Numbers Video

Here is a youtube video on how to teach the numbers. Here is the associations we use for teaching the numbers Learning the Letters and Numbers. This video doesn't show the very important part of learning the numbers, which is having your child find each of the numbers for you. Don't forget that you need to do a lot of this before they can tell you what they are!

Don't stop at ten!

Jake learnt all his numbers to ten long ago, but I was recently asked how he was going with the teen numbers and realised that for so long he had just been doing 1-10, with not much development beyond that. It is really common that the children easily get good at 1-10 and then just don’t progress further for a long time, so I thought it was a good idea to encourage you all to keep going! We have had lots of fun at home and school playing a little game with all the number cards from 1-20. Any child who has a fair ability to recognise the numbers 1-10 can do this game as learning numbers 14-19 helps reinforce the learning of numbers 4-9.

I start by laying out all the cards, telling the children what they are as I do so. 

Then, we play finding the numbers, but in order, so I start by asking the children to find me number one. After we have found it and placed it in the line, I ask them what comes after number one. Often as they get to the bigger numbers they need to go back to number one and count through to figure out what number comes next, so this is great counting practice too. I have them point to the cards in the line as they count for extra reinforcement recognizing the numbers.

When they have laid all the numbers out from 1-20 go back and count with them all the way through. Jake was really struggling to remember 15 when he was counting, but having the numbers in front of him helped to not forget any of them. We pretended the number cards were train stations and we needed to put them in order along the track. At the end we pretended we were the train going through all the stations and announcing the numbers…

Notes on teaching teen numbers

11 – remind them at the start it is a 1 and a 1 – hold up index finger on both hands

12 – I say t for two and t for twelve

13 – Th for three and th for thirteen

14-19 – Use the same associations for 4-9 and point to the one in front of it as you say teen.

Four – while tracing over the number say “number four, shut the door” (chopping through the number is shut the door)

Five – we have five fingers on our hand (hold up your hand and then make a hook with your fingers and thumb and show that it is a hook like at the bottom of the five. It is also fun to give them a high five and if they are at all interested in pirates you can say that we have five fingers but instead Captain Hook has a hook.
Six – silly, silly six is standing on his head with his feet in the air (he is so silly isn’t he!)
Seven – number seven, straight straight to heaven (trace over the number showing how it is a straight line)
Eight – eight like a roller coaster (trace around the eight showing how it is like a roller coaster going around and around. If your child doesn’t understand what a roller coaster is you can say it is like a crazy little dog, when you stand in the middle it runs around and around. Pretend that they are standing in the middle of the eight and show them how the crazy little dog is so excited that it runs around and around).
Nine – Sensible number nine (number nine isn’t like number six at all, he is very sensible. Number nine stands up nice and straight with his head in the air and his feet on the floor. Not like silly number six). *This is often a number that children get confused with six, so it is very good to accentuate the difference.

Here is a link to printable number cards in case you don't have any:

https://drive.google.com/file/d/0BwzunNaHHgjpLVJoUTVVcmVmQU0/view?usp=sharing

Counting!

Counting!

Jake is very confident counting to ten and identifying the numbers to ten. Now it is time for him to put the two together and take it to the next level, learning how to enumerate. We do this in everyday life whenever I see the opportunity, as well as in books we are reading. At school we love using what we call ‘counting sheets’ to help the children develop their enumerating skills. These sheets have the numbers written on them, in little boxes that the children cut out and stick on the corresponding boxes. This gives the children some cutting and sticking practice as well and gives them an activity to practice their number recognition in the most basic form, having only to find the number, rather than have to identify it outright.

If your little one is like Jake, keen to cut, but not really at the point where they can cut on lines without just cutting it all to pieces, help guide them by standing behind them and holding the scissors over the top of their hands. Make sure they are holding the scissors in the correct way as this is laying the foundations for successful cutting by themselves. If you know the tune to the song ‘Open Shut them’ you can sing along as you cut (you have to sing it quite slowly so it is in time for their little snips!)

 ‘Open shut them, open shut them, give a little snip!,

  Open shut them, open shut them, snip snip snip snip snip.’

