The Joy of New Learning!

Some of my students do the ICAS Mathematics papers with the University of New South Wales. They just like the challenge and it’s a choice for them if they want. Those that are good at Mathematics generally like to give it a go.

The following question in the Yr 7 and Yr 8 paper had the better students in my class stumped. As their teacher I was totally lost as well.  Teegan went home and asked her sister and she came back with an explanation that we couldn’t follow so being the end of term and year we left it.

However when the holidays came around it was something I wanted to find out about so I took the problem to my friend and a past Math’s teacher to help me.  Here was the problem.

35.                          4! = 4x3x2x1

                                5! = 5x4x3x2x1

                                Jess wrote the expression 20! – 19! on the board.

                                Which of the following has the same value as this expression?

(A)        1!

(B)        20

(C)        19x19!

(D)         20x19!

When first looking at it I thought maybe (A).  I was applying the only background knowledge I had which was  taking 20! – 19! =  and thinking of it as 20a – 19a =.          However having peeked at the answers I knew this wasn’t correct. I was worried by the top piece of information but I couldn’t find any pattern and in the end chose to ignore it.

                                                                   

                                                       

However now I have new information!   The ! is a special symbol, it stands for factorial. I hadn't known that. So 4! stands for 4x3x2x1.    5! as above.  6! would be 6x5x4x3x2x1.   Factorial is related to the word factor. So 6,5,4,3,2,1 are all the factors of 6!

I now had some helpful information but it took me awhile longer.  So….

20! – 19!  =  20 x (19 x 18……x1) – 19x(18x17….x1)

                  = 20 x 19! – 19!

                    = 19 x 19!          which is (C)

Factorial numbers get bigger quickly.   20! is 20 x 19!  so if we take away one 19! we have 19 x19!

20! is 20 times larger than 19!

The part in blue took me a little while to get.  Later in the day I went over it in my head and I said to my friend awhile later, “So I’m going over the factorial thing and this is what I think…

As he listened he said “I don’t think you have got this part, and he named the place where 20! is 20 times greater than 19!, so we chatted over that and finally I saw it.  Or at least I did, until I sat down to write this and then I had to go to his paper to look at the notes he had jotted down and then it came back to me.

Now to those that did Maths for high school and college this probably is a no brainer. But for me who was told in Year 10 that girls didn’t need Maths (1960’s) this was very new learning.  My love is reading and writing, however I need to teach Maths to Year 8 and I actually enjoy it too.
 

Why did I want to solve this problem?  Well firstly I was driven by the fact that I wanted to be able to teach my students about it.  That was my why.  It has no other relation to my life, and I have to say it probably has little relevance to a large part of the population.  So why would my students need it? Well obviously they are not going to get the message that girls don’t need Maths so it is a small step in the bigger picture.  Now that I knew the word factorials I was empowered to search further about them. A video on You Tube showed me a little more. 

I hadn’t seen them mentioned in Algebra at the Year 8 level but what’s the harm in going further? I was partly driven also by my need not to have my students say half way through the year “I haven’t learned anything new in Maths this year!”  Now while it wasn’t Teegan who said this, or indeed anyone in my class in 2011, I know I will get great joy in sharing my knowledge with her and the others who are ready for it.   Students who on the whole are showing through testing they are at Level 5 in the NZ curriculum but are still at primary school.

And learning for the sake of learning is actually very satisfying.  Now I need to share it in a way my students will get it, so that one day very soon they can go beyond me.  One thing I can predict is they are going to grasp this far quicker than I did.

The Book Whisperer.

I have just finished reading this excellent book by Donalyn Miller.  I found it easy reading, and was through it in a couple of days.  However I am now intending to do a re-read and gather up what I missed in the first reading.

                                                      

 I grew up in the'50s where I was forever scrounging and seeking out books that weren't there. No town or school library, and a meager class library. Oh to have been in such a classroom as D Millers. She believes that students should have plenty of books available to them to read, and that they should be of their own choosing.  She also believes that this type of reading can be done during the school day. Now that kind of thinking is not foreign to me, New Zealand schools have long been places where we could choose the materials we teach with.  We have no prescribed basal readers or course that we have to follow. Just standards our students must reach. During my teaching career students have always chosen their own books to read in class.  This said, D Miller is advocating more than that, and that is where I found her book helpful.

