Friday, July 25, 2014

Most popular posts from one year of blogging

The Math Switch began one year ago, in July, 2013. In that time, I have enjoyed sharing ideas on inquiry-based learning and on educational technology. In the last few months, I have been able to post regularly, at 3 Tuesdays per month. Over that time, the most popular posts have been:
  1. 9 Ways to Engage Reluctant Students, aka Tackling the Startup Problem 
  2. Harnessing Your Personality 
  3. Dealing with misconceptions, Part 1: Seven ways to handle misconceptions in the moment 
  4. Engage! 
  5. A Critical Examination of my Transition to Higher Mathematics course, inspired by Grant Wiggins 

Thank you to all who have stopped by to read the posts. A special thanks goes to those that have re-shared, or commented on the blog. 

Tuesday, July 15, 2014

An Introduction to 6 Apps for Quizzes and Polls

In this post, I discuss 6 apps and websites for quizzes and classroom polls. This is not a deep look, but I will tackle some critical basic features: the types of questions available, the kinds of resources that can be embedded in the questions, and what students or participants need in order to respond. All of these 6 apps are free, at least up to a certain usage level.

Readers may also wish to consult the comparison chart at (the chart dates from November, 2012), and to look at some of the information provided by Richard Byrne at and elsewhere on his site.
  1. Edmodo is a course management system, with quizzes and polls as embedded tools. Edmodo has multiple choice, true/false, short answer, fill in the blank, and matching quizzes, as well as multiple choice polls. Quizzes have a number of nice features, including the ability to embed links, video, images, and LaTeX (by enclosing the mathematics with [math]…[/math]). Polling is simpler, with just the multiple choice mode and no embedding. Students should have accounts and be set up in a class in order to use either polls or quizzes.
  2. Socrative has multiple choice, true/false, and short answer formats for both polls and quizzes. Quizzes can have embedded images, but not video or links or LaTeX (unless you create an image with LaTeX in it). Quizzes can be run as a game called Space Race, where getting answers right moves a rocket across the screen in a race with other participants. In a quiz, students can get immediate feedback on whether their answer was correct if the quiz is set up with the correct choices marked. Alternatively, if the correct choices are not marked, students do not immediately know if they responded correctly. Polls (“Single Question Activities”) can be run instantly, with no need to pre-load questions. In a poll, the idea is to set everything up without Socrative, and just use Socrative to collect votes of A/B/C/D/E, where the instructor can designate what each response means. Student accounts are not needed. Just recently, accounts have been switched over to Socrative 2.0. Socrative 2.0 adds a feature, Exit Ticket, which is pre-formatted with three questions: a multiple choice question about how well the student feels he/she has learned the day’s lesson, and two short answer responses, one a request to describe what was learned, and the second to answer the teacher’s question (which allows the teacher to pose a specific question, i.e., outside the app, in addition to the general one). 
  3. Google Forms are part of the suite of Google Drive tools. Forms support multiple choice, multiple correct, short answer, and fill in the blank. Forms can have embedded images, video, or links, but not LaTeX (unless you create an image with LaTeX in it, as I described earlier). Students do not get immediate feedback about the correctness of their answer choices. Auto-grading of the responses can be accomplished by installing the Flubaroo script in Sheets. Students do not need accounts. However, to get the maximum benefit from Flubaroo, it is a good idea to collect student emails in the Form.
  4. Quiz Bean is web-based, and not an app. It has multiple choice, true/false, and multiple correct formats. Quiz Bean supports embedded images, but not video or links or LaTeX (unless you create an image with LaTeX in it). Students get immediate scoring feedback as they progress through the quiz. Students need accounts and accounts should be set up into a class by the instructor.
  5. Quizlet is built more as a study tool. After setting up an account, users build virtual index cards and then practice quizzing themselves, matching the items in one of a few ways. The index cards can include images or text. 
  6. gFlash+ is similar to Quizlet in that it is designed for building virtual index cards. The “g” indicates that the index cards can be created from Google Sheets. There is no need for a gFlash+ account, but this app works best if connected to a Google Drive account.
Besides the ones listed above, there are many, many more. An incomplete list of them includes:
  1. Exit Ticket:
  2. Kahoot:
  3. Mentimeter:
  4. ParticiPoll:
  5. Poll Everywhere:
  6. TAPit:
  7. Flisti:
  8. Infuse Learning:
  9. Quiz Socket:
  10. Geddit:
  11. Top Hat:
I hope this spurs some ideas. There are so many ways to collect feedback from students!

Tuesday, July 8, 2014

Doing math on iOS

In this post, I describe my experience using various apps to do mathematical computations. This is focused on the kind of mathematics that arises in K-14 classes, and not research-level work.

