Critical Thinking on the First Day of School

By: Rachel Barry

Following up on yesterday's post on the ways teachers build relationships with and among students on the first day of school, I wanted to share a more in-depth look at my first day of classes.  

This past spring and summer, numerous math teachers around the district embarked on an opportunity to take a massive open online course (MOOC) from Stanford University called How to Learn Math for Teachers.  This course focused on how to change student mindsets towards mathematics, pedagogical strategies to promote active learning, and build critical thinking skills.  (Small plug...there were about 80 teachers across the district - math, science, special education - who took this course, and it was AWESOME!).  Prior to taking the class, I felt that I had a strong understanding of how to change the focus in class from grades to learning, however, this class gave me numerous more strategies to emphasize this more through how I communicate and how I create effective classroom activities.  Here are some activities that I did on the first day of classes to both build relationships as well as challenge students to think critically.

Would You Rather...?
In groups, I had students develop a "Would You Rather...? statement, one per group, and wrote it on their tables (see whiteboard tables here).  Then, the students rotated around the groups and voted at each table.  

In my AP Statistics class, I took this a step further and had students discuss the expected outcome prior to voting.  This is a key concept of statistics, so I loved being able to bring it up on the first day.  In this class, we continued the first day by performing a simulation where they worked in groups, getting to know one another, and getting introduced to statistics.

In my regular Algebra classes, I had the students calculate the percentages of tallies for each.  It was interesting to see the various methods that students used (proportions, decimals, etc) and whether or not the set up two equations or if they calculated one and then subtracted that from 100 to get the other.  We then had a class discussion on how many math problems can be solved using different steps or methods.  

This lead perfectly into my next activity...

Number Sense Activity
For this activity, I put this problem on the board and showed students how to solve this using traditional methods.  Then I challenged them in their groups to come up with FOUR other ways to solve this problem.  

Some students hit the ground running, while others sat back.  It was interesting when most groups got two right away (15 + 15 + 15 + 15 and 4 + ... + 4), and then they hit a road block.  Some students immediately started drawing (a grid of 15 x 4, four circles with 15 dots in each), and others sat back and observed.  Many students also separated or broke down the numbers (10 x 4 = 40, 5 x 4 = 20, 40 + 20 = 60 or 15 x 2 = 30, 15 x 2 = 30, 30 + 30 = 60).  The last method, though only two of my three classes saw it, was time.  

As groups were finishing up, I was having students share at the front of the board.  I have always struggled getting students (probably me coming up with excuses as to why it may not work) to do this regularly in class, so I decided to just start it on the first day, as a class norm.

I repeated this method with 25 x 7, and the students were much quicker, using other groups' methods.  Many students then saw the connection to money.

Rectangle Activity

For the next activity, I drew this figure on the board and asked students "How many rectangles are in this figure?"

Now that students were acquainted with one another, the brainstorming started much quicker.  In each class, after about a minute or two had passed, a student asked "Is a square a rectangle?"  YES!  Exactly what I'd hoped!  We then had a (short) discussion about the importance of asking questions and challenging me throughout the course by asking "Why?"  Then students continued working.  It was very cool to see students using colors, breaking down the figure, etc.  (If you want to know, there are 18!)

Fractions Activity

The last activity was for me to formatively assess students' prior knowledge of fractions.  Our first unit focuses on simplifying exponents and radicals, and if students do not fully understand the basics of fractions, they will struggle when we throw in variables, exponents, and square roots.  

I wrote random fractions on a bunch of notecards.  Each student was given a notecard and a partner.  Each pair was given a die.  Students were to roll the die, and if the die landed on an odd number, they added the fractions, while if it landed on an even number, they subtracted the two fractions.  Once they solved for the correct answer, one person traded their notecard with one of another group.  They repeated the process.  Next, they used the same notecards and rolled the die with an odd number meaning that they would multiply the fractions, and an even number would mean dividing the fractions.  They switched cards, and repeated.  

Survey

Finally, students opened their iPads, logged into Schoology and pulled up a Google Form survey.  In this survey, I ask them both routine questions (when is your lunch/study hall, who is your counselor, when is your birthday, etc.) and getting to you know questions (what are your future career goals, is there anything that I should know that would help me better teach you?)