I have recently become aware of the Daily Five and Café books by the sisters Gail Boushey and Joan Moser, and have implemented their ideas as well as I can. Of course as always, it was a fine tuning of my teaching rather than a radical shift, especially with the Café book.  However the Daily Five did involve some small radical changes – throwing out many desks for one!  The Book Whisperer calls for more fine tuning, and it challenges me as well.

Daily Five is working well, its magic, as all of we teachers who have implemented it can attest to.  In spite of this I still had a query in my mind as to the accountability of students in their reading.  The Book Whisperer answers this question for me.  If you are wondering about it then read the book, like me you will find answers.

I admit I have never been a great reader of children's literature, I enjoy the books I read to my class and there it stops. I now realise I need to read more of them, so I am starting with a goal of one per week. I have just grabbed from our school library Inkheart by  Cornelia Funke. D Miller mentions it in her book; also one of my reluctant girl readers mentioned it yesterday as a favourite book for her.  As this year has been a year of difficulty for me in trying to hook in some girls to reading, I thought this is a good place for me to start.

Some main points that I take from this book are:

·        The students need a wide variety of books to choose from – as each student will have differing tastes.  D Miller has her own vast class library that she has paid for.  I don’t have the time to build that library – I retire in a few years – however I have some books in our class library, we have a good school library, we visit as a class the local district library once a fortnight and we can loan 30 books from our National library for a 6 week time period. 

·        She has a very good system for organising her class books. She does this according to genre and has a system of stickers and numbers that easily allow for additional books with no changing around of the books already there.  I am going to organise the books I do have in the way she describes. It might not be until the summer break, but I will do it.

·        She has  high expectations for her students.  She sets the goal at the beginning of the year for the students to read 40 books.  Read that is! She allows that a reader will pick up a book and not like it and its okay to discard. ( I notice on Goodreads she has her own shelf for such discards.) Next term, is going to be short, I think I will set 7 -8 books for my class. In February as we begin our school year, it will be 40.

·        She has an effective system of accountability.  She has her students use a reader’s notebook and has a simple way of recording what they read.  I like this and I am going to implement it next term.  Once a week they write her a letter type response to the book they are reading and she replies to this. I need to explore that further in my second reread of the book.

·        She reads many children’s books so that she can match a student to a book.  I am sure that’s not the only reason she reads them, she is obviously a booklover full stop!  For me this is the most challenging aspect.  I am a booklover too, but prefer to read what I like in my own time.  As a result of reading this book though, I am going to change that, as I mentioned above.

I highly recommend this book to all teachers, and as one teacher on Twitter suggests, all administrators!

Writing in the Classroom

Recently I have been working on what good writing looks like, and what the teaching of that looks like as well.  Last summer holidays,- overseas readers  its just going into Spring down here- as teachers do, I was searching around for new viewpoints on writing.  I came across the Northern Nevada Writing Project.  It has some wonderful pointers on the teaching of writing in the classroom.

It takes the six traits approach to writing, and I find this really helpful in teaching the skills of writing.  When I went to school, we didn't learn that much about writing.  Once when my mother went to a parent interview the teacher said, "You would think her writing would be better with all the reading she does".  My mother came home and repeated that to me, and it's a remark I've never forgotten. It wasn't that helpful, and if I was being myself now, I would say, "So teach me to write!"  Back then, we were expected to learn about writing by osmosis perhaps? The Northern Nevada writing project which you can link to from the picture below, features children's books that can be a model for writing.

I noted this site, but it is only recently that I have returned to it and started to really make use of it.


There is also a Ning linked to this site, which again I joined but did little about until now.  You can check it out through the picture link below.  At present I am grappling with developing the skills of sentence fluency with my class.  Another post on that later.  Let us say I am coming to terms with the participle phrase, hoping that my students are at the same time.

It is said that what we need to learn,  is best learned by teaching it.  You see, it is not only my class that are developing their writing knowledge and skills, count me in too.  At present I am preparing a guest post on books for another teacher.  I just need the time to revise and edit it first!  I want to put into practice what I am learning.  Hope my class does too.

Were you taught about writing when you went to school, or did you learn by osmosis?

