Friday, January 12, 2018

#MyFavFriday - Proofs and More

Happy Friday, y'all!

Holy moly is it cold out there!  After some chilly weather to start back to school, we had a lovely warmup with highs on Wednesday in the 60s.  Then a cold front moved in again and we're back under freezing.  BRRR!!!  I am ready for spring to show up! :)  Seriously though, if it's going to be this cold, it really needs to snow - at least then, I have a chance at a snow day :)  Thankfully we have a long weekend, so I plan to stay wrapped up in blankets, working on lessons and reading.

This week had a few down points, but overall it was a good week.... now it's time for a look back at my favorite things from this week:


My Favorite Learning Strategy:
I already blogged about this strategy earlier this week, but I really enjoyed using the "sample student responses" in my AP Stat class to help students determine the success criteria for a "good" vs "poor" paper.  Asking them to reflect on the papers with a star / wish was a last-minute decision, but one that I'm glad I did.  The level of detail that the students noticed really made me realize that I need to let them "be the teacher" more often.  It almost makes me excited to grade their FRAPPYs this weekend.  (Notice I said *almost*... I mean, does ANY teacher get excited about a weekend of grading????)



My Favorite Lesson of the Week:
This reflection question is so difficult for me!  So many good lessons happened this week - proofs in Geometry, simulations in AP Stat, blood typing in Forensics - how do you pick just one???

In high school, I adored my Geometry (and later Calculus) teacher and she is a huge reason why I ended up as a math teacher.  However, I remember NOT caring for proofs, at least at first!  Before we could ever use a theorem, we had to prove it, so our notebooks were full of proofs.  Once I understood them, proofs became one of my favorite things and I still love them.  Over Winter Break, when I was working on how to introduce proof, I tweeted out a request for ideas and my former high school Geometry teacher was one of the responses I received.  Because of all of the great advice from the #MTBoS on proofs, it's been a fabulous week of logical thinking puzzles, vocabulary practice, flow proofs, and two column proofs.  The best part is that the kids are ROCKING it!  I'm so proud of them! :)  The picture above is a couple of proofs from Mrs. Newell's Triangle Congruence materials - have I said lately how much I *love* my dry erase sleeves? :)


My Favorite Question of the Week:
Do you ever have a situation where your favorite thing isn't because it was really good, but because you learned a lot from it?  That's the situation with my favorite question this week.

The question on the left was the Daily Reflection in my Geometry class on Monday.  We had worked that day on connecting vocabulary words to conclusions.  I know it's hard to read, but under each "given" statement was a 2-column table, meant to simulate the idea of a 2-column proof with the left box saying "What can you conclude?" and the right box saying "Why?".  I really did not anticipate any issues with these questions, but oh my... :(  The number of students that really struggled with articulating a difference in right angles and complementary angles was surprising to me.  But I guess that's the whole point of the Reflection, right?  For me to know if they have learned what I wanted them to learn... :)


My Favorite Student Response of the Week:
I had two favorite student responses this week - one serious and one that just made me smile.

The one that made me smile came first.  I have started Test Prep Thursdays in Geometry with 2 practice ACT problems.  I loved the student drawing with "Not to Scale" written next to it. :) :) :)

Today, the Daily Reflection Prompt was about #OneGoodThing and this student response helped me put things in perspective.  "Something good that happened to me this week is I'm alive.  We don't own our lives so it's a blessing that I receive which money can't buy."

That response was truly a *mic drop* moment... leave it to a 16 year old to say something so profound, that truly makes you step back, take a deep breath, and count your blessings.

People say I'm crazy for working with teenagers all day long.  I say I'd be crazy not to!  My students make me smile and laugh, get frustrated and cry, and everything in between.  But ultimately, my students make me want to be a better person and a better teacher - and that, folks, is what it's all about.

Have a blessed weekend!

Wednesday, January 10, 2018

How do you know what they know?

