Incidental Or Non-Conscious Learning

Most of our learning is non-conscious.

Schools make use of displays to communicate information to children. This kind of information immersion is used to good effect by advertisers. Just think how easily children learn a tune or pop-song.

At this stage we are making no conscious attempt to memorise facts and will not attempt to do so. Nevertheless your child will by now have made certain discoveries about the rods independently. These unconscious discoveries will have occurred while he/she was 'playing' with the rods. At the risk of becoming a bore I will repeat the mantra that play is an absolutely fundamental prerequisite for success. It is the source of rich experience that children will draw upon increasingly as new concepts are introduced.

By now your child will have discovered that:

• Rods of the same color are also equal in length.
• Rods of equal length are the same color.

•  Rods of different colors have different lengths.

• It is possible to make equal lengths by  puttingcertain rods end to end.

Your child will also have begun to acquire an unconscious understanding of number bonds to 10.

To 'know' that blue is the same length as pink and yellow placed end to end

is to 'know' that B = p + y

or that 9 = 4 + 5

Thus your child will also have begun to acquire an unconscious understanding of number bonds without even realising it!

At a later stage of the program when they are asked what two numbers make ten children will be able to visualise the pattern for 10.

Fingers will definitely not be needed.

If you observe children you may find them beginning to try and organise their work.

The pattern below reveals an understanding of the commutative property of addition.



Researcher Paul Torrance tested 182 students, aged 10 - 21, half of whom were sighted and half of whom were blind. Using words to stimulate their imaginations he tested their response and found that the blind learners scored significantly higher in creative imagery.

In the next post we look at an interesting and powerful arrangement of the rods you may well have seen your child construct.

The program is available at www.helpyourchildsucceed.com

Directed Activities And Mental Imaging

Before we consider the important roles Directed Activities and Mental Imaging play in developing your child's mathematical ability can I ask you to do one thing.

Type 'children playing with cuisenaire rods' in the Google Search Box. Set the search term to 'Images'.

The pictures that appear will all have one of two things in common.
What will be obvious is that the children in the photos are either smiling and enjoying the experience or totally absorbed in what they are doing.

They have entered the optimal learning state that Csikszentmihalyi describes as the 'flow state'. Children love the tactile experience of playing with the rods. Color engages them but all too often the material is discarded as 'child's play' far too soon and almost inevitably with long term negative consequences for the child. The fact is that Cuisenaire rods are such a precise mathematical tool they can be effectively employed at any level.

When I started teaching in the early 70's Cuisenaire rods were common in almost every U.K.school. What was lacking was any structured program that teachers could follow and consequently the rods were used either as 'toys' or in a very limited context as in 'teaching fractions'. Sadly in the U.S. and U.K. today teachers are so pressured into ensuring that children pass the 'tests' set by central government that they have little time or are too lacking in confidence to attempt anything that may appear to be 'outside the box'.

Hopefully 'Ensure Your Child Succeeds At Math' provides the guidance that will encourage teachers to use Cuisenaire rods on a daily basis and teach math at a deeper level than is possible without them. The process is so natural and enjoyable it can almost seem too good to be true. Surely learning math is about drills and routines? True, they have their place but it is very much of secondary importance to ensuring a deeper understanding of the underlying mathematical concepts.

Time to get off my soap box!

DIRECTED ACTIVITIES

After a while directed activities can be introduced along-side free play. It is important that at every stage of their development children are allowed time to simply play with the rods. When introducing directed activities try and link them to children's particular interests. If one child is a Star Trek fan then ask him to build the USS Enterprise. If another loves Noddy stories ask him to build Noddy's House.

Obviously the possibilities are endless but should always be tailored to the child's particular interests.

One of the brain's natural abilities is imaging. This ability can be used to create a retentive memory - a vital ability for anyone and especially useful when preparing for examinations. Begin to increase your child's capacity for recall by asking him/her to simply imagine they are outside Noddy's house looking directly at it, or about to board the Enterprise.

Draw on their other senses.
e.g. What might they hear, smell, taste? Get them to see the object they are about to create in their mind first. The ability to have a mental image of the rods is vital, as this will speed up progress considerably.
Apparently Enstein first conceived of the Theory Of Relativity while imagining himself travelling on a beam of light!

Increase the challenge by asking children to use only certain color rods. Not only will this improve your child's manual dexterity but also stimulate his/her brain at the same time.

Allowing your child tme to play freely with the rods is vital no matter what stage of development he/she reaches. You are the best judge of your child's likely concentration span. If you are not sure stop the free play sessions when he/she starts throwing the rods around!

Directed activities and free play sessions are continued together.
Regardless of age children never tire of playing creatively with the rods.

