Fraction A Day - Fraction Multiplication

Today I revisited Fraction Multiplication adding controls to the Fraction Multiplication visualization to simplify modifying the fractions.  So that when you mouse over the fraction controls appear to allow you to modify the numerator and denominator.  I also played around with larger buttons to make it easier on touch screens, but that still needs some work.

I would also like to make it easier to facilitate comparisons, so kids can compare 2/4 x 2/4 with 1/2 x 1/2 etc.  The goal being to make the comparisons easy to make so they can focus on the fractions rather than the artifacts of making copies of fraction images.

Fraction A Day - Day 36+ - Tangrams

Fun with Tangrams in Etoys.  Create shapes and stories with Tangrams.  You can also explore area and fractions.  Ed Emberly also has a wonderful activity using shapes here (click on the animation icon, below "Cut and Paste, then try it yourself).

Fraction A Day - Day 35+ - Multiply Me

Kids love pictures and especially pictures of themselves (don't we all). So this Etoy allows them to use their own pictures to play with Multiplication (and fractions).  By clicking on an image they can create multiple copies of themselves. Which can be used to ask how many of you are there in row 1, row 2, etc or what is the size of an image in row X if the image in row 1 is our unit size of 1?



Below is a copy of the script:

If you click "show code textually" (from the menu at the top left of the Script editor) you can see the smalltalk/squeak version as well.

Fraction A Day - Day 34 Is it Half a Star?

Using a gridded playfield allows kids to see the area for different shapes. Using the Fractionator (and a playfield with gridding turned on) I was able to get the images below, which are 1/3, but are they 1/3 of the Star? Let the kids ponder this for a while, then ask "What's your unit/whole/one?"

Fraction A Day - Day 33+ Half a Spongebob

"Stencils allow children to explore the math behind the patterns. It is difficult for them to perceive the difference between 1/8 and 3/8 without visual aids in the beginning. Unlike charts, Etoys is interactive. Unlike paper or cardboard, it allows children to repeat any number of times without waste."

- K.K. Subramaniam (who created the Stencil code in squeak to make this possible) 

So I used Stencils (which hopefully will be in an upcoming version of Etoys) to allow kids to explore fractions.  See the example below:

Fractionator  (2011-Jul-30 1:29 EDT) by Mr. Steve <mrsteve>  Tool for kids to create and explore Fractions.

Using this Etoy, kids, can create and explore their own fractions.  Fractions can be made using the "Fractionator" (using the Stencil functionality) or by drawing lines to separate parts of the set.

The line drawing tool, allows you to create multiple segment lines by hitting the key to add a new segment (actually it simply adds a new vertice). If you hold down the a, you can get a behavior a bit like drawing (would be interesting to see how this behaves on a touch screen).

The "Fractionator" lets kids specify the number of parts.  I would like to extend this so kids create their own fractionator tools by writing scripts to set the size of the Fractionator.

The last pages have an explanation of how the the "line drawing" scripts work.  I used a magnifier and speech balloons to explain what was happening, it would be good to add step by step actions as you highlight each scripting tile.

What do you think?  How can this be used? How can it be improved?  Leave a comment.

Another great use of stencils can be found here: http://community.ofset.org/index.php/Grab_area_button This was done by Susanne Guyader, an 80+ year old artist who used Squeak/Etoys to guide art teachers in France. 

http://community.ofset.org/index.php/Grab_area_button

A Fraction A Day - Day 3 - Color Blind/Dyslexic Fractions

During dinner at a friends birthday party, one of the folks there mentioned that she had dyslexia and had problems with the greater than and less than signs. She also talked about some of the tricks her father taught her to help deal with her dyslexia. Another friend talked about how his son had eye tracking problems and how hard it was to detect. So I started to think about how we could embed various "tests" into lesson plans. For example perhaps you could distinguish if a child understood which fractions are larger and smaller but had problems with the > and < symbols because of dyslexia. One possible way to do this would be to ask them to place the the larger fractions in the bigger box and then run a similar test asking them to choose the correct symbol (> or <).

You could also use "place them in a bigger box" as a starting task, then introduce the symbolism after, by asking them to choose the correct symbol, while keeping the larger and smaller boxes on the screen to give an additional visual clue as to the meanings of the symbols.

