#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!

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Constitution Day – Math and Politics

Sam: It’s a private poll. The press doesn’t have access to it… The only way they’d know what questions were being asked is if they were actually called by one of the pollsters and… Oh my god!

C.J.: Yes.

Sam: A reporter got called by one of the pollsters?

Josh: Wow. What are the chances of that?

Sam: The chances of that are astronomical.

Josh: We can calculate it. They sample 800 respondents…

C.J.: Would the two of you stop being amazed by the mathematics!

(2001). The Leadership Breakfast [Television series episode]. In The West Wing. New York: NBC.

 

Last month the faculty at my college received the following in an email from our Academic Dean:

 

Hello Faculty!

With Constitution Week this week (Sept 15-19), and Constitution Day approaching next Wednesday, Sept. 17, it’s time for all faculty to plan a small segment of their classes, relating it to any aspect of the Constitution.

We do this every year as required by law. Since I don’t teach classes that lend themselves to this kind of activity I have to be more creative.

This term I’m teaching College Mathematics, which is math for non-technical majors. This is the only math class that some of these students will take. It includes discussion of algebra, geometry, statistics, probability and financial math.

This week we’re covering statistics. Based on my firm belief that you can find math in anything,I did a search on ‘constitution statistics’. It led me to the blog Introductory Statistics. I found a post titled “A Statistical Look at the Amendments to the United States Constitution”. It included a table showing the proposed and enacted dates for all twenty-seven of the amendments. I copied the data into a spreadsheet:

 

Amendment Proposed Enacted No. of Months
1 9/25/1789 12/15/1791 26
2 9/25/1789 12/15/1791 26
3 9/25/1789 12/15/1791 26
4 9/25/1789 12/15/1791 26
5 9/25/1789 12/15/1791 26
6 9/25/1789 12/15/1791 26
7 9/25/1789 12/15/1791 26
8 9/25/1789 12/15/1791 26
9 9/25/1789 12/15/1791 26
10 9/25/1789 12/15/1791 26
11 3/4/1794 2/7/1795 11
12 12/9/1803 6/15/1804 6
13 1/31/1865 12/6/1865 10
14 6/13/1866 7/9/1868 24
15 2/26/1869 2/3/1870 11
16 7/12/1909 2/3/1913 42
17 5/13/1912 4/8/1913 10
18 12/18/1917 1/16/1919 12
19 6/4/1919 8/18/1920 14
20 3/2/1932 1/23/1933 10
21 2/20/1933 12/5/1933 9
22 3/24/1947 2/27/1951 47
23 6/16/1960 3/29/1961 9
24 9/14/1962 1/23/1964 16
25 7/6/1965 2/10/1967 19
26 3/23/1971 7/1/1971 3
27 9/25/1789 5/7/1992 2431

 

I emailed a copy of the spreadsheet to my students. I also sent a link to an article summarizing the contents of each amendment.

I have two hours each week with my students to cover that week’s topic. The rest of the class takes place online. The in-class session on Monday night sets the groundwork for the entire week. I have two major topics to cover this week:

  1. Using graphs to visualize data
    1. histograms (bar charts)
    2. pie charts
    3. line charts
  2. Measures of central tendency, ie mean, median and mode

With the amendment data, we used bar charts to see how long most amendments took to enact (one to two years). This led to a discussion of outliers. For example, the 27th amendment took over 200 years to enact. We constructed pie charts to get another view of the distribution and to confirm our earlier conclusion.

But there is also a time element built into the data – proposed and enacted dates. When you want to look at data that occurs over time, you use a line chart (or trend chart). In this case, we aggregated the amendments based on the half-century during which they were enacted. When you plot that into a trend chart, you get an interesting view of the last two centuries of the United States. You can then correlate the lines with social, demographic and political data.

You can find math in anything, if you look hard enough.