Travel Journal – Stories Everywhere

Every place has a story, sometimes the story is ancient and tied to the land.  When we arrived at our mountain mansion we knew little of the far reaching history of Tateyama and the mountain.

Omachi ShrineTuesday morning we stepped out the door, ready to explore, and our attention was captured by another beautiful shrine. Before us were towering ceders, serene green spaces, and dai-doro stone lanterns lining the path; it’s no wonder we are attracted to these spaces!

Next we came upon the Tateyama Toyama Museum. You may think we had our fill of places like this. Well almost, but we naively thought there was not much else to see in this location, so in we went.  This turned out to be a brilliant move because the museum gave us a framework for understanding more of what we saw the rest of this day and the next.

The first exhibits gave us the usual explanation of the geology of the area, showing how volcanoes occur, and telling that Tateyama is a volcanic mountain. It was after this, that things got interesting, and puzzling too.  We viewed displays with short captions in English and detailed explanations in Japanese. We tried to make sense of the exhibits that explained the faith that had grown and developed around this volcano, a Buddhist faith that included the concepts of heaven and hell. Both concepts were tied to the activity of the mountain, the beautiful green heights on one side of the valley and the sulphurous springs and odors so prominent on the other side.

One gratuitous photograph.*

One gratuitous photograph.*

This painting on silk, striking in its color and detail, is actually a frightening picture, showing people burning in flames trying to get away. And other people or beings in the sky above, whether they had escaped or were there to rescue the others I am not sure.

A carefully constructed diorama of the mountains, the valley, the shrines, and a beautiful red bridge caught our attention and next to it was a video showing a present day ceremony showing women sitting, listening meditativly to a priest performing ceremonies. Then the women dressed in white gowns, with their hands tied together were blindfolded, and walked together at a steady pace over a beautiful red bridge following priests or monks in deep blue gowns. The women were walking 3 by 3 on white cloths that guided them down the hill from the shrine over a red bridge. I found the imagery disturbing, mostly because the women were completely vulnerable and because of  my own lack of understanding about what all this meant.  (A Google search helped: Tateyama UNESCO Ceremony)

imageAfter the museum we continued walking down the forested road when unexpectedly we came upon the very red bridge we viewed in the video and in the diorama! “This is it, the red bridge!”, we exclaimed. All the places we had visited today helped us understand a little more of the faith expression that developed as a result of the volcano and the local religion. This beautiful bridge, over a deep gorge surrounded by green forest, was also part of the religious significance of this area. We were beginning to grasp the story around Mount Tateyama and the surrounding area. Little did we know there was more to discover the next day.

 

*Photography is not allowed in the museum, when I snapped this image I was told – no pictures! I offered to delete the photo but was told that I could keep it, soI felt free to share it here. 

 

 

Teacher Language Matters

As I listened to examples of number talks in the math classroom, this stands out, teacher language matters.

“I think I heard you say.”

“How did you know you should have…..”

“Where do you think your mistake came from?”

“So you are saying…”

“How did you figure that out?”

“Do we see it another way?”

“How do we see this one?”

The teacher’s language conveys that effort, thinking processes  and grappling with the ideas are what matters. Students have the freedom to explore the ideas.  Relational equity develops as each student’s contribution is valued and analysed in an effort to come to a common conclusion.

And there is more … students see that math is a beautiful, creative and connected subject.

 

 

 

My Mother and ‘The Number Talk’

My brother nodded in agreement and chuckled, “Yes our mother was great with numbers.”  She had the ability to use numbers fluently, a skill we we both easily acknowledged.

How well I remember standing next to my mother in a grocery store or bank as she quickly and easily calculated totals.  I would line up the digits mentally in my head, carry or borrow if needed, and try to remember the numbers as I worked.  What a cumbersome procedure!  She, on the other hand, already had the answer and cheerfully let the clerk know the amount required.  I recognized her skill and longed to have it.  It wasn’t speed I wanted, it was the ease with which she worked. Why couldn’t I do that?

Was it the education my mother received during the 1920’s in the Netherlands?  Or was it as a young, single woman when she worked for Unilever that she developed proficient number sense? It was not until later in my mathematical life that I learned her secret. Perhaps I would have benefited from a motherly ‘Number Talk‘.

A Number Talk?   Yes, the kind of talks I plan to use with students this year.  Parents certainly can engage their children in number talks. They’re fun!  And teachers of math will find them a best practice for developing number sense in students.

I observed a number talk as part of my summer math course. Here are my observations.

How Number Talks Work

The instructor sets the students up for the number talk telling them they are to figure out a math question.

1.The question is written on the board and students are asked to solve it. No pencils, no paper, they are to calculate their answers mentally. No comment is given on how to approach the problem.

2. Students are given lots of thinking time and respond with a thumbs up once they have the solution. A low key way to respond so that everyone can take the time they need.

3. Students then share their answers and explain how they arrived at the solution.

4. Through the discussion students are led to see the interesting variety of approaches used to solve the question.

Open ended questions such as these spur the discussion on.

“Anyone try something different?”, “Anyone else do that?” These questions give everyone a chance to explain their process.

“I think I heard you say.” or “How did you know you should have…..” These statements give the student opportunity to clarify thinking and communication. The teacher does not add to the student’s explanation she only repeats what she hears. The onus is on the student to ensure that the explanation is clear.

“Where do you think your mistake came from?” Helps the student clarify logic and identify the error. Mistakes are part of the solution process both acceptable and interesting as part of the learning.

 5. The process students use to solve the problem is written on the board so that it is easy for everyone to follow. This is important. Everyone needs to understand how the numbers are manipulated.

6. All solutions are represented on the board and students are asked to draw a picture of their solution and someone else’s solution. Another important step as it makes the learning more concrete and helps students see how they can work flexibly with numbers.

Screen shot from XEDUC115N How to Learn Math

Screen shot from XEDUC115N How to Learn Math

Number talks are one way to help students develop insight, ability and willingness to to break numbers apart and regroup them as they observe and discuss different ways to solve math problems.

Yes, the answer is important but it is not the most interesting part of a mathematical question.  As we show students that problems can be solved in different ways we teach them the very, very important building block of number sense, a skill that is foundational for the rest of math.

Ahhh yes,  a number talk would  have given me insight into the skillful mind of my mathematician mother but I think I am on to her secret now.