#MathEd – Math for My Nephew

A while ago I was asked to provide some resources I use to teach math for my nephew (well, nephew-in-law). I decided to gather them together into a blog post and thus get a two-fer.

Associations

Mathematical Association of America (http://www.maa.org/) – Their stated mission is “to advance the mathematical sciences, especially at the collegiate level.” Membership is open to students and teachers (K-12 and college), starting at $35/year (student with proof of status) and going up to $249/year (Member Plus). I’m a member and for me the real value of membership is access to a wide range of publications plus discounts on books, both e-book and printed. (Disclaimer: I currently write book reviews for the MAA web site but I am not compensated.) You can follow them on Twitter at @maanow and on Facebook as maanews.

National Council of Teachers of Mathematics (http://www.nctm.org/) – Like the MAA, the NCTM offers memberships to students, teachers (primary through college) and to organizations. They also offer the option of an ‘e-membership’ at each level for a slight discount. Membership annual dues range from $44 (Student and Emeritus) to $144 (Full Individual Membership). Membership gives you access to a host of instructional materials, NCTM’s ‘e-standards’ and NCTM’s E-Seminars, 60 minute on-demand video presentations on a variety of math education topics. You can follow them on Twitter at @NCTM or on Facebook as NCTM Illuminations.

Blogs

Math with Bad Drawings – This is one of my favorite sites. Ben Orlin provides an entertaining and educational view of math from a teachers perspective. The title comes from each post being illustrated by a series of stick drawings on a whiteboard. I wrote a review of his site here. I’ve used some of his posts as jumping-off points for discussions in my math class. You can follow Ben on Twitter as @benorlin. He’s also on Facebook but doesn’t appear to be too active.

MathBabe – Cathy O’Neil is a former Wall Street quantitative analyst who left for the wilds of higher education. She mainly blogs about Big Data and math education in higher ed. I wrote a review of her site here. A smart, interesting, fun site. You can also follow Cathy on Twitter.

Finding Ways to Nguyen Students Over – Fawn Nguyen is a California math teacher who has one of the best math blogs I’ve seen for primary and secondary educators. She clearly works hard to present math to her students in innovative and entertaining ways and she shares these techniques on her blog. (I wrote a review of her site here.) However, the real hidden gems of her site for educators are the affiliated sites like Visual Patterns, Math Munch and Would You Rather. These sites are a treasure trove of fun math problems and exercises you can share with your students or work on your own.

The NRICH Project – Not a blog per se, but The NRICH Project was started by the University of Cambridge, according to their “About” page:

“to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.”

(More here.) The content is divided into material for teachers and students. Each category is further divided into primary and secondary education. The idea is to present tasks that target multiple learning styles. These are known as “rich tasks” and you can get more information about them from this article.  Teaching materials are printable and downloadable for ease of use. You can also follow the NRICH project on Twitter  and on Facebook. You can sign up on their mailing list to get updates. They also provide a guide for parents and caregivers.

Project Euler – Also not a blog but a cool site for more advanced math fans. (Yes, there are some of us out there.) It’s a collection of almost 500 math problems, some of which may require basic programming skills. Each problem builds on insights gained solving previous problems so I advise doing them in order. I’ve posted a few of the problems on my site. Working on the problems presents interesting insights and is definitely mind-expanding.

Videos

NumberPhile – This is a nice resource of short, entertaining videos about specific math concepts. I do a short segment at the beginning of my classes called “Math Minute” and I’ve used several of these as inspiration for material. You can also follow them on Twitter and Facebook.

ComputerPhile – Not strictly related to math, but computer science is based on math. Similar to NumberPhile, ComputerPhile provides short videos about topics like undecidability, cryptography and how computers use math to do animation. You can follow them on Twitter or on Facebook.

I’m always looking for good math resources, both for my classroom and this blog. If you have any interesting leads, post them in comments!