When all the little boxes are cut out you can play finding them, checking that if you ask your child to find each number they are able to do it. When you have played finding them, have your child count the objects in the first box and then find the number, before sticking it in the box. If they are racing through counting at top speed, rather than taking their time and counting each picture, tell them that they need to give each one a number and that the (insert name of picture, such as 'Daddy Pig') will be sad if it doesn't get it's own number!). Try to avoid pointing to the picture and having them count, but if necessary hold their hand and help them point carefully and slowly to each number as they count. Carry on this way until the sheet is done. Your little one can colour in the pictures if they would like. Jake is especially keen to do one if it is a present for someone, but he is also in love with Peppa Pig at the moment so anything with her on it has instant appeal to him!

We are listening to ‘Musical Times Tables – It’s Fun To Multiply’ by Don Spencer, part of a pack I got from the ABC shop. I had a past student who at four years old, had amazing counting abilities, he seemed to be able to see the pattern and know how much was in front of him. If they were laid out in rows, such as four lots of 8 counters he could tell you it was 32, almost instantly! He didn’t seem to be counting but could just see the pattern and knew. His mother said she played a CD like this of times tables in the background once every day. It could be purely coincidental as he was an extraordinary child in other ways, but I do believe in the power of singing when wanting to learn easily. It is also a major part of Accelerated Learning and we often see the benefit of using it in the classroom. Montessori saw that the children went through 'sensitive periods' where something could be learnt easily and quickly if it was done during this window of opportunity. If they are learnt in song form, perhaps it is during this age of rapid language development that it is the ideal time to just 'absorb' the times tables. 

I was always quite good at tables, thanks to the painful experience of having my dad grill a reluctant younger me, on our drive to school and back every day! I would love for Jake to be able to absorb them in an easy and painless way and I do see him starting to try and sing along from time to time, so I live in hope! An obvious footnote here is that it may drive you nuts and you might also find yourself absent-mindedly walking around later singing these repetitive little chants to yourself…

I have attached some basic 1-5 counting sheets below, which I recommend starting with, even if your child is able to do something more advanced. Small successes will help build their confidence and regardless of their skill they will get some good counting and cutting practice. If you would like more advanced ones with 1-10 or 10-20 feel free to email me at admin@smartstarteducation.com.au.

https://drive.google.com/file/d/0BwzunNaHHgjpT2hJSjlkTUs1NGc/view?usp=sharing

https://drive.google.com/file/d/0BwzunNaHHgjpQ0hxdmZ6RUJMaUk/view?usp=sharing

https://drive.google.com/file/d/0BwzunNaHHgjpaHkzb2k2Q1diNGM/view?usp=sharing

https://drive.google.com/file/d/0BwzunNaHHgjpalZxTzZfYnk0Vms/view?usp=sharing

Treasure Baskets

Treasure Baskets            

Maria Montessori believed that children went through ‘sensitive periods’, which she described as ‘windows of opportunity’ for learning something specific, with the greatest ease. A lot of research has supported this idea. For example, we now know that children develop language skills far more easily in their developmental years, than later in life. Around the age of two or three she observed a sensitivity for small objects, where children were fixated on small objects and tiny details.  During this time you will be amazed at the things your child might notice, that you have overlooked, or wonder at how they can be so fascinated by things that seem so inconsequential to us! 

You might also wonder what it is that your child is learning during this period, what can playing with all these little objects do for your child’s development? Well, in order for your child to understand the bigger picture of the world around them, they need to deconstruct it and break it down to the smallest level. They need to understand the smaller pieces that make up this bigger picture, examine them in great detail and then see how they fit together. When you think of it this way I think it makes sense that it is so interesting for them, it is human nature to want to know how the world around us works and so much of it is incredibly amazing when you take a step back and see it from a child's perspective. When the child is interacting with tiny objects they are also required to develop their physical skills, their hand-eye coordination, fine motor skills, the pincer grip that will later be used to hold a pencil and a fine control of movement.

