High School Teachers Online Networking

I just wanted to pass along a link to a survey at the “An Old Math Dog Learning New Tricks” blog.  Lisa Henry is generating a Google Spreadsheet (is it a Google Drive Spreadsheet now?) of teachers Twitter usernames and a few other questions.  Seems like a great way to create an online support system.  Maybe if I ask she will add in a Google+ name!


Using Google Calender & Twitter on Your Class Website

I have been looking for a way to update assignments on my class website that would be very easy.  I was also hoping to figure out a way to update either Twitter or Facebook at the same time.  I was thinking that Twitter would be better because it seems that more students are using Twitter. Apparently all of the old people using Facebook has driven the younger generation away!

I told Lorraine what I was thinking and she suggested using ifttt.com. “If This Then That” is a website that automates actions on the internet.  So if I get an email from a certain email address a tweet will go out to the world.

The way I have it set up right now will hopefully make updating my website a little easier.  I create an event in Google Calender and have an email sent as a “reminder”.  This email triggers a Twitter post, and they both show up on my website.  I thought this would allow students/parents to check the website, subscribe to the calender, or follow my class Twitter feed.  All of these options and I only have to create an assignment once!

Here is one of the webpages on my site: http://joshmales.com/advancedalgebra.html  I don’t have much on it yet, but you can see how it will work.

If I post something to Twitter, it won’t show up on my calender. If I post something to my calender and have it send me a reminder, that gets posted to Twitter.

I did create new gmail and Twitter accounts.  The ifttt trigger will happen anytime a calender reminder comes in, so I didn’t want my “Take out the trash” reminder to be tweeted to my students!  I also created a calender for each class so that each calender doesn’t get crowded.

My plan is to update Google Calender at the end of the day with assignments and any up coming quizzes or tests. I’ll need to set the reminder to be emailed (you can make this default so you don’t have to do it every time you create an assignment.)  The subject of the email from the calender is what is posted to Twitter.

Here is the “recipe” for ifttt.com  You should be able to use this to create your own trigger.  The email address is the same for any Google Calender.

Let me know if you have any questions, or if you have suggestions for making it better!

Rounding Up Responses to “Is Algebra Necessary?”

The opinion piece “Is Algebra Necessary?“ in the NY Times on July 28 seems to have been written to stir up math teachers!  I won’t say much on it, other than to say that I think Mr. Hacker brings up the wrong issue.  I’m not sure that the traditional version of high school algebra is appropriate for most students, but I do think that students need to have a very solid understanding of a range of mathematical topics to be truly successful in a modern career.

While you should definitely read some of the comments after Hackers piece (there are well over 400 comments as I write this!), here are some responses that I thought are worth reading:

Probably my favorite one: “The Innumeracy of Intellectuals” on the Uncertain Principals blog writen by Chad Orzel.

Too innumerate” from the blog The Accidental Mathematician  written by Dr. Izabella Laba.

More Reasons to Learn Algebra” from the blog Wild Math written by Damon Hedman.

This one made me laugh:  ”The end of algebra” by Alexandra Petri on the Washington Post.

Between the comments and these posts, I should be ready for the inevitable “When am I ever going to need this?” on the first day of every unit!

Just Another Khan Academy Post

I was in the middle of writing about my own feelings and thoughts on Khan Academy when I saw someone else had done a better job than I  was doing!

The Washington Post has an education blog called the Answer Sheet, and they had a post written by Karim Kai Ani called “Khan Academy: The hype and the reality.”

Karim is a former math teacher, and does a great job of explaining why real educators have a problem with Khan Academy.

I will say that while I have problems with Khan being the great savior of math education, I do think his videos (at least the ones that are mathematically correct) serve a purpose and I have links to them on my class website for students that need help or just want to review.  This does make me realize that I need to have a discussion with my students and their parents about using these videos.

Does anyone have opinions on the videos at Brightstorm.com?  I generally like them better, but haven’t paid enough attention to say whether they are all mathematically correct.


Some Links

This is just a list of some of the math articles that have popped up in the last few week. I included the first paragraph from each.

Obama Aims to Develop STEM Master Teacher Corps by Erik Robelen- The White House today is turning its attention back to STEM education, as the Obama administration lays out plans to launch a national “master-teacher corps” to recognize and reward top educators in science, technology, engineering, and mathematics. The goal over four years is to identify 10,000 such STEM master teachers around the nation, the White House says.

