19.10.11 Oliver's sixth lesson ....

In just 6 weeks Oliver has developed sufficient understanding about what a number represents so as to have his own 'beginners tools' to really participate in the learning where he uses these tools to learn new concepts। This approach also enables a student to reason for himself and to think about how his own knowledge can be drawn upon to explore something new.

The concrete equipment used to teach the 'tools' still has a part to play in moving forward, although the active facility becomes a passive facility. This is equally important to the student because h/she requires a quick means of referencing or 'triggering' familiar knowledge in order to facilitate a new concept. An example of this is given below...

Adding 1 and 2 to a number

First Oliver was asked to order the Pattern Boards for reference purposes only. On the display card I placed 2 cubes (known pattern). Next I hid this behind a screen where I added two more cubes. Then taking the screen away, I said "What did I do?" Oliver replied "There's two more, it's 4!" It did not matter whether I added 1, or 2 cubes, or took 1 or 2 cubes away he was able to state exactly what had happened.

Note:The early pattern board activities in the Stern programme where pupil's learn to recognise, then build their own patterns, followed by ordering from the smallest to the biggest, then from 1 to 10, make these later tasks meaningful! They can see exactly what is happening. The visual imagery of the boards is extremely powerful and supportive.

My next activity was to vbuild 10, Oliver told me how many in an instant. Behind the screen I took 2 away. He was just as quick to tell me waht I had done and to give me the new total (8). I continued to remove 2 cubes each time where he said (6), then (4), then (2) and earned ***** stars!

Increased expressive language

Note:I have mentioned in past posts how Oliver was reticient to verbalise or ask questions, however, his increased confidence and the 'knowing' that he is learning, has made the difference. Today he showed some lovely spontaneous responses. The homework last week really helped to reinforce this emerging ability.

Counting in 2s

I could have introduced counting in 2's at an earlier point but to do so would have made it difficult for Oliver to grasp this concept. He would not have taken any meaning from a rote procedure. Instead, waiting until he has some understanding about quantity, as well as the support from the number structure he has internalised, this makes my task easier and Oliver's ability to comprehend. Rather than learn rote counting, which at best, would become a meaningless chant of number words. I have to help him make associations with what he knows and to understand why it is more efficient to count in 2s. A vital part of this is to continuously encourage a pupil's reasoning ability. Also my philospohy - learned from my years of portage work with my own daughter - is to see what the student already has in place in which to build upon..

We have the 2-blocks (quantity known); we have the set of structured pattern boards (quantity and order known); we have Oliver's ability to recognise patterns; we have his ability to colour and is something Oliver enjoys. There are sufficient skills here for me to top layer a new idea.

On the Display Card, using the same colours as the 2-block, I placed two cubes (associations). When Oliver named the quantity, I gave him a 2-block. We placed it horizontally next to the card. I then added two more cubes. Oliver told me it was now 4. I gave him another 2-block which was then placed underneath the first keeping a small gap for clearer identification. We touched and counted 2, 4. The 4-board was pulled down to also reinforce the quantity. These steps were continued up to 10, giving us 10 sngle cubes on the card, five lots of 2-blocks and the 10-pattern board.

More reinforcement of the concept Using a worksheet with images of 2-blocks in qunatities of 2, 4, 6, 8, 10, I began to place a 2-block on top of the first image sayiing 2! Moving to the next two groups I covered each image with blocks and counted 2, 4, then 2, 4, 6,. At the end of each count we found the correct pattern board to verify the count. and the 2-blocks we bgan the count. I Oliver took the lead with the count for 8 and then 10. Finally Oliver coloured the groups of 2's in each pattern. Following this, taking away all of the prompts, I scattered a quantity of 2-blocks where were I touched and we counted 2, 4, 6, 8, 10.

Estimating within ten - moving away from the structure then bringing it back to find the answer

The pattern boards are still at the end of the table for reference purposes. Oliver glances at them on occasions showing that he is mentally checking his thinking. Also I will refer to them in a prompting way to enable Oliver to find the answer for himself. I scattered a quantity of counters whilst Oliver made three columns on the white board for recording. We were fortunate to have David Cudworth Education Officer at Ups and Downs South West visiting, and like all visitors they get to join in the games. Taking turns, to guess how many counters, amounts recorded by Oliver, I would then move the counters, two at a time, into a Stern pattern counting 2, 4, 6, 8. The complete pattern was instantly recognisable by Oliver. David pulled down the 8-board for verification. Oliver checked his recording for the winner and assigned points which were agreed on at the beginning of the game.


In a previous game of estimating once counters had been scattered Oliver was able to state the exact quantity at a glance without counting or need to arrange the structure (subitization)


Bringing in 'even'numbers

A further aspect of number that also fits with this learning is the concept of even numbers. My student has already had an introduction to odd/even numbers in lesson 4 so our next task was to remind Oliver of tghe two explicit clues used to identify an 'even' and an 'odd' number. He was then able to recognise all of the even pattern boards. The pattern boards were already on hand and sequenced to facilitate this task.

Time telling practice

With the working clock on the all opposite my student I incorporate reading practice throughout the session. Today, using a worksheet with written moments of digital time Oliver read the first correctly then placed the clock hands on the practice clock correctly and read the time again. He went through the sheet 8:05, 6:15, 2:35, 1:55 (sc), 7:20, 9:10 (sc) 4:40, 6:00, 9:55, 12:00. The 'precise' point reading and recognition is going well, so today I introduced the first of the two phrases to encourage reading anywhere around the clock. 'It's just gone' or It's almost'. When the minute hand is between two 5 minute points as with 20 and 25 pupil's are encouraged to read 'It's just gone say 6: 20.' Whilst some pupil's can cope with the choice element this provides there will be some that find this too much to think about. In this case introduce one phrase first.

