Since, as @samjshah reminds me, we blog partly as an reflective archive for ourselves, I wanted to capture some of what I did in the new introductory logic unit I created for Geometry this year. I also wanted to capture some of who and what inspired me to do the things that worked out best!
I had no idea how prescient it would be to have an introductory unit that both adds tremendous rigor and depth while simultaneously being somewhat optional. These first two weeks of school have been somewhat chaotic as we discover who has been placed and scheduled correctly, who needs to be placed into a different section due to unavoidable schedule changes, corrections, or updates, how many new sections of certain courses we need, and so on. There were days when I felt like I didn't have the same students in any class two days in a row — even though some days this was more of a feeling than an actuality. So it was wonderful to have an adaptable "throughline" these two weeks — a river into which students might step, flow, or reenter without too much extra craziness. The unit was hard in the good way that students at my school really love — at the Zone of Proximal Development (ZPD), way up on a shelf just high enough above them that they have to stretch to reach it.
DAY 1 — Attacks and Counterattacks — What makes a mathematical definition?
We started with @samjshah and Brendan's Attacks and Counterattacks, which is now the recommended default starting unit for all Geometry students in our district. It was a great icebreaking activity, prompting students to activates their prior knowledge about what constitutes a definition. Plus it involved defining a narwhal, so how could that end badly, right? Table groups passed their definitions around the room, then used table-sized whiteboards to come up with a counterexample that broke the defining group's definitions. This involved both collaboration and presentation skills, as well as a good memory for definitional trivia. Did you know that the horn of the narwhal is ACTUALLY a tooth?
DAY 2 — Statements, Compound Statements, and Truth Tables
I also used this unit to set up classroom norms. Each day, when students come in, the "Welcome" slide is projected onto the board with introductory instructions and the Home Enjoyment (HE) assignment to copy down into your notebook.
We don't have bells at our school, so as an auditory cue, I am taking a page from the amazing @MrVaudrey and embedding a one-minute "welcome to class" music button that tells students this is a short, specific, and finite portion of our show and they know what they need to do. Thank you, Mr. Vaudrey! The theme music for Geometry (my 1st block class at 7:35 a.m.) is the music from Hawaii 5-0 (in honor of my principal and reminding me to ask myself, What Would @wahedahbug Do? with her brilliant mathematical classroom intro routines).
The instructions sometimes tell students to grab a handout from the handouts hanger but they always tell students to get out their HE and compare answers. I have realized that if I need to include homework review during a time of greatest primacy and recency, then I am going to make it count (thank you, @druinok and @pamjwilson!).
Next up was a dramatic table read of a deleted scene from the first Harry Potter movie. It's just terrible what ends up on the cutting room floor but, you know — Hollywood. "Harry Potter and the Logical Statement" was a SMASH hit. Students taught themselves the basics of statements, negations, equivalence, and truth tables and it beat the living crap out of giving them a boring lecture. After they were done, we summarized and organized what we had learned and I set up expectations for Home Enjoyment.
Day 3 —Advanced Equivalence & Rules of Replacement; Intro to Conditional Statements
The beginning of the truth table Olympics. Getting students to use what they know and extend it and — hooray — organize their work logically on the page was a huge win. Plus the kids liked learning something grown-up and hard. We did more practice set up homework review routines and expectations. Students are getting better about coming into class and getting started right away. Overview of the Professionalism score and expectation-setting.
Day 4 —Conditional Statements, Part II
Students discovered the Law of Non-Contradiction (Law of the Excluded Middle: A ⋁ ~A, but not both), and introduction to converse, inverse, and contrapositive using the basic conditional statement, "If I am Batman, then I am a superhero" (I'm looking at you, @mgolding). Whole lot of truth table whiteboarding going on.
Day 5 —Four Basic Laws of Inference
Modus ponens, modus tollens, simplification, disjunctive syllogism, and intro to proof. By this point are really getting into the technical language, to my great surprise. We start whiteboarding proofs and advanced truth tables.
Day 6 — Biconditionals & Definitions
We return full circle to where we started, with definitions, but now we define biconditional (iff) statements and how to prove them. Students start to groove on the idea that you have to prove both if A, then B and also if B, then A to prove a biconditional. There are lightbulb moments about the importance of counterexamples. Routines are starting to gel. Students are still transferring into the class and between/among sections/instructors, but other students help to indoctrinate them into our emerging culture.
Day 7 — Intensive Practice Day — Truth Table Practice aka Whiteboarding Madness
I give each table a sheet of truth tables to build and I use this activity as a Participation Quiz to further solidify our norms. Many groups start passing the marker around to ensure equitable participation. Everybody does splendidly on the Participation Quiz.
Day 8— Assessment
Home Enjoyment Packet #1 is due to be turned in. Students take the Unit 0 Logic test. It is a bear, but my students are "scared but prepared." Some students need more time so they come in at 7:15 a.m., during 3rd, 4th, 5th, or 6th block to finish. Their stillness and concentration is impressive. Algebra 1 students are doing their own crazy stuff all around them, but they persist and persevere. I am over the moon about them. They are proud of themselves for the advanced logic they have learned.
Day 9— Chapter 1 Launch: The Elements of Geometry — the poetry of primitives
We explore undefined terms, learn a little math history, and do some Think-Pair-Share. Next year I want to have another table reading/deleted scene activity for all this stuff instead of a boring lecture. But that is OK. Our routines are solid and we are moving forward.
Onward to constructions on Monday.
Now I have to score 73 logic tests (and 73 HE packets, but only for completion), but it was totally worth it. My Geometry classes are off to a great start, and we have a solid foundation to build from, even if my sections have 36 kids each.