Tag Archives: Google

Survey Results: Pace of Class

I just did anonymous student surveys via Google Forms today and, among other things, I found this little nugget of info:

The pace of the class was…

Way too fast (I was constantly behind) 1 2%
A little too fast (I was behind a good bit) 24 41%
Just right. 27 46%
A little too slow (I wanted a little more challenge) 5 8%
Way too slow (I wanted a much bigger challenge) 2 3%


I’m pleasantly surprised by these results (not all of my students were present today, but this represents a majority of them).

What do you think we should be shooting for as teachers?

I believe that, if possible, all students should feel a little “pressed” and “stretched”. I’m actually shocked more students didn’t feel completely overwhelmed[1]. I think it depends on the student whether they should feel “just right”. The student who can really identify when they’re learning knows that being just a little “pressed” or “stretched” is “just right”, although I don’t know how many of my students have that acute an understanding of their own learning.

If I had to pick any two categories to get 87% of the votes in, it would be those two, so I am definitely pleasantly surprised by these results. I definitely have SBG to thank for helping me identify whether the class, as a whole, is able to “move on”.

Now time to see if I can push just a little faster next year (I was “behind” where I was last year, when I didn’t do SBG).


[1] Perhaps those are the same students who would not come to class on the last day of school? Or not feel like providing any feedback and just pretend to take the survey?


1 Comment

Filed under Teaching

A Better Law of Sines/Cosines Project

A while back I had students finding distances on our school’s campus using the Law of Sines and Cosines, and I made the point that I thought students appreciated finding things out that related to their lives a little more.  However, this activity still seemed superficial to me because of (1) the ease with which students could look online to find these distances (using Google maps and a latitude/longitude distance calculator can be surprisingly precise!–see below), (2) after finding 1 or 2 distances it got old fast, and (3) I’m pretty sure this is not how surveyors do it in the real world.

I was talking with the father of a student in my Precalculus class, who happened to be a farmer, and “finding the area of his land” came up somehow.  Now a good chunk of the students live on the reservation and so it is very, very rural.  One thing they have, however, is land, and a lot of it.  I realized that breaking polygons into triangles is a cool theorem, and one that has practicality in finding the area of a plot of land if, say, you wanted students to use the Law of Sines, Cosines, and the Trig Area formula for a triangle.

I’m going to start with the following warm-up and hope that students recognize the connection between the project and the warm-up (I may have to spell it out for some of them).

I decided to turn this into an individual project for the students and use it in place of a test, since this would probably interest them significantly more and would demonstrate a deeper understanding of how to use the equations than “apply it to this triangle”.  I’m going to hand them this sheet below, show them how to find distances on Google Maps via Wolfram Alpha, and then let them go.

I’m hoping that students will solve this problem in a number of different ways.  One way that came to my mind immediately was, after breaking the land into triangles, find all the distances using Google Maps, then use Law of Cosines to find an angle, and lastly use the trig area of a triangle formula which involves two sides and the included angle.  Of course, if students are familiar with Heron’s formula, they could jump to that, hence the requirement they use 2 of the 3 formulas (is that too false a requirement?).

Lastly, you’ll notice I’ve made accommodations for the “urban” and suburban students as well: they can measure the square footage of their house/apartment or even a room as long as it isn’t a rectangle.

Let me know what you think, and in return I hope to show off some students’ work!


Instructions for finding Distance using Google Maps and Wolfram Alpha

1) First you should find the place in Google Maps.  Right-click and select “What’s here?”  You should see a green arrow now on the location.  In the search bar it will leave some coordinates, which are the very precise latitude and longitude of the place.  Copy these coordinates.


2) Next, go to Wolfram Alpha, and paste the coordinates as follows (and shown in the picture below):

distance from (35.528149 N,108.654796 W) to (35.52855 N, 108.656035 W)

Make sure you change +/- to N/S or E/W otherwise Wolfram Alpha will simply plot them as points and find the distance.  You’ll have to go back to Google Maps to select the other point and find the other set of coordinates.


One cool thing that Wolfram Alpha does is gives the distance is a number of different measurements.  And I’m not just talking about m, km, feet, inches, etc., but it gives crazy ones like “times the traditional length of Noah’s Ark” or “about the height of the world’s tallest tree” or “Light travel time in a vacuum” or “Maximum distance visible from that height”.  Crazy cool, right?


Filed under Teaching

Choose-Your-Own-Adventure Video Response Form

I really want to try flipping my classroom for a while, but the huge obstacle is that not all of my students have internet access at home.  However, my smallest classes have a large enough percentage that I think it will work out: Physics and my advanced Precalculus.  It will be slow at first, and I won’t be creating all of the videos, but I do have an idea that I think will improve student interaction with these videos.

I’ve used Google Docs to create a survey for students to fill out after watching the video.  They first tell me how much of the video they watched and whether they understood it all, and based on that I either make them answer a question that they could only understand from watching the video, or I make them ask a question that they have because they were lost.  I am trying this first on my advanced students and we’ll see how well they interact with the form.

Here’s my website where I will direct students to go for HW.  The form is at the bottom of the page.   If you would like to interact with the form, here is a copy of my form that you can test out for yourself (or copy for yourself) which won’t interfere with my students’ responses on my website.  Here’s what the results look like on Google Spreadsheets:


Ultimately, I think it would be awesome for a whole video series to be “choose your own adventure” to help students out with misconceptions, but that would require a whole community of people dedicated to educating through online video and it would probably need to be supported financially by someone like Bill Gates, and I just don’t see any organizations around like that…

If you have suggestions for ways to improve the form, please let me know.  Thanks!

Leave a comment

Filed under Teaching