific charges leveled there by serious academics,” he said.

via Stanford professor goes public on attacks over her math education research | Inside Higher Ed.

October 17, 2012 at 8:47 am 6 comments

IB reclassifies CS as an experimental science

Interesting: The International Baccalaureate program has re-defined computer science as an “experimental science” rather than as a “mathematics.”  Only a few states classify CS as a math or science for high school graduation, andGeorgia is the only one that (like IB) classifies it as a science.

The International Baccalaureate (IB) computer science course will be taught as an option in group 4, experimental sciences, from August 2012.

Computer science previously formed an option in group 5 of the Diploma Programme curriculum but now lies within group 4. As such, it is regarded as an experimental science, alongside biology, chemistry, design technology, physics and environmental systems and societies. This group change is significant as it means DP students can now select computer science as their group 4 subject rather than having to select it in addition to mathematics as was previously the case.

via Computer Science.

April 11, 2012 at 9:05 am 8 comments

Study: Some are born with math ability

The below links to the UPI story on this study, and the NYTimes just covered it, too.  The implications for STEM education are pretty interesting.  If you aren’t born with math skills, can they be developed?  Without that developmental effort, how well will the students without good number sense do in STEM fields? What other kinds of skills are critical for STEM learning, how do we identify them, test for them, and create developmental remediation if they are missing?

People can be born with good math skills, just as some are born with a talent for music, art or athletics, a U.S. study suggests.

Research conducted by Johns Hopkins University psychologists indicates math ability in preschool children is strongly linked to their inborn and primitive “number sense,” called an “Approximate Number System” — ANS.

via Study: Some are born with math ability –

September 1, 2011 at 4:09 pm 5 comments

New National Academies Report calls Science as important as Reading or Math

Interesting new report, which I think is probably more controversial than we might think.  The National Research Council is now saying science education is as important as reading and mathematics.  I don’t think that most people in the US will buy that. C.P. Snow’s Two Cultures are still alive and well.  There is a strong distrust of science in US society, as pointed out in the book Denialism:  Don’t get vaccines because they might cause illness; evolution is still an unproven theory; and humans are not having any impact on the environment.  I live in the South, where I heard a radio talk show just this last week about how the US “stifles” classroom teaching on creationism, and how other “more free-minded” nations (South Korea was mentioned by name) allow for classroom discussion that is critical of the “so-called science of evolution.”

Yes, we need more science education, but the adults that believe anti-science rhetoric are unlikely to agree that science is as important as reading or math.  Is this one of the barriers preventing CS education from taking hold in the US, that the anti-science bias extends to computer science?

State, national, and local policymakers should elevate science education in grades K-12 to the same level of importance as reading and mathematics, says a new report from the National Research Council. The report recommends ways that leaders at all levels can improve K-12 education in science, technology, engineering, and mathematics.

The report responds to a request from Rep. Frank Wolf (R-Va.) for the National Science Foundation — which sponsored the Research Council report — to identify highly successful K-12 schools and programs in STEM fields.

“A growing number of jobs — not just those in professional science — require knowledge of STEM fields,” said Adam Gamoran, chair of the committee that wrote the report and professor of sociology and educational policy studies at the University of Wisconsin, Madison. “The goal isn’t only to have a capable and competitive work force. We need to help all students become scientifically literate because citizens are increasingly facing decisions related to science and technology — whether it’s understanding a medical diagnosis or weighing competing claims about the environment.”

via Report Recommends Ways to Improve K-12 STEM Education, Calls on Policymakers
To Raise Science Education to Same Level of Importance as Math and Reading

July 12, 2011 at 12:44 pm 4 comments

Fear and anxiety over curricular change

Here in Georgia in educational circles, you often hear, “Thank God for Alabama and Mississippi!”  Because without them, we’d be 50th among the 50 states in educational standards.

Over the last few years, there has been a significant effort to improve standards and create a new, more rigorous curriculum.  It has parents up in arms!  “There’s no proof that this will work!”  No, there never can be .  Replicating another state’s program might work in the next context, but might not.  “My straight-A student is now getting C’s!” Now there’s the underlying issue.  When you make wholesale change, students have to adapt and teachers have to learn.  That kind of change is leading to exactly that kind of fear and anxiety in Georgia.

We’re not in exactly the same space with respect to Computing.  In most places, we’re not replacing anything.  However, replacing CS1 curriculum, among teachers (faculty) who have no incentive to change — that may be even harder.

Under the state’s new math curriculum, lower scores plus a quicker pace of instruction equal greater anxiety for both students and their teachers.

