Leocolor Books (Spanish Words in Color)

• Leocolor – Libro 1
• Leocolor – Libro 2
• Leocolor – Narraciones Breves
• Leocolor – Ocho Cuentos
• Leocolor – Para la enseñanza de la lectura

The Silent Way (Foreign Language)

• Teaching Foreign Languages in Schools The Silent Way
• The Silent Way – A Thousand Sentences
• The Silent Way – Eight Tales
• The Silent Way – Short Passages
• The Silent Way – The Common Sense of Teaching Foreign Languages
• The Silent Way Algebricks
• The Silent Way American English Fidel Large (42cmx60cm)
• The Silent Way American English Large Set (42cmx60cm)
• The Silent Way American English Mini Set (20cmx14cm)
• The Silent Way American English Small Set
• The Silent Way American English Sound-Color Chart (42cmx60cm)

Visible and Tangible Mathematics

• The Science of Education Part 2B: Awareness of Mathematization
• Visible and Tangible Mathematics Algebricks Large Box
• Visible and Tangible Mathematics Algebricks Small Box

Click on the individual products above, or Click Here to view all our products.

It should be noted that each child had their own large box of rods, in sufficient quantity to create several patterns to keep on their desk while they worked out the answers.

Most of the kids were getting correct answers, some very quickly.  Others were working slowly and needed some guidance.  I worked with one girl, new to the school, by asking some more basic questions such as which pattern do we need to look at to find the answer, what does the number on the bottom of ¼ tell us, etc.  She was then able to get an answer.  There were two other boys that were having trouble who asked for the teachers help.  I did notice that the teacher did not ask students who were finished, to help those that were having difficulty.  I think this would be part of Gattegno approach, but there may be some practical reasons why this was not used here. (I did not see students helping other students often in other classes either!) It would be interesting to hear from other teachers about how useful this is or problems with it (i.e. problems with students helping others who are having difficulty).  I have certainly seen that students helping students can be very effective in my small tutoring classes.

It should be noted again that the teacher had most of the students fully engaged in their work.  They all seemed very enthusiastic about the challenge!

After most students had finished the questions, the teacher asked them to cover up their patterns.  They were then asked to imagine the patterns and answer a few questions without looking at the rods.  If they can do these fractions without the rods, they have made an important step in moving towards a mental perception of the math and away from dependence on the rods.  I overheard some of them say “This is easy!”, which is I think, the mark of a successful lesson.

On to another grade one class….

They continued to work on multiples, but this time also with subtraction, first with the teacher using the Smartboard and magnetic rods (I must get some of these), with one student coming to the board to show how to solve a problem. (eg. 2P – 3r = ___ )  Again I watched the class get increasing restless – without anything in front of them to keep their hands busy – until they were asked to write down a list of questions using multiples.  Once they had written them down, they were allowed to get their individual boxes of rods and start working on the problems.  They were much more involved in their work once they had the rods, and were busy building the trains and patterns.  Some needed help, but most worked busily away and constructed  correct answers.  The students whom I helped would call me back for more help often; I tried to give them some direction, but then the next question they would have the same problem.  They had not “learned” how to solve the challenge.  I wondered if they were newer to the rods than other students, or if they just needed more time.  Maybe we needed to go back to the previous lesson with these kids ( on subtraction or difference) before we tried these problems again.  Without students helping other students, it certainly puts more work on to the teacher.

What was obvious in both these classes (besides the “subordination of teaching” approach) was the incredible usefulness of manipulative’s in keeping the students focused and giving them a way to understand and solve the problem!

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.

The first one, a game with dice, has the student building a staircase with rods and then rolling the dice to determine which rods they can take away from their staircase.  If you are working with just addition and subtraction for example, and you roll a 5 and a 3, you could take away a yellow and a light green rod, or a brown rod for (5+3), or a red rod (for 5-3) , assuming you still have the given rods still in your staircase.  The next player then rolls the dice and takes away a rod or rods according to the numbers or an addition/subtraction operation on the numbers.  Play continues until one player has no rods left.  Another way to play the game would be to allow multiplcatin or division on the dice numbers as well,  or to add another die and use three numbers in any expression with +,-, x, or ÷.  Many other variations on this game can be made.