#WeHateMath Blog Review – MathFiction

MathFiction is not strictly a blog per se but it’s unique enough that I felt it deserved a shout-out.  From the site description:

 

Do you like fiction and mathematics? Are you looking for a book or story that might be useful for the students in your math class? Are you interested in what our society thinks about mathematicians? Then you’ve come to the right place. This database lists over one thousand short stories, plays, novels, films, and comic books containing math or mathematicians.

 

The list is maintained by Alex Kasman, who teaches in the Department of Mathematics at the College of Charleston. I came across this site when I was doing some research for a blog post about using calculators in math class. I was trying to remember an Isaac Asimov short story that I had read which described a future where nobody is taught arithmetic any more since it’s all performed by machines. (“The Feeling of Power” [1957]) A brisk search of the Intertubes brought me to MathFiction and I was so impressed that I bookmarked it for my classroom tool kit.

You can browse through the material at your leisure or, if you have something specific in mind, use the search page, where you can either use the site-specific Google keyword search or power-search by author, title, summary, medium, genre, topic or motif. Entries are also rated by both math content (1 to 4) and literary quality. (You can search on these fields as well.)
As both a nerd and a math teacher, I have a feeling that I’ll be spending a lot of time on this site. So head on over there and tell Alex I sent you. (I’m trying to start a thing.)

#WeHateMath A Better Way to Teach Math?

Ever since I started teaching math, I’ve been trying to figure out why so many students (and non-students) seem to have problems with it and what I could do about that. With that in mind, I’ve been trying different techniques to see which ones are effective.

The first one was what I call the “Age of Aquarius” technique. It usually has me saying things like “Math is the secret language of the Universe” and “We’re all made of math” in an attempt to engage student imaginations. Unfortunately these work best with an audience that is already receptive and math classes are generally full of people who want to be anywhere else. As a result, saying these things makes them think that either you are high or you’re trying to make your job sound more interesting than it is.

I call the second method “Eat Your Vegetables”. This consists of explaining how learning math is good for you, usually by citing the Stanford Medical School study that showed improved brain function from the very act of learning math. In other words, even if you never use this stuff in your real life, it’s the mental equivalent of CrossFit. This also fell flat, being a bit too abstract for a group that just wanted to get through the class with a minimum of effort.

I decided to tackle this from the other end. I wanted to find the source of this distaste for math. I’ve always felt that hate is a fear-based emotion so if I can lower the general anxiety level in the room, I should get better responses.

One technique I used was to use tools to handle the mechanics of problem-solving. For example, whenever convenient I encouraged the use of calculators once the math portion of the problem had been processed. (If you understand the math well enough to explain it to a machine, this is a good thing.) For statistics, I showed how to use spreadsheets to quickly and easily observe the effects of different sample data on results as well as how to create different types of charts to visualize the numbers. For probability, I brought in decks of cards. I used a drawing program to sketch out problems and scenarios.

I also tried to minimize the use of jargon during class. While it’s useful to have a common vocabulary, I wanted students to pay more attention to the relationships and patterns than to worry about coming up with the correct terminology. We introduced terms as needed but it was okay if they had to use a few more words to explain what they were talking about or if they had to draw a picture or diagram.

This was the first term I used these techniques so it’s early days. But my last class session was today and overall I feel quite positive. Several students have remarked that this was the best math class they’ve ever had and my retention rate was pretty good. For math classes, it’s not unusual for half or more of registered students to withdraw before end of term. Out of an initial class of twenty one, I lost just seven and of those, four withdrew before the start of the term.

All in all, a good start. I’m teaching two sections of the same class next term so I’ll continue to refine my techniques and report my data here.

#WeHateMath Math without Calculations?

I ran across a couple of articles that discuss something that I’ve been pondering (and talking about on this blog) for a while now. That is, teaching mathematics without requiring that students do the final calculations by hand.

Here’s the basic idea. Computation (formulating solutions to problems) is more important now than ever. However, since we have calculators, computers and even Web sites to crunch the numbers for us, doing the calculations by hand is out-of-date and should be de-emphasized.

This idea was recently promoted by Conrad Wolfram, the head of Wolfram Research, which produces the software package Mathematica and the math engine Wolfram Alpha. Here’s an interview with Wolfram where he describes his idea in a bit more detail.