All day today, I kept thinking "I'm totally going to blog tonight... here's idea A, idea B, idea C, etc", but then 4pm came and the thoughts just disappeared or my after-school brain thought "That was a dumb idea... why did I think that would be a good blog post??"  It's so frustrating, but one of my goals this year is to #PushSend, even when I'm struggling.


Over the past few weeks, Pam and I have been slowly reading and discussing Embedding Formative Assessment by Dylan Wiliam and Siobhan Leahy. (Abbreviated EFA2) While there are parts of the book that have been fairly difficult to read, I've also been able to walk away with several usable strategies - and we're only on Chapter 4! :)

This year's theme of "What did you teach? What did they learn?" was inspired by this book and I have really tried to focus on this question each day.  A similar statement from the book was a reminder to stop worrying about the label of "formative assessment" and start thinking about whether your classroom activities will help your students learn more.  As a result of this book, I've really tried to focus on being intentional on "how do I know what they know?"  

In Chapter 3, the authors focus on learning intentions (aka objectives) and success criteria (aka rubrics) and it was this chapter that I've really focused on this week.  

Exit Tickets:  I've renamed my exit tickets as "Daily Reflections".  This week, when students arrived to class on Monday, I had a half sheet in their folder with space for this week's Daily Reflections.  Each day, I have really focused on my theme question of "What did you teach? What did they learn?" to guide me as I write that day's question.  I've tried to be intentional with the Reflection prompt as I think about the day's objective and what I hoped they would be able to do/understand at the end of the lesson.  Today, I tried a suggestion from EFA2 where students generate their own test/quiz questions, hoping to trigger what the authors call the "generation effect", where students remember responses they generate better than responses given to them.  

Success Criteria:  One of the other strategies I tried from Chapter 3 was one about analyzing student work.  The authors spent quite a bit of time in Chapter 3 referencing "success criteria" or rubrics for student work.  In general, I use rubrics for quizzes and tests that mimic the AP Exam style grading, but I remember trying to use an online rubric maker several years ago and I really struggled to understand the difference between "few / some / many" or other descriptors that are often used in those rubrics.  The authors instead suggest  that we should communicate quality work to our students by providing student work samples, not rubrics because rubrics rarely have the same meaning for students as they do for us.  The authors suggested showing examples of various quality to students and having the students give feedback.  For their justification, the authors said there were two main reasons to do this:  (1) students are better about spotting mistakes in the work of others than they are in their own work and (2) when students notice mistakes in the work of others, they are less likely to make the same mistakes in their own work.

I tried this strategy yesterday and today in my Stat class.  I like to start the 2nd semester with simulations because it's kind of fun and eases them back into our course; however, students often struggle with the written portion of a simulation.  I modified a previous AP problem and created two student samples of vastly different quality, and thanks to hubby's help, vastly different handwriting as well!  I asked students to pretend they were the teacher and read the two samples, writing feedback to Student A and Student B regarding what each student did well and what each student needs to improve.  After time to individually assess the student work, I had them share out in their table groups, and then finally as a class share-out of Star and Wish.  Finally, I had them close their eyes and use their fingers to show me what they felt each sample would have scored on the AP Exam on the 0-4 scale.  While I was pleased with the level of engagement each student showed and the quality of their discussions / critiques, the real power of this strategy showed up later in the hour when they had time to work on a problem set.  Many of them referenced the success criteria from the student samples, really putting effort into mimicking the work of the "good" paper and providing each other feedback regarding the quality of their written descriptions.  This was definitely a strategy that I will use again!!


Friday, January 5, 2018

#MyFavFriday - First Week Back

Happy Friday!!!  We've made it through another week - HIGH FIVE! :)

This was our first week back from Winter Break and thankfully it was a short week.  We started back on Wednesday, then I had to be absent yesterday as my mom had a heart stent put in (she did great!), then I was back for today.  This weekend is shaping up to be a busy one with several family events and lots of lesson planning! :)  Thankfully I don't have any grading to do yet!