Mental Imaging: Games To Play
You have already begun to develop this natural ability of the brain through directed activities. Now we need to consolidate this ability. To achieve this we introduce some games. These games are designed to ensure children can recognize the rods by touch alone. Although color is a powerful stimulus for memory recall it is possible for children with impaired, or no vision at all to derive tremendous benefit from the use of the rods. Children who have little of no sight usually develop their sensory ability to a very high degree. Eric Jenson in his book The Learning Brain suggests they are not dis-abled only differently abled.

Ask your child to hold his/her hand behind their back and give them two rods to hold. Can they guess which colors? It would be best to start with the smaller rods. For example, give them red and white. can they hold up the red . . . the white? Increase the challenge with different pairs of rods.

• As they become more confident increase the number of rods to three or four.
• You may find eventually that placing the rods in a bag, like those used in banks, will make it easier to increase the challenge while making it more manageable for your child. If the game becomes too easy they will soon get bored. Too difficult and children become discouraged. You are best situated to provide your child with an education totally tailored to his/her needs.

Once children have mastered these games and are now able to recognize all the  rods by touch alone they are ready for further challenges.

The ability to substitute one term for another in math is crucial to understanding. The next activity which is really an open-ended task will help develop this ability.

• Choose one of the rods and ask your child what two rods can he/she place end to end to make the same length as the first rod?

There are numerous combinations of rods that end to end make the same length as the blue rod. See how many your children can find.

In the next post we take a closer look at incidental learning.

The complete program is available now at www.HelpYourChildSucceed.com

Phil Rowlands

First Stages Of The Program: Vocabulary

Having given your child a set of the rods (or access to the software) he/she will have naturally begun to play with them exercising his or her imagination in a variety of ways. Through play your child is unconsciously garnering the experience we will draw upon later to introduce and develop math concepts.

By now the rods will have become a source of pleasure and delight. Children are frequently reluctant to 'break up' their creative designs and it can be a good idea to take a photo of their work. Alternatively they can create an exact copy using the software and save it in a file on the hard drive.

 It is at this point you can introduce the color names of the rods. The names we choose are important because they reflect the precise nature of the material and will be important during the ensuing stages. Please use the following color names:

Later, before we introduce math concepts we will refer to the rods by the first letter of their color name. Thus black becomes 'b', blue becomes 'B' and in order to avoid confusion the brown rod has been named 'tan' and becomes 't'.

Once the signs are introduced (gradually) your child will learn to construct mathematical sentences from what he/she creates with the rods using their Letter Names. Let's take a look at a simple construction.

During periods of play it is quite likely your child may have already discovered that the yellow rod is equivalent to green rod placed 'side by side' with the red rod.

At a later stage once the letter names and signs have been introduced this will be written as g + r = y

A simple form of algebra in fact.

Although this is jumpimg ahead you need to understand the importance of imparting the correct terms to the child for the different ways the rods can be physically aligned with each other.

Here are the important terms and phrases you should use:

Also 'length', 'longer', 'shorter'.

On a math forum recently a lady, who was trying to promote her own product in the face of many comments from teachers regarding the importance of using manipulatives to develop understanding, made a valid point. She said that manipulatives were often used merely as toys.

Sadly she was right. While the rods are a source of immense fun and pleasure their unique potential to develop mathematical understanding in children is often barely scratched. This program ensures that this potential is released in a way that allows your child to 'discover' math concepts for him/herself through a process of exploration and discovery with gentle promptings from you. The program will guide you along the way. Just enjoy the journey.

If you have not yet read "The 5 Most Common Reasons Why Your Child May Fail At Math" can I encourage you to do so. You may find it very enlightening.

For those of you who want accessmore information about the full program right away it is available at www.helpyourchildsucceed.com

In the next post we consider Directed Activities and the importance of developing Mental Imaging and games you can play to develop this ability.

So 'Math Anxiety' Does Exist? WOW!

In this post I was going to talk about the early stages of the program, the importance of vocabulary and directed activities but, to quote Gene Pitney, "Something happened to me and now I'm not the same any more."

Two things actually. The first was the a report of the study from the Stanford University School of Medicine in Psychological Science showing that children who experience difficulty with math exhibit an altered brain function from anxiety. Anyone who is in an anxious state suffers from altered brain function. How many of us recall the stupid mistakes we made when learning to drive because panic just shut down access to the part of the brain that accesses our higher thinking skills. Well at least now it's been given a label perhaps educators will begin to seriously address the root cause of 'Math Anxiety'.

The second was a discussion on the LinkedIn Elementary Math Group started by substitute teacher Laura Lynn Walsh* alarmed at the lack of practical understanding displayed by the 6th Grade class to a 'warm up' problem she posed.

