The Rookery

Letter of the Law

Just in time for Village, the Herons had a fascinating conversation about laws on Thursday.  We have a class guideline:  If the predicted high for the day is 70 or greater, you may wear shorts.  On Thursday, the predicted high was sixty degrees...so no one was wearing shorts.  But we went out for a soccer game and then recess and by the time we got back in, we were really hot.  

One student asked if he could take his pants off because he had put on shorts underneath when he got dressed in the morning.

The room erupted, "That's not fair!"  "He shouldn't be allowed to have shorts, the predicted high wasn't 70!"  Others disagreed, "Whatever...he should wear shorts if he's hot."  "You just think it's unfair because you want to wear shorts."  "If you had thought of it, you wouldn't have a problem with it." We were just entering lunch time and I let the conversation continue for a little bit.  "He followed the rule - he wore pants to school..."  "I think it's fine...if he gets cold he can put his pants back on and that's why we have the rule so that we don't complain of being cold."  

I chimed in at that point asking the students if they remembered why we had the rule, "You need us to be ready to spend an hour or more outside in case we're doing a lesson or something."

Had the pants/shorts child followed the rule?  "Yes."  was the response from everyone, albeit some were a little grumpy.  I introduced the concept of the "letter of the law" and the "spirit of the law."  He had technically followed the rule...is it possible that he had also followed the spirit?  After all, he could put pants back on if he needed to.  There was a lot of conversation about this.  "It's hard to learn if you're hot, too," the pants/shorts child pointed out, hopefully.

I asked the class if they would feel it was fair if I officially amended the rule so that students could wear shorts under their pants if they wanted to and could ask to change if they got hot.  The response was unanimous...yes, that would be fair.  So we have officially amended the rule - students may wear "just in case shorts" under their pants.  I think that the work of figuring out why a rule exists and what it's meant to do will be very useful as students begin to form ideas for creating laws in their own Village.

 

When the Students Teach Themselves

Another number talk, showing great flexibility...sadly, I did not record our negative number work.

For several years, I have been interested in "The Mathematical Habits of Mind"  What can I help students do as math thinkers to become more successful in math and to best prepare them for using math and learning math in the years to come?  What do mathematicians do and how can I translate that to a fourth and fifth grade classroom.  Elements of the common core speak to this - students are asked to explain why something works.  They are expected to uncover patterns and extend them.  They are asked to work with numbers flexibly depending on context and model them in a variety of ways.  In the common core, these are called "mathematical practices" and like several parts of Common Core, I feel it is a good fit for Prairie Creek.

Which brings us to Friday.  I have a visiting student from Cathy's reading class at Carleton.  He's going to be a math teacher so I was excited that he was going to be in our room for math as well as reading.  I decided to share a number talk with him - the Herons love them, he hadn't seen them before, and they are central to my understanding of how kids think about number.  We opened with 60-32.  Students are expected to do the problem in their heads and then share the approach they used to get the answer.  Students approached the problem in eight different ways, including one student who got -28 instead of 28.  She explained that she had done 32-60 instead of 60-32.  A child commented that it was cool that it was the negative.  "Does that always happen?" he asked.  I turned it over to the class, "Does subtraction always work like that where you'll get the negative difference if you flip the two subtrahends, numbers in the subtraction.  Or is this a coincidence?" I asked the class.  A handful thought it always happened.  A larger handful thought it was a coincidence and the rest thought we should test it out with more examples.

In math, making a hypothesis like "When you flip the subtrahends in a subtraction problem, you get the same answer but negative" is called a conjecture.  When things are going really, really well in a math lesson - students make conjectures.  They extend ideas and want to know if it works.  Then they test some examples to see (eventually they'll write proofs...but that's a few years down the road.)

So we did some examples and it turns out it does always work.  "What about one number minus itself?" a student asked.  We pondered this for a while.  "You always get zero," another child answered.  I pointed out they had just "discovered" a very important fact about subtraction called the identity property and that it took human mathematicians hundreds of years to realize how important this was.  "But why do you get the opposite number every time?" another student pressed.  We wrote out the problems using open number lines and this visualization helped several students have a "aha" moment.  It was hard for them (and me) to articulate exactly at first.  When you subtract A-B and get C.  Then, when you subtract B-A, you end up going back B to get to zero and then you have to continue to -C to have subtracted the whole quantity of A.  It makes more sense in numbers.  34-15 is 19.  If I subtract 15-34 using a number line, I start at 15 and go back to zero (subtracting 15 of the 34).  I then have to subtract 19 more to have subtracted a total of 34.  Using the number line, I end on -19.  As we drew out several examples more students called excitedly, "Oh! I see why it works!"

This wasn't a planned part of the lesson but the students were ready to use their math habits of mind to question and explore.  I could have taught them that when B is bigger than A and you subtract A from B, you just get the negative answer of A-B.  But that would have been a disconnected fact to memorize - by constructing their understanding, they don't have to memorize anything.  It just makes sense (and it's a lot more fun.)

The deep math work continued as we jumped into our math lesson.  We used Pascal's triangle and colored patterns based on divisibility (I wanted to review the key concepts of multiples).  Students quickly saw patterns in their work and used them to make better predictions about which numbers they needed to test.

