What Decade are we in?

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.

Thanks Sheryl

Viddler

Ok Blogger has a video uploader. This is a great step forward for us who use blogger. I have however just been introduced to Viddler. This is a service similar to Youtube and Google Video. Viddler allows you to add comments and reply to comments that have been left on uploaded video.

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.

pictobrowser

Darren just talked about pictobrowser Pictobrowser is an easy and I mean easy way to embed a flickr slideshow into your blog. Just go to pictobrowser, it will prompt you to a flickr account then your tag and give you the code. The result is below. For 3 minutes of work and most of that was typing this post easy peasy!!

video upload

Testing out the video uploader here at blogger.

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

Fosnot Institute Day 3

What a wonderful day. These 3 days have reaffirmed my belief in how I teach math. I have been given the tools and an extra jolt of horsepower to continue my path to having students talk, communicate and become mathematicians. I am also convinced that 2.0 apps and how they promote collaboration and publishing students work fits nicely into my new plans. I also love voicethread. Two years ago I was happy when kids went into paint and created an image. Last year slideshare, bubbleshare and slide.com came into their posts and math work. This year the posts will be kicked up a notch when students see that they can create movies and talking slides using the newest apps. Wow what will next year... wait next month... wait tomorrow's newest apps bring to their work. Now on to day 3 of the Institute.

Fosnot Day 3

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
Multiplying fractions

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

Contextsforlearning.com

The material I was being taught is from Fractions Decimals and Percents.

Fosnot and Dalk Mathematizing Institute Day 2

I had planned to podcast this session. I ran out of time. As it is this is a rough and sometimes hard to understand recounting of the day. I did figure out how to use voicethread. Perhaps I started to enjoy it a little too much.

Fosnot Institute Day 2

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
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.

Solution

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

Question 2

2 x 17 (double)

Question 3

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.

Sidenote

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.

String 2

1.) 2x18
2.) 4x18
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

String 3

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

String 4

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.

Fosnot and Dalk Mathematizing Institute Day 1

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?

·

As we watched the first video clip it was clear that the students were doing most of the teaching and the learning. The teacher was merely a guide to facilitate the learning.

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.