Wednesday, December 14, 2016

CMC North '16 Post: 2 of n

I am still mentally unpacking all of the great things I learned about and thought about while at Asilomar for CMC North '16.  I'm always besides myself with how many different things I could be doing differently and what those changes in my practice could look and feel like.

Let me start with the Mini-Conference session on a Transformational Approach to Geometry by Lew Douglas and Henri Picciotto.

One of my colleagues asked our Principal if he could go and he thought it would be a good idea if one of our Geometry team members went with him - so I ended up being able to go "early" to this wonderful session.

At the beginning Henri and Lew presented the idea that we'd have to (at least partially) re-define the way that we define specific Geometric terms and we would have to become more comfortable with students giving informal arguments because we should reserve formal proofs for the really important things (yay!).  I whole-heartedly agree.

When I took Geometry we spent almost all of our time proving.  While it was fun for me (I guess it shouldn't have been a really big surprise to me that I became a math teacher!) I now wonder about my classmates.  How many of them were turned off by the 180 degree turn into the land of proofs?

Students should always have to justify their reasoning (SMP3), construct viable arguments and critique the reasoning of others in all of their classes.  Math makes people reasonable, right?

But does it have to be a 2-column proof every time?  Can't a student explain something to me and that's enough?  If students are using language to convey meaning in a meaningful way then I feel plenty satisfied with that.

I'm a big fan of flow proofs so oftentimes when I begin to venture into the land of formalization I use flow proofs to soften the blow.  A tiny bit visual and a tiny bit less formal than the 2-column cousin.  I'm not saying we shouldn't ask students to write about mathematics and I'm not asking or advocating that 2-column proofs be stricken from classrooms but it was at least a little bit vindicating to hear others say that we should reserve the formalization for when we really need it.

Was that their main point?  No.  Transformational Geometry takes a different way of thinking about justifications for proof and it also takes a more relational-thinking approach as opposed to always thinking about properties and definitions.  Again, not that you don't use properties and definitions but it just takes a back seat to relations of objects.

What would happen if this was an angle bisector?  What does this mean for reflections?  What do I know about points that are reflections?  What properties are true for reflected images?  I really think this is a great way to get students to think about the relationships that different Geometric objects have with each other and to get students to create their own line of questioning in order to get themselves to the right place.  I can't verify that this will but I'd like to think that moving towards using Transformations as a basis for getting students to justify their reasoning by using their language and understanding as opposed to forcing them to use words that aren't naturally their own.

Just an opinion.  Agree or disagree - it's up to you.  Also, it would probably be rare (possible, not probable) that you sat in the same session that I did and it's my right to disagree with myself tomorrow even!  But these are the ravings of a almost-on-the-final-stretch-can't-wait-for-all-of-my-finals-to-be-over-teacher and it's getting late.  I apologize in advanced for any inadvertent craziness I may have typed.  

Sunday, December 04, 2016

CMC North '16 Post: 1 of n

Fresh off of coming back from CMC North 2016 I write to you while passively watching Gilmore Girls (original series, I'm not caught up enough for the new Netflix part just yet) and eating Mountain Mike's pizza :).

There's always so much to think about and debrief after CMC North so I'm trying to figure out exactly how to approach all of this.

I attended a huge variety of sessions:

  • Mini-Conference session on a Transformational Approach to Geometry by Lew Douglas and Henri Picciotto 
  • Co-Teaching: Mathematical Practices For All Students by Noirin Foy and Valerie Ruiz 
  • Computing Transformations Using Complex Numbers and Matrices by Henri Picciotto 
  • Building Understanding Through Discourse by Rick Barlow and Madison Miller 
  • Summative Assessment Without Testing: Successful Examples by Masha Albrecht 
  • Make the Way: Student Agency, Authority, and Identity by Brent Jackson and Joan Easterday
Of course there are also the keynotes too!  Amazing stuff!  I haven't even unpacked my bag or notes (and I've got a LOT of notes!)... I don't even think I've unpacked my car 0_o.  