Obviously I have my own opinion and was therefore delighted that many teachers who responded hit the nail, for me, fairly and squarely on the head. Here are a sample of their comments:

"As an elementary math teacher for the past 33 years, one complaint I constantly voice concerns the early abandonment of manipulatives. Why the rush to put aside the visuals and manipulatives and replace them with mathematical symbols only?"  - Jim Knight

"I love using manipulatives and getting the kids up to move made sense to me, but, as a sub, using manipulatives is very tricky. They usually end up being used inappropriately. Interestingly, I don't think regular classroom teachers use them much either. They are usually stowed away in inaccessible or dusty places." - Laura Lynn Walsh

"In order for manipulatives to be helpful, students need time to work with them. They need "play" time with them initially to understand what they represent. I think most teachers don't allow for this kind of time with the manipulatives, so using them ends up being a rote procedure, rather than a tool to develop concepts." - Sharon Voght

Jim touched on one of the root causes why so many children fail at Math. Mathematical symbols are introduced before children have grasped the concepts they represent. Number itself is an abstract concept. It does not really exist except in relation to something else. Children need hands on experience with manipulatives to gain this deeper understanding.

Laura identified another problem with manipulatives, they are often used inappropriately. For example I have witnessed Cuisenaire Rods, the most precise math model ever devised, being used as a sort of crude calculator. In fact the whole purpose of the rods is to lead children from concrete situations to abstract thought (problem solving, hypothesising etc).

Sharon offers a very insightful comment having identified the importance of "play time" with the rods. Play is absolutely fundamental and in truth that is what frightens most teachers because it exists outside the set curricula or scheme of work. It is ironic really that many teachers become anxious if children are seen to be playing rather than 'learning' while children become anxious because they have not been given sufficient time or direction with manipulatives to fully understand concepts that cannot be 'taught'.

Hopefully at the end of these series of posts you will have an appreciation of the powerful role manipulatives, in this case Cuisenaire Rods, can exert on the mathematical development of the child. What he will learn following this program will go deeper and further than can ever be achieved by a traditional approach. What is more it will be achieved using a material he has come to associate with play, creativity and fun.

No one ever got anxious while having fun!

In the next post we will take a look at the early stages of the program.

Phil Rowlands
+Phil Rowlands
*Read the full account on Laura'sblog at http://llwcontemplations.blogspot.com/

How To Use Our Free Math Software

The workman is worthy of his hire, except on the internet apparently. Everybody seems to want to give things away for free and even authors are undervaluing themselves by selling their books for just $0.99 on Kindle. So, you may ask, why am I doing the same?


The program I am currently blogging about took years to develop and perfect. It was trialled with children and parents and proved equally effective with both. It was even awarded Open College Network status. Recently it received a very positive review from the Old Schoolhouse Magazine. You can access the review here.


Play, directed activities and open ended tasks and challenges drive the program. Its basic premise is that math should be fun. Indeed all learning should be fun, a journey of exploration and discovery. However, because it involves a great deal of interaction with your child I appreciate it is not for everyone. Nevertheless, every child benefits from using math manipulatives, and Cuisenaire Rods in particular.

That is why I am making the software freely available. Even those parents and teachers who decide for whatever reason not to at least evaluate the program will probably appreciate the software as a learning tool. Should you decide to take a closer look at the program there is a link within the software itself. Just click this logo on the top right corner.

I chose Clickbank as the vendor because they offer a 30 day money back guarantee if anyone for whatever reason decides the program is not for them. Whatever, I hope you enjoy and find the software of some use.


In the next post we take a look at the very early stages of the program and focus on the importance of establishing the correct vocabulary and the role of directed activities.

Thanks once again for your company, have a blessed Easter.

A Word About You

This series of posts has been written on the premise that, as a parent, you want the best for your child. You would not have read this far if that were not the case.


Sadly many teachers lack confidence in their mathematical ability. I was once one of them. The radical approach outlined in this course can appear threatening.

Therefore in many of our schools day by day, week by week, month by month, and year by year children are led blindfold down the same narrow path that has been trod many times before. They proceed at the same pace, never allowed to look to the left or right, unaware of the rich landscape of pattern and relationship that surrounds them.

Research by Caine and Caine reveals that teachers who exert excessive control over the learning process merely succeed in reducing learning. Caine states, "If students are to be predominately self-motivated, they must be given the opportunity to focus on their areas of interest and to participate in activities they find interesting."

Much of our current educational practice is in danger of creating a culture of dependency. Motivated and informed parents (and teachers) can make a world of difference for your child.

