Thursday, February 23, 2017

Reflection

Ok, so I fell off the blog train for a few there and it's time to get back on!  I have been super busy working with teachers on all kinds of great math ideas.  We are exploring new ways to differentiate for enrichment in 4th grade, working on computational fluency and how it's assessed in 5th grade, and vertical alignment of our secondary math curriculum.  WOW.  All that and lots of STEM happenings.  Busy, busy, busy.

With all this going on, it's hard to take time out and reflect but I'd like to take a quick minute to share with you something I am working into my routine, and that is reflection.  Self reflection.  As a district coordinator it is hard to feel engaged with everyone all the time and very easy to get swept away with all the different projects that are going on at once.  Add all this to being a year one administrator and you can see how things can easily get out of control.

As part of my quest to be a better administrator (and person overall) I wanted to do some type of meaningful reflection other than my daily note taking.  I read an excellent article from ASCD with a just in time perfect suggestion.  This suggestion, from Baruti Kafele's "The Principal 50:  Critical Leadership Questions for Inspiring Schoolwide Excellence" recommends asking yourself some essential questions on a daily basis.  These questions include:

  • Who am I? (in the context of students and leadership)
  • What am I about? (purpose as a leader)
  • What is my most recent evidence? (in the last 24 hours that support ques 1 & 2)
These questions struck me as the perfect outline for self reflection.  Kafele suggests looking in the mirror and asking yourself these questions everyday.  I'm not sure that I'll ever have a complete answer to these questions but I do feel it is important to reflect on these things on a regular basis in order to arrive at the most complete answer possible. :) 

So far I have a kindergarten student that I can most recently think of that help me answer the first question.  When I entered their class recently one student said, "Who are you??"  and to that I replied, "I get to do Math & STEM throughout all the buildings in Exeter!"  Pretty simplistic and I'm sure that will evolve but thank you to that Kindergartner for giving me a starting point!  As far as leadership I feel my greatest purpose is to support others and provide a safe place for everyone to learn and grow.  My most recent evidence in the past 24 hours is the work we did with grade levels 3-5 in which they dove into the question, "What makes a good mathematical communicator and what does that look like?" 

I hope everyone has a moment where they can reflect on themselves, their purpose and their work.  I feel the three questions above can apply to a variety of people in many situations.  Great stuff, thanks Baruti!

Friday, January 13, 2017

The Progression of Multiplication HD

In the math world, the progressions of mathematical thinking and learning are still somewhat of a mystery.  This is not anyone's fault.  Classical teacher training programs are just that: traditional preparation much like how we learned math "back in the day".  We learned math by rote memorization through a bunch of procedures that we really did not understand and frankly hid much of the mathematics involved.  This is true and if you don't believe me ask around and see if your friends know why the standard algorithm for multiplication works!  I have always wanted to make progressions videos and low and behold I began searching online and found Mr. Graham Fletcher who apparently beat me to it!  Not only that but I think he does a wonderful job.  You can share this with parents (or teachers) who are asking why math is "different" now or with anyone who just wants to learn a little more about the natural progression of multiplicative learning in the elementary grades.  And please leave a comment if something strikes you or if you have a question! I'd love to chat with you about what you see here!

Happy viewing :)


Thursday, January 12, 2017

Counting...what goes on???


In our most recent short PD sessions, a topic of conversation came up...again.  Counting.  Specifically learning to count in kindergarten...and assessing counting skills.  There are so many sub skills that go into counting.  We don't think about it because we as adults have been doing it for so long and so often, but there really is A LOT that goes into counting.  K students learning to count must know the names of the numbers, the sequence of the numbers, one to one correspondence, how to keep track of counting, conservation or arrangement (also subitizing), and that the final number counted represents the amount of objects in the set.  WOW!  That's a lot of little skills that go into one big important skill, counting.

My daughter is three and knows the names of many numbers.  I attribute this largely to all the nursery rhymes and songs we sing!  The names of our numbers are a convention of language and usually taught at an early age.  Teaching the names of the numbers can be done through songs and rhymes such as "Monkeys Jumping on the Bed" and using numbers in everyday conversation.  The counting sequence can also be introduced the same way.  Using multiple representations when teaching the names and sequence can be very helpful.  You can show three things, show a picture of three things and then show the number 3 all while saying "three".  You can add one to three and say four, add one more and say five, and so on.  It has been recommended not to stress knowing the number symbols (digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) until children can hear and speak the names.

