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.