Last fall, I posted about wanting to use #MyFavFriday more as a weekly reflection post, but it kind of fell by the wayside as the semester progressed.  During the #MTBoS12Days challenge, I posted a fall reflection and I recommitted to trying it again, so here we go!

My Favorite Lesson of the Week:
This one is definitely a toss up...

In Geometry, my favorite lesson had to be on Wednesday, when we did several critical thinking puzzles to help ease us back into school-mode, with the main idea of logical thinking to move us into proofs.  These word chain puzzles were such a hit!

Then, today in AP Stat, we did Doug Tyson's Smelling Parkinson's activity to introduce simulations.  It was absolutely all I could do to keep a straight face as some kids swore up and down that the cards had different odors.  I can't wait to tie back to this lesson when we get to hypothesis testing :)


My Favorite Formative Assessment Strategy used this Weeek:
Last semester, one of the books I was reading was Total Participation Techniques and then Angela Watson had a Truth for Teachers podcast episode on the book as well.

One of the strategies mentioned was "Hold Ups".  In the book/podcast, the Hold Ups are more generic, but I've found them to be a great tool for feedback, especially in Geometry.  Today, we were reviewing triangle congruence from first semester and I had 10 or so triangle diagrams.  What I love about Hold Ups is that with quick glance around the room, I can easily tell which problems the students got and which ones we need to discuss more.

My Favorite Exit Ticket Prompt of the Week:
Based on some twitter discussions about a mid-year Teacher Report Card, my exit tickets this week were designed to elicit feedback from my students about what worked (and what didn't work) in the Fall Semester.  Today's exit ticket question was:  1) What was something (activity, structure, etc) that really helped you learn?  2)  What was something that did NOT help you learn?

My Favorite Exit Ticket Replies:
Asking my students for feedback during this short week has really been eye-opening and has given me a lot to ponder this weekend.  Below are some of my favorite replies from the prompt above:

  • While I dislike FRAPPYs they really do help you to better understand because you are getting the practice.
  • I dislike when we have to watch videos when you aren't here.  
  • Having you correct our problems right then was very helpful. [Edited to add:  VNPS]
  • Something that didn't:  The Kahoots - They're fun, but only as a tool for review; which is what we used it as.... nevermind! :)
  • I dislike getting up and doing problems around the room.  I really need to sit and do math and we had to stand and it was hard to write, etc
  • One test I was studying and finally remembered to use the Canvas page - it was like a whole new world!
  • Going around the room with whiteboards was awful for me.  I was always afraid that someone would see me doing something wrong.

What were your favorite moments of the week?  Share your post in the comments or on Twitter using the hashtag #MyFavFriday.

Have a great weekend, y'all!



Thursday, January 4, 2018

2018 Classroom Focus

In previous years, I have posted my "mantra" for the year, usually in August.  This year, I didn't post one because honestly I didn't know what my classroom focus would be.  I had plenty of ideas for my personal life, but very little for my professional life.

But, as always, it was @pamjwilson to the rescue.  (If you don't read Pam's blog or follow her on twitter - go do that now.. She's *amazing*)

Over Winter Break, I happened to catch a twitter discussion between Pam and Elissa regarding goals for the new year.  Over the next few days, Pam and I chatted a few times about formative assessment and some of our previous #EduRead books.  One of the books we discussed was Embedding Formative Assessment by Dylan Wiliam, a book that I had started a few years ago, but only read through Chapter 3 before life bogged me down.  :)

Reading this book was already on my to-do list, but after seeing the twitter discussion and Pam's goals, I moved the book to the top of my pile.  

I'm so glad I did, because I finally found my classroom focus for 2018! :)


Such a simple, yet powerful, set of questions to help guide my semester.

What is your classroom focus for 2018?

