12 2/3 + 7 3/5 = huh

The other day I was watching my intern teach a math lesson on using the algorhythm method to divide fractions. I was working with a young person who had no real concept of what a fraction was a month prior, indeed she did not understand what multiplication actually represented, much less her multiplication tables. We had been doing conceptual work such as open ended fraction questions (a la Dan Meyer) and manipulatives and diagrams so that she could visualize fractional numbers and problems.

She had made good progress in the weeks prior and now we were teaching the algorhythm method to divide fractions (invert and multiply, divide the top, then the bottom, etc.). As I worked with her, it became more obvious than ever that teaching the algorhythm alone is a tremendous obstacle to real learning in math. With this student, in this instant, I decided that if she could estimate the answer of a dividing fraction question, that would be enough.

On Friday, a few teachers had a discussion in my room as to why kids do not do well in math. I made the statement that much of it is due to the poor teaching methods of teachers. Alfie Kohn has posted a great article on Math instruction! He says:

"...that traditional forms of teaching, and an emphasis on the basics, contributed significantly to the low standing of older American students....instruction in this country still seems – compared to instruction in some other countries – more centered on students as passive absorbers of knowledge rather than as active participants who construct, transform, and integrate knowledge.”

He cites studies from Japan where math instruction may be different:

"...three out of five U.S. teachers said they were chiefly concerned with “skill building.” Only one out of four Japanese teachers responded that way: the overwhelming majority said they wanted their students to understand a particular math concept. That goal led those teachers to include deductive reasoning in their instruction, which played a role in 62 percent of Japanese lessons and 0 percent of U.S. lessons. Japanese teachers also explored the intricacies of specific mathematical concepts with their students rather than just naming those concepts, American style. In Japanese classrooms, fewer math problems were considered in more depth, and students participated actively in suggesting different ways of solving those problems. Also, interestingly, homework was rarely assigned."

Teaching the algorhythm alone seems to me to be the most unproductive way to teach math, or conversely, the most productive way to produce disengaged, confused math students! Much of what I read these days backs this up. In a recent post, Conrad Wolfram claims that we spend 90% of teaching time in math on computation and not enough on the conceptual and real life application. Kohn goes on to say:

"the research conducted on such programs has been concentrated in the primary grades, and it points to a result that can be summarized in six words: better reasoning without sacrificing computational skills...in one study, forty first-grade teachers in Wisconsin were given special training in how to make problem solving the organizing focus of teaching arithmetic. When achievement tests taken by their students were later compared to those of traditionally taught children, the results showed a modest, though consistent, edge for the former group. “A focus on problem solving does not necessarily result in a decline in performance in computational skills..."

I love teaching math and the challenges it brings. There are a world of educational opportunities out there for math teachers. 21st century learning applies to math in a big way.

Tackling Myths

People talk about technology affecting children in negative ways. Nick Sauers has just written a post on "1:1 Schools" to help debunk some of these ideas called "Tackling Myths". He gives statistics that do not support the following statements:

• People are losing their abilities to connect with one another in "real life" because they are living in an online world.


• Our language is being destroyed because of the language kids use while texting or while in chatrooms.


• Students won't be safe online!
  

The New York Times (Virginia Heffernan) has also published an article called "The Attention Span Myth". Heffernan argues that our modern fascination on the importance of attention span is ill founded. As one comedian quipped, "remember when having ADD meant that you had an imagination?!"

On the other hand, CBC television produced a video entitled "Are We Digital Dummies?" This video makes the statement that "no one is happy with the time they are spending with technology". This video is both convincing and one sided and well worth watching for an alternate view.

One of the most interesting things the film says is that over-use of technology causes anything from marital stress to work burnout. Families may talk less and work life is extended beyond the office. One example suggested workers prior to blackberries (32 billion worldwide!) worked 45 hours a week, post blackberry was 70 hours.

The film suggests that we are a nation of distracted technophiles. Brain research says that middle age multi-taskers make more mistakes. They also argued that technology can discourage creativity. This is because as soon as you get an idea you put it out there instead of taking it further with deeper reflection and research.


There is some suggestion that technology is rewiring the brain. This point was not well supported by the authors, yet is something for me to do further reading on.

I do like the concluding point in the film. We need too manage technology in our lives or it will manage us.

