Wednesday, August 29, 2007
Watch this video and try to figure out if there are similar arguments today about the 21st century school and what these folks were dealing with in the 1940's. I found the similarities .... disturbing. It is a powerful piece to show your staff.
Monday, August 27, 2007
I plan to use video often this year. If students can interact with the video especially if it has the curricular content this is what separates viddler from the rest. Here is an article (thank you Jason Hando) that explains what makes viddler different. Oh Yeah there is no 100 MB limit to the size of the video that you are uploading. You get a wopping 500 MB. This is handy when you are using bulky video making software.
Jason also pointed me to this recent OnlineVideo Screencast Comparison. I guess you could say that I am getting ready for the school year. Oh the percolations I am having. Lets the the year off to a great start.
Saturday, August 25, 2007
Friday, August 24, 2007
On a different note. I had the opportunity today to teach 30 teachers about the new math curriculum being implemented in Manitoba. They had a great time and my partner Greg and i put on a great show. Greg told the crowd about my blogging and wikiing with my students and very few OK only one of the participants had even heard of blogging and wikiing. I gave them some URL's to check out and told them about K12online06 and the upcoming K12online07 and maybe some will bite and check it out. I hope they find 2.0 apps and their potential to change their classrooms as interesting as the math material we presented today.
Still waiting for the video to finish processing. If this is a seamless and effortless as I think it will be then my goal of more movie production this year from the sargentparkmathzone team will be easier then ever.
Hey the video uploaded quickly. This can only be a good thing
Thursday, August 23, 2007
The math is not in the model to be seen but in the learners head. The learner is constantly trying to figure out and understand. Use real context this will give the opportunity for authentic learning.
So you teach fractions here are some strings for you
Think about a half? Elicit responses from your community. Many will come out but the first one I want you to think about is money.
First string think about $$
String 1 (coin strings)
1.) ½ + ¼ = (3/4 75/100)
2.) ½ +1/10 = 6 dimes 60 cents
3.) 2/10 + 1/5= (how many people thought of a nickel)(good for /100)
4.) 4/10 + 2/5 +1/4=
This is a very early string for fractions. These are landmark fractions. Landmark fractions are easy because you are dealing with whole numbers instead of dealing with fractions. Link to percents because of the $1.00. Get rid of the fractions and make it contextual.
String 2 (clock)
Draw the clock to represent the fraction
Calculate the minutes. You do not need to show the equivalent fractions because the clock model is there you do not need to show the equivalent fractions
1.) ½ + 1/3
2.) ¼ + 1/3 (anyone get 7/12)
3.)1/6 +3/12 +1/3
(1/6 is the kicker here) 1/6 is 10 minutes… start to look at the whole.. There was some breakdown here. The 1/6 was causing problems… get the community to provide the proof for the breakdown. This is key keep the kids talking and doing the explaining. Knowledge can be generated out of a communities talk. 4) 10/60 + 1/6 +1/4 +7/12
This problem was generated after the community was having issues. Free flow. Getting bogged down in some lcd’s
Pedagogy 10/60 and 1/6 are = this should be a good scaffold
When doing strings think on your feet and go with the flow… but not too much
This string again gets you away from fractions and into wholes… then you can get back into the fractional form.
Scaffold the landmark fraction(ability to use whole numbers) and coins.
String 3 (you choose the strategy)
Look at the numbers and choose coins or clocks
1.) ½ +1/3 (clock because of 1/3 $)
2.) 1/3 +1/4
3.)¼ + 1/5 ($$)
4.) 4/5 – ¼ ($$ because of the /5)kids will start to see which fractions are clockable and which are $$able
String 4 (double numberline)
Pick any number you want to be a guide on the track (numberline)
1.) 1/3 + 1/7 =
2.) ½ +1/4= Community will choose numbers to be the numberline total
(need to add the other aspects of the string) Kids will start to create common denominators What others numbers are easy numbers Lets pick a simpler number…. This gets to the common denominators. Work to prove conjectures. Name them after the student that came up with the idea. Use other examples to prove or disprove Double open numberline paves the way to common denominators…… Push to show equivalence
String 5 (Use an array to demonstrate)
1.) 1/3 x 1/5 left with 1/15(outer inner boxes)
2.) 2/5 x 1/3 (the whole remains the same one more piece doubles)
3.) 2/5 x 2/3 (double doubles) (use the playground context to be the building block)
Inner and outer rectangles show the algorithm
4.) 3/5 x 2/3 You can use the previous array (shows the pattern)
5.) 2/5 x 3/3 Curious leap here (new array) what happened to the inner rectangle. It shifted 2 by 3 becomes 3 by 2)
Can we swap the numerators to make a friendly question
6.) 4/7 x ¾ = 3/7 x 4/4
Division of Fraction
Use a ratio table see photo Use the ratio table to explain yours is not to reason why just invert and multiply
The use of the ratio table was brilliant. It should be the model used to bring understanding to why we invert and multiply fractions.
