Relational mathematics and Montessori

I’ve just finished reading this paper by Richard Skemp (nicely republished here on the Republic of Mathematics site) about the difference between instrumental and relational understanding when it comes to mathematics education. My first thought was, “this is what sets Montessori maths education apart from traditional mainstream.” The Montessori mathematics materials lay a groundwork for relational understanding. Eric, who’s 7, not only knows how to calculate the area of a rectangle (width x height) but why that calculation works, because he spent lots of time building rectangles with wooden cubes, and learning through building that the “area” of shape is derived from the number of cubes inside.

A few years ago, when Rachel was still in preschool, Gary & I attended a parent education evening where her teacher showed us the “binomial cube” material that she was learning. Of course, at age 4, she did not learn the binomial equation, but by manipulating the pieces of wood to fit them properly into the cube, she was gaining understanding that, years later, she could use to learn exactly how to solve the algebraic formula (a+b)³. The cubes and prisms in the binomial cubing material represent the factors of the equation.

I sat there and thought, “I remember learning the binomial cube expression!” and if I thought hard enough, I might have actually come up with the solution. Gary, on the other hand, picked up the material and immediately sorted out all the pieces and proceeded to show me how the equation was constructed based on those pieces. In case you’ve forgotten: (a + b)³ = a³ + 3a²b + 3ab² + b³

I understood it instrumentally, but he understood it relationally.

Dr Skemp, in his paper, argues (in a nutshell) that relational understanding of mathematics is better. I would have to agree.

Age

So, should I be feeling old now that our eldest daughter is on the verge of high school? Rachel yesterday decided that she will be attending Wairarapa College next year.

Seems only yesterday that we were enrolling her in her Montessori pre-school at age 3.

[at preschool]

[growing up]

‘Course, it might just be that I’m feeling old because today’s my birthday!

A blog post with no text and just an embedded image.

My blog to Buzz

This is really just a test to see how the linkage works. I’ve just connected this blog to my Buzz account and am testing how it looks.

Will it show this photo, for example, which is a mockup of my blog from Jan 2006.

It looks nothing like that now (whew!).

I was reading several buzzes today that made a point about permanency and blogging and it got me thinking that I’ve only updated this blog a few times in the last year, and perhaps I should be posting here and sending this off to my other sites. This blog has a record of my thoughts going back almost 6 years now, it seems a shame to leave it by the wayside.

Anyway, so here’s my test. My plan was to delete this afterwards, but I might just leave it. Maybe I should investigate a plugin that will post any buzz comments to here, given that I get more comments on Buzz than I do here!

Bic Runga Acoustic Winery Tour

3 Mar 2007 – We attended the final concert in the Bic Runga Acoustic Winery Tour 2007. It was held at Alana Estate winery in Martinborough. A beautiful afternoon/evening with some wonderful music. We really enjoyed it, and were lucky to have our blanket not too far from the stage. That, and my trusty Panasonic with its 12x zoom, got me some great shots of Bic and her sister Boh, who opened the concert.

Bic Runga Acoustic Winery Tour, posted with vodpod

Some of my Picnik Collages

Search results

Search results for picnik collages, posted with vodpod

Also, just testing a new solution for embedding a Flickr slideshow in a wordpress.com blog … using vodpod. Seems to work well!

Here’s how. Using Firefox. Go to Vodpod’s wordpress page. Drag the bookmarklet to your bookmark bar. Then, go to Flickr and run the slideshow that you want to embed. Click the bookmarklet. In the popup, you’ll see a sample of the slideshow. Enter your wordpress login details and any tags, etc, you want in your post. Then, press “send to blog” to create the post and open the wordpress.com editor. Make any additions to your post and you’re done. Publish.

Hope this helps those of you out there who have missed the ability to embed Flickr slideshows on wordpress.com.

Googly

Haven’t posted here in, oh, 6 months.

As you may have heard, the company I work for, Picnik, was purchased by Google in March. I’m still there… my position is Community Builder and I’m still spending my time on Flickr, supporting our community of Picnikers there. If you’re a Flickr user, be sure to pop into the Picnikers group.

I’m also spending some of my online time on Buzz (my profile).

So, busy busy… but I hope to start posting more often to this blog.

Wasp in Space

I was playing with the cloning feature on Picnik and my 6 year old Eric said, "put the moon on that apple". Thus, "wasp in space" was born.

I started with a photo of half-eaten apple on the tree (wasp included). I then found a photo I'd taken of the full moon.

 

Using Picnik:

1. Open photo of apple.
2. Create a "before/after frame". that gives me apple in 2 different frames.
3. Using the 'photo basket', drag the photo of the moon up on top of the right-side frame and resize it to be the right size for the apple.
4. Flatten the photo using "combine all items".
5. Use the clone tool to "paint" the moon onto the left-side frame. Use the brush feature to get it just right.
6. When finished, crop the image to leave only the left-side frame.
7. To get the black background, I used the doodle tool to colour in the background .
8. Finally, a frame and some text.

Eric had a good idea, didn't he?

A change in the air

more photos from curiouskiwi

So, anyone who knows me knows that I’m always on the lookout for new things to try. Several of my Flickr friends are leaving Flickr and have moved to 23. So, I’ve opened an account there (well, to tell the truth, it seems I opened the account back in Apr 2006, so I’ve “reopened” it) and am posting a few photos. I’m not leaving Flickr, but I don’t want to miss out on my friends’ photos either.

Using iPhoto ’09 to backup your Flickr photos

I’ve just come across an interesting “feature” of the iPhoto ’09 Flickr integration.

As background, when you upload photos from iPhoto ’09 to Flickr, the photos are put into a new set on Flickr, and that set is then set to sync with iPhoto. Any changes to the photos in that set are reflected in your iPhoto library.

I wondered what would happen if I removed a photo from the set on Flickr (but not on iPhoto), hoping that it wouldn’t delete the photo from iPhoto (as that is what happens if you change your mind and delete the photo on Flickr… the photo is deleted in iPhoto as wellremoved from the Album in iPhoto).

It seems that if the photo is removed from the set on Flickr, all ties to the ‘flickr album’ on iPhoto are broken, and any title/desc/tag changes on Flickr do not get synced back to iPhoto. The photo is removed from the Flickr album but is not deleted from the Library.

However, if you then add the photo back into the Flickr set, a brand new original-sized copy is downloaded and imported into your iPhoto library (so now you’ll have 2 copies of the same photo). I thought, ooh, I don’t know if I like that… but, it dawned on me that this could be a good feature if you are trying to backup a lot of your flickr photos and their metadata.

showing "pending" backups into Library from Flickr set

Simply upload one photo from iphoto to flickr to create a new ‘synced’ set. Then, using the Organizr, add the photos you want to backup into that set. Go back to iPhoto and sync that Flickr album and it will go out and grab the largest file on Flickr, including all tags/titles/descriptions, and import them into iPhoto.

The filenames will be the same as the photo original on flickr, eg., 176709303_026f53b3c0_o.jpg.

If you leave the photos in that synced set, any further changes on Flickr (ie, new tags etc) will be synced to the copy in iPhoto. Or you can simply copy those new files to another drive or backup disk, remove them from the set on Flickr, and delete them from your iPhoto library.

Voila! A quick backup of your photos, including their titles/tags/descriptions from Flickr.

Disclaimer. This worked for me but you might want to test it yourself.