Musings from Mrs. Galvan

Every year I reassure my geometry students that once we get to congruent triangles, that they will feel more confident about the course. They tend wax nostalgic over predictability of solving equations in algebra and lament the feelings of confusion they experience when learning how to use upwards of 30 theorems and definitions. Learning how to use all these rules in 6 weeks is hard. Students start to feel better we we begin triangle congruency proofs because the goal of each proof is more predictable. Compiled with the fact that those 30 rules are more rehearsed and deductive structure no longer feels like foreign language, their comfort and confidence increase. As eager as I was to get to this part of the course (despite preaching daily on effort and learning from mistakes), I didn't want to just hand them the triangle congruency theorems. I have done just that though in years past, using my excuse of only having 135 forty minute classes each year to relieve my guilt of not doi...

T his year in geometry, I am striving for a more constructivist approach. Many concepts (like perpendicular or supplementary) are familiar. The challenging part is to write the definitions in polished, conditional form and then integrate them into two column proofs. Approaching new material this way is more engaging and promotes retention. Rather than announcing the definitions from on high, I have been having students discuss the terms and attempt the if-then form in small groups. Sometimes instead of discussion, they investigate the concept using geogebra or math open ref . Then we collect the attempts and discuss as a class. Once we agree on the ideal wording, they add it to their flash card deck with an accompanying diagram. Most lessons close with students using the new theorems along with ones they already know to write a two column proof with their partner. Starting class with more generative activities, making time for retrieval practice (with their flash cards) a...

Way back on March 13, I used a less directed approach to teaching the discriminant than I had in the past. The Monday before, I was visiting a school in Houston. In one of the math classes, the teacher did a lesson that did a bit of discovery. which inspired me to change things up a bit. In the past, I have done a quick lecture on the topic and set my students free to practice in pairs as quickly as possible. I mean the discriminant is way boring so best to go quickly so the teenagers don't realize this! Building on the idea that initial struggle correlates with eventual retention, I made this quick and easy change. Students work in pairs. One student is in charge of graphing the functions on desmos . They use this guided handout and develop the rule. How does it match up to my (ever evolving) inventory of what makes a good an engaging lesson: fun and interesting it's a game with prizes problem based inquiry based connected to an application doesn't ...