Class Engaged in #Daily5.

My class have all voted in favour of the way we are managing the Literacy section of the day. I vote for it too!

Implementing Daily Five.

Three weeks into the new school term and Daily Five is beginning to take shape in my classroom.  I am still finding my way and I still have questions, however I think that when I begin to grasp the way it works and how I might operate within it, it is going to be all I hoped.

The actual design of the classroom, with many of the desks removed to the storage dungeon, on the whole is working well.  The main drawback is that I have allotted places around the room for students to store their books and pencils etc.,   at times there  are bodies all trying to get to the same place at the same time.  So we are learning about waiting and taking turns, rather than walking on top of one another, ( as one student does)!

The students like the layout, and there were many dropping jaws and visitors from the next room coming in to see what had happened in Room four, on the first day back.  Just a week ago, after school, Sandy, a teacher from the other end of our long corridor came in and exclaimed, “Where are all your desks?”   With glee, I told her what I had done with them.

I now have Reading to Self, up and running successfully. This was not difficult as the students were already reading for 20 minutes of self-choice reading in the day. However I went through the Daily Five introduction and we practiced doing it correctly, incorrectly and correctly!   Writing was next on the list and we went through the same process, followed by Working with Words. 

At present I am working on Reading to Someone.  We are at the stage of building the I chart and practising it.  By the end of the week I hope it will be there as a choice.  I am a little nervous of this one, as it will introduce more sound into the room, so I think I will need to take my time with it.  At a class level where students are 10 to 13 years old perhaps it could be argued it isn’t a needed skill. That most of them are fluent readers.  However not all of them are, and those that are, do not necessarily have the expression and variety of a good oral reader.  I will probably request that it be chosen two times in the week and observe how that goes.

Listening will be introduced this week and up and running by next week.  I am not going to make this a compulsory aspect as I think it will appeal to those it needs to, and less to those who don’t need it so much.  However I do believe we all benefit from being read to, and I won’t stop anybody from making the choice. I have used Ministry listening materials, and have also collected some other places the students might go in my Livebinder.   We have another time in the day when we all listen to a story together.  At present we are listening to The Lion Boy by Zizou Corder. 

This week I am aiming for four days using Daily Five.  Because I am giving more time than I might normally to Literacy, I am keeping Friday to cover other aspects of the curriculum.  I am giving a ten minute input, and then students choose what they are going to work on.   On a good day I hope to have four input sessions, followed by four choice sessions.  As all teachers know, not every day is a good day.  Take tomorrow there are school photos!  Tuesday the students are off to technology and so it goes…. 

The hardest aspect for me to organize I think will be how I spend that time while the students are involved in their choices.  At present I am using it to Running Record some students to find out what would be good next steps for them.  I am also meeting individually with writers, and I am beginning to grasp that.  However once I start integrating group times, it will be something else to juggle.  I want to use my time wisely and where it will make the most difference.  I suspect this aspect of Daily Five is going to take the longest to implement effectively. 

I am keen that students will be able to tell me what they are choosing to do and what their goal is as they leave the gathering place.  Some students are well able to identify their goals, others are going to need more support. 

I see how our key competency of self-management fits very well into the Daily Five.  I have completed a taxonomy for students to place themselves on at the end of each session or day, in relation to this.  Indeed I should do one for myself.  With over 35 years of teaching experience it is very difficult to leave go my roving eye and word of caution, and allow the students to practice self-management!

Classroom Changes Afoot.

Holidays are when ideas begin to mull around in my head.  The summer holidays usually are the worst!  I make huge plans, and then I return to school, and reality hits!  It’s then I find the nitty gritty of implementing those plans takes a lot more than I anticipated in those lazy, hazy days of summer.

However, this isn’t the summer break, it’s the two week mid-winter break.  Ideas of how I want to make changes are entering my mind.  I am blaming it on the fact I sat in an office for last term instead of a classroom.  Normally my mind is mush at the end of a term and ideas have fled.  Oh, and the second culprit, Twitter.  It brims over with such great ideas.

Firstly I got drawn in by the idea of the Daily Five.  It’s a way to organize and structure the literacy programme, as shared by Gail Boushey and Joan Moser in their books, The Daily Five and The Café Book.  I see there is a possibility of structuring Maths in a similar way; however I will leave that for the time being. 