Here are some sample pictures to give you an idea of what I mean:

FYI, I am not a doctor nor have a I ever played one on TV, but I think this may have some merit and seems easily testable.  We would need to connect to experts in the fields to come up with good tests.  In any case while far from perfect these could act as early indicators of possible issues.

A Fraction A Day - Day 2 - Cut the Cake Riddle

Day 2, here is a fraction embedded in a riddle.

Below is a link to an Etoys project which has hints as to how to solve it and lets you "play with" the fraction to try and discover the answer yourself.  Try it, you never know what you might learn.

Cut the Cake Riddle

A Fraction A Day - Day 1

I have heard some writers talk about writing every day, I have decided to take this approach with curriculum development. And will be creating a Fraction a day, to support an OER (Open Educational Resource) for mathematics education I am working on with some folks from OLPC (Randall Caton and
Edward Cherlin).

Rather than a complete curriculum/textbook/OER for each grade (which should be an end goal) I would like to tackle things one bite at a time, with the first bite being Fractions. Why? Its a subject kids struggle with and therefore teachers and parents worry/care about.  I do not want to re-invent the wheel here.  Lets use good existing ideas and it is possible to teach first graders to solve problems like: (1/2 x () + (2/5 X 10) -(1/2 x 8) = ? (see Lore Rasmussen et al - Lab Sheet Annotations and Mathematics for the Primary Teacher, pg 140).  If we can provide good materials to help kids understand fractions and get evidence that they work we will create a good entrance path for the rest of our materials.

So a couple of tasks:

1. Identify XO Activities we can use to teach fractions (I spend most of my time in Etoys, but we should use Turtle Art and others)
2. Identify existing lessons we can refer to or re-render (ex: http://illuminations.nctm.org/LessonDetail.aspx?ID=U152)
3. Identify virtual manipulatives needed (I have cuisenaire rods and pattern blocks in Etoys, here is a nice one at Illuminations)
4. Identify physical manipulatives that can be used (and id how can be easily and cheaply created by kids/teachers)
5. Identify no computer, concrete activities kids can do (ex: 1) Fold a paper in half and cut, 2) Label as 1 piece of X needed to make a whole sheet; repeat)
6. Create/Identify a lesson, manipulative, blog pos or video each day. Okay ambitious, but do-able (for short sprints). It helps me keep the perfect from being the enemy of the good and gets me focused and moving.  I look at it as the equivalent of some writers practice of writing something every day.
7. Identify Models of Fractions and how we can present these different models in concrete forms as a kind of Fraction Exploratorium
8. Identify common mis-conceptions learners have about fractions and using them and identify ways of addressing these mis-conceptions.

Area Blocks - A Tool For Teachers (and Learners)

This post started as an OER Glue test (a promising new tool to "Gather content, stitch it together, and engage learners w/o reinventing the wheel.").  But I figured I'd add some educational content as well.

So (if you have Etoys installed) you should see an Etoy open up inside the page below. If you don't see it, get it, its free, its cool and its one of the best things I have found for creating educational content, letting kids learn, explore and express ideas.

Tools to Play/Learn/Teach with - M&M Fractions and Multiplicaiton

M&M Artifacts for Multiplication and Fractions
(you need to download Etoys to play/view)

download  launch

Etoys is a media-rich authoring environment that encourages deep learning through experimentation. 

Children use Etoys to make their own models, stories, and games, which keeps them engaged because it's a lot of fun. But Etoys isn't just child's play. Etoys makes abstractions more palpable, allowing children to visualize and explore new ideas. 

Etoys allows you to construct things from a set of basic building blocks which is its strength and also (IMNSHBOWO¹) its weakness.  It requires that you build everything from those basic building blocks.   I wanted to explore the idea of providing higher level "artifacts" that allow the user to play with ideas without having to start from first principles.  So I am working on a set of "Tools to Play/Learn/Teach with" (or to Think with or Play with) that allow kids, teachers and anyone else to play and learn.

I created this Etoy to explore how we can help kids with ideas such as fractions and multiplication.

My end goal is to see Etoys and the higher level artifacts used by teachers, kids and parents to facilitate and improve learning.  You are free to modify the tools you see here and/or create your own. As such they are Creative Commons licensed under the Share and Share alike  (see sidebar for license for all content on this site).

¹ IMNSHBOWO - In My Not So Humble But Often Wrong Opinion