The boys elected to spend most of our three hours there at the playground, and with the seals.
Well, okay, not "final", final, but final for now... "until the new year", which has become our favourite phrase this past week, as we try to squeeze in all the "one lasts" before we head home to Canada next week for Christmas!
The boys elected to spend most of our three hours there at the playground, and with the seals.
As would be expected, the recently-released results of the PISA math test have resulted in a flurry of media responses.
Everyone's an expert, it seems, not so much on the math necessarily, but on the best remedy. (Ontario students didn't do so well.)
This article from the Globe and Mail discusses the problematic "new math", often painted as less formal in structure...
"The OECD report noted that the top performers had more exposure to formal mathematics, algebra and geometry than the word problems used in “discovery learning,” which advocates that children can learn math more effectively when they are given opportunities to investigate ideas through problem-solving and open-ended investigations."
As someone keenly interested math education, especially at the elementary level, I am troubled by comments like the one above because it implies that a problem-based approach to teaching math is inherently inneffective in providing a rigourous mathematical education.
I would argue that the problem isn't so much the pedagogical approach itself, but rather the way in which it is manifested in a classroom. Many teachers know the words "constructivist" and "problem based", but -- in addition to lacking confidence with the math itself -- they may lack a firm understanding of the theory behind these terms and practical experience in implementing these approaches effectively.
This doesn't necessarily mean that problem based learning is a bad thing in and of itself, but rather perhaps suggests that teachers need to develop strengths and confidence in this area in order to teach math more effectively, incorporating both the mathematical skills and the broader learning skills into a rich, holistic program.
Interestingly, I attended an online professional learning session this evening with Cynthia Nicholson, on "Infusing Math Learning with Critical Thinking".
After exploring a quote from John Van de Walle, on how we teachers cannot "think for our students", one teacher commented that "if we can provide opportunities for our students to discover math truths, that will be more valuable and far reaching for them" than the skill and drill and kill model.
Of course, in order to provide said opportunities, teachers must be both masterful facilitators and knowledgeable math teachers.
The truth is that teaching is complex! And the average teacher -- even a very committed "average" teacher who takes the odd PD workshop -- has a wee bit (or more) of math phobia. This was confirmed in tonight's session, where several teachers "blanked out" and "shut down" (their words, not mine) when confronted with fairly typical math word problems incolving proportional reasoning and unit rate at about the Grade 4 level.
More rigorous mathematical instruction for pre-service teacher candidates is perhaps a critical componant. (I shudder to think how little I understood about even basic mathematical concepts when I graduated from Teacher's College nearly two decades ago!)
Still, being "good at math" is not enough.
If we don't equip our students with the tools for critical thinking and encourage them to develop a growth mindset (Carol Dweck), then those who struggle with math may give up rather than persevere with mathematical challenges. Taking the time to teach students "stick with-it-ness" as well as specific mathematical tools (how to draw an effective picture to model mathematical thinking, for example, or, how to ascertain when something "makes sense") will help those students who are not rote learners to stay "checked in" in the math classroom.
(Of course a reasonable depth of mathematical understanding on the part of the teacher is vital in order to be able to do this effectively.)
If we want students to fluently rattle off facts they have memorized but with minimal understanding or ability to apply, then we should "return to the basics" as some in the article mentioned above insist, and focus on traditional skill-based, rote-only teaching. But if we want our students to "learn to think and think to learn", then we had better inform ourselves about the math, AND ALSO nurture thoughtful communities, frame critical challenges, teach intellectual tools, and assess thinking and performance.
The recipe for solving the disappointing PISA results problem includes two main ingredients: A more solid foundational understanding of mathematics for teachers, and a deep comprehension of how to effectively teach critical thinking in the classroom.
Both are needed if we are to effectively educate students for success in the 21 century.
One thing I've been thinking and reading more about this year is gender equity. The ongoing oppression of women around the world is an often-overlooked fact in North America, where many cajole themselves into thinking "we're all equal" (all you have to do is look at the income gap between men and women in the same jobs to dispel that myth!)