Jake has been quite fascinated by small objects for the last few months. We have a box of assorted objects at school, which we play ‘I Spy’ with, a game where the teacher will spell out a word, C – A – T and the child will have to hear the word and find the object. Jake has for a long time, loved to take out the box and line the objects up, talking about them and looking at them for extended periods of time. He has also loved doing this with small toys at home like little cars and animals.  A month or two ago I started putting, what Montessori called, a ‘Treasure Basket’ on his shelf at home. A treasure basket tends to be a basket with a dozen or two assorted items inside it for your child to investigate and explore. They can have a theme and it is nice if they can have different things within it that appeal to all of the five senses. They can be tailored to any age, when Jake was a baby I had a basket of different miniature (but big enough nothing could be swallowed) kitchen items for him to explore; a small wooden spoon, mini whisk, little pastry brush etc. I have seen people make baskets with all the objects the same colour so that they can focus on teaching their child that colour, or all the objects made of a certain material such as wood or metal. At school we often have a treasure basket of different containers, which the children love. They practice opening and closing the lids, learning to match which lid goes on which box and they like to smell the containers and talk about what was in them! 

I often have parents say that their young child needs to be sitting with them at all times when they are playing or that their child can’t concentrate on something for long before they move off to the next thing. I really think this is a great activity to put on the shelf for any child like this. If you want to extend the amount of time your child can concentrate and work independently, this seems to be a fantastic way. In order to keep it a fascinating exercise for your child you will want to swap some or all of the objects every week and experiment to find what kinds of things they are really interested in. I found that just adding to the treasure basket is not a good thing, a limited amount of objects is best or it becomes overwhelming and they end up tipping it everywhere and making more mess than they are happy to clean up at the end of the exercise. Just like with their toy collections, less seems to be more. You can show your child how to take the objects out and stand them up, talk about what they are and what they do/ are used for/ noises they make etc. If you can see your child is interested and absorbed take a step back and see how long they are happy to work independently. As an extension for older children who want you to be involved, play the I Spy game, spelling out the letter sounds and seeing if they can make the word.

                                                       

 It isn't necessary to have a theme and mostly it is easiest to keep it fresh if you just have to rummage through some drawers for a new bunch of odds and ends. Here are some ideas for themes if you feel like it:

·         Bottles and containers - you can put some little moon stones or marbles inside the containers as the children seem to love this extra element of discover

·         Magnetic vs not magnetic – I have just given Jake a magnet and he has explored what it attracts and what it doesn’t

·         Floating and sinking - Might be a good one to do outside if you want to allow them to work independently without a huge mess being created!

·         Animal/ Dinosaurs – good for learning the names and sounds animals make

·         Colour baskets – all the objects of the same colour

·         Metal, wood, cloth – all the objects made of the same material

·         Lego is great because there is so many little fiddly bits to click in and out. Jake loves fiddling with Lego, not really building, fiddling away connecting trailers, clicking people on and off etc. He also quite likes Barbies, talking about the body parts, fiddling with all the little bits that come with them, putting on shoes and clothes, they are all great fine motor skill exercises and grab his attention.

                         

                               

The next time you go to the effort of taking your little one to somewhere like the zoo and they just want to look at the gumnuts on the path or watch the ants, don't be frustrated, try and see the world from your child's perspective and marvel at how amazing every little component of it is! 

"Enjoy the little things in life, for one day,

you may look back and realise they were the big things" 

                                                     

Art Explosion!

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A few weeks ago Jake got his hands on a Crayola marker and had a great time drawing with it, first on the table/his body, and then on paper, when I spotted the new activity… He seems to have a new level of interest for drawing now and really sticks to it, doing a few pages at a time. He enjoys me drawing with him, showing him how to draw animals or shapes and the likes. It is all very basic scribbles at the moment, but drawing is still a fantastic activity because he is developing his hand strength, coordination, concentration and pencil hold. Drawing and colouring is an activity that can help your child pick up writing so much faster and is a really worthwhile activity to incorporate into your day, not to mention a lot of fun.

Mess!!

I recently saw an advertisement for Crayola Colour Wonder, a set of markers that only show up on special paper so that they can't stain other surfaces. I scoffed at the mother proudly announcing that she had allowed her four year old to draw with markers for the first time, as the ad pans across a child lying on a fluffy white rug, drawing happily. However, I have to admit it does seem to be a messier process than I expected. He is compelled to draw on the floor, table, his body etc! It takes time and reinforcement to really make sure that they understand that they are only allowed to draw on paper. We talk about it every time we get the pens and paper out and he is getting better. At school after we have someone drawing somewhere they shouldn't we quiz the class on places they can draw, ‘Can we draw on walls? (no)  ‘Can we draw on jobs? (no)’ ‘Can we draw on paper?’ (yes) ‘Can we draw on books? They are paper’ (no), ‘Can we draw on other people’s drawings’ (No, just your own paper, from the craft shelf). Etc…

What to buy?      