Number Bond work

I gave Oliver and David a 10-Box each and asked both to tip out their blocks. I also placed a 10-block horizontally in front of them. The next instruction was to find two blocks that make 10 and place them alongside the 10-block. Oliver quickly selected both 5s saying 5 plus 5 equals 10 and wrote this down in his column. Taking turns with David, both selected their block partners saying the number sentence, verifying by placing alongside the 10, then Oliver recorded his and David's facts.

Observations: Oliver found all ten pairs quickly. He was able to place them on the table top without the support of the box. He also found, named and placed the reverse facts, as with 2 + 8 and 8 + 2. Also, he picked up the 10 block and said that 10 and zero make 10 and zero and 10 make 10! A further activity also highlighted this emerging understanding and was such fun. Whilst I was on 'oven duty' so as to bake the baguette for oliver's snack/break, I gave both men an empty 10-box and asked them to shout out the numbers as they place all ten facts into the box. Oliver had certainly overcome his shyness to do this verbal task! My student has demonstrated his increasing understanding of the bonds for 10 from memory. next week we will look at playing memory games to help trtansfer this concrete understanding to numeral/abstract equivalents.

Handwriting practice

Handwriting sheets are still going home for writing practice.

This was a very exciting and satisfying session where new concepts have been introduced - with the added attraction of David whom Oliver adores !

Vikki Horner

12.10.11 Oliver's Fifth Lesson ...

Oliver has made rapid progress with size, position, order and number names to 10. All is developing from using representations in the form of blocks and the work in the Counting Board. Oliver has a strength with pattern and thus the Pattern Board structure has enabled him to internalise most of the patterns (9 still requires more practice) and grasp the pattern order from the smallest pattern to the biggest as well as their number names to 10. Assigning number names is now 95% accurate. He is building his 'tool kit' which is enabling him to take an active part in the learning process.

The language strand is progressing nicely, Oliver's understanding of language concepts is

growing. In today's session he showed good understanding of 'most', 'least', 'how many more', 'how many less', 'whose in the lead?' The Snake game is great for this to take place....

Concrete teaching and learning from the array of equipment I use is extremely powerful... It gives clear images and 'clues' so that a pupil can make sense of what is being taught, to make connections, as well as link new learning to every day experience children have. For the practitioner, we can build and broaden from seeing a pupil's emerging understanding with each action taken. Because of the regular use of the equipment I know that all of the above tool gathering is being constantly reinforced.

Today I am introducing Oliver to numerals related to the Stern blocks and patterns because he now has a sufficient amount of number knowledge to 10. This will begin the process of transferring concrete understanding to abstract use. We see it as filling numerals with meaning. graphically, unzipping a numeral and filling it with what has thus far been learned. These small incremental steps encourage a pupil to make connections. Further games included matching pattern cards, in the same structured format, such as cubes of only one colour, cars, stars, lips, smiley faces.

Adding 1 to a number gives the next higher number

As Oliver knows the patterns we can draw on this to show how a single cube (different colour) at the bottom of each pattern brings instant recognition of the next number pattern! This is his first exposure to addition.

Bond work in the 10-Box

The pattern work and the Counting Board work is in advance of the bonds but it will catch up. Having said this Oliver has some understanding of some of the bonds already: 1 and 9, 4 and 6, 5 and 5, 7 and 3, 8 and 2, 9 and 1 and 10 and 0. The Hiding Game is a great way for the pupil to show you the combinations he/she knows because each player has to select a known pair and hide them. Next whilst showing one of the parts, a clue is given. "I have 10 altogether, in one hand I have 6, 6 and what make 10?" At a glance then one can see if the selected pair is correct or not. If not, it is not necessry to say "It is wrong..." There is a built-in means for a pupil to figure it out for h/herself. Have an empty 10-Box nearby, and ask the pupil to quickly check his blocks. Usually when the first block is placed in the box the pupil jumps to and self corrects because the box or empty 'gap' triggers the image of the correct block. The exchange is made and we are back in the game. There are so many games for bond practice. Okay here's another one. The pupil builds the stair 1 to 10 in the box. Then finds the partners for each step. Once complete take an empty 10-Box and place it over the box as a 'lid'. Ask "What does 1 need to make 10?" (9), then slide the lid so the pupil can check h/she is correct. They love this game! Continue until all ten combinations are named.

Handwriting Practice

This topic continues to be part of our sessions, although Oliver's written numerals are very much improved.

Teaching Time

We are still working with ONLY digital moments of time. You may remember that we began with the 3-step method, however Oliver quickly consolidated this. He simply looks at the clock face and states that moment in time. Guidance or self correcting is mostly to do with the bigger numbers from 45 to 60. This is coming along nicely.

I will try to post the next three lessons in my drive to catch up so that currrent sessons are quickly posted, especially as it only took a further three lessons for Oliver to have all the number bonds for 10 firmly in place!

Vikki Horner

Stop Press! Hayley Rydon Has Mastered Telling the Time...

Congratulations to Hayley in New Zealand who has been using the Charlotte Clock method to learn to tell the time. The working clock has been part of the 'kitchen' furniture for three years so that she has everything visible for her to reference. The practice clock enables her to have hands-on experiences. Looking good Hayley!!

I have just heard from mum Bronwyn that today is a special day in the Rydon household because the Charlotte Clock is being removed and replaced by a basic single digit clock. Why ? because 12 year old Hayley has mastered telling the time ... three cheers! hip hip hurray... she no longer requires the visual prompts provided by the Charlotte Clock special features.

Of course everyone is very proud of Hayley's achievement and Hayley, so are we, You've rocked it..... and you should be very proud of yourself too! the last word comes from mum who said

"We could not have done it without the Charlotte Clock method, so thanks Charlotte and thanks Vikki."

