# In Problem Solving 1, we make use of the entire classroom to engage students in a number of teaching and learning modes.

The primary purpose of this course is to introduce our students to a wide variety of problem solving themes and techniques, as well as to practice skills that will stand them in good stead throughout their years at Proof School. To this end we are steadily progressing through a sequence of topics including tiling problems, crafting precise definitions, proof by coloring, symbolic logic, the Pigeonhole Principle, elementary counting, and many more topics to come.

To make effective use of our classroom space, Sachi and I have developed a number of "teaching modes." For instance, at times the entire class sits on pillows on the floor surrounded by white boards. This mode allows for engaged thinking and whole class discussion. At other times students work at tables individually or in pairs on sets of problems designed to lead them through a new mathematical idea. On occasion, Sachi and I split the class in half based on students' prior knowledge to teach separate (but typically related) lessons.

In order to expose students to the spectrum of classic math questions and solution methods, we also run an IF-AT (Immediate Feedback Assessment Technique) three times a week. Students work on a set of five multiple choice questions in randomly selected groups of three, which are shuffled each week. Once a group agrees on an answer they scratch off the corresponding silver rectangle on their "scratch-and-win" answer sheet to see if there is a star underneath, indicating a correct answer. Besides being entertaining, this exercise teaches students to explain their reasoning in a convincing manner, instills the habit of listening carefully to others in order to learn how to solve a problem, and promotes collaborative decision-making.

Our evaluation of each student's performance in the course will be based on their engagement with material during class time, the quality of their written work, the level of completion of the contents of their math folder, and on in-class assessments given two or three times during the block.

-Sam Vandervelde