Here is the list of iOS apps I have tried for doing math of various sorts on my iPad:
  • TI-Nspire CAS is the most valuable app for the iPad. Although it is pricey at $29.99, it is designed for extended exploration in a way that most other apps are not. This has been my go-to app in my work doing mathematical modeling (e.g., linear regression) with middle school teachers. Some of my favorite features include the ability to graph multiple functions or multiple regressions on the same graph and the ability to export files to Dropbox or elsewhere. The export feature allows me to input data to a spreadsheet and share it, thereby saving everyone else from entering data (and making typos).
  • Wolfram Alpha is versatile, as long as one is interested in looking at one object at a time. By this I mean that one can easily graph any function or set of functions, plot a data set and perform regression, or do standard calculations, but it is not possible to store the results within the app. Instead, it is necessary to take screenshots or copy-paste information to another location (Evernote, for example). The app also makes it difficult to edit information because it is not possible to scroll through a long command line that has been entered. On the other hand, if given an equation, it can show the steps involved in solving the equation. The app can also serve as a search tool to answer questions or provide information. The app requires an active internet connection at all times.
  • MyScript Calculator is a lot of fun for basic calculations. It transforms hand-written mathematics into typed math script and performs the calculations indicated. It should be noted that getting formatting correct is sometimes difficult, say if there is a rational expression with exponents in the denominator, but it works well for quick scratch calculations.
  • Geogebra is a spectacular app for the desktop or laptop, but the iOS app has a long way to catch up. What is missing are the settings. For instance, I have never found a way to use a non-square scaling, such as I might need for an exponential function, where the outputs grow much faster than the inputs. Neither does there seem to be a way to adjust the labels (e.g., to show the label on a function), or to display a table of values. Unlike the Nspire or Wolfram, Geogebra does not render 3-dimensional graphs. Still, the app is free, and is good for a lot of Euclidean geometry and 2-dimensional graphing, and it offers sliders for dynamic exploration as well.
The following are apps that I have used, but not extensively:
  • Geometry Pad uses the freemium model. I have used only the free version, which includes the ability to draw basic geometric objects. The premium version adds a lot of features, including the ability to do calculations, graph functions, and a lot more.
  • Sketch2Graph takes a hand-drawn graph, converts it to a plot of a linear or quadratic function or conic section, and outputs the equation describing the plot. The function graph can then be manipulated by hand. This enables some nice exploration of these graphs and the relation between the graph and the equation.
  • Algebra Tiles is designed for illustrating or manipulating algebra tiles in an app. The interface has three modes, basic, equations, and factors. This app works as a tool, and is not built to give practice problems nor does it show how to use the tiles. It does serve as a functional replacement for using actual tiles.
Readers, what have I missed?

Tuesday, July 1, 2014

Taking notes on iPad: Evernote, NotesPlus, and Notability

In this post, I briefly describe situations in which I find I need to take notes on my iPad, and the apps that I find most useful in these situations: Evernote, NotesPlus, and Notability.

There are two recurring situations in which I find I need to take notes with my iPad. The first is in meetings. In these situations, usually I am able to type notes as the meeting is happening. In this case, I use Evernote. Evernote is perfect for typing notes because I can open the app and start a note almost immediately. Occasionally, there may be a one-sheet handout as well. (Generally, if the handout is longer than one page, the presenter will share it via email.) I have scanned a number of handouts and the scans have been clear. In addition, items scanned into Evernote become searchable. Occasionally, someone hands out a business card, in which case I scan that in too. For certain recurring meetings, I have a particular notebook where I keep all my meeting notes, or I have a tag for the committee that I use to make sure I can find the note later.

The second situation in which I take notes is during class. In this case, I find I prefer to handwrite my notes, rather than typing, because I may need to write mathematics. Sometimes I am writing something that I want to share with the class, and other times I am making notes about what is happening during presentations or group work that I want to remember for later discussions or follow-up. This includes the possibility that I photograph student work and then annotate it. I use Notes Plus or Notability for class notes. I can recommend both apps. For NotesPlus and Notability:
  • Both can be backed up to Dropbox. 
  • Both offer an eraser as well as an undo button. 
  • Both offer a close-up box for writing. 
  • Both apps have always retained everything I’ve created. I have never experienced disappearing notebooks or pages.
  • Both apps offer a variety of pen thicknesses and colors as well as a highlighter.
  • Both apps offer the ability to add audio recordings to notes.
  • Line segments are handled differently. In NotesPlus, drawing line segments is integrated into the note. For instance, if I want to draw a rectangle, I begin drawing it, and it appears where I put it. Usually, NotesPlus auto-detects the line segments and gives me control points to adjust the placement of the segment. In contrast, in Notability, when drawing segments, the app takes me out of the space where I am working, and then I have to insert the line drawing back onto the page. When I insert the drawing, there is white space around it, so it feels like inserting a picture into a document. 
  • Typed notes are handled differently within each app. NotesPlus offers text boxes that can be inserted anywhere, whereas in Notability the options are to insert stickies or to move the cursor around on the page. 
  • NotesPlus has a built-in web browser, in case one is looking to clip information from websites to insert into notes, a feature not present in Notability. 
Together, this set of tools has really helped me get the most productivity from my iPad.