Bronwyn Rydon, New Zealand

The Charlotte Clock method was developed around the Down syndrome learning profile, and designed as a bridge to moving on to telling time with a basic clock face. It is a simplified method that takes away the complexities of abstract time concepts and is successfully teaching time skills to thousands of children with SEN in the UK and abroad, at home and at school.

For further information go to www.mathsextra.com or email enquiries@mathsextra.com

It's a small investment with HUGE rewards.......

05.10.11 Oliver's Forth Lesson - Continuous Progression with Five Teaching Strands....

I believe that we should be providing children with the 'tools' to enable them to move into the 'empowerment zone'. This means they would be able to actually participate in the learning process because they have some idea about what numbers are and what we can do with them as well as how to combine numbers and know their totals. Then we have to make sure this knowledge is embedded in the child's long-term memory so he/she can access it instantly, not by figuring it out every time, using up space in working memory, when this is required for other processes.

Although I am still building these 'tools' with Oliver, the teaching programme is flexible, yet logical, is visual and hands-on and IS moving him forward. This requires that I have many 'balls' in the air at any given time. AND, regardless of having NO understanding about numbers when we began our sessions, Oliver is more and more able to cope with it all.

There are opportunities for me to build and broaden any new understanding, as well as provide practice for previously learned topics. Whilst there was much reticence from Ollie with vocalising - an important part of the programme - he is doing more and more of this spontaneously. AND he is already showing me examples of being empowered by his new knowledge. The purpose of this blog is to diseminate information week by week of my student's progress, and although there are a few weeks of reporting still to post to demonstrate the journey - I am finding some really exciting moments that can only be described as magical.. Here's a preview of what happened during our 16th lesson or approximately one school term... You also need to factor in that this student has spent the past ten years in full time education where he made little or progress. So yes, magical and it shows that pupils with SEN can make sense of numbers.

Magic Moment... At the end of last weeks lesson, we had a wonderful experience whilst working with 2-digit numbers.. "I know!" (you will see in the following blog posts how this topic was brought into my teaching). Ollie announced that he was 15 and his sister was 23, I asked him to show me both numbers in the Dual Board. Then I asked him if he would like to find out how much older Anna was than him. Ollies eyes lit up, and eagerly said yes so we proceeded to do so. This led him to ask about his mum and dads age and wanted to figure out this difference too. However, the magic came from Oliver's ability to transfer his thinking when he asked "What if Mike was 85 how old would mum be? and a further "What if Mike was 100 how old would mum be?"

Back to the 4th lesson which began with work in the Counting Board - Oliver is now 95% accurate when naming the Blocks and the Pattern Boards by their number names, and 95% accurate when ordering the blocks. Early vocabulary is in place and today he showed accurate understandng of new words and phrases; 'most'. 'least', 'how many more'?', 'how many less/fewer?' 'whose in the lead?' Given this progress, I am keen to introduce numerals and link them to our current work as follows:

The Counting Board - This is great because it has a vertical guide board with written numerals 1 to 10 to draw on. Charlotte was free today and so after the teaching aspect to introduce numerals 1 to 10, we all played the 'snake game' which is brilliant for reinforcing quantities. Oh you want to know how to play the game? okay... select a numeral, name it, place it correctly in the board, name the block below, if all this is correct the pupil takes the block and begins to build a 'snake'. This can be played with two teams, or two or three players. After each go, I can ask who is in the lead? who has the most, how many more do you have than (whoever is playing). With each next go, there is always a diferent configuration and so the reinforcement continues..... Note: Oliver was able to tell me the correct number of units of difference, at a glance, even if the last block was 'partitioned' demonstrating that Oliver was seeing 'size' of units beyond the equal point of both 'snakes' regardless of colour.

Consolidation and transferance - We do this by making connections within individual teaching strands matching blocks and pattern boards, then blocks, pattern boards semi abstract cards, finally, blocks or pattern boards with numeral cards to 10, ultimately games with numerals alone.

Note: Oliver's ability to order the boards to 10 is almost there, although he is still self-correcting the 7 and 8, or 9 I am pleased with progress and so feel Oliver is now ready to be introduced to odd and even number concepts in the next session. Also, because the pattern boards were designed for this purpose, Oliver will continue to get further practice in ordering patterns to 10.

Combinations of 10 - Olivers development in other areas of number knowledge is in advance of his bonds to 10 learning. Therefore I am giving this more attention and it will be the task at home, and if possible, during the numeracy lesson at school. It should be the first task as the student will be fresh and keen. I want to give Oliver more modelling and more opportunity to articulate the bonds - 'seeing', 'saying' and 'doing'. Remember for facts to embed in long term memory the student needs to have both addends and the total, contained in a number sentence, DO NOT simply accept an answer, eg: you might say "What does 8 need to make 10? and your student says... 8... The number is not attached to anything and will quickly fade away. Taking the role of the 'teacher' means that your student has to begin the task and then ask you to do something..... We also incorporate the game where blocks 1 - 9 are placed on a surface nearby. The student selects a block from our group on the table then is asked to go and find the partner/number that makes 10. This encourages memory and you will see examples of developing receptive language when the task is completed correctly.

Telling the Time - We used clock face 2 as a means of building five minute blocks of time. We used cards to set the hour hand and then the spinner with template in 5s to set the minute hand. The 5-pattern cards where then used to physically build that moment in time (30). Using the red outer numerals we said the numerals together 5, 10, 15, 20, 25, 30. This is to be our first introduction to counting in fives.

Handwriting practice - Include a worksheet. Whilst our focus here is mainly 5, 7, 8, Oliver wanted to write a row of all numbers to 11! I gave Oliver a sentence to say out loud as he wrote each numeral.