Many times we take part in activities and professional development that is lacking in so many ways. These 3 days out of my summer break were stimulating and exciting. I can hardly wait to use my knowledge of 2.0 apps and push the limits of what I learned this weak. Oh Yeah you can annotate and draw while doing a voice thread. That is too cool for school.
For those of you who want to get the Fosnot material here is the web address
The material I was being taught is from Fractions Decimals and Percents.
Wednesday, August 22, 2007
The day started answering some questions following yesterdays session that dealt with Math in Contest. Yesterdays session make us partake in a group activity in mathematizing. This activity would take a whole class. Todays session was more about the "drill and practice" if you could call it that.
Strings are minilessons. They should take between 10 to 15 minutes of classtime. These activities focus on a students ability to do "mental math". That does not mean that they have to do all computation in their head. Mental math is giving students strategies to solve questions in a variety of ways.... the way mathematicians would.
Strings of computation problems where numbers are chosen for a reason to connect in giving a student a feel of numeracy.I jump around her a bit. I hope it is clear.
Questions and comments that arose out of string 1
10 x 17 = 170
Question is... How did you know?
The zero trick… Why does it work.
Why is it like magic?
Talk to your partner?
This discussion with partners within the learning community is important. Some prompts the facilitator can give are:
Did the person next to you say something interesting to you?
Did the person next to you say something that made you said WHAT?
Why does adding a 0 when x10 GENERAIZE?
Pull this information out of the community of learners.
Switch the question instead of 10 seventeens lets think about seventeen 10’s. Ah the good old communicative property. This is a rule that generalizes
17 x 10 = 17 x 10
2 x 17 (double)
12 x 17
12 is 10 and 2 so use this to help you multiply the more difficult question.
Use and array to illustrate this question.
Eventually you can use and open array to show the multiplication on all kids strategies.
(draw rectange with 10 by 17 then underneath it do a 2 by 17 show the two combined to show the new array 170 and 34 is 204
Mental arithmathic is to break the habits of pen and paper. Mental math is more to break the bonds of the traditional algorithm.
Get kids to build on their strategies instead of putting them into our strategies.
Mathematicians play with what they know about number and go with it. They are not restricted to just using the traditional number algorithm. Multiplication and the array is so important for understanding the multiplication of polynomials. (x+6)(x+3). Many of us learned the FOIL method. You can use the array to display the multiplication better.
When we teach the students the traditional method of multiplying what happens is the opposite to what kids need to know when multiplying polynomials. The traditional way of multiplying ends up being LIOF the opposite of FOIL that they will need in middle and high school.
Distributive property and the array much more effective.
Strings and how they built.
1.) 10 x 17
2.) 2 x 17
3.) 20 x 17 (doubled the 10 x 17 (draw a double array 10 x 17 twice) Show the array over again )
4.) 22x17 is the next part of the string
Next part of string is 19 x 17 Which strategies will kids choose? I chose 170+90+63 because I can multiply but you can see another strategy that would be 20x17-17….or -10-7
5.) 19 x 117 next part of string just 100x19 more than the previous string
Towards the end of the string take the strategies away
6.) 13x22 but the strategies you have been working on will be the helpers
Come in with a string but be prepared to go with the flow of the learners.
3.) 8x18 (doubles)
4.) 16x9 (double half or x10-16)
5.) 4x36 (4x30 4x6) strategies are honoured even if they are outside the 48x3 (could be 4x12x3 use the factors to make it easier) make an array
This string takes into place the associative property
When kids get the distribuive property and the associative property they get multipication.
