Blog #6

Use technology tools and resources, such as interactive whiteboards, graphing calculators, and math apps, to enhance teaching and learning.  There is a WIDE range of opinion when it comes to using various forms of technology in the classroom.  So let me be up front about where I stand right from the beginning.  I am a proponent of using technology if…

• It can help me be more efficient as a teacher.

• It can help students to grasp complex and abstract math concepts.

• It can make learning math more accessible (and maybe even a little more fun) for my students.

I do not use technology just for the sake of technology, or to show off some bright, shiny, new toy.  But if technology can help me be a better teacher and can help my students be better learners, I am on board.  I cannot begin to comment on all of the possible resources available to secondary math teachers these days, but I will comment on a few that I have used personally and that I believe fit one or more of the above criteria.

Interactive Whiteboard

I used a Smartboard about 8 years ago in my high school math classes.  It didn’t last long, however, as the school was moving to large touchscreen TVs that we could connect to through a toggle or HDMI cord.  At my most recent school, we had projectors aimed at the whiteboard, but also had screens that would lower in front of the whiteboard.  We connected to the projector through Apple TV and a control box in each room.  I share this with you to let you know that I have been around long enough to experience a variety of technology options for presenting my lessons.   Personally, I was not a fan of the actual interactive whiteboard (Smartboard).  My pen was always glitchy and it was frustrating to use.  (I realize it was a while ago and that the technology has probably improved.  I hope so for any of you who use a Smartboard now.)  I actually preferred the TV or the projector, especially when I got an iPad and could connect it to the device.   I would design slides containing notes, images, and the problems that we would be addressing in class.  I would create the slideshow on my computer so that I could utilize the full functionality of PowerPoint, such as transitions, design elements, links to websites or videos, etc.  I saved the lesson in my Microsoft 365 account.  Then I would connect my iPad to the TV or projector, open the PowerPoint app, and open the slideshow from my account.  What I loved the most about this set up is I could use my Apple pencil to write on the slides on my iPad, allowing me to face my students, rather than turning my back to them, as we worked through problems together.  For my multi-section courses, I would choose NOT to save the writing until the end of the last section.  When the last section was dismissed, I WOULD SAVE the writing, then export the slideshow as a pdf and post it on my LMS for students who were absent or just needed a second look.  Added bonus at the school with Apple TV, since there were no cables to attach to, I could hand the iPad to a student and ask them to write out a solution on the iPad.  My point with all of this is…you do not need an actual interactive whiteboard to use technology to present more interesting lessons.  You can take whatever you have access to at your school and use that technology to make your lessons more engaging for your students and more efficient for you.

Graphing Calculators

Handheld Calculators  A handheld graphing calculator is an amazing tool for allowing students to explore ideas and transition from concrete to abstract understanding of math concepts.  But students need to know how to effectively use this tool.  That is why I advocate for graphing calculators to be available to students starting in Algebra 1.  That DOES NOT mean that I allow them to use their calculators for everything.  I write most of my assessments in two parts, a no calculator part and a calculator part.  One reason is I believe there are certain foundational skills that students must demonstrate on their own, and there are more complex problem solving tasks where I want to assess a student’s thinking process, not their calculation skills.  A second reason is that I usually teach in schools that offer Advanced Placement courses as the highest level courses in a subject area.  If our goal is to prepare students for the AP courses in math, they need to practice taking tests that are partly with and partly without calculators, and they need to learn what the calculator can do and how to use it properly.  I believe that should start as early as Algebra 1 so that students are comfortable with their calculator when it comes to high stakes assessments.  I am personally most familiar with the Texas Instruments calculators (TI-84 and TI-Nspire).  As I mentioned in a previous blog, Texas Instruments has a library of calculator activities at education.ti.com that guide students through exploring and making connections.  The activity guides can be downloaded as Microsoft Word or pdf, so you can edit the Word document, if you wish, to meet your class goals and needs. 

Desmos (graphing calculator) If your students do not have access to handheld graphing calculators, I would recommend using Desmos.com (website or app).  Even as a teacher, using Desmos can have advantages over the handheld.  First, it is easier to display by projecting from your computer/iPad than the handheld.  Second, you do not need an account to use it.  However, if you create a free account, you get some additional features.  In the upper left corner, when you click on the three horizontal lines, you open a library of pre-made examples.  You can also save your own graphs and they will be listed in this library.  In the upper right corner, if you click on the arrow coming out of a square, you have options to share a link, print, export image, or embed whatever you have graphed.  If you choose to export, you can choose size of image, thickness of the lines, and whether to download as a PNG, SVG or Braille file.  This is super useful when creating worksheets or assessments and you need images of graphs.  Also in the upper right you have the help icon where you can learn about using features like sliders or tables.  There is also an icon for choosing your preferred language.  Just below these icons is a wrench icon that allows you to set the interval of values for the x- and y-axis, indicate the spacing for tick marks (including exact radian angle measures), and choose if you want grid lines, arrows, and radians or degrees.  One disadvantage for your students, however, may be using Desmos on assessments.  You will need to determine how comfortable you are with them using their computers on an exam, and, if allowed, how to do so with academic integrity.