(5): Down and round, give it a hat!

(7): On the DOT, straight to the cupboard, STOP and DOWN!

(8): Big 'S' up and join.....

Oliver was writing the 7 in reverse. to encourage the correct strokes I find that by first making a dot, a pupil can place his pencil on the dot then move the pencil to the right horizontally, but he needs another prompt to know the direction to go in. Look at what is on the child's right side and use that. For us it is a large cupboard. Threfore I demonstrated the action - placing my pencil on the DOT I say "On the dot, straight to the cupboard, STOP and DOWN," without taking the pencil off the paper. He quickly got the hang of it, completing a full row or 7's. Next we tackled 8, by writing a large S, pausing then diagonally going up and close. These two parts work really well. We tried drawing the curves and diagonal stroke with our hands in the air, so the 'S' can be a big as possible... You can also try writing in the sand or on smooth sandpaper or any other rough surface. These physical experiences always help! Oliver's 8's were an instant success!! Then Oliver thought we should look at 2 which toppled!!!! "We had such fun trying to think up the phrases .... They became 'Mike's fat belly on a skate board'. !!!! don't knock it if it works!!! haha.

For writing homework Oliver was given some writing exercises in Pupil's Workbook 2.

Feedback on all lessons is always written up and sent to parents as well as the teaching assistant to follow my lead in school. It's a good partnership.

Vikki Horner

28.09.11 Oliver's third lesson ....Part II

Following the Counting board work recorded in Part I, we moved to working with pattern.

PATTERN BOARD WORK

Moving this along form our previous lesson I reviewed Oliver's ability to recognise all 6 number patterns, before introducing him to sequencing. You will see the boards are placed on our 'HomeBoard' resource. Once the teaching task is complete, Oliver then repeats this himself and when necessary has the (sc) aspect to enable him to figure out the correct order of the boards. So to recap, Oliver can recognise the patterns for all 6 boards, he can also build his own patterns from copying a selected board, now he can order the 6 patterns. Notice we have not yet used number names, this is a normal aspect of the programme. However, with older pupils I am keen to introduce the 'naming stage' quite quickly.

I introduce the 7 pattern in a specific way, to further progress a child's developing relational

understanding. On my display card I build the 6-pattern, which the pupil recognises. Holding the 7-pattern board I explain that this next pattern is the same as the previous one (pointing to and circling all 6 cubes) with one more cube! I then place a different coloured cube underneath. Looking at the photos, you can see that Oliver was able to still see the 6-pattern jumping out as well as the overall 7-pattern (which he recognises from our previous work with pattern) being the same as the 7- board. Pattern Boards 8, 9 and 10 are also introduced in a specific order so as to emphasise the relationships with each other. As you would expect, sequencing practice with all 10 patterns follow. Also some building of patterns 7 to 10, both for recognition and for self construction, is also necessary in order to internalise the whole series of patterns.

NOTE:

In just two lessons, Ollie was already spontaneously 'seeing' the number names of some of the boards. Younger children would need more practice to get there. I observed some very good examples of internalisation of Oliver's developing sense of pattern, which is a building block to understanding number, as well as naming and ordering the boards to 10.

NUMBER BONDS USING THE 10-BOX

'Turn taking' is an important aspect of the STERN pedagogy, because the practitioner models the task so that the pupil will know what is expected and can grow to be confident and competent. Many chidlren with additional needs who are struggling with maths get to the point where they know they are failing.... even if they can't articulate this feeling. This can often bring about behavioural issues. I have experienced this with my student, so much so that I make a point of letting him know that a task is new, that he has not yet been taught it, so how could he know it! I tell him that after we work through the tasks together he WILL know how to do it.... This explanation seems to make sense to him and so he is more willing to participate, although I still dip into my arsenal of Boffs and High Fives on occasion, long my they reign.....

We continued from the previous lesson where I place a block into the Box so that Ollie finds the partner. He still uses the self-correcting feature, which is an errorless way to learn. Once a pair of blocks is found it is important for the student to say the full number sentence such as "1 and 9 make 10." In order to embed a fact in long-term memory it requires both addends and the answer as a contained phrase. It is also the same when finding the missing addend - 4 and what make 10? Often children simply say (6) which is not attached to anything and as such will quickly fade. Therefore after a combination has been found or the missing addend has been given, RECAP together - pointing to each block you both name the blocks in this number sentence "So 4 and 6 make 10." Oliver was not too willing to verbalise this and thus I had to resort to ..... you guessed it ..... "Okay Boff let's do this one together!"

HAND WRITING

As mentioned earlier, as a direct result of noticing that Oliver's L/R directionality was poor and seeing examples of his handwriting of numbers to 10, I felt we could help improve this writing formation of numbers. I have a series of physical movements that involve large sweeping arm actions which Oliver did not want to do. He was too embarrassed to do these with me. Therefore we opted for practicing forming right and left curves, vertical and horizontal lines using a mini white board so that we had a edge. This task was also practised during his numeracy lesson on a Monday at school, as well as at home. Our focus was mainly on 2's that toppled, 5's with long necks, and two cirle 8's.

TIP:

These pre-writing activities are worth doing because it encourages fine-motor ability and strengthens muscles for better dexterity. We constantly get told by parents that their child has better dexerity since using the Stern equipment - all that manipulation on a daily basis. The writing exercises also reinforce this. A parent told me that her 14 year old daughter (DS) who had fine-motor delay, after working with the equipment for a term, not only began to make progress in her maths ability but she suddenly was able to do up her own buttons on her blouse...... such a small step you may think, but a huge achievement for her and for more independence........ Well done you!!!