“In my classes, I have 60 kids and only 17 are passing. You know how stressful that is on me?” said Donna Aker, a veteran math teacher at South Gwinnett High School.

It’s a problem common to many metro Atlanta schools. Nearly one in five ninth-graders in metro Atlanta last year got an F in Math I — the first year of the state’s new math curriculum in high school.

via New curriculum: Math anxiety for students, teachers  |

May 25, 2010 at 7:56 am 3 comments

Wright and Wilson: But where do we learn literacy?

In Ant Lovers Unite! Will Wright And E.O Wilson On Life And Games : NPR, E.O. Wilson and Will Wright discuss (among other things) the future of education, which Wilson claims will be all about games.

So the first question he asked Wilson was if he saw a role for games in the educational process.

“I’ll go to an even more radical position,” Wilson said. “I think games are the future in education. We’re going through a rapid transition now. We’re about to leave print and textbooks behind.”

Wilson imagines students taking visits through the virtual world to different ecosystems. “That could be a rain forest,” he said, “a tundra — or a Jurassic forest.”

Wilson said that for the most part, we are teaching children the wrong way. According to the biologist, “When children went out in Paleolithic times, they went with adults and they learned everything they needed to learn by participating in the process.”

That’s the way the human mind is programmed to learn, Wilson said.

That’s a romantic vision, and I remain a big fan of apprenticeship approaches to education.  However, Paleolithic children didn’t have to gain literacy — in mathematics, textual language, or computation.  How do we, in an apprenticeship/game-like fashion, develop the ability to take advantage of the symbolic (and now, symbol processing) languages in which so much knowledge of our culture is stored?  Some learning is slow and reflective.

September 2, 2009 at 12:10 pm 3 comments

Fashion counts: Cell phones vs. Calculators

My advisor, Elliot Soloway, appeared in the Atlanta Journal Constitution this week, which made me proud. Education columnist Maureen Downey wrote a piece on “Cellphone as Teacher” in which she talked about Elliot and his quest to make cell phones into useful and powerful educational tools. The idea is to “capitalize on children’s natural affinity for technology and the omnipresence of cellphones.”  The article talks about how the cell phones might be used: “Students measured the area of a school hallway, recorded the geologic stages of the rock cycle and found mean, median, mode and range from a group of numbers. They sketched and even animated on the phones.”

My kids started school this week (Georgia starts waaay early), so I’ve been spending lots of time in Target and Office Depot picking up school supplies — including calculators.  Have you looked at calculators lately?  They are amazingly powerful!  A $30 calculator provides a list interface to input sets of numbers, and then does regression analysis and solves simultaneous equations.  The $100 calculator that’s required for the high school does graphing, animation, and includes a digital periodic table.  These calculators can easily be used for everything Maureen describes.  A $100 calculator is way cheaper than a cell phone plus minutes. There’s a huge amount of curricular materials for calculators, and the teachers now do welcome calculators into the classroom, unlike cell phones. Maureen quotes Elliot saying, “Now, we truly, finally have personal computers that are going to fit in our pockets.” Calculators have been there for years.

So why not push calculators, rather than cell phones?  They are cheaper, more powerful, the curricula already exist, and teachers already accept them.  I’m pretty sure that I know how Elliot would answer: you start from where the kids are.  Calculators are not cool, are not interesting.  They are out of fashion.  As Maureen’s piece says:

“Laptops are very ’90s,” says University of Michigan researcher Elliot Soloway. “They are your daddy’s computers.”

He might as well have said, “Calculators are very ’80’s.  They’re your grandfather’s computers.”

I think about that with respect to computing education (and the next blog post I’m planning).  I’ve argued that no student gets engaged anymore by seeing the word “Hello World!” appear on the screen.  In MediaComp, the equivalent of “Hello World!” is to open a picture and play a sound.  That’s a minimally interesting unit of computation.  But what will it be next year? In five years? In ten years?

In contrast, I look at my kids’ math books, and social science texts, and even science books.  I recognize the pedagogical methods, even some of the figures and diagrams.  There is change there, but there is also a sense for what makes education work.

Will we ever get there with computing education and educational technology?  Our field is so influenced by fashion, by the latest and greatest thing.  What’s cool engages. What’s out of fashion is rejected by students.  Why does fashion seem to influence other disciplines less?  Maybe it does influence engagement there, too, and not changing is a downfall.  On the other hand, there are lots of kids taking Calculus AP, and few taking CS AP.  Math Ed seems not to be a slave to fashion.  How do we get to the point where we can talk about computing education that works, period, and that we can keep using for decades?  Or does the continual upheaval in the field force us to always be on a treadmill of creating the next trendy educational technology or computing education initiative, none of which will last long?