6.) 4.8 x0.3 (make it 48 x 3)
7.) 3 1/2 x 14 (double and half so that it is 7x7)
8.) 3 1/3 x 150 (x3 divide by 3 becomes 10 x 150)
Now for some Division
1.) 130/13 (10’s rule)
2.) 26/13 (doubles)
3.) 52/13 (26 doubled answer doubles)
4.) 182/13 (52 and 130 from above using partial quotients)
Partial quotients uses the distributive property (inverse of multiplication.)
5.) 195/13 (just 13 more)
6.) 260/13 (doubles)
7.) 247/13 (260-13) one less
What we have been working on is Associative property.
Distributive property and how it relates to division and partial quotients
1.) 100/4 (four quarters)
2.) 200/4 (just doubles)
3.) 200/8 (divisor doubles but the divident remains the same it halves)
Partial quotients are helpful when there are no common factors or if one of the numbers is a prime
Simplifying are effective
4.) 400/16 (double double) equivalent fractions
5.) 800/32 (fractions again)
6.) 300/12 (use the first question and create equivalents)
7.) 1200/48 (simplify)
8.) 3.6 /0.9 make it simpler
These are great warm-up and mini lessons. Highly recommend that you go and buy the books buy these authors. This is the way math was meant to be taught. I am looking forward to the last day and the school year.
Tuesday, August 21, 2007
What a terrific day I had today. With the exception of the fire alarm that interrupted the afternoon session great learning was had by all. Here is my recap...
Fosnot Institute Day 1
Starting to use math with context. It is important for students and teachers to learn math with a context. Allow students to be mathematicians learning and explaining. For too long teachers have been the be all know all.
Here is the context. The teacher poses this question to the class.
A rectangular lot in neighbourhood A is 50m by 100m. Of this lot ¾ of it will be a playground. Of this playground 2/5 will be blacktop.
A rectangular lot in neighbourhood B is 50m by 100m. Of this lot 2/5 of it will be a playground. Of this playground ¾ will be blacktop.
Which Park has more space for blacktop?
In pairs you now attack this problem. As a teacher you stand back and take notes on the conversations happening between the students. This thinking time is important for the mathematical ideas to take place. A push or prompt needs to be held in instead of giving that helping hand.
Here are some photos of our finished work
It was fun to work with a partner and talk math. Together we worked out the problem and were chosen to speak for the math congress. Hmm not bad for my first day back thinking about math.
Following this work time students post their work which had been done on chart paper for a gallery walk. During this time students are encouraged to post notes using post-its on the other pieces of chart paper.
Students need to be trained to have good gallery walks. Choose similar and different solutions. Teachers need to use guided questions to start this process.
· What was done similar to your solution. Is it clearer on this paper?
· What do you not understand on this solution. Is there something missing?etc
Next to the congress. This is a part of the lesson where students become the teachers. You could call it double learning. Students are reinforcing their learning when they are teaching the rest of the class.
The teacher based on the gallery walk chooses examples that will further the learning process. This does not necessarily mean the best examples but examples that add more context to the topic.
During the congress it is important for the teacher to remain on the side lines. Instead of asking Do you get it? The teacher needs to ask;
How many people and put in there own words what this group has said?
Giving a group a second chance to explain a topic will give them another chance to reinforce their knowledge. The second time around concepts are easier to explain or at least seem to be more coherent.
During this congress after the group presented there was time for a pair talk. Are 2 fifths equivalent to 4 tenths. Questions that arise during the congress are the avenues to deeper contextual understanding and avenues to further discussion and scaffolding.
It is not the presenting groups responsibility to explaining the new topics arising from the congress. Other students take turns explaining using their own words and pictures on the assignments hanging up throughout the room.
If students get bogged down in these instances the teacher then jumps in and tries to rephrase the topic. (pictures can be a powerful manipulative)
The congress develops a sense of community in the classroom. It is important to recognize the importance of math to students. Celebrate questions and explanations explaining to students the mathematizing they are doing.
Side note Create a classroom space for working and congresses. Find a way to separate the two pieces of the problem.