THE CHARLOTTE CLOCK

Our 'time telling' strand is continuous and Oliver is reading moments of time independently now he has grasped the three step method: Todays readings were: 7:40 4:50* 2:40* 10:55 and 7:40. the two STARS were for brilliant working out. Oliver simply read out the time in one step! "It's 4:50." "It's 2:40." Fantastic! He, as with others using this method, needs to practice reading time from his Charlotte Clock at home to support what is done in the lesson because the opportunities can be limitless......

Vikki Horner

28.09.11 Oliver's third lesson....Part I

Today is our third lesson where we began with reinforcement of the block positions and vocabulary from level 1 teaching in the Counting Board.


This is moving along at a pace, so I have incorporated assigning number names from level 2. This will broaden my acitivities as well as build on Oliver's emerging understanding. First, he showed understanding of size and of position of blocks to 10 when asked to order the blocks from the smallest to the biggest and in reverse order. He self-corrected (sc) 8 and 7 otherwise was very accurate with the position of the remaining blocks.


The next task, introducing number names, was to model the procedure. It consisted of touching the 1-block then asking Oliver to name it (1) (Everyone knows this cube is called one!) Then pointing to the 2-block he named it (2), then as I pointed to each next block Oliver and I named them together up to 10! GREAT!


NOTE:
Don't miss this step out - remember that at assessment during my first lesson, Oliver did not know the count to 10, and missed out numerous names. Therefore I don't take anything for granted, I let the pupil show me what and how he tackles a task where there are clues for him to feel secure in his actions.


TIP:
When a child gets stuck on a name and thus begins to count the units of a block, DO NOT allow this to happen, distract by pointing to the 1-block, and ask the child its name, then keep pointing tio each next block as h/she names it up to to the block where the difficulty arose. The objective here is to teach childrne to see a number as a whole idea, ready for efficient calculation which will begin shortly. Counting practice will come through other activities.


As the practitioner, you will begin to see which names are secure, then use them as stepping stones to get your pupil to figure out the answers h/herself. For example, Oliver was secure with 6, but got mixed up with 7 and 8, therefore I pointed to the 6 and asked, "What number comes after 6" pausing for a second or two to give him a chance to answer, but not too long because I don't want him to feel 'tested'. If he is not able to answer, I simply point to the 1-block again and ask him to name it and whilst I continue to point, he names the blocks up to 6.


Here, I ask "So if this is 6, what comes after 6?" (point to 7). These clues help children figure things out for themselves. Carrying on then, "This is 7 (point) what number comes after 7?" (8). Same for 9, then before I could get ot the 10, Oliver quickly named it wothout hesitation. (When an answer is known - ALL children are keen to answer with speed!) On another round you can give the instruction to order the numbers from 1 to 10, and again from 10 to 1. See how the initial task of sequencing by size, has become a sequence of numbers to 10! The next build up layer will be to simply count up to 10 and back to 1 with eyes closed, although the pupil is encouraged to 'see' the blocks in the board. Great support and great development of visualisation ability.


The above technique takes a little patience but is well worth it becasue you are reinforcing numerous aspects simultaneously - reasoning ability; positional vocabulary; number sequencing; number names and counting.


NOTE:
Oliver seems to enjoy starting from 10 and not 1. this is okay and indicates choice. I simply ask him to begin from 1 with the next round. Actually children do not get sufficient practice with counting back, so see this as a bonus! This task provides rhythm and practice with additional support. Through the visual imagery from the lengths of the series of blocks, the child 'sees' a picture of blocks reducing by one unit each time. This visual information is being absorbed at a subconscious level and plays a part in a child's ability to mentally count back to zero. We repeated the task still maintaining the 'naming blocks' focus; Oliver was accurate with 1 to 5, 6 (sc) 7, 8,9 and 10 were named correctly this time! Well done Oliver!


PRACTICE IDENTIFYING BLOCKS BY NAME

After observing the accuracy and confidence displayed by Oliver, the next task I introduced was the 'Calling Back Game' where we shared out the blocks - mum joined in too. Next, I called back a number. Whoever had that block placed it in the board. Ollie absolutely loved this game and asked to do it again and again, in fact 8 times in all! (All that rtepetition and practice!!!)

TIP:
to get you thinking about the need to continue to stretch a child's emerging ability; try these ideas... after the second round (of 8) my observations were that Ollie was naming the blocks accurately, he was also placing the blocks correctly and his positional understanding was also accurate, SO I began to broaden the task by asking "Calling back 2 and the next number! what is its name?" "Calling back 10 and the number before 10? What is it called?" You can see how easy it is to give lots of extra practice with different elements as in this case with number relationships. It was such fun.... Oliver was a STAR and he knew it! How lovely is that?

Before ending this work I gave him another couple of tasks - 'The Stand Up and Stand Down Games' which is another means of identifying blocks by their names. These games enable me to give instructions focussed on 6, 7, 8 repeatedly. the best thing about these cheeky tactics is when Oliver suddenly realises what I am up to by saying "I've done those before!" and I say "Are you sure?" ha ha ha.....

The lesson continues with Pattern Board work and will be recorded in Part 2.


Vikki Horner

NUMBER WORK – PATTERN BOARDS AND CUBE PATTERNS

This resource makes learning extremely visual and is enormously helpful when teaching children about number quantities, properties and simple addition and subtraction. At a glance the unit parts of each number are displayed as a group of structured cubes – ‘painting a picture’ of the meaning of numerals 1, 2, 3, 4, 5, 6 and so forth to 10. Properties such as 'odd' and 'even' numbers, are vivid and are represented as ‘the odd man’ or needing a ‘partner’ this unforgettable imagery and easy description make the ideas memorable. Simple addition and subtraction tasks are also carried out with this support.