Brain pioneer Hart says, "It can be stated flatly . . . the human brain is not organized or designed for linear, one path thought . . . " and . . . "Once we begin to look critically at this notion of teaching in a logical sequence, we can see that usually a further giant . . . and utterly wrong assumption has been made: that if a subject is fragmented into bits . . . and the student is then presented with the bits . . . the student will be quite able to assemble the parts and emerge with the whole - even though never given an inkling of the whole."

If anyone is starting to panic PLEASE DON'T!

The course follows a logical sequence but at each stage your child will be free to explore the often infinite possibilities at his/her own pace and in his/her unique way.

 Learners should always be presented with the BIG PICTURE or GLOBAL OVERVIEW. When you go on a journey by car to a strange place you refer to the map, the global overview. The BIG PICTURE is always at the back of your mind even when focusing on some specific part of the route.

With the rods you are immediately giving your child possession of the BIG PICTURE. each step you take will lead you into new, exciting challenges and sometimes you may meander off the planned route but you always have the BIG PICTURE to refer to.

Learning with the rods will be sequential but never prescribed.

In his excellent book, "The Learning Brain", Eric Jenson states that 75% of teachers are sequential, analytical presenters. Unfortunately 70% of their students do not learn that way! He suggests a better approach would be to start with a more global overview and then move to a more sequential approach. Cuisenaire Rods lend themselves perfectly to this method. 

Hopefully by now you are beginning to appreciate the immense potential for mathematical discovery the Cuisenaire Rods hold for your child.

As your child learns to manipulate the rods another 'hidden' benefit is being reaped. While producing their constructions with the rods he/she will also be actually stimulating his/her brain.

 Dr Jean Houston's work proved that stimulation of the body can stimulate the mind. The later work of Kandel and Hawkins confirmed that exercising the extremities of the body produced a positive effect on the brain.

Next Week we take a look at a software I developed to simulate the Cuisenaire Rods. Although it is no substitute for children using the rods it is a versatile tool that they, and you may enjoy using.

REMEMBER At this stage all your children need to be doing is simply playing with the rods. We will discuss First Steps in the post after next.

I am currently creating an instructional video to accompany the software and when it is complete I shall be making both the software and the video freely available for a limited time - so please check back.



The Importance Of Color Before Number

In the last post we took a look at Cuisenaire Rods. We saw they are simply ten colored pieces of wood or plastic so why are they so powerful a model for introducing math to young children?

Color is one very important reason. Later in the program we will often  refer to white as1, red as 2, and so on but at this stage it is color that must take precedent. This is because number itself is an abstract concept. What do I mean by this? Imagine I ask a child to run an errand and fetch me five. Naturally the child would inquire, "Five what?" For young children number only has meaning in relation to something else, five drinks or five pencils etc.

This is certainly not true of color and therefore children are best introduced to math concepts through the attributes of color.

A study by researchers Backman, et al. and Allen revealed that color was a greate stimulus for memory recall than verbal cues or objects. Color could and should play a far more significant role in the learning process.

Color evokes a response. Calming colors are light blue and light green. Red is an engaging and emotive color while yellow, beige or off white stimulate positive learning.

Weiner says that darker colors lower stress and increase feelings of peacefulness. In contrast, red, yellow and orange spark energy and creativity and can also increase aggressive and nervous behaviour. Apparently the most neutral color is a textured light grey.

In his book 'Now Johnny Can Do Arithemetic', Caleb Gattegno relates an interesting story:

"In a village where there had been a mining accident, all the children next morning used dark colors and severe outlines, many being churches and crosses.. The sadness in the atmosphere was reflected both in the colors and pattern chosen."

Children delight in playing with the rods, blissfully unaware they are familiarizing themselves with a precise mathematcial tool. They are simply having fun. I have often heard parents say, "As long as my child is happy . . . ", often unaware that they have expressed a deep educational truth.

Children, and adults, need to be in the right emotional state if quality learning is to take place. The ideal state is one of relaxed alertness. A positive emotional state is probably the single most important condition necessary to ensure learning is an enriching experience.
Anxiety, stress and other negative emotions make it impossible for us to access the higher level thinking skills.

Play with the rods provides the challengingly creative, open-ended experiences that stimulate the brain and help create a positive learning environment. It is when learning is also fun that it is most effective.

You may well be amazed at the intuitive knowledge and understanding your child displays when playing with the rods. Some children will attempt to create complex patterns, others delight in trying to copy real life.
The rods introduce your child to a rich and vibrant universe where the only limitations is his/her imagination.

Apparently Albert Einstein first became interested in the Theory Of Relativity after imagining himself travelling on a beam of light. Day dreaming is one of the brain's most potent abilities.

Have you ever bought one of your children an expensive Christmas present only to find they were more interested in playing with the box than they were with the content?

In the NEXT POST: A Word About YOU.

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