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Showing posts from 2015

Drawing Shapes

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.


Starting Congruent Triangles

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 doin…

Median, Not a Median

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 and divides the op…


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 to be the…

Digital Portfolio: MAP's - Baseball Jersey with Desmos

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.

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 the domain... they struggled with accuracy. Luckily, we have Desmos.

Desmos also made …

Geometry weeks 4, 5 & 6...

This 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) and free recall s…

Hilights from Weeks 4 & 5 & 6 in Algebra (Really getting behind on my blogging)

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 working…

Week 3: Defining Midpoints

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 rather than e…

Back to School Day 2015

It was so nice to meet my new students' parents and say hello to former students' parents on Saturday. Back to school day is always a joyful, energizing day, though rushed too as I attempt to fit a 20 minute presentations into 10 minute slots!

In addition to introducing myself and discussing course content, I want parents to know why I teach the way I do. It is difficult to explain problem based learning, game based learning, digital portfolios, mindfulness, neuro-plasticity, cognitive science backed learning strategies, growth mindset and standards based grading in 10 minutes... From my experience the last few years, it is actually impossible! Hence, writing a blog post to sum it all up is on my to do list.
For parents who missed my break-neck speed presentations, or for those who want to check out the information again, they are below.
I am looking forward to a great year of learning with your kiddos!

Week 2: Paired Problem Solving FTW

True, to form, it is has taken me to the end of week 3 to finish my week 2 post...


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.



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 late last week, right before school started, I read about another method for Paired Problem…

Week 1

Having long decided that 180 blogging won't fit my working mom of two life style, this year I am going for weekly blogging. It is important to me to blog to model ongoing learning for my students - I blog to reflect on my teaching and to have a place to receive ideas and feedback.

I am already behind as I had planned to do this over the weekend, but I can blame grad school (this time) as I spent time working on my research project.

Last week was great. The beginning of the year is typically a simultaneously draining and energizing time and this year was no exception. On top of getting into the rhythm of my new schedule and meeting my new students (who by the way this year seem to all be named Isabella or Madison or Ryan), I also sent my own son to school. William (I know, a far more unique name) started kindergarten and suddenly, I am a mom of an elementary kid. I am breaking all the rules from parenting books on how to get your kid to talk to you by grilling him everyday on the car…

Transformations with Geogebra

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.

What will this day be like...? I wonder....?

So tomorrow is the first day of school. I am at the point in my to do list when it is time for me to let some things go - I can't do everything I'd like to on day 1.

I did make a presentation to explain Standards Based Grading. Inspired by Bowman, This prezi gives a basic overview of what SBG is, why I use it and how it will work for my students.

Apparently in my post grad school haze I completely missed the TMC15 inspired month of blogging (Blaugust). I also missed discussion on all the awesome things people learned at TMC15, including using my favorite read of 2014 - Make It Stick both to structure class and as a teaching tool. Julie R. blogged about how she plans to teach her classes strategies from the book and even shared resources for doing so (which I plan on stealing and using).

I also missed several Global Math Department webinars including this one on suggestions for the first day of school.

So now that I am catching up on what I missed, my to do list is growing and …

Better Questions

Yesterday I saw Sam's tweet:

I thought, yes I want to improve my questioning skills.

I just so happen to be reading some good questions in Ritchhart's Creating Cultures of Thinking, so this evening I wrote this. Check it out over on the collaborative BetterQs Blog.

Back in LA

I have been home for two weeks. It has been a quick transition to reality, both in regard to family and school. Today is my last day as summertime stay at home mom so I don't want to take up too much time writing a long, thoughtful post. Instead I will share my to do list:
Finish interleaving algebra problem sets Watch Tinkerbell and the Neverbeast with the kiddos everyday Make posters for both of the classrooms I will be teaching in this year Write PD grants for conferences that I want to attend Finish presentations for back to school workshops Decisively answer continual requests to watch a show or to have snacks Swim everyday with kiddos Host casual dance parties to the music from Tinkerbell and the Neverbeast Finish writing learning targets for Geometry and make the course more fun Buy fancy shades for windows Renew passport Sign kids up for soccer Make family photo book for 2014 Clean the house (lol) Plan a trip to Lego Land Plan play-dates for the kids Work on grad school re…

We Never go out of Learning Style

Three weeks into grad school and once again last night I was sleepless at 1 am, second guessing my ability to learn new things quickly and participate intelligently. Why can't I make connections quickly and speak my mind in class?