For those who finished and didn't want to explore another number, I offered a new activity of drawing

Collecting and testing conjectures on the white board

loop-de-loops.  You use graph paper and choose three numbers, say 2,4,5.  You go to the right two, up four, left five and then down two, right four, up five, left two, down four, right 5 and up two, left four, down five (and you'll be back where you started.)  Quickly, the Herons began to group patterns.  "This one doesn't have a square in the middle."  "These two have squares in the middle."  "Wait! If it's odd, odd, odd, maybe it always has a square!"  "Let me test this one!"  "What happens if you switch around the numbers?"  Within five minutes they had made multiple conjectures, tested them and modified them.  Our time was up far too soon.

Now...how to design a test that enables students to demonstrate this learning!

mmm

 

So gross...so cool

"Oh!  I have a skull!  Come quick."  "What is this?!?"  "COOL!"  "Ewww..."  "MICHELLE!  COME HERE NOW!"  "Intact vertebrae...I have intact vertebrae!"  "Dude!"  An audio feed from our owl pellet dissection yesterday would have been a hoot. (Sorry.)  There was a lot of enthusiasm as students' owl pellets revealed treasure after treasure.  For some, it might have been the highlight of the year.

Continuing our informal study of how bodies get rid of things we eat but can't digest (my "fourth" grade model project this year was on scat), the Herons dissected owl pellets yesterday.  In February, several fifth graders told me they couldn't wait to dissect pellets at Wolf Ridge.  Sadly, it wasn't on our schedule this year.  Thankfully, I have the freedom to pursue students' interests in our curriculum and with a quick visit to pellet.com we had a nice addition to our recent adaptations theme.

We learned about owl adaptations and how pellets are formed and then ("Finally!" as one student said) we got our pellets.  As students discovered bones, they compared and sorted them using a bone identification chart.  We looked at the anatomy of the different animals we were discovering - including the ball and socket joint we could re-construct with pelvis and leg bones of the rodents we found.  Using our jewelers' loupes, we took a closer look at the cancellous bone structures inside the skull.  Two students found mole skeletons and we were able to look at the huge difference in the forearms of moles compared to rodents.  A favorite find was orange rodent teeth - made orange by the iron that strengthens one side of the tooth so that the back side wears down to an edge and a sharp, knife-like tooth is made.  We also found rodent teeth that were over an inch long but slipped inside the bottom part of the jaw - and we spent a long moment contemplating how weird it would be if our teeth continued to grow indefinitely the way our hair does.

As we wrapped up our lab, students recorded how many different animal skulls and bones they found in their pellets.  Today we compiled the class results and discovered that 89% of the meals our owls ate were mice, 4% shrew and 7% mole.  We considered how scientists might use data like this about owl diets in an area.  And finally, we shared questions that our work prompted and what we would want to find out next (a fair number of those questions focussed on just how pellets are made.)

All but one Heron would like you to know that they would be very pleased to receive owl pellets for their next birthday or holiday gift.  (The link is provided in paragraph two).  Have fun!

It Starts Young

Last week, right after the honoring fair wrapped up, the Herons went down to our Dove bird buddies to help with their initial personal project research.  The Herons helped their Dove buddy record questions of wonder and then they read information books together.

Their work had come full circle.  The Herons had questioned, learned and taught and now they were teaching younger children how to do the same thing.  Back in the day, a giant fifth grader had settled in next to them to read, too.

About eight years ago, personal projects was the focus of a year-long professional development focus.  During that work, we aligned what we did at every grade level so that we used similar language and techniques during the research process.  At each grade the work deepens in its scope - from answering three "dot" fact questions in kindergarten to the thirty minute honors project presentations.  The constant is children pursuing subjects they are passionate about and teaching others what they have learned.  Also constant is that the process of learning is a social one, whether you are reading with your bird buddy or studying with your mentor.

  

Question, Learn, Share - Creating a Culture of Curiosity

This is one of my favorite weeks at Prairie Creek.  The students would probably say, "That's because you're not doing anything!"  And there is some truth in this.  I'm not the teacher this week...they are.  And what a joy it is to see them take on the role of "expert" with such confidence.  Four Herons taught today as part of their honors projects - and each held their audience's attention for a half hour.  Their topics ranged from the orphan trains to Andrew Lloyd Webber to chess to the classification system of Carl Linneaus.

How, I wondered, did these kids ever come up with these projects?  Then I listened as their peers asked question after question - specific questions springing from a genuine interest and a desire to know.  I went downstairs to watch a few fourth grade projects - and I saw a group of Chickadees rotating through presentations on video games, the violin, vaccines, basketball and the arctic.  Each audience of fourth graders and kindergarteners was also asking questions (my favorite being, "Ummm...what are the signs that you might be catching smallpox?"  The presenter assured her she wasn't.)

During personal projects the students are immersed in a culture of curiosity.  Everyone around them is interested in things.  Everyone is asking questions.  Seeds are being planted for future interests and passions.  Just as importantly, everyone is teaching.  We are learning from each other.  Students see that knowledge isn't something imparted by a wizened few.  It is something that they can discover and share themselves.

This sense of agency, of being a creator of knowledge, is central to the success of the progressive classroom.  We don't use grades or stars or even praise to motivate students.  Instead, they motivate themselves through the desire to figure things out. They want to know.  From a very early age, they have seen how others question, learn and teach and they themselves have questioned, learned and taught.

This week culminates in Honoring Night (6:30-8:30 pm) to which everyone is invited.  To me, it celebrates the fact that these fifth graders have proven themselves ready to question and discover independently.  They are ready to learn (and teach) anywhere they go.  We couldn't be more proud.