From the congress here were some things I heard… Lets prove it.
Of means multiply…(use pictures that are out there in the congress)
- to prove it you need to disprove it. Find a math sentence that uses of in a different way other than x.
- two of 5 or 2 out of 5
- groups of means x?
The use of arrays proves this …?
Facilitator needs to stop this and give this as homework journal. (blog it)(move it back to the individual level instead of the group)
Multiply numerators and denominators the demomenators give the number in the gird(array)the numerators multiplied gives you the amount of the whole.
Communicative Property 2 times 5 is the same as 5 times 2
All the above were ways in which we took the contextual problem and stretched it further our understanding.
Take away the AHHA’s and kids will never want to be mathematicians.
Petagogy… make the kids do the explaining. Take your time and have them do the explaining…double learningl.
In the afternoon we broke up into two groups. We were with Maartin D talking about the landscape of learning. This landscape takes into account
Building the landscape of learning.
What do children really think and do….
What is it that I as a teacher want my students to talk about
Building context…what content can I steal….
What is the order
Big ideas take time to create
What models are used
In their supplemental material that is provided Fosnot and Dalk give many examples of teachers and students interacting in mini-lessons and math congresses. This gives educators a chance to see this mathematizing in action. The CD's have the ability to cut and paste video lessons and parts of video lessons into your own customized clips which you can then add to your landscape of learning for the unit you are creating. We went through this task in the afternoon and I was pleasantly surprised with the ease at which we started to create our own landscape to improve our learning experience.
As you watch the many different video clips that are provided you will be able to deduce for yourself,
- What is the role of the teacher
- What are the children saying and the math behind it(this is how you neeed to see the footage we watch)
- What is the big idea being discussed in the video blip?
You want the students to start to use the model with a context to understand a variety of different situations.
I went home with a positive attitude and a desire to return the next day and continue my journey into mathematizing and the joy of seeing students be key instruments in their own learning.
Message of day one... Context is important, kids need to be mathematicians.
Tuesday, August 14, 2007
Here are some things I like about Podcast People.
It is easy and free.
You can add authors to a central podcast page or hub.
Part of your page includes can include feeds from flickr,
All of these easy to set up and use features makes this site worth a further look. Hey stay tuned I will create a podcast and upload it soon.
Wednesday, August 08, 2007
What went right
Class blogs Students used the class blogs to do growing posts and scribe posts. This was a good introduction to blogging for most students. I was able to use these activities to prepare them for what was to come. I also made commenting part of the scribe post assignment. Students were given a list of other classes that scribe or use blogs and were asked to leave a comment behind. I found that many of my students were great commenter and started to comment more on their own school blogs. Problems.... Not everyone participated in their class blogs. It was hard to get the "less" motivated students to participate and do a scribe post. I also found it hard to find the time to comment regularly on these posts.
Class hub After switching to the "new blogger" at the beginning of the year the class hub was a great communicator with the students. I had my skype availability, chat boxes and email on the hub for students to use. Students skype chatted with me and g mail chatted regularly. This allowed the room to be open beyond the 330 bell. I would have students asking me questions up until my sleepy time it I was in front of the computer.
I liked hub post like "what did I do wrong?" This got the class thinking and doing different types of problem solving.
I will use the same hub this year. I am hoping that students will continue to use this hub as a place to get the class information that they need.
Wikis This was my first season with wikis. I used them to do student led conferences and the first and second unprojects. Students liked the feel of wiki's because of their familiarity with other apps like facebook and myspace. They created some amazing content and blinged it up using applications they learned on their own. This was a complete success. Wiki's got all of the students participating in communicating mathematically.
This year I will start the wiki's earlier and integrate them more into everyday homework, and assignments.
Darren mused about "expert voices".
This got me thinking. What do 13 and 14 year olds want to be experts in or more importantly how can they show that they are experts. My solution were unprojects. I called them unprojects because the only part of this assignment that was in my control was the topic and the amount of information needed to be provided so that a student could be an "expert". The rest was up to the students. The communicated math in so many different forms. Some sang, made movies, created wikis or blogs. The most important aspect of these projects was the participation rates. Over 90% of the students created some kind of unproject. All of these students pushed their own limits to new heights, some by just participating and others by going way beyond the call of duty. I found out during this assignment that once students have a grasp of some 2.0 tools out there they will start to do math work at home that is meaningful to them.
