Knowing the How but Not the Why

Guilty.  I can do a lot of procedures, but when asked to put it in a context or explain WHY it works…I may or may not be able to do it.  Or at least at that point in time. 

For example, a colleague who subs in our building is finishing up an education certification. As part of that program, they are currently enrolled in a math methods/problem solving course.  They had a question about a problem…

2/3 divided by 4/5

Getting an answer was not the issue.  We both knew to invert the 2nd and multiply.  They were asked to put it in a context and then follow up with a different interpretation as well. 

I thought for a bit and said, there is a lesson sequence in the Vn de Walle book but mine is at home.  “Oh! I’ve got that book!”  So they ran to get it.  By the time they returned, I had found an article I remember running across a couple of summers ago.  Measurement and Fair Sharing Models for Dividing Fractions by Gregg & Gregg. It was essentially the same lesson, modeled after the Van de Walle lesson.  Christopher Danielson has a very nice post here that references it as well.

Basically, I went through the lesson sequence.  Just as when we teach procedures, if we don’t provide opportunities for student thinking to develop, they are stuck with meaningless, rote steps.  As part of this sequence, I realized how much easier it was for me to divide with like denominators.  Honestly, I had never considered it before.  Shameful, I know.  But noone had ever led me to do it that way and I had never taken the time to consider it. 

Along with Jo Boaler’s course, I wonder how spending some time thinking about how elementary and middle grades teachers develop concepts would impact my own teaching.  I realize how important it is to allow time and provide a structure for students to make those meaningful connections on their own.  I am there as the support to help them along their way.  But in order to be successful, I might need some of my own productive struggle in order to answer the WHY and provide some meaning.

Unit Organizer Update & Feedback Only Grading

Its been a good, very good, no, great start to the year.  Almost scary how smoothly it has begun.  But I will take it and be happy. Very happy.  I always have amazing kids.  They make me smile.  They make me think.  They make me love what I do.

I have read about comments only grading multiple times.  A colleague shared more research as part of an action research project last spring.  Reading and chatting Wilham’s Embedded Formative Assessment this summer convinced me I needed to give up grades on student work and offer feedback only.  So far, so good.  When I pass target quizzes back, I allow some time for students to mark on their organizers where they consider they are based on feedback I have offered.  I will definitely be sharing updates.

I shared a unit organizer here a couple of weeks ago.  It’s gone well, though I knew I wasn’t satisfied with it.  But this afternoon, Crazy Math Teacher Lady shared this

My thoughts are to modify my booklet style organizer to include this on the inside.  I appreciated the graph for each target.  This goes right along with some research from #efamath chat this summer.  It reminds me of something similar I had seen on @druinok’s block a while back.  I like how Lisa has a place for students to record multiple assessments.  This is a great layout!

I plan on keeping a vocabulary knowledge survey on the front as suggested by Math = Love.  Here is a sample of mine

And keeping the assessment grid on the back for personal reflection…

I re-intoduced an old assignment from a few years ago in my first units…students were asked to write their own unit assessment using our learning targets.  Most seemed to put good effort in to interpretting what each was asking.  Offering written feedback gave me a chance to address some of their misconceptions, mostly notational issues in diagrams they had included or clarifying some vocabulary.

My intentions were for them to go back through their INBs, notes, target quizzes.  A couple of times in class, I fielded specific questions they had.  Based on what I observed, I believe it was a useful task.

I am looking forward to my new organizers!  Thanks to Lisa, Sarah & @druinok for sharing such awesome ideas!

INB Unit Organizer

I wanted to create a unit organizer than encompassed several aspects but would also be narrowed to one page, fiting in to the INB.  Here’s a list of what I wanted:

vocabulary
unit overview/schedule
learning targets
record of assignments
track their own assessments/learning
place to record questions/big ideas
opportunity for end of unit reflection

Here is what I arrived at for a first attempt, copied front to back and folded in half, this is the order students will see the booklet. 

The vocabulary pre-assess was a great tool.  I saw this idea over at Math = Love earlier in the summer.  It went so well. It only took students a couple of minutes to self-assess their vocabulary knowledge.  As I walked around, I was able to see several terms had 3s & 4s.  We compiled a list of our 1s & 2s words.  I explained, as they learned a word or gained better understanding, they should go back and put a +.  Before the end of class, students were asking if they could go ahead and update their chart.

If possible, maybe completemthis part a day before beginning a unit, in order to make needed adjustments based on student responses.

I included the correlated CCSS # for each target.  Eventually, these may be beneficial when looking online for a resource on a specific standard.

I am not fully satisfied with this chart yet. Assignments made for specific targets can be listed, a note if completed (stamp) and place to monitor their assessment for each.  A second line has been included in case RTI/enrichment is needed.

Finally, the back side has a place to record reflection.  Ideally, I would have them complete the reflection at least 2 days prior to unit assessment, allowing to address any needs the following day, prior to assessment.

As always, this is a work i  progress, suggestions and ideas are welcomed!
PDF:  http://db.tt/DWfJUqLL
Foundations in Geometry doc

Intro to Matrices:

Intro to Matrices pdf
Intro to Matrices doc

INB – Extension Pages

Several folks seem to be planning INBs for this year.  I had lots of questions last summer. 

I learned a lot this past year and feel that round 2 will be more successful.  The first point of confusion for me last summer was, how could I possibly interact with every single student via the INB?!?!  I finally realized through some great instruction from Megan & Elizabeth, the purpose was actually about students interacting with the new information I provide them.  After reading a little on Cornell Notes format and some INB brain research connections, I felt I had a better understanding. 