Beating Back the Math Demons by Marilyn Depietto- “I just hate math so much! I’m so bad at it!” the student shouted. Leibnitz, Euclid and Pythagoras stared at him from their places on my classroom walls, and a small laugh escaped my throat at the surprising volume of his voice and the severity of his declaration.

Common-Core Writers Issue Math ‘Publishers’ Criteria‘ by Erik Robelen- The lead writers of the Common Core State Standards in mathematics have finalized a set of guidelines for curricular materials that seek to promote “faithful” implementation of the new standards at grades K-8. The 24-page document, to be published online today, is intended to guide the work of educational publishers in developing textbooks and other instructional materials, as well as states and school districts as they evaluate and select materials or revise existing ones.

Can’t we all get along? by Keith Devlin –  Unless you follow several mathematics education blogs or subscribe to certain Twitter feeds, you may well have missed the recent revival of the US Math Wars. The protagonists in the latest salvo are not the traditional foes, Mathematically Correct versus NCTM and MAA, but two groups who are making use of new technology in education, with Khan Academy squaring up against a number of web-savvy, younger mathematics and science educators who believe the US can and should do a lot better (and differently) in math ed than we do.

 Critique of Khan Academy Goes Viral by Katie Ash- By now, you’ve probably heard of Sal Khan, the educator who began by creating videos to explain math to his cousins, which has grown into a library of over 3,000 assorted educational clips with more than 150 million views on YouTube. The resulting Khan Academy, a nonprofit organization that aims to provide students with free access to all those resources, has received grant funding from educational philanthropy giants like the Bill & Melinda Gates Foundation.

Introducing Right Triangle Trig with a 10cm Circle

What better time to think about something new for next year!  I did this for the first time last year and I really thought it was an excellent intro to right triangle trig.  I thought I did a good job of showing the relationship between similar triangles before, but this does a much better job than anything I had done before.

Last year I was involved in a PD class called Project Prime that met 5 times throughout the year. The class was focused on geometry topics that integrate algebra concepts into the class.  This activity was probably the best thing that I picked up during these sessions and made all of it worth it.

This intro to right triangle trig using slope angles comes from Henri Picciotto’s website.  I have the links listed at the bottom to jump to certain portions, but it is worth checking out his website.

The idea is to use similar triangles and the slopes of the segments to introduce the tangent ratio (the name tangent doesn’t come up for most of it) and use the circle as a built in protractor to find angles.  I really like that this introduction brings up an Algebra 1 topic and really hammers home the idea of similar triangles, but I really love that it takes the mystery out of those crazy numbers the calculator comes up with for the tangent of 30 degrees.

Below is an image with two segments drawn in to use as an example.  For segment 1, I drew a segment through the 30 degree mark and found a slope of 5.8/10 or .58 (go ahead and check your trusty calculator…pretty close!).  Students would put this into a table to use to solve some problems using these ratios at the end (I have links below to find the worksheets that go along with this).  For segment 2, I drew a segment in that had a slope of 10/7 and found that it had an angle of 55 degrees.

I found that some students like to draw their segments to the edge of the circle and use that point to find the slope.  This works just fine, but I found it much easier to go to the rulers on the side and top.

In the directions, students are directed to label their circle with cm and degrees.  I decided to do this before I copied it for them.  I thought it wasn’t worth the class time to have them label it themselves.  I would recommend it because it does take awhile.  I also copied the text from the web-pages into a Word document and reformatted them, and changed the wording on some of the questions.

After seeing this activity I smacked myself in the head because it seems so simple, but I had never thought of it before.  I really think my students had a better idea of these “magic” trig ratios and their purpose.  While there were still some struggles with solving equations, inverse trig functions didn’t require much of a conversation because they made so much sense already!

We also took the next step and used this same 10cm circle to look at the sine and cosine ratios.  When doing this, I found it much easier to use the point on the circle (the radius of the circle is 1) to make the ratios a little more palatable.  I had some students that insisted on going to the side rulers, and they were happy to use Pythagorean Theorem to find the length of the hypotenuse.