I resurfaced on Twitter over the conference so that was good.  I think that's what I've appreciate the most about CMC North.  It re-awakens me to rethink many different aspects of my teaching practice.  
During @Zakchamp's Keynote on Sunday morning the "we should test less and assess more" vibe was prevalent.  This really dove-tailed with some pieces I got from @Rickbrlw and @MatheMadison session about discourse.  

SO, for now all I know is that my Warm-Up routine for tomorrow will probably change.  I don't want to "make it through" the next 2 weeks but for my sanity I at least have to survive through them.  With a good nights' sleep I can ensure that my students get the best version of me that I can present to them tomorrow and I can go from there.  Lots of moving pieces but I know that debriefing the sessions one by one would probably be best for me.  

While I was there I did mention that someone should put together a Google Doc with those URLs from all of the sessions.  It'd be good/great for someone to compile a list like this.  Maybe with a Google form or something?  idk.  Something to think about?  Anyone want to volunteer for this?  

Thursday, December 11, 2014

Students helping students

Today was interesting... I feel like that's what I say at the end of every day.

So I do this after-school tutorial/re-teach for Geometry.  The original format of this tutorial is that there is a topic that we go over on Tuesday and then on Thursday students are allowed to do re-tests on that particular topic area.  Teachers receive their own students tests, grade those tests themselves and life moves on.  

Unfortunately, life doesn't work like clockwork.  So I end up with a room of many different students all with different areas they need help in, all coming from different teachers, all with different attitudes about math.  Also, since most of them are not my own students I don't know a lot of their names and they don't know all, or really any, of my own classroom rules.  

There are several of my own Pre-Calculus students who come to volunteer their time to help out with this tutorial.  They help everyone sign-in, get oriented with what group they want to work with, sometimes they tutor students themselves.  This definitely helps the process of what I need to do.  This also helps my own students to increase their own mathematical confidence too - a very big plus.

So even though there is a bit of a coordination-mess, sometimes my room looks like a hurricane went through it and the janitor says my students are making more work for her because they make a mess in the hallways too :( - I still think we're making progress and I have to believe that progress is success. Eventually those students will take their renewed understanding to their classes, eventually the "regular" tutorial kids will teach the others how to clean up after themselves and things will iron out.  Right? Right.  Well, one can only hope.

My only fault with this process is that even though we are meeting 1 need there are so many others we aren't meeting. What are the programs your school offers? Pros//Cons of those models?  Trying to figure out how to restructure ours so it can help those who need help with homework, remedial skills and also not-so-long-ago re-takes.  

Saturday, November 15, 2014

Collaboration is Key

This morning it all started with a simple yet elegant infographic

Teamwork, collaboration, goal-setting.  All of these ideas are right up my alley!  I love trying to keep directions simple for students because it really makes ideas cement in - ideas that are cross-curricular and transcend all subject areas.  This means when your Geometry teacher tells you that your groups need to turn into teams, she isn't kidding.

But I really do believe my students think I'm blowing hot air.  The intelligence of 1 dominates the groups, the students who won't do things normally are still not doing anything, this frustrates the students who care about their grades and is causing a lot of friction.  I wish I could do something about student X who is absent so often that they never know what is going on when they come back.  Or student Y who even when "present" is not fully present.  Attendance is such a key factor in achievement that I think that alone is impacting the way the groups work.

Teachers say group work for the sake of group work is not good.  Tasks need to be enriching, engaging, etc.  But when I try to switch from group work to, say, whole-class instruction - the ship sinks.  I do not believe that students listen to me.  Mind you, exit tickets say otherwise.  Ok, when I *do* an exit ticket it indicates that students understand what I am saying.  But during the process of whole-class instruction/guidance there are students who are not paying attention, fiddling with their phones, putting their heads down, etc.

Best Learning Position Ever... 
I know math is not everyone's bag but... c'mon!  Putting your head down?  I'm not *that* boring.  Or am I?  I have been wrestling with this idea for a while now really.  I'd say 95% of my students are making progress on learning goals, paying attention, engaging themselves with content, asking really good questions, participating actively, even *asking* when we will do 4 corners or other similar activities again - and then there are 5% who really don't care.  They are not in this class because they want to be there, they don't want to put forth effort into something that doesn't matter to them, their mind/brain is completely somewhere else, they have 1 or 2 jobs/activities that dominate their time and they are tired and no amount of interesting mathematical facts/applications or really funny jokes (no really, my jokes *are* hilarious) or gimmicks or anything will hold their attention.