This structural idea appeals to me:

ü It encourages students to be responsible and independent. 

ü It allows me time to work with individuals and groups. 

ü There are also times when I can meet for whole class input. 

ü Once I get organized each student will have their own goals that they are working towards.

ü  The Daily Five ensures that students keep those goals before them daily.  We have often previously set goals and somehow during the term they have been lost, only to be remembered when we reflect towards the end of term.

So that leaves plenty to get organized.  And I also need to make a general large picture of the social studies unit to be entered into for the coming term.  There are plenty of other ideas also rolling around inside.  Not new ideas, others have all been there before me, but I am walking the path for the first time.  Fortunately great teachers have shared places on the internet to explore and obtain more information.

Subsequently I looked at the two sisters website and noticed the designs of some of the classrooms. I heard in my head, “What if…..?”  What if I made some changes in the layout of the classroom. (I am a structural control freak, you need to know that!) I decide where the students sit, I carefully craft a seating plan each term.

But what if…. Every student didn’t have a desk.  Computers are wonderful in the classroom, but they take up room and they have to be where they can be cabled into the internet ports, although a wireless upgrade is hopefully coming very soon. I use a rather large kidney shaped desk, that I like but has a dangerous wobbly bit on it.  So I am thinking:

ü Get a jelly bean shaped desk I can use.

ü Find a two seater couch

ü Rearrange the class library

ü Organise how to store student gear.

ü Remove some of my filing cabinets

ü Gather up some cushions

ü Make up some listening boxes

ü Put my dibs on a  low table or two

ü Wonder how many actual desks to leave

My classroom is generally the last thing I organize.  My walls are never anything to write home about.  There are other things that take my time and energy.  But this could make a difference to learning and I am rather energized by the thought. 

There is a thought going around in my head about how students will cope with this.  I am thinking that I will pre prepare but nothing too radical until the students return.  Then I will get them to think about the classroom and what if…?  I will ask them to come up with a design, and get their thoughts on how many desks we need, where we could place things.

I already have my jelly bean desk.  I spotted it on Trademe, now I just need to organize the transport.  I will be able to use it for working with groups of students and it can also double up as a working area for them when I am not using it.  I have my eye on a 2 seater couch that will be local and easily picked up, and very cheap.  Nice.

Evernote - Teacher Helper.

Evernote is a free web tool that I recently came across through reading Richard Lambert’s blog . Later I listened to a prerecorded webinar given on Wednesday eT@lking by Graham Clark. 

Evernote is for

            PC

            Ipad or Ipod Touch

            Iphone or Android.

If you have it on two or more such devices it will sync automatically and notes you put in using your PC will be found on for instance your Ipad when you next open it up.

Evernote allows you to keep notes that include text, photos, and audio. I cannot see any way of easily creating audio on your PC, however on the other devices it is in the toolbar and is very easy to add a voice to the note.

 If you pay $5 a month you can include all kinds of documents and video.  At present I am only using the free tool, however as I begin to collect information I may move to the paid version.  The free version allows you 60mb a month.

While I will use it to collect, sort and tag a variety of information I want to use it to collect data about students in one place so that it will help me to track what they are learning through the year.  For example the class has just finished a Science Fair project.  I have photographed these and put them in students’ notebooks.

Evernote can be downloaded from their website.  Apps are downloaded from the app stores.

There is a web clipping tool which should also be downloaded.  It sits on your tool bar and gives you the option of clipping the url, the whole article or the page.

If you set your preferences under Tools you will also be able to choose from a drop down list which notebook you want to put the note in.

A clipping tool is also added to your email and if you want to save a special email you can put it into you notebook.  For example I just did it to remind me of a password I want handy for a website.

If you are on your ipad you can also clip to your notebook using the email address assigned to you by Evernote when you join.  The following video shows you how to do this. I haven't yet mastered this aspect!  Clipping from your PC is far easier.

If you are starting a new notebook this can be done from the tool bar at the top. Once the new notebook is made you are ready to start adding notes to it.

The new note can then be clicked on, a title given to it and it can be tagged. Some teachers choose to tag by student name within a notebook.  I prefer to set up a notebook for each student.  I then tag as well, so that I could for example find all science information if I wanted.