Math Apps

Desmos (activities)  As a teacher, if you have an account for the Desmos graphing calculator, you can use that same account to access the Desmos activities at teacher.desmos.com.  I have mentioned the Desmos activities in previous blogs as well.  There are a wide variety of tasks like Marbleslides and Polygraphs (see last week’s blog) and much more.  What I want to talk about here is a bit more about why I think this website is so great.  You can set up classes on the platform and give students an access code for any activity you assign.  You have a dashboard where you can see all tasks you have assigned, by activity or by class.  You can also add co-teachers to any class to allow them to view and manage the activities.  When you as a teacher open an activity, you have the option to preview it as the students will see it.  At the bottom of many of the preview screens there is a tab for “Teacher Moves” and a tab for “Sample Responses”.  These will help you prepare for using the activity with your class.  Back on the main page of the activity, you can click on the assign button to assign the activity to your previously set up classes, or get a single session code that you can share with students as a one-time thing.  At the top of the main page, to the right of the title, you can click on the three vertical dots and choose to edit or copy and edit the activity.  I have used this if an activity was too long, or if there were questions that did not correspond with the focus that I wanted for that topic.  Finally, when you are ready to use the task with your class, click on the “Teach” button.  This will open up command central for you as the teacher.  On the summary tab, you can see every student who is signed in and how they are progressing.  In the teacher tab, you can see all of the students’ responses to any particular slide and can decide whether to show correctness of responses or not.  You can click on a student’s response to provide individualized feedback, and you click on student names to take a “snapshot” of work/responses you want to highlight. In the student tab you can see the same screen that the student sees (like it was in the preview).  In the snapshots tab you can see all of the snapshots you have taken for that activity.  In the upper left corner, you can pause the activity and control the pace at which students can progress.  My favorite feature in the Anonymize button.  This turns all of the students’ names into names of mathematicians, which allows you to show slides or snapshots without students necessarily knowing who’s answer is whose.  Every single activity has these features…EVERY SINGLE ONE!  And with the ability to edit as you like, it is an amazing resource.  Remember, although you can search within Desmos, the best way to find activities to match your topic is to go to a search engine and type the math topic followed by “desmos”. 

Geogebra (calculators & activities)  If you go to the website geogebra.org, you will enter a world of math and science applets that can be useful for helping students “see” the concepts they are learning.  This website also has calculator options.  If you click on the “Start Calculator” in the middle of the screen, you will be directed to the Graphing Calculator platform.  However, if you click on the Calculators drop down at the top of the page, you will have more options like a 3D calculator, or a Geometry calculator.  These calculators remind me more of the Geometer’s Sketchpad that used to be available years ago.  I think that makes it a bit too complicated for the general math student to navigate on their own.  But if you are into creating your own applets, or if you like guiding students through the process of manipulating these types of applets, then I highly encourage you to check this out.  This is not, however, what I use Geogebra for.  I use it for its pre-made resources.  Similar to Desmos, there is a huge library of applets already created that you can use in your class without needing to create an account.  If you click on resources, the applets are arranged by common core areas and only show grades 4 – 8.  However, if you search for a high school topic on the website, or in a search engine with “geogebra” after it, you will likely find applets that will match your search.  Different from Desmos, however, is that these are not set up as step-by-step lessons.  These are just visual representations of math concepts that you can use in your class, which can still be very helpful, it is just a different approach.

Socrative  Socrative is a platform that allows you to quickly assess students and provide immediate feedback.  It can be accessed through their website (socrative.com) or their app.  Teachers may sign up for a free account or upgrade to a pro account.  You are assigned a “room number” with your account.  This is how students will log in to your task.  You can create questions ahead of time to use with your students during class.  Or you can use “quick questions” that allow you to ask a multiple choice, true/false or short answer question on the spot and receive student responses.  The question sets that you create are saved on your Library page, but you can also explore other people’s tasks and question sets on the Discover page.  You can choose to interact with the questions as a “quiz” or a “space race”.  When you launch a quiz, you have the option to choose Instant Feedback, Open Navigation or Teacher Paced.  You can also choose settings like requiring names, shuffling questions, and so on.  Students can access Socrative on their computer or through an app on a smart phone or tablet.  They enter the room number and their name, if required.  Then they begin working on the task in the manner chosen by the teacher.   I particularly like the Teacher Paced format during a lesson, because I control how quickly students move through the questions.  I can also show results of each question (without names) so that we can discuss any misconceptions before moving on.  If you launch a “space race”, then you will choose settings for creating teams and working through the problems as a competition, with rockets on the screen showing each team’s progress.  When either of these tasks is finished, the teacher gets a results table to summarize how the students did.  If you launch the third option, an exit ticket, the students answer three preset questions:  1) How well did you understand today’s material? (multiple choice)  2) What did you learn in today’s class? (free response) and 3) Please answer the teacher’s question (free response – opportunity to ask a lesson specific question).  The exit ticket also summarizes responses in a table so that you can quickly check on student understanding and plan accordingly for the next lesson.  This is a quick and easy platform and students like the different approach to paper and pencil.  Great formative assessment tool to get and give quick feedback.