I definitely recommend this as a way to introduce right triangle trig, but be sure to go through it yourself before jumping in with your students!

These links will take you to specific parts of Henri’s site:

Digital Textbooks – Some Hopes and Worries

It is no secret that I consider myself a “curriculum materials” person. I have always enjoyed using good materials and have been an advocate of not throwing out the book. However, I am also a proponent of learning to use curriculum materials flexibly. Doing this requires a lot of skills and without these skills I do believes that teachers may become “text-bound” which is what the anti-textbook folks are worried about.  In 1988 Ball and Feiman-Nemser wrote about how many teacher education programs were giving students the impression that if you were a good teacher you did not use a textbook, but created all of your own materials. I think that in many places this idea is still being espoused. I think that this is particularly important now as digital textbooks become more and more available. Now anyone can download iAuthor and create their own text. Although I am an advocate of teachers taking inititiative and designing their own stuff, I find this idea SCARY! This week, at NCTM,  I went to a presentation by Barbara Reys and Amanda Thomas from the University of Missouri who talked about the Promise and Reality of Digital Textbooks. One of the challenges that they mentioned in regards to digital textbooks is curriculum coherence. I have been at a few schools who have thrown out textbooks and have opted to do their own thing and I often found that without the time, support, and knowledge, these “original” curricula lack the kind of coherence that helps students understand the big ideas. With the advent of digital technologies I think we have the chance to enhance students’ experiences by embedding materials with things like applets, graphing and CAS utilities, Dynamic Geometry software, and spots for collaboration and assessment, but I wonder about the coherence of materials that may be designed by anyone and everyone. As someone who works very closely with those that design curriculum materials (and not those designed by big publishing firms, but ones that are designed by teachers and researchers) I know the endless time and eneregy that goes into creating and researching the effects of each and every lesson. Of course, I have a lot more to say about this, but I want to know what you think.

What do you see as some of the advantages and challenges of digital textbooks?


FluidMath Review

We have been having some technical difficulties over the past few weeks.  Basically we finally got tired of our old host and have been transferring our site over to a new host.  There were a few false starts getting WordPress working, but I hope we are all good.  This post has been ready for awhile, just waiting for things to be set.

I heard about FluidMath a couple of weeks ago and I had to try the free trial.  I played around with it for about a week and I really like it.  I’m pretty sure that I’m just scratching the surface, but I thought I would put a couple of videos up that show me messing around with it.

FluidMath allows you to hand write math (either on a tablet PC or interactive whiteboard);  it then interprets your handwriting and does the calculations or graphs the function (actually relationships, since it will graph implicit relationships as well.)   It does this all very quickly.  I thought it was pretty cool that you could go back in and change the original function and it would update everything on the fly.  You can also do some dynamic graphs with sliders, all very quickly and on the fly.

If you haven’t see FluidMath before, check out their video here: http://www.fluiditysoftware.com/index.php?option=com_content&view=article&id=27&Itemid=7

I was impressed at how easy it was to use and figure out.  The only time I really had trouble using it was getting it to recognize my handwriting a few times.  This really wasn’t a big deal, and after using it for 30 minutes or so I had corrected most of my mistakes.

As an example of the intuitive way that it works, I wanted to put a second graph on the same coordinate system and I wasn’t sure how to do it.  I thought it would be good if you just connected it with the first graph, so I tried it and it worked!

After talking to some fellow teachers at school about this program I went and looked at the pricing more closely.  When I was first checking it out I saw $75 and thought it wasn’t bad for something so awesome, but after looking again that $75 is for the subscription fee.  So I would have to pay $75 a year to use it.  This seems a little steep, but hopefully the price will drop after the company gets going.  I can’t imagine many districts putting up the money for a whole math department to use this, and if they did I would feel like I had to use it everyday!

Which leads to the question “Would I use it everyday?”  You can switch between math and drawing, so you can hand write notes that you don’t want to be turned into math and quickly switch to math input when you need to.  One thing that I didn’t look into is the ability to import Excel files, and I did enough to figure out you can copy and paste graphics into the file.  I use OneNote in class most of the time and I really like the ability to import PDF and Word files into the program to write on them, I’m not sure if you can do it in FluidMath.  I do like that FluidMath also uses tabs, this will make organization much easier.