The lesson
With the first 6 Pattern Boards I placed them randomly in front of Oliver. I began to build a cube pattern on the display card pictured below. Oliver was asked to match this to the same board. Initially I used the same coloured cubes as the Pattern Board, offering two opportunities for success – matching by colour or by pattern. Oliver was able to recognise the pattern and so a different colour set of cubes was used.

The checking up factor proved interesting. Oliver was given the display card containing the cubes and was asked to place them in his chosen board. From this action children learn to develop cognitive skills such as left/right directionality, hand-eye coordination and 1:1 correspondence as well as strengthening fine-motor manipulation. With a student as old as Oliver, I would still be looking to see if these skills are firmly established. However, Oliver had different ideas! He wanted to take the quick route and so picked up the cubes in two’s and tried to ‘drop’ them into the empty insets. I had to explain that I needed to see if he was able to place the cubes separately into the board first ....THEN he could do it his way… compromise accepted - High five!!

Sequencing
Oliver moved on to ordering the boards from the smallest to the biggest which he did with a couple of self corrections. More high fives! At this point it was 11.00 and Oliver was hungry! This led to a lovely opportunity to encourage some clock watching and reading practice, so
as to feed that man!!!. I reinforced the procedure once more using the practice Charlotte Clock placing the hands at 1.00, Oliver followed this correctly then was asked to go to the oven, I showed him how to turn the two dials in order to bake a baguette for his much loved
cheese sandwich. This done we took our break and looked at Oliver’s bird’s of prey book. He turned the pages to his favourite birds and named them with amazing skill. He clearly has a passion for nature and David Attenborough is a favourite in his house…..

Bonds of 10
Oliver had NO understanding of the bonds of 10 - not even by counting on. No matter BECAUSE I know that in a short space of time he will build his understanding of the combinations of 10 - and that’s not all, he will know them and use them as recall from memory. So watch this space…..

To begin….. we spent the last part of the session finding pairs of blocks to fit into the 10-Box. The box is the same height as the 10-block and contains 10 combinations that make 10. I would put in a biggish block and Oliver would find one to fit the gap. The same self-checking principle applies. Each time a block was placed in the box that did not fit, the immediate visual feedback ‘told’ him in which way it did not fit, enabling him to simply take it out and try another one thus each task is a success. No feelings that he can’t do something, only feelings of satisfaction and achievement! AND high fives BOFF all round! Not too sure which of us is BOFF though?…..

We certainly finished the first session on a positive note where Oliver was definitely familiarising himself with the equipment, listening and following instructions, and completing tasks.

You might like to know that during our first 2 hour session, Oliver covered the work highlighted in blog posts dated 22nd and 24th of November as well as the contents in this post.

Vikki Horner

This entry was prompted by the number of families I spoke to last week, all have concerns about why their child cannot make progress with maths..

You will be surprised how many times I hear – “He knows his numbers to 10 but he does not know what to do with them!”

To gain insight into why this is, we have to go below the surface and look at the underlying issues…..

When a pupil has no real understanding of number knowledge or facts to 10, and is operating within the Performance Indicator levels (P Scales), try working through the three levels of the first Stern programme using the supporting equipment. This is often referred to as the ‘tool kit’ for moving forward. There are other factors to consider because it's not simply about the maths content that makes it impossible for a child to learn about numbers and arithmetic.

Cognitive processing systems and skills – are central to ALL learning. To explain what this means I like to use a computer analogy.‘Human beings’ are the ‘hardware’ and the 'cognitive processing systems' are the ‘software’ Let’s say you wish to create a beautiful power-point presentation with all the bells and whistles. If the software is not there, how can you create your beautiful power point presentation? Likewise, if we have deficits in our cognitive processing systems then we would find learning, on many levels, difficult and for some, almost impossible. Simply put, we ALL need to draw on these systems everyday for all our ‘thinking’ and ‘doing’. Imagine if for some reason your memory ceased to function properly?

The Stern equipment stimulates and strengthens these systems- every single time the blocks and cube patterns are handled a child is developing h/her spatial, discrimination and sequencing ability. The unforgettable visual imagery is stimulating a child's visual-perceptual processing ability. Moving blocks on to a table nearby and giving the instruction - "Go to the table and bring back 3 and the block one bigger than 3." encourages receptive language as well as memory. These are examples of how these functions develop and as they do there will be progress in other areas and other subjects.

Something simple like being able to button up a blouse came as a result of strengthening a teenagers fine-motor ability!

Numerals, number concepts, the number system – are abstract by nature, maths is also the fastest moving subject on the curriculum and very quickly moves into abstract notions and this is the point where children can be left behind. Further, deficits in cognition can mean that the child does not have the ‘infrastructure’ for abstract thinking and yet is still being taught abstract concepts. Would this not be bewildering for the child? Try to imagine learning maths in Russian because to the non-Russian speaking individual this would be as abstract as it could be? then you would begin to understand the raft of emotions these children may be feeling every time they have maths.

Numerals are abstract symbols - where are the clues to their meaning? yet young children are exposed to numerals very early, beginning in the home where parents may teach them to say a string of names and some even learn to recognise the symbol, but many spend years trying to crack the code. Imagine if I gave you a sheet of heirogyphs and asked you to tell me what it says. Where would you begin? How would you decipher the code? What emotions would you be feeling? Not easy is it? Wouldn't it be better to have a set of number blocks representing numbers to ten so your child can hold a block and feel its size, and have a board to put it in? They would discover where all the blocks live and begin to order them... first, in go the small ones. Next come the bigger ones, then the biggest! Learning through play and discovery provides children with insights that they would never get from numeral cards or sheets or rote chanting. The boards act like a puzzle which is appropriate for all young children and so important for children with special needs.