                                         

I think for young children who are starting out, thick Crayola markers are probably the best product to go for. The thickness means they are easy to grip and even if your child wants to bang them down on the page (Please discourage!) the nibs don't seem to get wrecked or pushed in very quickly. In my mind one of the great things about an early childhood education is that the child starts primary school being good at everything, which in turn encourages them and empowers them to tackle any learning opportunity without the fear of failure. We all love it when we are great at something! These markers give an instant result, they can fill a page with drawing without needing to have the hand strength to push down hard or really control the pen well and that gives them a lot of satisfaction. The downside to the markers and the reason we try and use pencils in the classroom with older children is that they do need constant help/ reminding to put the lid on and they are messier. The lids are a bit hard for Jake at the moment, he can get them off and put them back on, but doesn't quite click them all the way shut. I think for now, just putting the lids on is a good start and I can click them in for him when he is finished with the activity.

      

 

 Painting is also lots of fun, we are just using a little water colour set at the moment because it is so easy to get out and doesn't need lots of prep/clean up. I think the easier, the better, so that you can feel happy about them getting it out whenever they want it. I tend to put a bit of water on each colour when he isn't looking just to get the colours loosened up and ready to go. A big favourite at school is for us to fold a piece of paper in half and then draw the outline of half a butterfly on it. The children cut along the line and then paint on one side of the paper, before they fold it in half and rub it together. It creates a great symmetrical butterfly. With Jake we have just been trying it with folding the paper and creating symmetrical pictures, like the one hung in the left frame below, so do some experimenting.

Stop bad habits in their tracks

It is a lot easier for your child to learn the right pencil hold right from the start than to have to unlearn bad habits later on. I have so many children start preschool with an ingrained way of holding their pencils with their hand upside down, with a fist or right at the top of the pen, rather than close to the nib. Jake is generally good, but started turning his hand upside down recently. I just quickly swap the pen around to the correct way and tell him to ‘nip nip’ his pen and he seems to have realised that it is easier and has gone back to holding it right. If your child is in the habit of holding their pencil wrong, get onto it as soon as possible, helping them to hold it right every time they pick up a pencil, until the correct hold comes naturally to them.

You are now an art gallery manager! 

  

                                    

                      

​You are quickly going to have a large pile of ‘artworks’ so think about ways to display it that will encourage your child. I really love how children’s drawings are transformed into serious art, by being framed and hung on the wall. I think Jake's scribbles look fantastic, framed on the wall :) However, at this point I think Jake’s art is in the quantity, rather than quality phase and he will be able to more independently display large quantities by having a string to peg them on. So I have started with just a few frames on his bedroom wall and hung a little rope along our hallway with some pegs on it. I used the removable stick on hooks because I thought it would be good to be able to move the string higher as he gets taller, but possibly I should have drilled some hooks in,  I have already had to rehang one of the hooks as he pulled it down while rearranging the pictures… I am working on teaching him how to not pull on the rope and hanging up his pictures carefully, so do what you think will work best for your child. 

Talking about colours

Jake hasn't really been very interested in talking about colours up until recently, everything has just been yellow when we have asked him! However, over the last month or so it has started to sink in. I think talking about different colours while we are doing painting/drawing has really helped, so use this time to get some colour practice in. We find having little associations for the colours, like 'green like the grass', 'pink like a pig', 'brown like chocolate' etc. is a good way to help them remember the colours, so try using the same phrases each time you talk about it to help them remember the colour. 

Sign it

 If you want to start increasing your child’s recognition of their name, start writing their name on their pictures and spelling out the letter sounds as you go. If they have a combination sound like sh or ch, underline those and sound them out as the combination so that they start to become familiar with it. With Jake I draw an arrow to show him that the ‘e’ jumps on the ‘a’ to make it say it’s name instead of the sound.

 Demonstrate

 In the classroom we are amazed at how the children can draw pictures that are so much more advanced when we show them step by step how to draw the creature they are wanting to draw. There is a vast difference in skill between different four year olds and the ones who are fantastic usually have parents who can draw and do it with them regularly. Don't worry if you aren't fantastic at drawing, keep drawing lots of very simple pictures that they can observe and copy and you might just improve as they do! With the young children at school and even Jake, the first step we are trying to help them achieve is to be able to form a circle. Once they can do that they are well on the way to being able to draw a lot of things so try and teach them a circle and then see what you can do with it. 