A Little Calculus  This is an app for phone or tablet.  It contains several applets with visual representations for precalculus and calculus concepts.  Each applet has directions for how to manipulate the graphs and images.  The app has A LOT of applets, including, but not limited to, 2D Graphing Calculator, Polar Curves graphing (and how it is related to a trig graph on a Cartesian plane), Transformations, Conic Sections, Trigonometric Functions (and how the graph on the Cartesian plane is related to the unit circle), Inverse Functions, Limits, Intermediate Value Theorem, Derivative of a Function, Mean Value Theorem, Antiderivatives (slope fields), Riemann Integral, Volume by Cross-Sections, Disk Method, Washer Method, Sequences and Series, Parametric Curves, Multivariable Calculus, and SO MUCH MORE!  If you have a way to project your phone or tablet for students to see, the visuals on this apps can be invaluable for helping students transfer concrete examples to abstract understanding.

ZipGrade ZipGrade allows you to grade multiple choice questions quickly and easily through your phone or tablet.  You will access ZipGrade.com on your computer AND with an app.  Teachers can create a free account which allows them to score 100 papers per month.  In this account, you can set up classes, if you like.  You will create a “quiz” using a 20, 50 or 100 questions answer form (but you can have fewer questions than answer spaces).  If you connect the quiz to a class that you created, you can print off “bubble sheets” that already have each student’s name and ZipGrade ID number on them.  This is helpful for getting more specific analysis of the quiz results after the papers are scored.  When you save the quiz, you are directed to the dashboard for that quiz.  This is where you will create the answer key.  This is also where you will see the analytics after the quiz is scored.  Once students complete their assessment and fill in the bubble sheet, the teacher can use the ZipGrade app on their phone/tablet to scan and grade the answers.  The results are stored in the app and on the website.  Then you will see the statistics regarding how students did.  Also on the dashboard page for a given quiz, you can explore options for setting up and scoring the quiz online.  If doing an online quiz, you can upload a pdf of questions that corresponds with the answer key, and students can then see the questions and click on their answers in a split screen format.  This is ALL on the FREE version.  There is a $6.99 pro version and the only difference is unlimited papers per month.  All other features are available on both the free and the paid versions.  I found this particularly helpful with AP courses where I wanted my students to practice taking multiple choice sections on their assessments in preparation for the actual AP exam.

Appointlet.com  This last website, Appointlet.com, is more of a productivity site than a math site.  I have found that many students are hesitant to approach me about setting up a time for extra help.  A few years ago I set up an appointment calendar so that students could sign up for a time without talking to me directly.  I only set up times when I was available, so they did not need to check with me first.  There is a place to tell me a reason for the meeting if they want to, but it is not required.  I can connect the Appointlet calendar directly to my Google calendar so that 1) the requested meeting immediately shows up in my Google calendar, and 2) the calendars sync to avoid double-booking.  I include a link in the signature of my email and on my LMS so that students can find it easily whenever they want to make an appointment.  Students seem to like this arrangement and are more willing to sign up to get help in this way.  If you are looking for a way to encourage students to seek outside help, this could be something to try.

I have mentioned a few other websites in my previous blogs, like NCTM’s Illuminations, Mathsbot.com, and Deltamath.com.  If you are interested in these and have not read my previous posts, I encourage you to check them out.

I realize that this is a long post compared to my other blogs to this point.  But I want you to feel confident with using technology in your math classrooms, especially if you are someone who has been hesitant in the past.  There are so many resources available these days, but that can be a blessing and a curse.  It can take a lot of time to preview new resources, learn how to use them, and start implementing them in your lessons.  Many of us don’t have that kind of time.  My goal with this week’s blog was to give you a variety of resources that I have used, that meet at least one of the criteria I outlined in the beginning, and that are relatively easy to use.   I hope I have succeeded and that you will choose at least one of these to try in your class in the very near future.  Email me if you need support or have any questions.  I am here to help!