Wednesday, January 3, 2018

A #Teach180 Reflection

Technically, this post is based on the #MTBoS12Days prompt list to share a #teach180 photo and lesson, but over the break, I didn't have my resources to really post a complete lesson.  Sadly, I didn't quite make my #MTBoS12Days challenge, but I blogged more in 2017 than I did the year before, so I'm declaring it a success! :)

#Teach180 Lesson Reflection

Today was our first day back with kids and I don't know about you, but the January Back to School day is almost more difficult than the August day!  In August, kids are fairly eager to get started, to see what their teacher / classes are like, but in January, the kids already know you and motivation can be lacking when it's super cold outside.  We are coming off a super cold spell - today was the first day above freezing since last Friday, so that didn't help at all!  Also, in August, I have spent weeks cleaning and decorating my room and preparing lessons, but in January, I haven't thought about school for 2 weeks, let alone try to remember what we were learning back in mid-December.

So I knew that I wanted today to be a semi-relaxing day, nothing majorly stressful, but something to get them thinking again to ease them back into the swing of things...

In Stat, I did a modified version (1st semester topics only) of the Wedding Story Activity that was shared a few years back at the AP Best Practices, but I didn't get any pictures of that :)

But in Geometry....  oh my, we had fun! :)


We finished up Triangle Congruence in December, which means we are starting this semester with Proofs.  At some point in the next few days, I'll post my proof plan, which is mostly stolen from the #MTBoS :)

To start them out, I wanted to emphasize logical thinking, so our warmup was the sequencing activity you see on the left.  They were given 12 photos, out of order, and as a group, they had to put the photos in a logical sequence.  (File)  I really enjoyed listening to their discussions as they argued about why their order was the best.

From there, we moved on to some other logic puzzles, including this Logic Area Puzzle that you see on the upper left.  I took this puzzle from the Holt textbook that we used YEARS ago at my school.  Again, I loved listening to the kids as they worked to remember perimeter vs area of squares and I'll admit I did not let them struggle the way I should have here.  :(

On the flip side of the Logic Area Puzzle was a "Flow Story Proof" from Math Teacher Mambo to help introduce the left to right logic of a flow proof.  I don't know that I would keep this activity in this sequence next year - I think I would rather use it as a warmup on the day I actually teach flow proofs.

The activity that I absolutely LOVED was the Word Proofs from Don't Panic, the Answer is 42 and you can see them on the lower left.  We didn't get very far into these, but I think they will be our warmups for the next several days.  The structured reasoning of here's where we start, here's each step (and the reason), and finally here's where we end was such an amazing way to think through the proof process!

The last few minutes of class was a 2nd semester Feedback exit ticket for Keep / Change / Start / Stop.  I'm not sure that I received a ton of useful information from them, but I brought them home to ponder some more over the next few days.  

It was such a good morning and one that I enjoyed quite a bit.  :)  Only 100 more days to go! :)

Tuesday, January 2, 2018

Geometry Reference Sheet - #MTBoS12Days

EEEKKKK - It's my last day of break!!!  I didn't quite make my 12 posts goal, but I was close - this is the 10th post, not counting the prompts post! 

#Made4Math - Geometry Reference Sheet

I know it's technically not Monday, but in my defense, I came up with the idea yesterday, just didn't get it together until today! :)

We start back to school tomorrow, but I have to be absent on Thursday because my mom is having a stent put in.  What do you do when you are absent on the 2nd day of a semester?  EEKK!  I already had planned to put together their notebooks that day, but in Geometry, that doesn't take too much time because we don't have a ton to tape in like in AP Stat.  I know!  Let's make a Reference Sheet!

So when I went to school today, I grabbed my first semester notebook, then I sat down with a blank piece of paper and started planning out a reference page.  This doesn't contain EVERYTHING we did first semester, but it has the most important things, I think... :)  If you see something missing, please let me know!


After taping in the few pages they need to tape in, the students will use their first semester notebook to complete the reference sheet.  Hopefully it will be a useful tool this semester!