Pack away away away away away

One of the things that I always notice at the start of a school year is the amount of time we need to spend reinforcing to the children that they need to pack away, after they have completed an activity. In the first few weeks we wonder if certain children will ever get their heads around the idea and stop putting all their skills into play to avoid the dreaded task of putting a tray back on the shelf! But, a month passes quickly and suddenly we are really impressed that the children are taking responsibility for their environment and understand what we mean when we say it is tidy up time!

It’s funny though, as one parent mentioned to me a few days ago, often the children learn to pack away and tidy up after themselves at school, but the skill is not transferred to their home environment. The parent quickly added that he did understand that it was because he had never enforced it at home. This is a valid point, if you want your child to pack away after each activity, you do need to make it part of all your routines, from bath time to mealtime and of course after every activity. If you do it every day, constantly, it becomes a habit. It is hard to begin with, there is resistance, they would much rather run off to the next thing, but as it becomes a habit they start to stop questioning you and just get on with it. It takes about 21 days to form a new habit, so remember it takes time and persistence, but I think it is definitely worth it if you can help your child become responsible, tidy and organised. 
                    

    
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Songs are a great way to teach your child, at playgroup our leader sung a song that we also used to sing a Gymbaroo so you may have heard it before. I sing the song every time it is time to pack away and it gives Jake another cue that it is time to tidy up.

The words are:

 Pack away away away away away,

Pack away away away away away,

Pack away away away, we are finished for the day (or ‘thanks for helping me today’)

Pack away away away away away

And it is sung to the tune of ‘If you’re happy and you know it’

Modelling also seems to have a lot more success than just directing. If I jump in enthusiastically to start packing away, singing the song, Jake is much more likely to join in, than if I just tell him to start tidying up. The same is true in the classroom. At the end of the morning when all the children need to tidy up, there are always ones that will mill around and not help out. If I say let’s all pick up ten pieces of rubbish, counting loudly as I pick up the ten pieces, I generally get a large group of followers. Whereas, I can walk around the classroom endlessly trying to tell the ones who are milling about to come and join in and really not get anywhere! If Jake ever sees me sweeping he demands to have a broom as well and seems to really like sweeping up leaves with a dustpan and brush. It is quite tricky for them to begin to use a dustpan and brush so I guess a big pile of leaves helps children to easily fill the pan and get quick results. The leaves make a lovely rustly sound too, so it is probably just a nice sensorial experience! My inside microfibre mop had a problem with the handle a while ago so I unscrewed the top part and now it is just the right size for Jake to push around. Mostly it isn't really helping to clean much, but he enjoys mimicking what I am doing and gives him practice to develop the skill.

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The other thing is making the tidying up process doable for your child. This means keeping the toys to a limit, having low shelves for toys to be put away on and organising your shelves so that everything has a place to go back to. After we came back from our holiday there were lots of new things we had found on our travels as well as Christmas presents that didn't have space on the shelves. It was suddenly a big mess. We cleared out some things that weren't capturing Jake’s attention and it was so much easier to stay organised. Tidying up also needs to be a constant activity, leaving it until the end of a week or a day means that there will be a really large job to tackle so doing smaller, more frequent tidying up makes it a lot less daunting task for your child. 

If you haven't got your child's work/ play area organised, check out http://smartstarteducation.blogspot.com.au/2015/01/developing-organisation.html if you didn't already get an email from me about it. Tim Seldin's book 'How to raise an amazing child' is an excellent resource that has a chapter on how you can organise all the rooms in your house to help your child become independent and tidy. Dig around in the shed/garage/cupboard/ grandparents house/ op shop/ kmart and get some trays or baskets and make it really obvious to your child what goes with what and where it needs to end up after they have played with it! A small table and some little mats to use as work space is also a great addition. In these first weeks back to school there is always someone who wants to pull their activity off the shelf and do it right there on the floor in front of the shelf, rather than take it to a table or mat, so practice at that is also great. 

If you have about a thousand stuffed toys, despite a concerted effort not to end up in this place, I really recommend a toy net that you can hang up in your child's bedroom. We made one and it is great to keep the toys available to him limited, while still having all the beloved toys close. It is easy to vary what stuffed toys he can play with, if he asks for one we can get it down and as we tidy up, just chuck any that he doesn't seem to be interested in back up there so that he isn't wading through toys!

