Visit to the Bronx School – Day 3

My first class this morning was grade 3’s working on equivalent fractions.  When I arrived the students had just picked up their personal boxes of rods and were starting to build individually, their patterns for 12, 16 and 20,  using only trains of the same colour.   On the board the teacher makes the patterns for 12 and 16 using the magnetic rods.

Students were able to look at a pattern and hold up the rod that shows 1/3^rd in the 12 pattern (purple),   or with the 16 pattern –  2/4 is 2 purples.   They could separate the rods that showed ¾ and tell us  equivalent fractions such as  6/8  and 12/16.

With more and more equivalent fraction challenges the kids got more and more excited to provide their mostly correct answers!

Next it was time for the “Math Challenge!”

(1/3 x 12) + (2/4 x 16 ) + (1/4 x 12)  = ______

The teacher asked for the  strategy to get the answer.  Four different kids give their strategy, which mostly involves getting the answer from the twelve pattern for the first part of the equation (1/3 x 12) and so on.  The excitement builds as the kids want to say the answer.  Finally they get to say the answer!

Another challenge :  (½ x 8 ) + (2/4 x 20) + (4/8 x 16) = ______

and then another   (2/3 x 9 )+ (¼ x 8 ) + (1/3 x 6) each time many students could describe a correct strategy and then provide the answer.  They seemed to be having more and more fun with each challenge.  A few of the kids had trouble, but most seemed comfortable with the math.

As I sat there and watched the attention, the high level of engagement, and the building excitement and enthusiasm of the students in the lesson,  I was thinking,  this is what should be happening in all classes. This is the way learning should take place.  It was very impressive to see how much they enjoyed it!  Event the teacher was enjoying the lesson! I  noticed she was smiling, even as she tried to get some of the students to contain their excitement to give the answer.  It is a smile I have felt on too few occasions in the classroom.

After a visit to another grade 1 class doing math and multiples, I sat in on another seminar by Dr. Bruce Ballard on Words in Color with a kindergarten and grade 1 teacher who had some questions on using the charts with their class.  Participating with them in the process of how to teach vowel sounds that go with the “r” sound gave me some more valuable experience in seeing how useful the charts can be.  The amount of support and professional development available at the school is far beyond what is available at most schools.  In two short visits with Dr. Ballard, I learned some of the basic ways the charts can be used in the classroom.

Tags: Bronx School for Better Learning, math, Visible and Tangible Math, Words in Color
Category Gattegno Math | 1 Comment » | Mike Hofer

Visit to the Bronx School – Day 1

I have been tutoring grade 4 math for three months, using Cuisenaire rods and working from a few of Gattegno’s math books attempting to teach in a way that is fun, challenging and promoting a deeper understanding of math.  It has been frustrating at times, I believe due to my inexperience teaching math, using the rods, and trying to use a new teaching approach all at the same time. I felt it was time to get some more experience and ideas on how to use the “subordination of teaching to learning” method.

I also know that if I someday use Words in Color and the language charts I should see how they are used in a real classroom!   So what better place to go to fulfill these needs than the pre-eminent school in North America fully dedicated to using Gattegno’s approach, The Bronx School for Better Learning.

This blog will document briefly some of the experiences and learning I had there.  Out of the many different activities I observe each day I will highlight the ones that apply most to the teaching approach and tools of Gattegno.

Monday Jan 25^th

I arrived on Monday morning just as classes were starting.  I was invited to sit in on a grade 1 class.  When I arrived they were working with shapes and blocks at group tables – a sort of free play with blocks and other shapes– and obviously busy and having fun with the task.  After some time the teacher asks them to come over to the carpet area and sit quietly.  Once they are settled and quiet he asks each in turn what they did with the materials they were using. Some made patterns, stairs,  many made spinners, one girl described building a castle to protect the King and Queen.  I noticed that they were very attentive to the teacher and each other during this time.  They wanted a turn to say what they did and hear what the others did also.

The Spanish teacher arrived to give a 30-minute lesson to the Grade 1’s using the Spanish charts.  The teacher used the Fidel to help the class say some of the vowel sounds and other word charts for numbers.  The kids were very excited to be using their Spanish words and often shouted out answers and repeated their answers several times. While the class was working on some Spanish numbers, one group of kids started using their knowledge of Korean numbers and started a discussion on that!  While it was all a little less “orderly” than some lessons, the level of interest and engagement of the students was very high and many were working hard to learn to say the words well.

During two visits to grade 1 classrooms to see English language arts lessons, I observed students who knew the color rectangle chart very well.  From the teacher’s silent direction of pointing to a sequence of colors, they were able to say the words.  The lesson was handled on an orderly way; each time the teacher pointed to a sequence, many hands went up, all excited to tell their answer.  Next, some students came up to point to the colors to show the word they wanted the class to know.  The teacher did not tell the student they were right or wrong but asked the class for a vote.  This seems like a clever way to delegate responsibility onto the class for deciding on correct answers.  It was very energizing to see the teacher and students using the charts so comfortably!

At the end of the day I was fortunate to participate in  a seminar for new teachers on using the language charts.  Two teachers, new to the school, had some questions and concerns about how to use the charts effectively.  They suggested the charts were difficult and possibly confusing to use with some students.  One question asked was about the order of the words on the charts and the order of the charts themselves.  There was also some concern about the order of letters on the Fidel.  Rather than addressing these concerns directly, the seminar leader simply led them through the approach that they could use with the materials.  He started with the “quay” (pronounced key) and led us through the steps of how to say it correctly, then showed us using a table and wall what it a “quay” was.  We also worked on how to pronounce “blackguard” using the Fidel.  The point I believe, is that the colors help them through the process of how to say some words.  They can then be asked to use the words in sentences to show meaning, and so on.  The colors (the Fidel) help them solve the problem or the challenge of learning English.

We then worked on using the Fidel to say the sounds, sliding our arm/pointer down the column of different spellings for the same sound as we did so.  The leader of course did not once tell us how to say any words or sounds correctly.  He did not “model” the sounds!

This was only the second time I had seen how the charts could be used to advance vocabulary with correct pronunciation. Although I came to this seminar just to observe, I found myself eagerly particpating in the learing process.  At the end, we all had a more clear idea of how use the charts and a better sense of their rational organization.

Looking forward to the next day!…….

Tags: Bronx School for Better Learning, caleb gattegno, deeper understanding, math, math tutoring, tutoring, Visible and Tangible Math, Words in Color
Category Gattegno Math, Re-inventing Education Blog, Teachers Education Blog, The Silent Way, Words In Color Blog | No Comments » | Mike Hofer

Upcoming, “The Science of Education summarized”

Caleb Gattegno began work on The Science of Education series of books in 1940. After decades of research and real-world experience teaching all kinds of students to read, write, and do mathematics, he released The Science of Education Part 1: Theoretical Considerations in 1987. This book is renowned for its deep consideration and enlightening conclusions about the problem of education, but it is also a notoriously challenging read.  I have decided to take on the challenge, and to summarize each chapter according to my own understanding. I hope to express his ideas clearly and succinctly, without losing the powerful concepts his original words evoke. My next post will be summarizing Chapter 1: How a Science is Born. Wish me luck!

Tags: math, reading, The Science of Education, Words In Color Blog, writing
Category Re-inventing Education Blog | No Comments » | Amy