I remember some brain research for study habits for students, if you can get them to interact with new information in a purposeful way 3 times within a 24-hr period, it increases the likelihood to retain/recall the inrormation.  The right hand input, the left hand do something with the new information, and follow-up the following day in class with reflection or assessment. No, I don’t have a link, but when I find it in my old PD notes, I will cite and link!

My biggest fear was when I heard someone suggest everyone stays on the same page…what if my notes ran over…flipping the page was not allowed! What?!?!? I, personally, found this rule something that made the INBs a success for my students. Whenever a student was looking for info, another might tell them a specific page to look. To each his own, I would never judge you if you had a different rule. Whatever works best for your students!

But Megan taught me about extension pages…be careful! Tell students to take their notes BEFORE attaching the page. Tape top of extension page to bottom of INB page…

Then fold it up…

It folds flat and no bulk when INB is closed.

#TMC13 my take-a-ways

I have started this post and deleted it multiple times this week.

I have read so many others’ posts – all different approaches and points of view.

TMC involves so many aspects – it is surely impossible to entail it all.

TMC is so many things to so many people.

I sat this morning, flipping through my notes, still feeling overwhelmed with all the few days in Philly offered and asking what parts of TMC will have the greatest impact on my classroom this year?

No big surprise that My Favorites remains My Favorite.  What I appreciate most is that 5 minutes feels doable and offers an opportunity to share for some who are just dipping their toes in the water…

Orange-Mellows

When Nicole asked what was in the bag…the look on Anne & Rachel’s faces said it all- “Well, duh.  Isn’t it obvious what’s in the bag?”  Its taken me a while to truly realize what seems obvious to me, usually, won’t be obvious to my students.  I must consider what the lesson looks like from a non-mathy brain perspective.  How will what I’m doing / saying look to my students?  I appreciate her orange-mellow model for combining like terms.  Yes, its obvious to me and you, but using her simple model will likely make it more obvious for our students.  I will definitely share this will my colleagues in lower grades.

I was wondering – for operations with irrational numbers – would the same idea work…possibly let a student choose an amount of marshmallows, say 5, then take a bite out of another marshmallow.  How many marshmallows do they have?  More than 4, less than 5 but not quite sure of the exact amount.

Questioning

David Wees impressed the importance of Wait Time – something we’ve all heard about and know but still it just feels awkward when trying to be intentional.  He also discussed 3 types of questions students ask – Stop Thinking – question students ask when they want the answer, so they can stop thinking and move on.  Proximity – you are nearby…he suggests to stop answering these two types.  The third – start thinking – those questions that will lead to more thinking…are the ones we should focus our time on.  My thoughts are to take some time to process a student question – determining which type it is, then responding appropriately.  David is scheduled for Global Math this fall – take some time out and attend this meeting!

You Be the Ref

I have used different types of tasks that ask students to look for and address mistakes, but I liked Adrienne’s take on this idea.  Not telling students which are correct / incorrect in a set of problems with solutions – but allowing them to decide, explain the mistake, then do the problem correctly.

4 to 1

Jenn Crase shared a placemat activity called 4 to 1.  The idea is to have students placed in groups of 4, they solve a give problem, add their answers and teacher checks this one.  If its incorrect, its not telling them which one has made the mistake – but forces them as a group to determine where their mistake is.  I also like how she used assigning problem #’s to specific students as a differentiation strategy.  This is a very versatile task.

What is a ________ ?

I will definitely using this idea shared by Chris Lusto.  Allowing students to create definitions, his example was a circle.  Then asking classmates to create a figure that matches the given definition, but is not a circle.  I can see some fun discussions coming out of this – by taking the time to observe student responses, then selecting and sequencing them to share-out with the class.  I must add a side not here – I was very impressed with Chris’ excitement as he shared.  Seeing him speak in person, it was obvious his excitement for the math education and creating engaging learning opportunities for students.

desmos

Another person who impressed me with their passion for education was Eli Luberoff.  His face lit up with a huge smile when faced with reactions from the crowd of teachers.  He was excited to share the cool new things desmos is offering our students.  I really loved when he said they print off tweets and shout-outs from classroom teachers – posting them on a board to serve as their inspiration…we are why they do what they do.  I left with a new appreciation for Eli and his amazing team.

Dan Goldner

This session was nothing like I expected.  Yet, it still has me thinking about my classroom and how my decisions may / may not match what I think my educational values are.  It seemed almost that Dan did nothing except intro the activity – yet what he did had every single person in that room thinking, deeply at 5:00 pm on a Friday afternoon.  Our task was to look at 6 different classroom teachers and their policy/procedures – looking at what each scenario told us – and also what we felt it said about what they valued in their classroom/students.  He is scheduled for Global Math in September, I believe – mark your calendars.  I plan to share the same activity we used in his session with my department/colleagues.  The only thing I believe could have improved the session – more time to have carried on those conversations we began.    Take some time to look up the resources we used.  Its a great use of time for reflection on your classroom practices.

Again, there are so many more take-a-ways from TMC13 but these are the ones I feel will have the greatest impact for student learning as I begin a new year next Wednesday.

 

 

 

 

#EFAmath Reminders

Earlier in the summer, I shared a binder with sports card protectors where I filed formative assessment strategies as a quick flip for reminders when lesson planning or even in the midst of a lesson.

I picked up a couple of business card organizers.

Each has 12 pages with 4 slots.  you could purchase perforated business card sheets or quickly cut out your own.

@druinok’s flip card chart is still pretty awesome too!!!