While walking to class this morning, I was re-listening to an episode of  This American Life called Is This Working on the role of punishment in the School to Prison Pipeline. It opens with a mother talking about her preschool age son being suspended unfairly. Even though I had heard this before, it brought me to tears.

It also made parts of what we have learned the last three weeks come together for me. Specifically, how Nodding's ethic of caring points to the shortcomings of some No Excuses schools to help students grow emotionally by learning from mistakes versus facing no-tolerance punishment. How do strict discipline practices in No Excuses schools fulfill their responsibility to complete the sense of caring within their students?

It isn't a…

Should be reading....

I want to write about my school choice class, actually I need to also for an assignment, but instead we are exploring the city. The Empire State Building is tall and the Natural History museum is huge.

Phase 2

Dave and the kids are here. I think I spent all of Friday evening cuddling their faces, smelling their hair and telling them how much I had missed them. Having finished the big paper, we spent the weekend exploring the city: Central Park, the Village, 9/11 Memorial, Brooklyn, the High-line and Wil's favorite, the subway.

I started two new classes - Privatization and Research - both are, surprise, heavy on the reading. This experience is challenging my ability to process vast amounts of information, stay up late, write efficiently, participate (at all - not going for eloquent at this point), and my confidence overall.

I am grateful for my spouse. He has supported me from the moment I thought of applying, cared for the kids in my absence, carted them all over the city via stroller and subway (with a backpack loaded with their supplies), cooked meals, proof-read papers and provided much needed reassurance. <3

Things I do when I don't want to write a paper...

1. Laundry
2. Check Facebook
3. Take out the trash
4. Use the foam roller to painfully, stretch my IT band (when did this become a thing??)
5. Clean the stove
6. Sun Salutation
7. Make coffee
8. Google vegetarian dining options
9. Ballet
10. Check Instagram (I refuse the Twitter temptation - too prone to suck time)
11. Stellar kickboxing routine the tune of Eye of the Tiger, choreographed on the spot
12. Gaze out the window to watch the pigeons
13. Write silly blog posts

Always choose Tacos

Tomorrow will mark the end of mt first two weeks in New York. My family arrives this evening. I am both incredibly excited for their arrival and a teensy bit nervous about balancing the workload with my desire to spend time with them (BTW apparently "teensy" isn't a word but "weensy" is - what's with that?). Today then seems to be the shift from being a mom set loose in the big city to learn and grapple with being alone to being a busy mom trying both to learn and have fun with Dave and the kiddos.

It seemed appropriate then to take a break from writing the 10 page ethics paper to write a blog post. Somehow I have become a person who takes a break from writing to write something else.

I mentioned in my last two posts that things have been making more sense. Yesterday, our class on ethics ended and I am no longer in a quandary over ethics, or rather I am at peace with its vagueness. I finally have a sense as to the possible meaning(s) of the word aesthetic a…

Chatting not about Heidegger, but wine...

My weekend was super productive, go me! Which means I didn't make time to blog. 
The recap:
Friday - Excellent Happy Hour with cohort (is it happy hour when it lasts for four hours), my voice is still hoarse from excellent conversations
Saturday - Walked and walked around the UWS a bit in the morning (pictures below) and wrote a paper in the afternoon
Sunday - had coffee and yoga with two new friends in the morning and read ethics all afternoon
Today This morning's Ethics class was illuminating in a basic way for me - I realized that all of the philosophers we had been reading believe(d) in Virtue Ethics, that the goal of thinking and questioning is in pursuit of the good life. I think my classmates understood that last week, but better late than never. 
We also watched a movie on philosophy called Being In The World. It tried to explain Heidegger. Rather it did explain Heidegger and I tried to follow. Here is my attempt at a synopsis:
One understands objects by using them.  One …