I believe there are thousands of children who go into school without special needs and they get their special needs in school!

Young children learn about their world from what they see, hear, touch, taste and smell or from using their senses, better known as the ‘sensory-motor’ stage of development. This is why learning through play is so important from nursery through key stage 1. Children with summer births would have almost one years less development of cognitive functions, yet are expected to keep up with the rest of the class. They would still be operating within the sensory motor stage, and if using Stern's approach this group would keep up and move forward because of the cognitive stimulation and the VAK input.

The Stern programme was developed by child psychologists & mathematicians who carefully designed the equipment and activities so that teaching would follow a child’s natural stages of learning and development. This is the key to the successful nature of the Stern programme.

When no progress is made – I have many examples of children who have made little or no progress in five years, eight or even ten years! There are many schools in the UK who have numbers of pupils in this group. These children are still operating at the sensory-motor stage and require learning to be ‘concrete’ ‘visual’ and ‘tactile’. Numbers need to be presented in visible form to enable children and young adults to handle them and 'see' the meanings that lie within.

We believe that if a pupil is making no progress with maths, regardless of chronological age, h/she needs to switch to a concrete, multi-sensory, structured form of learning without abstract notions until understanding is evident, then one can begin to use other resources in a way that takes the concrete knowledge to a secondary resource which I call 'semi-concrete'until the child demonstrates transfer. Still further resources - semi-abstract, again looking for indication of transfer. Ultimately arriving at the point of introducing abstract resources enabling the child to use h/his newly acquired knowledge with fluency. Then it's back to the concrete structured form to learn another topic. We can also teach children to recognise some that they already know in other learning. For example the Stern pattern number structure is very distinct, making it easy to lean about the oddness and evenness of a number. Once the pupil is fluent we can introduce counting in twos using the even number patterns. The 6-Pattern - we can count 2, 4, 6. The 8-patttern 2, 4, 6, 8 and so on. Later on this understanding will form the basis of the two times table. I recall a 6 year old once exclaiming "Hey! there's three twos here.!! after building his 6 pattern with cubes. He had discovered a multiplication fact, but would not know it as that at this point, never-the-less it will be stored in his memory for later use.

consistent factor of the Stern programme is evidence of progress in cognition and number understanding in one single term. That said, it can take some schools over one year before they implement this programme, if they do at all. How much learning could have taken place in three terms? How about this example …. using our structured Charlotte Clock programme, my own daughter, who has Down syndrome and was 12 at the time, took approximately one year to master telling the time using both digital and analogue formats using a mix of formats!

Progress in 9 months - Stewart is a Year 2 pupil with moderate learning difficulties. Despite the level of carefully targeted support, using a range of materials and being in classes with very
experienced and skilled teachers, he was still unable to count with 1-1 matching and with no real understanding of number values. Stewart began working with Stern and within a nine month period he has gone from having no understanding of number values to being able to confidently add and subtract and record his work.

Progress in 5 months - 12 year old Peter, with Down syndrome, moved to his secondary school still operating within the P levels for maths. His parents recommended the Stern programme to school and they put him on the programme. After using the programme for 3 lessons a week in school, and at home, Peter made significant improvement. He was assessed five months later as operating at level 1, with his number bonds securely in place.

Progress in 6 months - We started using the Stern programme 6 months ago with an 8 year old girl with Down syndrome. She has shown remarkable developments in maths skills and in understanding of concepts. For the majority of topics she has such a solid grasp of what she is doing that she regularly completes assessments without the Stern equipment.

The above factors are the main causes of delayed progress, get these right and your children will begin to move forward with confidence, enjoy learning about numbers and maths AND without wasting so many vauable years of learning potential. We ALL need to develop the basic arithmetical skills for everyday living ....................

Vikki Horner


(See the structure of teaching with the Charlotte Clock Resource pack, and Stern Structural Arithmetic Kit A. http://www.mathsextra.com/)

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Oliver

First teaching session - 14th September 2011

One of my first tasks was to begin developing Oliver's time telling skills, now fifteen he really does need to have this skill in place. To do this, I use the Charlotte Clock because it was built around the Down syndrome and SEN learning profile. We begin with digital time, mastering this to 90% accuracy before moving on to analogue format. During our first meeting Oliver's mum told me he has recognised the quarter and the half past positions on occasion but has no understanding of the concept of time. So this will be great when moving to work with analogue time.

Quickly then, let's look at the face. There are two sets of numerals, clock hands are labelled - 'hour' and 'minute' . We use a three step method to begin with which quickly consolidates to two steps then I find, as was the case with Oliver, that children mostly look and read the time. Using the practice clock (same face), after talking about the elements on the face, and how to set moments of time, Oliver got to work: 2:10 Oliver placed the hour hand at 2 (black) and the minute hand at 10 (red), then was encouraged to say the two numbers together 2 10, then to put it into a time context..."So the time is 2:10." Next, 2:45 hands placed correctly, then read together 2 45 (it is important to point to each number as a prompt). "So the time is....?"

Because Oliver has not been exposed to numbers in the higher decades, he found it tricky to name some of them so I would say a number first. He soon got the hang of naming the red numerals to 60.

Further, I have a working clock (same face) on the wall opposite to where the pupil sits, where I monitor the time to give him reading opportunities at precise five minute points. Mum also has a working and practice clock at home so Oliver can practice between sessions. School too is using the same resource and provides more practice during his numeracy sessions two days a week. This arrangement seems to be working well. I was very pleased with his initial readings, Well done Ollie!

Next, we moved to work with numbers to 10

There is a lot to be learned about numbers before a child knows what they are and what can be done with them! For example 'size' 'position' 'relationships' 'number properties' and 'number concepts' number bonds, number facts to 10, There are 120 addition and subtraction facts with numbers up to 10. Who has fogotten this???