So in a load of about 160 students maybe 8 total across all of the classes don't seem to get it or even *want* to get with the program.  Why do I let it sour the pot so much?  Why can't I just let it go and be happy with all of the students who are responsive to what I *am* doing?

Collaboration *is* important and even if they don't see it now I think students are starting to get the hang of working together.  Maybe, just maybe someday they will transfer these skills to other classes.  Maybe they will use these ideas as adults.  Maybe they will see the benefit some day and come back and caution the other students to pay attention because they wish they did and maybe some day that will resonate with my lone 5% and then I can reach 100%.  Maybe someday I will be happy with 95% and develop confidence in my practices.

Ok, enough ranting - now to problem solve.  So, what makes the group work effective?  I can't find but do recall someone somewhere saying something about turning groups into teams (non-educational "how to" found here).  I do have a little acronym that helps orient students to the basic fundamentals of what groups do, but maybe this isn't enough.

  • Get Along 
  • Respect Others 
  • On Task Behavior 
  • Use Quiet Voices 
  • Participate 
  • Stay with your group 

In September I was fortunate enough to go to the UC Davis Math Project.  At this first session for the year we discussed group/team work and providing roles for students.  Something as simple as roles in a group seems superficial - but stick with me for a little bit here.

The presenter, who works for CPM, recommended that students not necessarily have to do that specific thing but be in charge of making sure that specific thing gets done.  I don't personally use CPM materials - although I am sure they are good and have heard fantastic things about them.  But from what I have heard they are very group/team based and everything she did say made a lot of sense.

So the recommended roles she put into place were:

  • Resource Manager 
  • Task Manager 
  • Facilitator 
  • Reporter/Recorder 

She did a really cool thing with task cards that helped remind students of what their main role was, some questions to ask themselves throughout the task and also a color-phrased mnemonic device to help them remember to work towards the goals of their work.

After a quick Google search about the whole idea of turning groups into teams I came across this article from Harvard about what does make a group into a team.  They say: "A team is a group of people who do collective work and are mutually committed to a common team purpose and challenging goals related to that purpose." 

Common purpose and challenging goals.  Maybe I haven't driven home the idea that they are working together for the common purpose of solving problems, making progress and developing understanding.  I think those are pretty challenging goals, if I do say so myself.  I always remind my class that there is 1 of me and 30-something of them.  They need to learn how to communicate with each other so that they can rely on each other for help.  But maybe I haven't done enough to help them mold their sense of purpose and duty to each other?

I am inspired by this collaborative chart from Maureen Devlin that outlines a good way for students to keep track of their collaborations.  My students maybe need a little more frequent check-ins so hopefully I find time today (between all of the wonderful grading I have to do!) in order to make a half-sheet sized version with a few less layers.  Maybe have students zero in on a few targets every once in a while until they feel confident with those and then move on to other targets.

I always say progress is success and I truly believe that.  Bite-sized pieces will hopefully get them addicted to the elation you feel when you know that you've got it and until then I hope they all show up to get the material that they need in order to make their progress.

I won't hold my breath, but I'll just keep taking deep breaths in hopes they all show up to learn.  Until then, I'll just keep Twittering (and blogging!) on.

Sunday, November 02, 2014

Sunday Musings

Yesterday I went to the UC Davis Math Project and got to meet a group of really wonderful teachers.  We worked on a lot of problems, I meet @JessicaMurk13 in person.  She writes The Mathy Murk and presented a really cool lesson on different ways she fosters Problem Solving in her Geometry classes.

It got me thinking about my own practices (as one often does) for fostering math conversations and it got me really buzzed about the training I went to earlier in the month: La Cucina Mathematica by @MrVaudrey and @Jstevens009.

So I may have overwhelmed the people at my table with my "Yea! Get on Twitter! It's Awesome!" enthusiasm but I really do think tweeting has helped me immensely.  Since La Cucina I've been checking on Twitter, following people, reading different chats, responding to a few things here and there and really trying to orient myself about it.