In my research on said topic, I came across a website created and maintained by a fascinating woman in India who calls herself, simply "Indian Homemaker". IHM blogs on a number of issues relevant to women around the world. In this piece, reblogged from another source, she shares an interesting perspective on rape:
Why do we have entire dossiers on How to Not Get Raped and no
guidelines for How to Not Rape People? We need a cultural revolution.
Here’s a list of Sexual Assault Prevention Tips Guaranteed to Work:
1. Don’t put drugs in people’s drinks in order to control their behavior.
2. When you see someone walking by themselves, leave them alone!
3. If you pull over to help someone with car problems, remember not to assault
4. NEVER open an unlocked door or window uninvited.
5. If you are in an elevator and someone else gets in, DON’T ASSAULT THEM!
6. Remember, people go to laundry to do their laundry, do not attempt to molest
someone who is alone in a laundry room.
7. USE THE BUDDY SYSTEM! If you are not able to stop yourself from assaulting
people, ask a friend to stay with you while you are in public.
8. Always be honest with people! Don’t pretend to be a caring friend in order to
gain the trust of someone you want to assault. Consider telling them you plan to
assault them. If you don’t communicate your intentions, the other person may
take that as a sign that you do not plan to rape them.
9. Don’t forget: you can’t have sex with someone unless they are awake!
10. Carry a whistle! If you are worried you might assault someone "on accident", you
can hand it to the person you are with, so they can blow it if you do.
Thankfully, as far as I know, rape does not seem to be a major concern here in Buenos Aires. Nevertheless I figured I'd share these helpful tips in case someone out there can benefit from them.
While Tats' Spanish is growing in leaps and bounds, the boys and I continue to wrestle with numbers (Did she say $3 for that bottle of water, or $13?!) and basic phrases.
We've been pretty diligent about using Duolingo and Memrise, two free, online options for language learning, but it seemed like time for something new and exciting. So, when I discovered Cat Academy, my interest was peaked!
Described by Forbes as a merger between "mind, meme and meow", Cat Academy is an app developed by Memrise, so I already knew and respected the "brand", so to speak. It uses photos of cats in cute and ridiculous predicaments to help "hook" words and phrases. Comic-like cats also praise and encourage you as you play.
Interestingly, the app "detects" what you have mastered, and what you still need to work on, and gives you relevant challenges as you go. The teacher in me loves this differentiated approach!!!
I also like that the "write your own" phrases in the training are comprised of click-on words that incorporate your device's touch screen, rather than requiring the player to type on that too-small keyboard.
I must say, I was a little skeptical when I first downloaded this app, despite the fact that it was only 99 cents. To be honest, it seemed a little gimmicky. (Spanish from Cats, really, people!) But, three days in, I can honestly say I already feel much more comfortable with the phrases I am learning. It's quite amazing. And, the boys have already announced that it's their favourite new language learning app. ("It's so fun, Mom, not stressful at all!" quoth one boy to me spontaneously over lunch yesterday.)
So, don't delay, learn Spanish -- with cats -- TODAY!
Many who visit Buenos Aires will notice the men, women and -- sometimes -- children who separate and sort through the city's garbage.
These are Cartoneros. They collect pretty much anything that can be recycled. Their industry is an intriguing one, its history rooted in the country's 2000/2001 economic crisis, when many Argentineans from across the social classes lost their jobs, and were left with the challenge of finding alternate sources of income, or face homelessness and hunger. (Despite the illusion of grandeur in some parts of this cosmopolitan city, approximately 30% of Argentineans are currently living below the poverty line.)
Often misunderstood, the Cartoneros here face grueling work days and endless prejudice from their fellow citizens, many of whom see them as "dirty", "beggars", or "thieves".
The boys and I, interested in this part of Buenos Aires's daily fabric, decided to do a little research on the city's "cardboard people". Alex and Simon will be sharing their findings and interpretations via an Explain Everything presentation, to be posted soon on their respective blogs. Stay tuned!