Video recording is built in (well, after you download an encoder if you don’t have one already installed) which makes the whole flipped classroom a breeze!  It’s also nice to record a lesson for those absent students.  Although, you would have to figure something out for recording sound.

So I think I could definitely start using this on a daily basis.

You need to send an email to get your trial copy.  I was surprised to get a response from the CEO, and ended up having a little email conversation with him about FluidMath.  Turns out that they have been working on a Calculus enabled version and he let me try out a beta version.  I included some video below to give you a look.

I recorded these videos after playing around for about an hour, so they are not polished FluidMath use!  I thought it would give you a good idea of the learning curve necessary for this program.  I couldn’t get the actual video to embed, so the pictures are links to the video that are on our SmugMug site.

Above is a link to a video showing some of the basics.  I left some of my mistakes in so you can get an idea of how easy it is to correct those mistakes.

 This is a link to a video showing some of the dynamic graphing capabilities.

This is link to a video showing some of the animation capabilities of FuidMath.  It did take me a couple of tries to get this working correctly.  Once I figured it out I think I can reproduce it pretty quickly. 

A link to a video showing the Beta Calculus enabled FuidMath.  This is a recreation (I forgot to start the recorder) of the first thing I did when starting this program. I had played with the regular version for a few hours so I had some of the basics down.  

Sharing A Few Links

I thought I would share a few links to things that either got me thinking, or that I thought were cool.

This is a link to the video Inspirations by Cristobal Vila.  After watching it, check out the Maths portion.  This is another video by Cristobal, Nature by Numbers.  Here is the link to the Maths.  I think I saw these on Lost In Recursion’s Facebook page.  I haven’t had a chance to watch these in class, but I’ll be making use of them in my geometry class in the next few weeks.

I just found out about this software program called FluidMath today.  Watch the video demonstration and you’ll be amazed.  I really like teaching with a Tablet PC, and think that iPad’s just are not that useful for a classroom teacher.  Programs like this are the reason why I feel like this.  I am going to get the trial version to check it out, but it will definitely be worth $75.   It looks like FluidMath also works with an interactive whiteboard so it has some wider appeal.  I can’t believe I’ve never heard of this before, I feel like I’m up on these sorts of things…I totally dropped the ball.  Maybe I’ll blame the company for not advertising enough!  Yes, I think it’s their fault.  I’m also excited about the new Windows 8 Tablet/Slates that are coming out.  I think you can use any Windows program on them, and I’ve heard they have a digital stylus.  The chance to use this program with a little tablet rather than my big old tablet PC will force me to break open the piggy bank.

Onto something not as fun, but more thought provoking.  I read a blog post by David Bressoud about the President’s Council of Advisors on Science and Technology (PCAST)  report to President Obama on undergraduate Science, Technology, Engineering, and Mathematics (STEM) education.  I plan on reading the full report over spring break but I thought I would share the link now.  David’s summary got me thinking and could start some healthy arguments…I mean discussions.  I feel like the disconnect between college and high school math is pretty big, maybe this will mix things up.




45-45-90 Without Rationalizing the Denominator

I was at a conference this week that focuses on using algebra in geometry classes.  We spent a lot of time doing some activities developing the Pythagorean Theorem, and then started talking about the special right triangles.  Everyone seemed to be pretty used to creating an equilateral triangle to find the legs of a 30-60-90 triangle with a hypotenuse of 1.  I’ve started using a similar thing for the 45-45-90 triangle that a number of people seemed to really like, so I thought I would share it.

The idea is to avoid the need to rationalize the denominator when finding the legs.  I’ve never been convinced it is really a worthwhile frustration for freshman and sophomores in high school.  So here we go…

Start with your triangle with a hypotenuse of 1 unit:

Create an isosceles triangle…

Notice that your isosceles triangle is actually a right triangle so you can use the Pythagorean Theorem to find the hypotenuse.

Students are usually quick to recognize that the leg of the original triangle is half the length of the new hypotenuse.

I’ve had much better success doing this rather than using x^2 + x^2 = 1^2.  I have also found it’s a great way to show that 1 / sqrt(2) and sqrt(2)/2 are equal.

Do you think it is worth the frustration of rationalizing when we generally stop caring about it once a student gets to Calculus?