I'm very fascinated with the #mtbos and found this NaNoWriMo-ish (National Novel Writing Month) post about blog posting.  So let's give this a whirl.  National Blog Posters Month!  (I'm assuming) well if that *is* what it is - I'm in.

I'm challenging myself to be more reflective and collective.  I want to collect resources I use, share them with others and get feedback before and after using them with students.  This may mean a couple of blog posts a day (one to say what I will do and the other to say how it went) but I think I can pull all of this together to see how it goes.

I'm especially inspired by this recent tweet from @mjfenton

I got into the conversation a little late in the game because it started with this simple

So simple yet so profound.  If you can't find what you are looking for where you are looking then you need to look elsewhere, right?  So ... here it goes.  I'll try to reflect and forecast for the next month on the daily.  I've tried multiple times to do something like this and wish I was more consistent on a regular basis but all I can do is control my time now.  I'll try not to be too wordy but... well, I am.  So here's hoping for a great November to everyone!  Keep Calm and Tweet/Blog On!

Sunday, October 26, 2014

Supplies, supplies, supplies

A recent tweet from @RPhillipsMath made me start thinking about the necessary supplies for a math classroom.  Last year I taught 7th grade, the years before that 8th or even one year it was 7th and 8th.  This year I'm teaching high school (Pre-Calc & Geometry) and I switched schools and even districts.  There were a lot of luxuries that I had at my previous school that I didn't realize were luxuries until... I didn't have them.

At the beginning of my 1st year at my old school they gave every teacher a "New Teacher Supply Box".  This box contained things like:

  • Stapler
  • Tape dispenser 
  • Extra rolls of tape 
  • 3-hole punch 
  • Markers 
  • Colored pencils 
  • Lined paper 
  • Elmer's glue 
Our district had a contract with Office Depot so the supplies came from there. 

We also had $250 (per year) that we could spend on whatever we wanted.  Over the 5 years I used a lot of things, purchased more things, collected some very useful items from eNasco Math like: 

We did have some supplies that we shared, like a class-set of graphing calculators.  

I even wanted to get some of these things: 
Now I'm at a school where I'm starting with a clean slate.  I inherited a classroom from another math teacher who left so I had some supplies (not very many) in the room when I came in.  There were broken compasses, small metal protractors, no markers, no colored pencils, no construction paper.  A lot of the supplies I was used to using weren't around anymore so... what's a girl to do?  

Write a DonorsChoose grant of course!  So now I have 2 DonorsChoose projects with some supplies that I have considered essential for instruction. 
Supplies will always be something teachers have to contend with, but hopefully with clear communication everyone can get what they need to make the classroom feel alive.  

Saturday, October 25, 2014


So we're in the middle of Midterm Madness at school.  The 1st Quarter ends on Tuesday and my students are psyching up for their midterms.  Well, maybe psyching up is an over-exaggeration.  Freaking out maybe?  So I took this opportunity to... well, teach my students a lesson.

This is my first year at a new school and although I really love it, I'm not sure I feel as effective as I could be.  It could be that I'm just tough on myself.  I feel like math is accessible for everyone and that given the correct set of circumstances anyone can learn it if they put some effort into it.

Well, no surprise to teachers out there - some of my students have been sitting back, coasting in the process of their learning, not really applying themselves,  So I decided to shake it up a bit.

Every student took 1 piece of paper, folded it hot dog and hamburger until they had quarter pieces of paper.  Then, we looked at the Chapter 1 and Chapter 2 questions and students were asked to write questions they had on one of their quarter pages.  These problems were taped on the board and either I or students who knew how to do them did them.  We had some music playing, students were up and out of their seats solving problems and the tempo was very productive.  Our 2nd day of review followed the same format but with a topic list so they were more focused with their question-asking.

I think this strategy was more effective at getting students to do problems on the board than anything else I've tried this year.  I want students to get into the habit of explaining things to each other and making sense of math but there seems to be an inverse relationship between mathematical confidence and actual confidence in my class.

Any suggestions on other strategies you use to get students to explain math to each other?  I want students to be engaged in our activities and for students to become more confident about their math abilities.