This year is going to be different. I have a class of students that has not blogged before and will be raw. They will need some extra pushes to get the creative juices flowing. I am confident that great things will continue to happen this year in the Sargent Park Math Zone. My goals are to do more interactive slide shows, make movies and podcasts and incorporate all of these pieces into the greatest Student Led Electronic Portfolio's my school has seen. As more and more 2.0 apps appear on the horizon it is going to be fun to mix them into my math teaching pedagogy.
Thanks to my former students for being so inspiring. To this years crew..
It is going to be a great year. Thanks you in advance.
As I sit in my Google Reader and Bloglines accounts and read all of these 8 things about you memes it makes me think..... is this a good starting blog post for kids. The idea of the meme, liking it to others to keep it going and the creativity of answering some questions could be interesting to students.
Beginning bloggers could learn how to link to other pages, learn what to put into posts and what to leave out (that dreaded personal information stuff..) and you could even use Google Docs to type the questions and import them into your blog.
Of course all of this is percolating in my head because how many of us ask our students to tell us what they did during their summer vacation etc on the first day back. Now here is a way to get the students to write and learn blogging.
I know many adults find the meme tedious and somewhat intrusive. Many call it viral. If my memory is accurate I think many students find these memes novel and interesting. Would this not be a great way to start off an interactive collaborative project. Two groups of kids and multiple memes. If you kept them short you would have some excellent ice breakers introducing the kids to each other. I know that Lynne memed her students with the latest 8 things meme.
We need to create some student friendly memes. Now that many of us are getting back to work and thinking about school is this a way to start off the year?
Think about it.
Monday, August 06, 2007
Mathematizing is solving problems, posing problems, playing with patterns and relationships and proving their thinking to fellow mathematicians. It was so fun to see these ideas in action in the classroom video clips from New York.
There is a diference between activity and genuine Problem solving. So we need more than "Hands ON" Discovery Learning.
Classrooms become communities. Children meed in groups and as a class to present and talk about solutions to common problems. There is "no wise one". convincing arguments are made to the group. Knowlege emerges in a community of discovery.Doing math is like climbing a mountain. You take it one step at a time. Sometime you can take many steps before seeing the vista and all its beauty. For students to continue to climb and enjoy the journey they need to undertake this journey themselves. Only then will they continue to climb instead of staying at one leve
Many techniques were used with the young learners. They were always placed in pairs and the pairs were carefully selected. You did not want to put the best student with your worst a A and Z pairing. You wanted to do a A and C parining so that there was a difference but not a vast gap.
The students would receive a large problem on a large piece of paper and then in pen put their answers to the question. The teacher would choose examples of the student work and have the students present to the class. The students would lead the discussion and ask quesitons to the presenters. The teachers role was to facilitate the conversation to hit petagogical ideas.
Teaching was done in the form of mini lessons to activate strategies and ideas. Learning was always group based and fostered math language skills.
I am going to create a wiki and do blog posts about this course. Her books are a must read for teachers who teach elementary math or middle school math.
To prepare my sons for this experience I borrowed the Garmin and took my kids out looking for a cache. As luck may have it there is a cache at the top of my street at Brock Cordova Park. The cache SKAVENSQ is located just a half mile away. While we were searching for a a local reporter was having a picnic with his family and asked what we were doing. I said looking for treasure. He was interested and asked if we would like to be on TV. So....
Today Monday August 6th we were filmed looking for the cache and interviewed on tv. Hmm Pretty cool for the second time out geocaching ever. My kids like it. I like it. There are over 500 caches in the city of Winnipeg. I know what they will be doing in there spare time!!
Now I have to go watch the news.
Update. Here is the spot with me and the kids. I did not mean to sound like a pirate. Global News link.
Victoria Beach where my wife's aunt has a cottage. This cottage was built by my wife's father so there is a family connection there.
After we returned home I created a bunch of movies from the wee little digital camera that I own. They can be found at Youtube. As I was playing around in Imovie I found that I could save the movies to my Ipod and the quality was much better than at youtube.