Another game involves a 5 x 5 table of numbers.  The numbers result of an operation or operations on, for example, four numbers such as 7, 6, 9, and 3.  The table can be prepared ahead of time.  Any and all correct equations using the numbers and the four operators  +,-, x, or ÷ could be used.  Examples are 7+6+9+3=25, (3×6) + (9-7)=20, (3×6) x (9-7) = 36 and so on.  With the twenty-five numbers arranged on the table, students must then find a number for which they can write the equation to get that answer.  If they find a correct equation they get a point and circle the number on the table.  Additionally they get a point for each box in the table that is already circled and is adjacent to the  this correct answer.  Once all the boxes are circled, the player with the most number of points wins the game.

The game could be simplified by using only addition and subtraction and using smaller numbers, or made more advanced by using exponents and factorials.

There must be many more games that educators have developed over the years.  It would be great to have a compilation of all these games somewhere!

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!…….

Chapter 1: How a Science is Born

In this first chapter, Gattegno discusses what a science is, the role of awareness in every science, and then how awareness became a science of its own – the Science of Education.  Below is just one interpretation of the messages in Chapter 1: How a Science is Born.

Firstly, to address awareness, we need to acknowledge the inner dialogue inside our minds. Humans have always had inner dialogues with themselves, at every age, in the past and present.  A “need to know” drives these inner dialogues.  Talking to ourselves in our minds is extremely important – it is what translates the world into the visible, audible, tangible, and mechanical world we each recognize. Awareness makes us human, and also makes science possible.

The accumulated experience of our ancestors, from the first humans onwards, is not designated as a science because their experience was not recorded in scientific journals and has not been accepted by academic pundits. Yet what early civilizations found led to the basis of all work ever done by humans. We now see these findings as natural, and common knowledge, but they are truly the results of human awareness.

Our ancestors had a need to know; they had to survive in their environment, and they had to pass their findings on to others. They learned how to work the soil to produce food, they discovered materials like clay to make art and household items, they discovered hunting and how to kill an animal with tools they created, and they discovered how to make their inner self go further, to push themselves to run faster, climb higher. These people discovered the Science of Optics. How can we trust what we see? What is light? What happens when it bounces or absorbs into various media? They also discovered the Science of Acoustics. We take for granted now that a sound sounds differently when moving through different substances like solids, liquids and gases, and that it has different qualities like pitch and intensity. An inner dialogue with the self is needed to know about any of these things, and so it could be said that early humans were constantly involved in scientific activities.

The mind does not want to fool itself, or be fooled by anything else.  This made people watchful and skeptical, which translated itself into repeatability. Whatever one person found, another could find too, and these became the “facts” of optics and acoustics that we take for granted today.

Today’s scientists are only concerned with the contents of their awareness, the “facts,” and not the awareness itself. This is illustrated well with mathematics. Mathematics is based on the awareness that relationships can be perceived as easily as objects, but mathematicians mostly focus on the result of the awareness. Pure mathematics focuses on creating statements that are equivalent to another statement; this only proves that there are a number of possible inner dialogues someone can have when considering a relationship. Since we focus on the result, we have lost contact with the maker of the answer – the mind conversing with itself.

All sciences are human endeavors, and they change as humans contribute new ideas. Some viewpoints are altered, and some are abandoned altogether. This tells us that “knowledge is the working of knowing.” Or perhaps that knowledge is knowing in progress.  Gattegno writes that, “the history of every science is a history of awareness,” and therefore, “everything could be the source of a new science.”

For example, astronomy became astro-physics, cosmology, radio-astronomy, spectro-astronomy, planet evolution, star evolution, galactic systems and more. This can be seen as specialization within one enormous challenge, but it could more accurately be seen as the ways various scientists prefer to address themselves with questions. Different inner dialogues produce different sciences.

Sciences are imprinted with the mind that proposed it. A science is as dependent on the scientist’s inner dialogue as it is dependent on “scientific method.” It is an illusion to believe, “that reality is totally fathomable and that it will be possible to reach a stage at which eternal unalterable knowledge will be available if the ’scientific method’ is used more carefully.” Reality grows and changes because it is only, “the construct of the minds who dedicate themselves to it.”

For example, 200 years ago, electricity was only a reality to a handful of people who imagined it. It started as thoughts, ideas and projects in minds, then as experiments, which turned into factories, stations, and machines. No one can deny the existence or reality of a concrete factory. But neither can anyone deny the existence of a person’s mind in the factory – after all, it was man-made.