I’m not saying this is a bad idea, but I can see that there are any number of ways for someone to take this in a negative way. It takes a while to think this through for those of us who (like me) were raised and educated in the traditional math curriculum.

I teach undergraduate math, so I’m always on the look-out for ways to improve my classroom content. That means that sometimes I use my classroom as a lab for a little empirical research.

For example, this term I’m teaching College Mathematics. This is a 100-level class aimed at non-technical students (we’re a career college) and my students are in a mix of majors like Medical Assisting, Graphic Design and Business Administration. The course description is as follows:

 

This course develops problem-solving and decision-making strategies using mathematical tools from arithmetic, algebra, geometry, and statistics. Topics include consumer mathematics, key concepts in statistics and probability, sets of numbers, and geometry. Upon successful completion of this course, students will be able to apply mathematical tools and methods to solve real-world problems.

 

So it’s essentially a course in functional numeracy. For most of these students, this is the only math class in their program.

I decided to test the theory that the thing most people who claim to hate math actually hate arithmetic. My personal opinion is that arithmetic is unnatural and mechanical (since the learning strategy consists of memorization) and that math places more emphasis on creativity, intuition and critical thinking. With this in mind, on my first day of class I did the following:

  1. Explain the difference between math and arithmetic.
  2. Set a policy of ‘no arithmetic by hand, unless it’s absolutely convenient’. (For example, I’m not going to grab a calculator to multiply 9 by 5.)

For each session, I start with a “Math Minute” where I present a short puzzle or thought experiment to get students thinking and discussing some math concept. For the rest of the period I discuss this week’s subject (I can’t change the text or the lesson plan). However, I keep the conversation focussed on concepts rather than calculation. When we work through problems, we spend most of the time thinking through the set-up and then use a calculator (or spreadsheet or Wolfram Alpha) to get the answer. (This is only for problems where the calculation isn’t obvious. See 2 above.)

As you can see, I haven’t made any big changes (evolutionary, not revolutionary). I still have to pay attention to different student learning styles, encourage group participation, share problem-solving tricks and all of the other classroom techniques I’ve been using for years now.

As expected, there was some resistance. I was taking an unusual approach by de-emphasizing those parts of a math class that are traditionally the focus. But overall the response has been positive.

Now I don’t think that all classroom math should be abstracted to machines. In my class, we still use decks of cards and dice to talk about probability, count floor tiles to think about surface area and lots and lots of whiteboard work complete with diagrams. The point is to get students to connect with math and I’m just shifting that connection to the problem set-up process and I’m a fan of whatever works.

 

#WeHateMath Blog Review – Finding Ways to Nguyen Students Over

Ever since I started this blog, I’ve been on the lookout for other sites that talk about math and math education. I’ve covered a couple before now, but Finding Ways to Nguyen Students Over is my latest crush. Fawn Nguyen is a middle school math teacher from California and judging by the tremendous amount of great content on her site, she has apparently discovered the secret of going without sleep.

Not only does it have some great classroom exercises but there’s a good, common-sense interview with a middle school teacher about Common Core and one of my favorite posts, entitled “Blessed”, where she shares a couple of lovely hand-written notes from her students. Here’s a quote:

I’m crying and thinking I should quit teaching because it can’t get any better than this — like quit while I’m ahead.

As if that weren’t enough, there’s a section known as Math Talks, where she shares student voices as they discuss a math problem. It’s great to see the different ways that students take to approach a solution and it’s a good reminder that everyone has a slightly different learning style. In fact, there’s so much available here that I’d encourage anyone to just click on over there and start digging. If you’re like me, you’ll come out hours later wondering where the time went and you’ll be a better person.

By the way tell Fawn I sent you. (Trust me, I’m trying to start a thing.)

#WeHateMath Blog Review – Math With Bad Drawings

As readers of this blog can probably guess, I’m very interested in math education. I teach undergraduate math and I’m always on the lookout for a fresh perspective. One such is the blog Math With Bad Drawings by Ben Orlin.

