Musings from Mrs. Galvan

This is now the 3rd year my students in Algebra and Geometry have made digital portfolios using blogger in my 1:1 laptop classroom. Posts range from simple summaries of in class PrBL tasks to elaborate projects. In geometry, students make constructions using geogebra and embed those on their blogs. Over the summer, for about a month I had "have students in algebra make interactive notebooks?" on my to do list. I was inspired by Sarah Hagan Carter and the sense of ownership her students must get from creating their own mini textbook via Interactive Notebooks . Additionally, her students are making a convenient and interactive study resource. I ended up deleting the to do item and moving on as I didn't want to give up on digital portfolios and I thought that having both seemed like too much. Yesterday in class I was thinking about how students can find a sample problem of an older concept when working on one of our interleaved problem sets? We don't use a textboo...

Today my geometry kiddos used our favorite Geogebra to construct a line through the center of a circle that is perpendicular to a chord. Directions: 1. Draw a circle 2. Draw a chord (use a segment) 3. Construct a line through the center of the circle that is perpendicular to the chord. 4. Add a point at the intersection of the line and the chord; measure the segments. 5. What do you notice? Make a conjecture and publish via digital portfolio.

I was really happy with last year's reboot of the space diagonal (aka diagonal of the solid) lesson, but my story about the prince craving the ideal bread stick wasn't the best. This year I changed the story to my (true) childhood story of visiting Disneyland and wanting candy. For next year, how might I add an open middle? Can this be morphed into a 3 Act Lesson that incorporates a prediction?

Here are a few of my favorite student video blogs. I assigned each kid a different proof from our book to demonstrate. Lucas Samantha Uma Annie Will Gaia Maddy Prompt: Tips for making video blogs and embedding 1. Must be typed, including diagram, symbols and tick mark notation (I suggest using Google Drive's Drawing App) Must have decent "watchability" Copy/Paste diagram and proof into slides of a presentation, adding a new step on each slide (make sure diagram is always visible) Energetic Explanation NEVER type out reasons as you talk... add tick marks as your prove congruencies 2. Must use a screen capture tool like jing that will record your voice and your typed completion of the proof Practice. Find a way to inject humor and energy into this video. I have to grade like 50 of them. Make yours pop! Remember that you can pause jing 3. Must be embedded in your blog - control the size of the embed 750 x 750 ish is great 4. As always,...

New year! Among my resolutions include trying to blog more. Given grad school and school and family, it falls to the bottom of my list, but I really miss it. There is something about taking the time to reflect about my teaching that feeds me. I can't explain it other than to say that I am a major reflector. Today my geometry kiddos dove into the new year with discovering one method for proving a quadrilateral is a parallelogram using geogebra. Geogebra constructions are great for getting students to make sense of the theorems and for getting students to do a bit of inquiry. They are getting more proficient at using geogebra and publishing their creations on their blogs so it took 20 minutes for them to get to the point of publishing. Here is the  Prompt . I will try to remember to add student examples once they turn things in.

Students added this geogebra construction to their digital portfolios today. Prompt . I will add examples of student work when they turn them in.

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

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 was our 3rd 4 day week in a row, making this feel like a slow starting school year. Three weeks in and I haven't given a significant assessment. Perhaps that is okay as I have given several small skills quizzes to Algebra and two in Geometry. They are getting feedback from me and I know which topics to spend more time on. This week in geometry included learning more basic terms, triangle inequality  (activity inspired by someone in the #mtbos), starting proofs and developing definitions for midpoint and bisect. I really like how my lesson on the definition for midpoint and bisect went this year. I facilitated a math talk punctuated by discussions in pairs. Step 1: Show them this image and ask them to come up with an If-then definition for point M that is general and doesn't name any points or segments from the diagram. Step 2: Gather ideas from the class and polish the grammar until it makes sense. Other possible items to clarify might be using congruent ...

True, to form, it is has taken me to the end of week 3 to finish my week 2 post... Highlights: Tuesday  in Geometry, students learned to use Geogebra while also learning about transformations - prompt here . Wednesday  in Geometry was spent reviewing for a quiz and writing their own chains of reasoning blog. Prompt: Examples: Annie         Andrew       Caroline In algebra, we are spending a lot of time taking questions on homework. Sometimes 10 minutes, which in a 40 minute class, is a significant potion of time.  Interleaved problem sets are harder, which is the point. The reasoning behind mixed over masses practice is that having to go from topic to topic forces the learner to concentrate more. More thinking = more retention. So yes there are lots of questions as they are remembering a lot of different concepts, but the time spent for homework review is  valuable. I am reading Creating Cultures of Thinking and lat...

Tomorrow we will learn to use geogebra. Students will use transformations and publish their results on their blogs. Here are my instructions . Here is my sample. Criticism: My instructions are pretty specific and don't leave a lot of room for exploration. I am hesitant to give less structure though as this will be their first time with geogebra this year.

So one of my favorite people I have met since discovering the #mtbos is Jed Butler . At Edcamp earlier this year we got to chit chat in person and in just a few minutes, I had several ideas that I wanted to implement, including doing a variation of his assignment called Recycle Robot. Last year (see old prompt ), I had my geometry students find an object at home to measure and calculate surface area and volume. Then they wrote a blog post about their item (see student sample ). This year, I wanted them to create something and the Recycle Robot was a good match. I made a few slight changes, including a requirement to convert the surface area to units of post-it notes as I wanted them to connect this project with the day we spent on File Cabinet . I reread my short reflection on how this assignment went last year and my goal for the assignment holds. Like last year students are doing more than calculating something from a textbook. They are interacting with the object in a way that ...