What we know about our current sciences is very important; we need all of the sciences in order to define the reality of our time. But that’s not enough. New sciences must be born to define new awarenesses.

The Science of Education is an example of how a science can emerge from the raw material of human experience, and progressively become a presentable system of thought. At the basis of the research of this science is the fact that humans are capable of being aware of their awareness – there is an ongoing dialogue of the mind with itself.

Sciences bring to light awarenesses that we receive as facts, like the ones in the Science of Optics or Acoustics. Since all new sciences begin with a new awareness, the Science of Education took awareness itself as the subject.  The science is actually the awareness of the awareness of awareness (using the word three times is necessary).  In other words, this science is not about looking at something. It is about looking at looking (at something), and knowing what the self does as it looks.

This science does what no other does, yet can follow the attributes of the established sciences. These attributes are: domain, approaches, methods, presentations, and verifications. Verification, for example, takes the form of continuous feedback.

This science has been worked on since 1940, but is still very new. Over the years, decades, and generations to come, it is hoped that revisions and alterations will be made to the science presented in the next chapters.

Special thanks to Gladys Doebeli Rocourt for being in touch with us and her comments on my previous blog on Aux Alizés.  A clarification that the maths materials are actually ‘new’ materials for math teaching and not ‘translated’ materials.

Aux Alizés, a school in Petion Ville, is run by Raymonde Rocourt and her daughter Patricia Rocourt.  This school opened in 1997 and operates using the Subordination of Teaching to Learning in all subjects.

Gattegno’s materials can be seen everywhere, in multiple languages, charts, rods and teaching approach.  The school was started by the three Rocourt sisters who came from a family of teachers, and had a longtime dream of opening a school.  After meeting Caleb Gattegno in Switzerland, Gladys Rocourt became a proficient teacher and trainer using his materials and worked at the International School in Geneva before returning to Haiti. Prior to starting Aux Alizés, Gladys travelled rural Haiti doing teacher training in French and Creole literacy, and mathematics. 

During this time, Gladys Rocourt collaborated extensively with Dr. Gattegno to develop a full blown Words in Color curriculum for Creole called Lekti an Koule Kreyol.  These materials are still in use at the school, which goes from Grade 1-6.  Gladys Rocourt also successfully translated Gattegno’s math curriculum into Creole, and aligned it with the official Haitian curriculum. 

Mme. Raymonde Rocourt spoke about the initial resistance her school encountered in the early years, with these colorful materials, and non-traditional teaching styles.  In 2009 the school’s reputation is one of the best in the community and standardized test scores of 100% pass for the past 9 years demonstrate their success, and needless to say acceptance as a leader in educational innovation.  Mme. Rocourt is even considering expanding the program to grade 9 in the future.

What an incredibly beautiful country!  The mix of languages here is amazing … The Haitians we have met are so fluid changing from French to Creole and English.  This may be one of the [only] positive outcome of colonialism.

The Mathematics Teacher Training Project in Haiti is officially underway.  Although the in-class training starts tomorrow, we met with the several of the partner groups, NGOs and schools, today for a very productive kick off meeting.  There were several comments throughout the day about the desire of the population here to be educated.  Some families will spend up to 40% of their household income sending a child to school.

Educational Solutions has been selected by ELAT, CAFT and other grassroots development groups to participate in mathematics  teacher training program in Haiti, December 6-12, 2009.  ELAT, an acronym for Elevating Learning Above Teaching, is a not-for-profit organization whose goal is to train teachers with a view to creating a local network of teachers who can train other teachers.  Esaie Pierre and Dr. Arthur Powell came to Educational Solutions with a proposal for this training, and we have enthusiastically agreed to participate.

ELAT has chosen the pedagogical approach and materials of Dr. Caleb Gattegno and Educational Solutions in its developmental projects, knowing that the materials apply in a variety of difficult educational circumstance and can easily overcome local language challenges.  ELAT’s international experience combined with Educational Solutions’ business, educational and operational skills are a recipe for successful training in underdeveloped regions of the world.   The December 2009 project involves training teachers in mathematics.  Future projects will include literacy and foreign language learning.

I will keep a log of our activities, and post updates from Haiti.

Sima Gandhi