Musings from Mrs. Galvan

The other day in geometry we defined medians and altitudes . Today they used their definitions to draw them, as accurately as possible. This activity consistently takes my students longer to do than I think it will. They struggle with drawing the altitudes especially. The struggle is good for them and deepens their understanding of the vocabulary. They added their drawings to their digital portfolio. Alex  Lucas Donovan Stephenie

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...

Inspired by Sam's Attacks and Counterattacks , my lesson on medians and altitudes was much more student centered than before.  To begin class, I showed this image and asked students to work with their partners to write an if-then definition for median.  After, they passed their paper to another pair with a new goal to try to draw diagram that fulfills the definition before them but that clearly isn't  a median. Some definitions weren't specific enough (omitted the word triangle or "from the vertex").  While others assumed that all triangles would be equilateral and hence that a median bisects the triangle. I walked around and helped students who needed help thinking of ways to disprove faulty definitions. Then the papers were returned to their original owners for them to improve their wording. I gathered student responses and together we agreed on a definition to add to our flashcard deck: "If a segment is drawn from the vertex of a triangle...

Hello readers (all three of you)! I am so excited to announce my most recent pedagogical discovery. The key to learning new things is flashcards. I know, this discovery is cutting edge and innovative. Students make a card for every theorem or definition that has a diagram and/or a given statement on the front and the (correct) If-Then statement on the back. Then, they use the flashcards to quiz themselves or a friend. I know that I should immediately run out to publish my discovery in a journal. Maybe I should present at an upcoming conference? The world needs to know!!! All silliness aside, learning many new rules day after day is hard. They not only need to know the correct wording, they also need to master when to use each one so that they can correctly draw conclusions. In years past I hadn't required flashcards, but inspired by increased attention to learning strategies that are supported by cognitive science (read Make it Stick , you just have to), flashcards seemed t...

Last week in Algebra (well the week before retreat) we started our unit on graphing linear equations. Generally we begin with tables and move quickly toward graphing via intercepts, the slope formula and slope-intercept. This year being my first time through with truly interleaved daily problem sets , they had already had several opportunities to remember from pre-algebra graphing via tables and calculating slope via counting rise over run from a graph. Hence, right away we were able to dig in to more detailed tasks. On day 1 after playing polygraph (lines), they began thinking about MAP's  Comparing Value for Money: Baseball Jerseys . From: http://map.mathshell.org/lessons.php?collection=8&unit=8200 They worked in pairs and quickly established that the price per t-shirt corresponds to the slope and that the one-off print set cost was the y-intercept. Actually graphing on paper was harder as I gave them a graph that went from 0 - 500 for the range and 0 to 25 for ...

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...

So every year around this time, my school shuts down and takes all the kids on retreat. I typically accompany upwards of 200 9th graders on a canoe trip down the Colorado River. It is an awesome trip and a great way for the class to bond. I have this year off though and while I will miss being part such a formative experience for my students, I am so excited to sleep in my own bed and get caught up with work and blogging. Week 7 = catch up on grading, planning, blogging and interleaving project. The last few weeks in algebra have been challenging for my students as we have been exploring complicated word problems. We worked on showing our thinking by writing and labeling all helpful expressions for a problem. The most challenging were the coin problems, interest problems and mixture problems. For each type, I lead my class through a discussion on how to translate the verbal expressions to algebraic ones. While it wasn't lecture, it also wasn't inquiry. A few days after w...