How far is Beijing leads to an investigation into longitude lines

Our investigation into China has deepened.

We started our investigation into Mandarin, learned a few phrases and the students went home with much enthusiasm to have conversations with their families.  The next morning they all greeted each other with Ni Hao!  They were so excited to learn Mandarin that they were asking for all sorts of new words.  I know very little so we moved towards the numbers, they soon saw how the pattern worked and began counting, they now know up to 99! Further questions are how to say zero and 100.

In a constructivist classroom it is easy just to  "go with it", to let the project evolve completely from the students leanings, but I must also be sure to listen out for those ideas that will lead the investigation further and deeper.  As we were working on the numbers a child asked about the One Child Policy in China, another asked if we could actually go to China.  Both of these questions are very valid, and both could lead to deeper investigations.

So which way to go?  Which one would be more interesting, which one would lead to the goals I had set for the investigation?  We decided to go with "going" to China.

This led to a fantastic discussion into our world.  The size of the earth, how far Beijing is from Richmond, Virginia and would it be possible to fly all the way there without stopping.  The general consensus was no it seemed too far.   We looked at scale, and on a world map calculated the distance - about 8000 miles - still too far was the opinion.

We then looked at airline route maps, it seemed that by going via California we may be able to get there, still not sure though.  Then a student brought in the proof - her father had traveled all the way to China without stopping and she showed us the route - yes it could be done!

Then the children became interested in the globe, looking up the route and investigating the markings on it.  Soon the words longitude and latitude were coming up.  What do those words mean I ask.  And as in an earlier blog, I noted that the students had learned a vocabulary word but had no real idea of the meaning of it. They knew they were lines on the globe, but nothing further.

So, an investigation into the longitude lines on the map ensued, groups of children gathered around globes, observing the lines and numbers they saw.  It was noticed that there were 12 longitude lines on one globe.  When this information was shared, we found all the globes had 12 lines, could this be to do with time, one student asked - YES, of course time zones, it must be!

In the constructivist classroom, it is always important to acknowledge the ideas of the students, right now it really doesn't matter whether the longitude lines have anything to do with the time zones, or that there may indeed be more than twelve of them.  It is not time for the teacher to reveal that information yet.  But I have been asked to find a time zone map, and we'll see if the time zones do match up with the longitude lines.

Using popsicle wrappers to start an investigation of China

So what can you tell about China from a few wrappers?

We started our investigation into China last week and the initial provocation was for the students to investigate some popsicle and candy wrappers.  They had to describe the wrappers, try to figure out what was inside, then comment on what they can glean about China from the wrapper.

Well - these are some of the ideas:

It must have been hot when I was there because so many of the wrappers are from popsicles.

Chinese people eat popsicles.

Chinese people eat some of the same candies as we do.

A different language is spoken in China.

Chinese is written using different letters than English.

Words are written using Chinese letters and numbers are in English.

The Chinese like to use cartoons.

Some Chinese foods are familar and some are unfamiliar.

Apart from the flavors, that are still a mystery - this we will investigate further another day, the other main interest was the language of Mandarin.  One of the wrappers was for Mentos so one student commented that if we know the letters that make the word Mentos in Chinese we could use those "letters" to make other words.  Then we would be able to read other things in Chinese, and maybe figure out some of the unfamiliar flavors.

I was interested in the misconception about the Chinese language of Mandarin.  Students will always build on previous understandings in their construct new ones.  All of the students were familiar with Spanish, which uses the same letter system (for the most part) to English, and they had applied this knowledge to a language new to them that of Mandarin.

So, on to speaking Mandarin.

Making Equilateral Triangles Outdoors

On Friday morning, our class bundled up and headed out to the outdoor classroom for math.  Cat was with us that morning as we continued our investigation of geometry and measurement.  The first challenge was to break into groups of three and then create an equilateral triangle using only yarn, scissors and their bodies.  A few students asked for tape measures, but the challenge was to construct the shape without a standard measurement tool.  

So why take this outdoors?

This is certainly an activity that could be done indoors, but this group has demonstrated that the level of ingenuity, problem-solving and cooperation is greater in our outdoor classroom.

So how did they solve the problem?

I noticed one group that started with a length of yarn.  The students positioned themselves in a triangular shape, estimating that they were an equal distance from each other.  I asked, “How do you know it’s an equilateral triangle?”  They responded, “We know because we’re standing the same distance from each other.  I pushed a little harder, “But how do you know for sure that the sides are of equal length?”  They then folded the yarn into thirds but quickly saw that their lengths were not quite equal.  A simple adjustment guaranteed that the sides were now congruent.

 Another group insisted that the only way to build an equilateral triangle was to measure using a standard tool.  Because the logs of the community space had already been measured at 15 feet each, the yarn triangle they created was an exact copy of the logs.  T said, “We already know this one is equilateral.”  They used their bodies as vertices, pulling the yarn behind their backs at the waistline.  Cat noticed that this distorted the shape somewhat, and C said that they could turn “sideways”, making it “thinner” and therefore closer to a point.  He also said that if they used their fingers, it would be “even better”.  What if we had not gone outdoors?  Here, they were able to build on prior experience to guide them in their cooperative problem-solving.

Cat asked them if it would be possible to make an even smaller equilateral triangle, and they struggled to come up with a strategy.  N came over and told them about how her group had accomplished it.  They had cut off a “random length” of yarn and then used that piece to measure off two identical pieces.  

By not allowing the students to use a standard measurement tool, the students got to the nature of congruence (equal measure), of measurement itself, and of proving something definitively.  Even the students said that they thought it would be “much easier” than it was.  After all, they could name and describe an equilateral triangle.  But building one was an entirely different matter. Years from now, in high school geometry, they will have to construct an equilateral triangle –again without using measurement tools– and prove how they know the sides are congruent.   