One to one correspondence is a skill in which children understand that a (spoken) number in the sequence represents one and only one object in the set and helps children count accurately.  Children who need to work on one to one correspondence may skip over an object all together, count an object twice, or run through the counting sequence without regard to the objects at hand at all.  Making this idea explicit while counting can help children learn that each number stands for one thing.  For example, when teaching one to one correspondence, we can point out that we say one number and only one number for each of the items we're counting, and we're careful not to skip any items.

Keeping track of counting is related to one to one correspondence.  In order for students to accurately count, they form ways to keep track of objects in a set, sometimes by touching or moving each object.  Students develop this sub skill differently but for those who are having trouble, arranging the objects to be counted in a linear arrangement first (versus scattered) may help them move from left to right so that they know what they have already counted.

Conservation of number is knowing that even if we move three objects into a different arrangement say linear versus scattered, it is still three objects.  With enough experiences children will be able to subitize (or automatically know by looking) small quantities up to three.  Research tells us that babies as young as 6 months old can subitize small quanitities!  The more exposure children have to seeing quantities in different arrangements, the better they will be at subitizing.  Subitizing can be used to count by counting on from the amount which is just known by looking (ie counting 5 as three by knowing three and then two more, 4, 5).

Knowing that the last number stated in the sequence tells the amount in the group can be difficult for  children at times.  When children have more experiences with conservation and counting, they will come to realize, it does not matter what order you count the items in or if you move them around, but the proper sequence that is important in correctly identifying a quantity.

As students progress through kindergarten though, how do you keep track of their ability to count?  Students can sound like they have the counting sequence down but put objects in front of them and they may count some time or skip some.  Ask them small sets and they may be able to subitize small amounts.  Make sure that they have the conventions of counting down (ie the names of numbers and the correct counting sequence).  Make connections to the ways they manipulate numbers and quantities.  For example, discovering that 5 is 5 whether we count 3 and then 2 or 2 first is the foundational building block for understanding the commutative property!

Finally I leave you with an amusing story...Anyone know a kiddo like this???
In his book Tracking The Automatic Ant (Springer, 1998), David Gale writes:
Once upon a time there was a little girl named Clara who was barely three years old and had just learned how to count. She could tell how many chairs were in the living room and the number of steps from the front porch. One day her father decided to test her. "Look," he said, "I've brought you these four lollipops," but he handed her only three. Clara took the lollipops and dutifully counted, "One, two, four." Then she looked up a bit puzzled and asked, "Where's the third one?"

Tuesday, January 3, 2017

Happy New (Math) Year!


I recently read a great challenge on a former colleague's blog.  AJ Juliani has tasked us all with his 30 Day Blogging Challenge.

After reading this and contemplating how to scale my impact and make my work and the work of the math world more accessible to all, it dawned upon me that a blog would be a great way to get the word out there (on the interwebs), specifically about math teaching and learning.

I've always wanted to write about the work I do everyday and about the struggles, trials and tribulations that I have encountered and continue to encounter in the math world.

As many of you know, I started out teaching in a 5th grade classroom in New Jersey, not knowing much about teaching (or learning) at all.  I was prepped through my undergrad program to work in the field of psychology and had no "classic" teacher training whatsoever.  I also had very limited content knowledge in the area of mathematics (although I never knew it).  You see, I was always told I was smart and learning came easy to me.  So when I asked questions about why we do things in math and my teacher told me just do it, that's the way it is, I did not press any further, I just memorized what I needed to and moved on.  Fast forward to my first teaching job in the 5th grade classroom using Everyday Math as our primary resource.  I was teaching things to 5th graders as I myself was learning them for the very first time with true understanding!  It was amazing.  It was also frustrating.  Teachers around me did not like that my students were doing well in math.  "How do you do that?" they'd ask.  "I can't get my class through Unit 2 and you're on Unit 4, you need to slow down!" they'd tell me.  I didn't think I was doing anything extraordinary and the truth is I probably wasn't.  However, what I still didn't know was that I wasn't learning new things in math because I hadn't been classically trained to be a teacher, but rather because I had never fully comprehended the concepts when learning them as a learner.  And neither had most other people.

Since my time in the 5th grade classroom, I have earned a master's degree in Curriculum & Instruction: Teaching Children Math, worked as a math coach, worked as a math intervention specialist, and now as a K-12 Math & STEM Coordinator.

I am challenging myself this year to make it a New Math Year.  I am going to do something outside of my comfort zone in the area of mathematics each week and blog about it right here for everyone to see!  👀 I would love to know if anyone (teachers, administrators, students) would like to join me in this venture?  If you do please comment here and we can chat about what you would like to accomplish in this New Math Year!