If you want a copy of it, here it is in PDF (to preserve the fonts) and in DOC (if you wish to edit)

Saturday, December 30, 2017

Feedback and Formative Assessment #MTBoS12Days

Yesterday's post about effective feedback definitely started my wheels going...

Feedback & Exit Tickets

After reading the Educational Leadership article yesterday regarding effective feedback, I started Googling various things to see what I could find that might help me solidify my thinking and I found a couple of articles that really made me pause...

One of the first links I found was this article on Deep vs Impression Feedback and a few things really hit me in the first few paragraphs... learners rarely take the time to read comments, teachers rarely give time to read the comments (or act on them), and the same comments tend to show up time after time, indicating that the feedback isn't doing a good job of moving learning forward. These are not earth-shattering and most teachers can attest to the truth in these statements, but for some reason it hit me pretty hard, especially my role in giving time to read and act on the feedback.  I obviously feel that the feedback is worthwhile or I wouldn't spend time writing on each student paper, but do I demonstrate to the students that I feel that feedback is worth *THEIR* time as well?

One of my goals with effective feedback needs to be developing *descriptive and actionable* feedback for students.  In order for increased learning to take place, time should be provided for students to take action.  In my classroom, my students do quick checks several times a week, which I have regarded as a positive thing because I can get a snapshot of how well the students understand the concept.  However, once I write feedback on their QC, I don't ask them to *do* anything with it.  What if I asked them to turn over the QC and do something actionable on the back?  Either reflect on their errors or rework the problem or make up a similar problem and solve it?  This has the potential to be really annoying on my part, handling the same papers over and over, but it's still a thought worth pondering.  How could I develop an actionable process that isn't time consuming?  I've worked really hard this year to find a good balance, so I don't want to disrupt that too much, and I know from experience that if something is too unwieldy, I won't follow through, so how can I manage this process well?

Further in the article are some specific strategies for Deep Feedback vs Impression Feedback.  I really liked the "Met / Not Yet / I noticed" strategy and the "Traffic Lights" strategy for feedback.  I've used Traffic Lights for students to self-assess, but I've never given feedback or assessed students using this strategy.  With Traffic Lights, I like that the suggestion was for students to work together to determine why something was rated as Red, Yellow, Green, which brings up the "detective work" that Wiliam mentioned in the EL article.  I need to dig into these strategies a bit more and see how it might work in my classroom.

Continuing on my Google search led me to Mathy McMatherson's blog post on Why I Switched to Exit Tickets.  This blog post is probably the thing that made me ponder and reflect the most over the past 24 hours.  I haven't been really pleased with how homework (or lack thereof) is working in Geometry.  I try to give a lot of practice throughout the class period, but one struggle there is that a lot of practice time in class is collaborative and not individual.  I need to figure out a better way to really dig into what my students know after a lesson individually.  I have gotten away from exit tickets this year and I'm not happy with that either, but it seems like I often run out of time to do all that I want to do. 

From Mathy's post:
I realized that these few homework problems were really the only thing I valued about the day-to-day implementation of homework in my classroom – so why wasn’t I doing it every day and why was I letting it be optional? This was one of my motivations for switching to exit tickets – take those first few problems from a homework assignment, make it an exit ticket, and make every student do it in class in front of me. Then, if students struggle with it, put problems like this on the bellwork tomorrow. Either way, I’m forcing every student to try these problems and learn how to do them.
I definitely agree with this!  Why not pick out a couple of problems for students to work RIGHT AWAY for quick feedback?  It would help inform my teaching on a regular basis, allow for student feedback, and utilize that time at the end of class in a better manner.  This is similar to how my quick checks currently work, but QCs are normally the following day and that's a whole other frustration because absent students don't have a clue what to do.   The key element to this plan is that it is actionable.  When I respond to the exit ticket, then students can immediately use that feedback on the next day's warmup, which also ties in to the 'Curve of Forgetting'.

I'm not quite where I want to be yet, but I am starting to formulate a plan for this upcoming semester :)

What are your thoughts?