If students had their own devices they could have Evernote on say their Ipod Touch and they could track their own work e-portfolio style. 

I like this free tool and I can see that it is going to be very useful.  I am looking forward to using it next term when I return to my classroom.

If you don't already use it I suggest you give it a go.  There are many uses for it outside of education.  Try it.

Making Time to build Your PLN.

When we are starting out to build a PLN the idea and task can be a little daunting.  It did to me at the beginning.  And really I still am at the beginning!  It does take time, but it doesn't need to be a lot of time.

In the most recent Edublogs PLN challenge Sarah Poling mentions the idea of spending 15 minutes a day, which will over a period of time make you very competent at what you are learning. For myself I then take this and say well I will spend some time most days.  Sometimes it will be more and sometimes less.

photo © 2010 Eric Lockheart | more info (via: Wylio)
I started out in a small way and joined the classroom Edublogs blogging challenges run by Sue Wyatt, for the last few years.  I didn't realise at the time that I was beginning to build a PLN.  I thought I was just getting into the world of classroom blogging and it was away to connect with other teachers and classes. My eyes were opened to the learning going on in other classrooms and I wanted that for my class too.  At this time I was introduced to the use of Google reader, firstly to follow blogs in the challenge, then my student blogs and finally I now use it to follow teachers who I want to learn along with.

Earlier this year I joined the Edublogs Teacher blogging challenge and through that I found more teachers, learned along with them, or was amazed at what some of them were doing far beyond where I was.  Through that I became aware of some of the webinars that were available from such sources as Techtalk Tuesdays and I have joined in occasionally with those.  Recently I could not be at the live webinar but I connected in later to listen to an Evernote webinar.  Afterwards I spent some time setting up Evernote to track my students, as I had seen suggested my Richard Lambert on his blog.  He had presented a webinar on Digital Storytelling, I attended that, have since bought his book and want to start out on that particular journey.

During the Teacher Blogging challenge I decided to join Twitter.  This came as a result of seeing how teachers in the blogging challenge were using it.  I have started very small.  I usually link into it quickly a couple of times per day.  I am still learning the conventions of Twitter.  I was working with a student recently, and was having to remind her about putting in full stops.  During our last session she said, "Right now I put in a full stop." Then  had to be reminded again later.  I thought to myself why can't she do this all the time.  However I was reminded of that little thought later in the evening when I sent off a tweet without the hash-tags it needed. I had used them properly in another tweet, but forgot again.  I then understood where we both were in our learning steps!  It helped me be far more compassionate towards both of us.  Today I have been learning about the Structured Overview of Learning Outcomes (SOLO) and the experience made even more sense to me.

As you may be able to see, I think I am building a PLN in a way that is particular to me.  I am finding that as I  participate in something I am meeting up with people I have met up before so I am deepening links with some people.  It is then leading to something new, joining up with something new.  And so the journey goes on.  One thing leads to another. I want quality rather than quantity. So my goals for building my PLN are:

1.   Spend some time on it each day.
2.   Comment on people's blogs that I follow.
3.   Spend a little time surfing through the latest updates on Twitter.
4.   Click on links that interest me in a tweet.
5.   Connect with others on Twitter as I see the opportunity.
6.   Each day spend time with one idea gleaned.  Explore it and decide it I am going to depth it.
7.   Recognise when I have a sense of fullness, small bites will be enough.
9.   Track how gradually my PLN and my own skills and knowledge is growing.
      (For example my New Zealand contacts have grown as I have consciously set about to develop this.)

photo © 2010 Hartwig HKD | more info (via: Wylio)

So what about actual time?  Sometimes in the morning I spend a little time glancing at my Google reader or Twitter. In the afternoon/evening  I might read on Twitter or engage in blogging. The weekend sometimes gives me some time as does school holidays as well. However I have less time for reading, watching TV, chores, and in person people time. It’s rather like budgeting with money, if you buy this then you can’t buy that..

To some extent what I choose is governed by what is going on around me or within me.  However I find that whatever I am passionate about time isn't a big factor.  I just need to remember I can't have it all.  We are time bound creatures!  However we have the gift of choice.