I like this project because it gets students looking for what we learn in class outside of class. It also gets them writing creatively and is a cumulative record of all the theorems they've learned this year. I have assigned this for many years, initially with students handing in actual photos in albums,  and have steadily made improvements.   Last year's improvement was having the students publish their safari journals on their blogs as it was my first year having students create math blogs.This year I added the rubric and the google presentation requirement. For next year, I would like to work with the English Department to make the writing assignment portion better. Perhaps we can research the literary requirements of a quest to help them to write better stories? Honestly, I am not sure why a lot of their stories are wanting. Does the geometry make it seem contrived? Are they waiting until the last minute to write? Did I not spend enough time talking about how to writ...

After 8 years teaching Geometry from this textbook , I finally made the lesson on Space Diagonals more interesting than saying: Do Pythag twice. Sure  I always do the Space Diagonal Dance, to much laughter, but the PrBL model wins. No, I don't have a video of the dance (that I know of). I happened to have brought donuts for a meeting so I had this box. I made up a story told them the legend of the Prince who made his butler leave the castle on a quest to find a delicious bread stick, the crunchy kind. The Prince told his butler that he was not to return until he found the longest bread stick that would fit in the box. I gave them the box dimensions, put them into groups and handed out the white boards. It wasn't as easy as I thought it would be. They discussed and argued for about 7 minutes before coming up with the solution. I walked around and monitored, giving feedback and hints. A group presented their approach before starting independent practice, er a worksheet, ...

Since I started looking beyond the textbook for problem solving opportunities for my students, I am continually reminded how much I used to over teach and over model. My traditional daily class plan had been: Review homework, new lesson, guided practice, homework. Repeat. Quiz. I know that I had been leading them too much because now that I am giving them richer tasks, I am surprised by how difficult they find some of them. Fourteen years in the classroom and my judgement of the degree of challenge in a problem still needs calibrating. For example, recently we did the task Viewmongus from Mathalicious to explore applications of Pythagorean theorem in Geometry. Given the diagonal length and the aspect ratio, calculate the dimensions of the TV. I looked at the materials before class and judged it a 10 minute problem. I budgeted 15 and reasoned that they could blog it for homework. I was surprised (and happy) to see my students struggling to use the 16:9 ratio to find the dimensions ...

As mentioned, I have gotten behind on blogging. Three weeks ago in Geometry, we were discussing similar triangles. Usually when I teach this, I am in a hurry to get to right triangles. I would make the excuse that they did a lot of ratios in pre-algebra, so let's just do similar triangle proofs and get to trig already! This year I did a few things that made class a lot more engaging. #joyful 1. As mentioned before , I had kids do problem solving in groups using white boards. Five Triangles is a great source of problems to use to mix it up. 2. The Blob - I filed Fawn's golf problem remix away when I first read it last year and I am SO glad that I used it this year. I followed her script, instructing them to draw a blob somewhere in the rectangle, a point H on one side and a point B on the other. I collected them and made copies. The next day I gave them the copy and gave them the challenge. Jonathon's wasn't possible with three triangles... I let him dra...

My classes for most of the month of January have been kinda boring. Sure, students listened, took notes, stayed organized, practiced concepts and demonstrated understanding on assessments, but save a game day or two and a Socrative Space Race, things haven't been fun. We haven't even added to our digital portfolios! Excuses: 1. Grades and comments were due January 21 2. Polynomials 3. My husband, two kids and I got the flu for a week 4. I had to go to meetings 5. Not enough class time (yes, I always use this one) Effect: My geometry students took the biggest hit. They learned about the interior angles of polygons without doing much exploration or any application. Similar polygons was covered with a boring lecture in which I presented one example. Then they did a worksheet at their seats. I have made my peace with the fact that not everyday can be a trip to Disneyland, but I do think I take my students' motivation and good study habits for granted. Recovery : ...

My geometry students recently did their 2nd video blog. I assign them each a different proof and they create a diagram and explain how to prove. See two of my favorites from this year and the prompt below. Jayla Bridget Tips for making video blogs and embedding  (Links to an external site.) 1. Must be typed, including diagram, symbols and tick mark notation (I suggest using Google Drive's Drawing App) 2. Must use a screen capture tool like jing that will record your voice and your typed completion of the proof 3. Must be embedded in your blog 4. As always, creative title and 1-2 sentence introduction 

Last Wednesday was fun thanks to an early morning lesson reboot. Usually in Geometry I give the following directions on a review day:  "Do these review problems with a partner and ask for help as needed."   Instead, I copied the same problems on separate papers to quickly make a game of Solve Crumple Toss (it went well in Algebra ; again thank you to Kate  for the idea). The goal, reviewing key topics from chapter 4 (diagram-less proofs, detour proofs, perpendicular bisectors, coordinate geometry, oh my!), was the same. The execution made for a much more engaging, dare I say fun, class. Today's reboot was not last minute (go me!), because earlier this month I saw Julie's blog post about Jessica's Dance-Dance-Transversal idea. Then Justin tweeted that Kate posted the power point and I was set! I love the Mtbos! Anywho, the kiddos had fun dancing and everyone knows their angle relationships. I am no longer feeling bad about my geometry ...