The easiest 'tool' I have used with children with SEN in building up this knowledge, is the Counting Board filled with graded unit blocks to 10. There is a special place for the numerals or number markers 1, 2, 3, 4, to 10 (see photo), but first we work with only the block representations to gather information about each block. Understanding relationships is a crucial building block, so is developing a child's natural sense of numbers.

Differentiation

In school when helping children with SEN to understand numbers, learning is differentiated to accommodate the difficulties by making the tasks smaller or simpler and often involves working with number 1 to 3 or 1 to 5 only. How can the relationships taking place with the whole series to 10 then be seen or grasped? How would a child see that 5 is in the middle of the series, or which consitutes the small numbers and those that are bigger? What about knowing that 4 comes before 5 and is one unit smaller, or that 5 comes after 4 and is one unit bigger? How would this information be learnt from using numeral cards 1, 2, 3, 4, 5, 6, etc., where there are no clues as to the size, position, quantity, oddness, or evenness for example?

The Stern programme is totally differentiated in the way it is taught and through the small step progression, as well as the apparatus. These aspects enable children to work with all numbers to 10 (representations) simultaneously. The differentatiion is done like this; a task is set with a single focus, the objective here is learning about 'SIZE', Therefore, matching blocks to empty grooves is simple, meaningful and easily within the capability of ALL children, but there is more...... Whilst doing this children are developing their ability to scan and judge 'sizes'. They repeat this action ten times thus introducing repetition. A further aspect is in developing a child's reasoning ability and making the task as independent as possible. To do this, the child learns to self-correct any action when necessary WITHOUT the parent or teacher saying it's too big, you need a smaller one..... . When placing a block that is too big into the groove, the immediate visual feedback speaks to the child. they can see why it does not fit, and often a child will say it's too big, I need one less, or a smaller one. If the placed block was too small they can see the gap. This visual cue leads them to try other blocks until they are successful. Errorless learning! The confidence boost that follows can sometimes be imeasurable.

As well as this there are other aspects that children are exposed to such as seeing 'small' blocks 'living' at the beginning and 'big' ones at the end. The biggest block comes last, the smallest one comes first. Then the next smallest, and the next, and so forth. All these facts are EXPLICIT. In contrast to working with numerals 1 to 10, or when counting, or when working with groups of teddies or other objects. A large part is due to the structure of the devices, because all Stern equipment is designed to make the learning as certain as possible.

Oliver wizzed through this task, with the occasional self-correcting. The prompts from me were, "Oh does it fit?" "NO" "Okay try another one." Children find this unthreatening and very satisfying! Moving on to an in dependent task, I asked Oliver to put the blocks in the board in order from the smallest to the biggest - first part of sequencing by size. I placed the 1-block in the board to start him off. He did this with great concentration, with a couple of self-corrections (better they do this for themselves than their teaching assistant!). The objective here it to encourage children to reason for themselves. Everything stays put no matter how long it takes a child to process a piece of information or complete a task. Oliver then decided to repeat this task starting with the biggest block working down to the smallest one! marvellous...

Early Vocabulary

I wanted to see if Oliver's understanding of positional vocabulary was secure or indeed transferring to our situation. I placed the 1-block into the board and asked which comes next, and the next, and the next, each time Oliver selected the correct sized block. The accuracy of this task comes from the 'measuring' of the empty groove with his eyes, then scanning (discriminating) for a block of the same length. The repetition that comes from doing this with all ten numbers, allowing the meaning behind the word to be 'seen' and 'felt'. With the second round I introduced the word 'after' in the same way, as well as the 'next biggest' and the 'next smallest'.

The follow-on Blog looks at how we can adjust the programme to accommodate an older pupil, as well as the pattern work we did together and with getting to grips with the bonds of 10. See you soon!

Oliver!

Overview:
Oliver’s operating levels were within the P levels for maths when the tutoring began in September. Until this term he was attending full-time at a Special School in Somerset. Now in his GCSE year, his schedule has changed. Oliver is a keen photographer and his love of photography has been encouraged by his parents. This term he is attending College one day a week as he hopes to take photography at GCSE. His main source of teaching for this is from private tuition with the lovely Mike, Oliver’s step father. He will continue at school for two days and the remaining day is when he makes the journey to me for a two hour maths lesson.

Focus:

Our focus is on building his understanding of foundation knowledge and facts, and basically going as far as he can in the time we have. We will also be developing his ability to use money in real life situations as well as learning to tell the time. Our work will be supported with a numeracy lesson on both days he is at school. Oliver has a great teaching assistant who is responsible for these lessons. There is also input at home reinforcing teaching tasks through games.

First Lesson:
Our first maths session took place on September 14th. I’ve known Oliver since he was 2 years old, now this tall, handsome teenager, walked into my kitchen with his encyclopaedia of animals and birds of prey tucked under his arm. “This is to look at, in the break,” he informed me. “I shall like that.” I told him, and so we began........

Assessment:
Initial assessment tasks gave me insights into Oliver’s understanding of numbers, and the lack of it…. I wanted to see how he performed with counting; positional vocabulary; number properties; cardinal and ordinal aspects of number; number bonds and operational understanding. Generally, the children and young adults I see don’t much like this part because on some level they know they're failing, even though they may not be able to articulate it. Therefore we moved swiftly into the fun part working with the apparatus. We will be working with different pieces of maths equipment which makes numbers visual and tactile. The learning follows specific stages to ensure that knowledge moves from concrete understanding into abstract understanding with success at evey stage. Our approach is multi-sensory teaching and learning in its truest sense.

In the next post we begin working with the Charlotte Clock reading digital time. .......