Gamifying the Unit Circle

Introduction

Precalculus students must be able to evaluate trig functions quickly and easily in order for them to be able to handle later trig topics better. To assist students in that respect, throughout the years I have made sure that students compete in groups against one another in a game called UC Bowl. Below is a description of the game and how it is managed in class.

The Details!

• The class was broken onto three competing teams.
• Each team was allowed to have an ID sheet along with a UC chart.
• Everything else including calculators had to be stashed away.
• And each team was given a small whiteboard to write down final answers to shouted out problems.
• Each rounds will involve a different team member acting as the scribe who would write the answer and quickly raise the board when prompted by me.
• I am standing in the from of the room with a TI calculator and a rubber-head hammer as a gavel.
• The TI calculator runs a Trig UC program written by a former colleague of mine (Thank you Eric Kamichke.) The calculator draws random Trig or Inverse Trig questions for students to answer as quickly as I allow for time-wise in any given round.
• I hit announce the problem to be solved, hit the rubber hammer, the students begin solving the problem, I give a warning to write final answer, and then I hit the hammer once again to have the scribe raise the boar immediately.
• Delays in raising the board results in a zero earned by the group and a word answers leads to a zero as well. Right answers are awarded one point each.
• The scores are tabulated to keep track of the scores.
• Between rounds pauses are taken to allow group members to reflect and discuss amongst themselves.
• The winning group earns sweets and cool treats that vary from year to year.
• Below is a sample of images showing some of the items listed in the above bullets.

Table Set Up for a Group in UC Bowl

Another Group's Table Set Up for UC Bowl

More Table Set Up for a Group in UC Bowl

Scoreboard for UC Bowl after some additional rounds!

Final Scoreboard for UC Bowl after the last few rounds were played!

Closing Remarks!

• The engagements was wonderful by all teams.
• The competition was fierce and even one team emerged as the wild posse team. The members dancing whenever they score points.
• The team that came last had a good comeback in the second class day that the UC Bowl was conducted and they still have chances to redeem themselves.
• The importance of UC and knowing values of trig and inverse trig functions began to sink in as an important part of learning trigonometry.
• In later edition of the game, the trig ID sheets with its UC chart will be removed to allow students to do everything in their heads.

Final Note: Please, use the comments area to share your thoughts on this activity and what kind of games you engage your students in math to make their learning fun and competitive in a healthy way. Thank you

MTBoS Mission #1 Blog Post: Clickerisms & Conceptual Understanding of Mathematical Ideas

This blog is my contribution to the Explore MTBoS Mission #1 [The Power of The Blog] initiative by our good fellow math bloggers Tina Cardone (@crstn85), Julie Reulbach (@jreulbach), Justin Lanier (@j_lanier), and Sam Shah (@samjshah).

Specifically, this blog addresses "What is one thing that happens in your classroom that makes it distinctly yours? It can be something you do that is unique in your school… It can be something more amorphous… However you want to interpret the question! Whatever!" of Mission #1 as stated by Sam.

Clickerisms! Using a set of clickers (class response systems as some folks would call them and they are shown below), I have always challenged my students with conceptual questions that would enable them and me gauge their deep understanding of mathematical concepts. The process goes as follows.

* Clickerisms as Unit Starters: My students are required to read a given section/chapter prior to start of coverage and a set of of true/false questions are presented to gauge students' understanding of what they read. Following are examples of such questions that precede a unit on number sets for more questions (check #precalcchat posts where I put sample questions from trig.)

*** Start of 1st Clickerism Set ***

1.  Answer True or False. The sum of two irrational numbers is always irrational.

A)  True

B)  False

2.  Answer True or False. The sum of any irrational number with any rational number is always irrational.

A)  True

B)  False

3.  Answer True or False. The division of an irrational number and a non-zero rational number is irrational.

A)  True

B)  False

4.  Answer True or False. The square of an irrational number is always rational.

A)  True

B)  False

*** End of 1st Clickerism Set ***

Students work on these problems individually at first, commit their answers to the output area of their respective interactive notebooks (INB), then a rapid fire sequence of clicking of answer choices would follow to obtain a set of bar graphs that would show the distributions of students' answers to each of the questions. Students are then asked to discuss the questions, that had no consensus class-wide, with someone who answered differently than they did. An updating of students answers would ensue. If the new distributions reflect a consensus, then the said questions would be skipped for now and the rest of the questions would become a springboard for delving into the topics at hand in greater depth by me.

** Clickerisms as Lesson Pulse Checkers: After the above process is completed, new activities would start to guide the students' learning process of the related concepts. But, before the lessons are considered done, a new set of Clickerisms is presented to check how well the concepts that were investigated earlier are well understood. These Clickerisms are more like mini quizzes that are generally extracted from whichever textbook I use for the given class or I generate them from encounters with Mathematical Blasphemies (MB) in previous years. Since, I use Axler's Precalculus textbook, here is an example of such a Clickerism as it appears in one of my PowerPoint slides that relates to the same topic mentioned above. Notice the three follow up questions that include a final question that sometimes I have students click anonymously to help me gauge their feeling about their level of confidence in understanding the underlying concepts of the questions at hand, the processes that went in completing them, and the final outcomes. 

*** Start of Clickerism ***

*** End of Clickerism  ***

The Clickerisms are a consistent set of formative assessment tools that I use to ensure students' deeper grasp of mathematical ideas they have read about and then have worked on in class. 

Thank you for taking the time to read this blog entry and I hope it would provide you with a possible way of increasing your students' confidence in what they learned and your confidence in their deeper conceptual grounding in mathematical understanding. Please, comment and add suggestions that would improve my teaching and my students' learning.  

  

When Trig Meets Series and Sequences

Combining the ingenuity of one of the problems posted by Maths Challenge site, "Corner Circle" and the versatility of Desmos this problem led to further neat sub problems that end up connecting trigonometry to topics of series and sequences. Below is the link the investigation "Mr. Le Nadj! Desmoses "Corner Circle" Problem." 

Please, give this activity a whirl in your class and report back as to how it goes for your students. Thank you

Updated Unit Circle Investigation in Desmos

Once my students worked on Unit Circle Investigation 2, new cool things emerged that I decided to add to the first two investigations and committed them to Unit Circle Investigation 3 within Desmos. Please, check out this new investigation and provide feedback and how did it work for your students? Thank you

Unit Circle Desmos Investigations

I have just posted two Unit Circle investigations at desmos.com, Unit Circle Investigation 1 & Unit Circle Investigation 2.

Please, take them for a spin, assess their educational value, and then post some feedback in the comments area. If you use these with your students report back regarding its success or lack thereof. Thank you

1st #precalcchat Script

Thanks to my partner @untilnextstop, the first Precalculus Chat materialized tonight and this is the link to the chat tweets for anyone who missed them. Tweets about "#precalcchat"

Thank you to all who attended and contributed and we look forward chatting with you and other fellow Precalculus teachers in the following weeks at #precalcchat.

Invitation to a Twitter Chat #precalcchat

All Pre-Calculus teachers, instructors, and professors are cordially invited to the launch of a series of twitter chats that would address everything Pre-Calculus. The first chat is Thursday, August 22nd starting at 8:30 PM. 

Event Title: "1st Week Matters," & it will discuss topics such as syllabi, pre-tests, technology, TIs, opening activities, etc.

Event Time: Thursday, August 22nd starting at 8:30 PM

Event Hosts: @MrLeNadj & @untilnextstop

Event Sponsor: Global Math Department with Cool Initiative of @jreulbach

Event Twitter Location: #precalcchat

We look forward having you and happy new Pre-Calculus school year!