August 14, 2009 at 11:31 am 3 comments

Aligning Computer Science with Mathematics by Felleisen and Krishnamurthi

The July 2009 Communications of the ACM has an interesting article by Matthias Felleisen and Shriram Krishnamurthi Why Computer Science Doesn’t Matter with the great subtitle “Aligning computer science with high school mathematics can help turn it into an essential subject for all students.”  The argument that Matthias and Shriram are making is that we can use programming to teach mathematics better, and help students learn both.  In so doing, we prevent marginalization of computer science and support an important goal of the American education system, the teaching of “‘rithmetic.”

It’s a good argument and one that I support.  I am dubious about some of the education claims made in the argument, like “we have already seen our curricular approach…help students raise their alebra scores” and “Formal evaluation shows the extremely positive impact this curriculum has…”  (I’ve been searching through the sites given in the article, but can’t find peer-reviewed, published papers that support these claims.)  But these are really minor quibbles.  Having written one of these pieces, I know that the tyrany of 1800 words is severe, and the authors can be excused for not providing background citations to the studies supporting their claims.  Instead, I’d like to provide some of the background literature that supports their claim.

Can we use programming to help students learn mathematics?  Absolutely!  Probably the most famous study supporting this argument is Idit Harel’s dissertation work on Instructional Software Development Project (ISDP). Idit had fourth graders write software in Logo to teach fractions to third graders.  She found that a real synergy occurred between the concepts of programming and the concepts of mathematics, and her students ended up learning more about both compared to another class.  Yasmin Kafai (who just moved to Penn from UCLA this last year) continued this project, exploring novel collaboration models (e.g., the fourth graders become fifth grade “consultants” as another cohort of fourth graders helps another cohort of third graders) and expanding from mathematics into science.  My own dissertation explored the synergy between physics and programming.  My results weren’t as strong — I had good physics learning, but not good computer science learning.  I suspect the problems were the challenge of making real learning in only a three week summer workshop, and not having the kinds of IDE’s that Matthias and Shriram are calling for.

“Our community must realize that minor tweaks of currently dominant approaches to programming won’t suffice.”  Completely agreed, and the best argument for this point came from Bruce Sherin’s powerful dissertation (with Andy diSessa at Berkeley).  Bruce taught two groups of students lessons in physics, one using programming and one using algebra.  (Andy would probably argue with Matthias and Shriram, “The ideal language and the IDE for imaginative programming are still to be designed.”  Over 20 years ago, Boxer implemented much of what they’re calling for.)  Bruce found some really interesting differences between what was learned via each form of notation.  For example, programming was better for figuring out causality and sequencing. An algebraic formula like x = x0 + vt leaves invisible to the novice that the t is what will typically vary in that equation.  On the other hand, algebra was better for understanding balance and equilibria.  A formula like F=ma works in both directions:  increase the mass or acceleration and the force increases, or if the force declines, then either the mass or the acceleration must have declined.  Most programming languages do not make evident how constraints work in the world.  The media extensions that Matthias and Shriram describe help address some of the challenges Bruce found when students had a single physics concept (e.g., an object moving because it’s location changed) being represented by multiple lines of code.

“As computer science educators, we must also demand a smooth, continuous path from imaginative programming to the engineering of large programs.”  Alan Kay has been making this argument for years.  He refers to the concept of Omniuser who can move from scripting in E-Toys, to changing how the levels close to the metal of the machine work, all with a single system and (hopefully) a single notation.  His STEPS effort is seeking to build such systems. In particular, Alan and his team are exploring “systems math” which is a kind of powerful mathematics that can only really exist in the powerful medium of programming.  Thus, STEPS gives us a way to go beyond just support “‘rithmetic” to support powerful new kinds of mathematics learning.

I’m a big fan of Scheme and consider DrScheme to be one of the finest pedagogical IDE’s ever created.  TeachScheme is a brilliant curriculum.  My guess is that careful studies of the effort would support many of the claims being made by Matthias and Shriram.  More importantly, though, I believe that they’re right that programming could actually improve mathematics learning.  Doing it in such a way that students’ mathaphobia doesn’t drive even more students from computer science is a real challenge.  An even bigger challenge is doing it in such a way that can gain the support of organizations like NCTM and that meets the mathematics standards in our schools. As they say, “Any attempt to align programming with mathematics will fail unless the programming language is as close to school mathematics as possible.”  It’s more than just the programming language — the whole package (curriculum, IDE, language) has to look and feel like mathematics to make it successful with the mathematics education community.

July 7, 2009 at 7:44 pm 4 comments

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