As the name suggests, it’s kind of hard to describe this blog with words. Each post is illustrated with photos of a whiteboard with really crude drawings (stick figures with giant heads and cartoon text bubbles) but together with the content it somehow becomes something quite sublime.

For example, his latest post is The Calculus of History, a contemplation on what sort of paper he’d assign to his calculus class. It begins with this line:

 

Forget the history of calculus. Write me a paper on the calculus of history.

 

Orlin then goes on a wonderful journey of pondering the implications of viewing history through a mathematical lens. Consider history as an integral, an infinite series, a solution to an enormous set of partial differential equations. It’s not a long piece but it’s poetry.

Not all posts are this philosophical. Some are downright funny. Consider The New Math Teacher (hint: he’s a TeleTubbie whose stomach plays Khan Academy videos), A mathematician is a machine for turning coffee into theorems (not to mention cookies into corollaries) and The Argue-About-Anything Club. He mixes these in with insights from his teaching experiences.

One in particular I love is 39 Ways to Love Math. Orlin went to a recent mathematics conference in Baltimore and put out papers, markers and the following invitation:

In one sheet of paper, capture why you love math.

Then he posted the results, creating a truly charming read as all of these very smart people try to communicate through words, pictures and sometimes equations their passion for mathematics.

So go over there and give his blog a read. Tell him I sent you. (He has no idea who I am, but I’m trying to start a thing.)

 

 

#WeHateMath #TheMelvinProject – Common Core Math Testing

Last week, Stephen Colbert did a bit on the Common Core called “Common Core Confusion”, which was both funny and painful to watch (like most good satire). He took a couple of questions from a Common Core math test and riffed on how weird and confusing they were. He was right, they were awkwardly phrased and asked for odd input from the student. (One of them told the student to write their friend a letter and explain the math problem to them.)

“Great!”, I thought to myself, “I’ve got a topic for the blog, ready-made!”  All I had to do was dig up some of those goofy questions and talk about them and offer perspective and then something something freedom + comedy. So I happened across a site that offered Common Core test prep and thought I had it made.

There was only one problem.

I actually read the questions and they were nothing like the ones that were presented on The Colbert Report. In fact, they were perfectly reasonable and written in a clear, understandable way. For example, this one from Grade 6 Mathematics:

 

The balance on your savings account is -50, which means that you have $50 of debt. A monthly charge increases the amount of your debt. Which of the following could be your new balance?

  1. 60

  2. 40

  3. -40

  4. -60

 

It turns out that the goofy questions that Colbert cited (and the ones floating around the Internet) are not Common Core questions at all. In fact, the Common Core standards do NOT specify how the subjects are taught. Every school district (or state or whatever appropriate local education body) is free to present the material in any way that they feel works best for their students. In fact, this is stated right on the front page of the standards document:

While the standards set grade-specific goals, they do not define how the standards should be taught or which materials should be used to support students. States and districts recognize that there will need to be a range of supports in place to ensure that all students, including those with special needs and English language learners, can master the standards. It is up to the states to define the full range of supports appropriate for these students.

So the questions that have been going viral all over the Internet are actually the result of really bad curriculum designers.

Now I’ve worked on curriculum committees. I’ve done course design. It’s a lot of work and you really don’t know if you’ve got it right until you’ve presented it to your students and get their feedback, both through their comments and how well they end up understanding the material.

The point (and I think I have one here somewhere) is that bad teachers are not the fault of Common Core. Bad course designers are not the fault of Common Core. Scam artists who suck up taxpayer dollars and deliver crappy materials and when caught, point fingers at Common Core have been around since before there was Common Core.


Yes, there are legitimate concerns with Common Core (and not a few illegitimate, insane ones). But what this recent brouhaha tells me is that national standards for primary education is just the beginning.

As Thomas Jefferson said:

“I know no safe depository of the ultimate powers of the society, but the people themselves: and if we think them not enlightened enough to exercise their controul (sic) with a wholsome (sic) discretion, the remedy is, not to take it from them, but to inform their discretion by education. this is the true corrective of abuses of constitutional power.”