Thinking with a strength

At Sabot at Stony Point we feel it is important for children to draw on their strengths to help them take their ideas as far as possible.  We are writing fiction stories and the children have the option of drawing their ideas, or cartooning to write an illustrated story. One of the students had been having trouble writing in the details, so during his first draft he had chosen to illustrate instead.  I typed his story for him and left spaces for his pictures.  However, as he was revising and editing this final draft I noticed that he had chosen to take some of the pictures out, and instead include the detail in his writing.

This was an unexpected step.  But, it really made me think.  We do need to allow children to think and organize in a language that makes the most sense to them.  They may not choose to use it in their final presentation, but by drawing, this student allowed himself to add detail, and make his story more cohesive.

How tall is a tree?

Every Friday we go to the forest, this is in addition to our time in our outside classroom.  Sometimes the children have specific science activities to do and sometimes they are presented with a challenge.

This week's challenge was how tall is a tree, or indeed how can one measure the height of a tree.
I had a basket containing tape measures, yard and meter sticks, string and yarn, protractors and set squares,  and safety goggles for the children to use if they needed.

Well, as usual my class went at the task with gusto and I enjoyed watching the various ways they solved the challenge.

So how did they do it?

Find a small tree and measure it with a measuring tape or stick.

Find a dead tree and measure along its length with a tape measure.

Find a thin, bendy tree, pull it down from the top, attach a tape measure to it and let it spring back up.

Measure a tree that is leaning over.  - I added a question for this group - did you measure the height of the tree or the length?  They realized they had in fact measured the length and redid it measuring the height.

Get a group of students together, one person climb the tree, the other hand them a measuring stick, and yet another hold the tree trunk steady.

Find a really long tree branch, use it to measure a tall tree and then measure the branch.

Eyeball a tree, think it is about three times the height of a student - so estimating about 12 feet tall.

The idea of measuring shadows came up and caused a lot of discussion.  The conclusion grade was, that measuring with a shadow would not work because shadows change in length throughout the day. They also noticed that at the time their shadows were longer than them so it wouldn't be an accurate measurement.  One student actually got down on the ground to see if that would make his shadow match his height, but noticed it didn't.  - I did wonder that after this experiment whether they would take it further, noticing just how long their shadow was compared to them, then using that same ratio with a tree, but they decided shadows were not going to work, so moved on to a different idea.

What I liked the best about this challenge was the range of ideas the children came up with.  It worked whatever their ideas were, it worked for all kinds of thinkers. They stayed focused, they measured many trees, they worked in teams, they understood the importance of safety, shared ideas with each other, discussed tough questions and also had a lot of fun.

Art in the forest

Friday was a beautiful day in the forest.  After a forest recess bustling with activity I set the class a challenge. A book on contemporary art had been generously donated earlier in the day and we were investigating how artists use different materials to create works of art.  The challenge was to create a work of art that used only the materials in the forest.  These are some of the beautiful pieces that were created.

Zen
G created this piece on a hidden rock.  
He noticed the spots of rain adding to
the beauty of his piece.

Face
T created this piece in the crook of a fallen tree using two different colored soils.

Ocean in the forest
L used a mushroom cap to create her seascape.

Temple
The pair created two gates and added a top and leaves.
They then blew on the leaves to create a
performance art piece.

Untitled - a shelter in the forest
E created a tiny dwelling- complete with a bed inside

Fallen Tree
This group were inspired by a fallen tree that they had been playing near. They represented it with rocks and twigs.

Following the students' lead

In the last post the class identified two problems with the outside classroom.
One was the cold and the other the boy's shelter.

We capitalized on a warmer day last week and started out to help the boys with their shelter problem before embarking on our science activities for the day.

The boys began by describing the problem and the class went off in search of more tsll sticks to add more space to the shelter while others went off searching for seating possibilities.  The seating group came across a huge and very heavy log cut from the wood for the triangle.  The first thing one student did was measure the log with his arms to make sure it would fit the space and then called for help to carry it up the hill.

Once again the entire class responded, with students taking on leadership roles and all working together they lugged the log up the hill.  Next problem, the branches sticking out made the log too big, so a plan was made to bring the handsaw next time.

Another problem that had come up was the idea of a roof, we decided that maybe we could weave small branches to make a panel.  The question of weaving came up, so we decided to have a minilesson.  While the children were at lunch I gathered together some pine needles and had a provocation ready, I was working on a weaving as they returned to the room and everyone wanted to give it a try.  Those ready to go, shared needles and found a space to start. Those a little nervous or needing a starter lesson in how to weave started with paper.  One student made a chess board with his newly acquired skill.  Next was to take it outside.  One student had tried weaving with rulers and discovered that in order to work the materials had to be "bendy".  So in the hunt for bendy sticks students also found bark.  Groups set to the task of weaving small sticks, large sticks and bark.  They worked at it for a good twenty minutes before all declaring that it wouldn't work.  The sticks were either not straight enough or not bendy enough, and the bark needed to be more similar pieces to work.

So is this failure?  NO!  We discovered a problem, we came up with a solution idea, we learned the skill, transferred it to natural materials on a small scale, discovered the necessary properties for the solution to work and set to work on the actual materials needed.  What we learned was that we still were not there, we still needed to figure out how to make the wood more flexible.  Some suggested making the wood wet, others to put it in hot water to see if that work.  The investigation continues.

Once again, I see totally engaged students, solving real problems, cooperating and being a successful community of learners.