                                                      

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Freedom

I recently spent a week in China on my summer holiday, which was lovely, but also very frustrating. Frustrating because I seemed to have no freedom when it came to what I wanted to do on the internet. I couldn't check my work or Gmail emails, couldn't share photos or videos from my trip on Google Plus or Facebook etc. It reminds you of how important freedom and the ability to make your own choices are, when your freedoms are taken away.

Freedom is a big part of a Montessori classroom, having this freedom allows the child to develop self-control and self-regulation.  The children are encouraged to seek out activities of their own interest, to engage with these activities for as long as they need, and to manage their own daily routines and activities. Rather than being herded from one activity to the next in groups, children individually choose activities that spark their interests. This individualized approach enables children to control their own choices, movements, and activities.

Another great thing about your child having the freedom to choose what they would like to work on is that it means they will be doing something that they are interested in, something that captures their full attention, which in turn develops their concentration span. It might look like your child is just playing, but they are developing one of the most important skills that they can. In the classroom everything we do is geared towards developing their concentration span or dependent on the child being able to work away and concentrate for extended periods of time.

To ensure your child is extending their concentration span, make sure your child has plenty of activities available to them that spark their interests and capture their attention. Montessori said that at this age children have a tendency to be fascinated by small objects and that they seemed to capture their attention, so fiddly little activities seem to be a great option, the popularity of Lego is evidence of this.

I just had to take the photo below, despite his toilet training related nudity! Jake is in love with vehicles at the moment and he had spent such a long time, taking these cars off their shelf and arranging them in a line all next to each other. I have no idea why he chose to do it or what was so satisfying for him to keep taking cars out and lining them up so carefully, but the concentration and desire to work without any encouragement or direction was fantastic to see and he was clearly very happy with his handiwork! It might look like just mindless play, but I was thrilled to see him showing an interest in repetition and precision, two human tendencies that the child should naturally have. Without repetition and precision your child will not excel at things that need practice and take time to learn, so naturally it is something that we should be overjoyed to see them exhibit as well as foster whenever we can. When you see your child working away busily and so absorbed that they have no interest in what you are doing, you know you have hit the jackpot (and not just because you get a few minutes to do something uninterrupted!).

 This all said, the freedom and choice is not unlimited in the classroom. We only put activities into the classroom that we believe will help the child develop a desirable skill, the adults are still puppet masters, subtly manipulating what the children learn. People talk about 'learning through play', I believe all play leads to the children learning something, we choose what they learn through the toys and activities we make available to them. Question what is your child learning from each toy you buy. Most of the time if they love something you can put it to good use teaching them all kinds of things. Playing with a bunch of little cars seems fairly uneducating, but there is a lot you can do with them, learn colour names, sort them by colours, match colours, count them, enumerate with them, learn the names of different parts, different types of vehicles etc. Following your child's interest will always help them to be more interested in what you are teaching, so use it to your advantage. 

There are also certain skills that we would love for the children to acquire and want to integrate into their school day. We hope that the children are always keen to try everything, but often children are lacking in confidence or have insecurities about trying some things. We rule out the option for negativity by giving them a few options rather than a yes/no question. For example, if we think a child would benefit from developing their fine motor skills, rather than asking 'would you like to come and do some drawing with me?', we can tell them that we really would really like to do an activity with them and ask if they would like to do some writing with us, or some drawing? Usually with an option of one or the other, rather than the option of refusing to try, a child will happily make a choice and come away from the experience feeling like they had the freedom to choose what they wanted to work on. 

If your child seems to be worried or reluctant about trying something that you would like to do with them, try giving them some options to choose from. Even if it is a few jobs you need to do in the day like load the dishes or hang out the clothes, ask they what they would like to help you do. I think young children are very frustrated by not being in control, Jake is very much like this and desperately wants independence and freedom, resisting really strongly and showing great frustration when I try to control his movement or take away his freedom. Little reinforcements to make them feel in control should help to reduce their frustration at feeling like they are not in control. If your child is also strong willed enough that fighting it seems to be a waste of time, give it a try to make them feel like they have control over their life and have the ability to choose their own direction.