8 Videos to Help Teach Innovatively

The Innovative Educator has posted a blog entitled "8 Videos to Stimulate Conversations about Innovative Education". These are great resources for you to use in PD opportunities for your staff and also for your own learning. The videos titles are:

1. High School 2.0


2. Progressive Learning Environments


3. Cells in the Classroom


4. Internet 2 and High Bandwidth Connectivity


5. Facebook, Youtube and Other Mainstream Tools


6. The Impact of Social Media in Schools


7. Disruptive Innovation


8. 21st Century Skills
   
   
   
   
   
   
   
   

Real World Math and Computers

Check out this TED talk by Conrad Wolfram on "Real World Math and Computers". Conrad Wolfram is the co-founder of the Wolfram Alpha website and he gives an amazing perspective on the teaching of math. This video is a must see for those with a real desire to change the way math is understood and learned (see Dan Meyer, Alfie Kohn posts).

Wolfram says there are four parts to teaching math. They are:

1. posing the right question


2. taking a real world problem and changing it into a math formulation


3. computation


4. taking the math formulation and applying it in a real world verification

He says that 90% of what we do in the class is computation which is the least beneficial and the most painstaking. He uses the example of teaching beginning calculus to very young students. it is not that hard for them to get the big ideas of calculus but we don't teach them because we get too involved with the onerous calculations of calculus.

When people like Dan Meyer and Conrad Wolfram talk about the changes needed in the teaching of math, I feel like they have been in my classroom!

Have a look at the video! Read more of Alfie Kohn and Dan Meyer.

"Wikipedia is Bad?!"

The other day a note came home from one of my kids teachers explaining a research project. In it they gave some guidelines for how the students should be conducting on-line research. The note was not in depth, a few short notes about using different search engines such as google or yahoo, not terribly helpful. I assume most of the teaching occurred in the classroom.


One particular statement on the note caught my attention. The statement said, "Wikipedia is bad, anyone can edit." I wrote a note back that said I believed that they did not quite understand the worth and significance of wikipedia as a tool and as a symbol of 21st century learning. I offered to provide them with information to support that statement and refute theirs and to come to their class and to talk to the students about the nature of wikipedia and 21st century learning.


I know of many teachers who routinely dismiss wikipedia as not to be trusted. This drives me crazy as I think so much can be learned from it as outlined in many books on 21st century learning. I decided to do some quick googling and to list the reasons wikipedia is extremely important and successful. Here I go.

1. collaborative construction of truth


2. as accurate and reliable as traditional sources (Nature magazine)


3. more current


4. people (adults) use wikipedia first


5. 15 times the word length of Encyclopedia Brittanica


6. most successful in world


7. over 10 million articles in over 233 languages (2007)


8. goal is the sum of all human knowledge


9. editable


10. changing, improving


11. collaborative vs. proprietary


12. warnings given when article is in dispute or not referenced properly


13. not editable if vandalised frequently


14. perused by thousands for accuracy and mechanics


15. second most visited site after google


16. represents a new way of learning and business


17. many contibute to one article instead of a few

There are possible flaws as there are in traditional sources of information.

Potential Problems

1. errors


2. vandalism


3. lies


4. writing is not always good or consistent


5. writing too complex for younger readers

I would love to teach my son's class the pros and cons of using wikipedia. Are you in your classroom?

10 ways to encourage students to take responsibility

I was tweeted Ed Ustanges's posterous post on the 10 ways to encourage students to take responsibility. I have listed his top ten, for more details see Ed's post. Great work Ed! I think I will ask my intern to evaluate me on Ed's list. I hope I pass.

1. Don’t make all the decisions

2. Don’t play guess what’s in my head

3. Talk less

4. Model behaviors and attitudes that promote learning.

5. Ask for feedback

6. Test less

7. Encourage goal setting and reflection.

8. Don’t over plan.

9. Focus on learning, not work.

10. Organise student led conferences

Kim Cofino, Finding the Right Fit: International Schools

I was tweeted a great post by Kim Cofino called "Finding the Right Fit", which is about applying to teach in an international school. Kim's post is very well written and makes me want to apply. I know I will keep her post in mind as I plan for the future. There are a world of opportunities out there. Have a look at her post!

I have included the promo movie for the school she is at, the Yokohama International School(YIS).

An Introduction to YIS from Yokohama International School on Vimeo.

Blooms and 2.0?

I got this schematic from a retweet (http://www.usi.edu/distance/bdt.htm). Have a look at it, click on it to enlarge.


While I think it is interesting, why would we think that using voicethread or glogster would involve the higher order thinking and creating of Bloom's taxonomy? I have seen many projects done with those tools which were all about knowledge consumption and lower order thinking rather than knowledge production. What do you think?

Public Education?

Joe Bower has posted a video on preparing kids for kindergarten tests. Watch the video and be amazed. Is this some people's dream for what school should be?

It reminded me of a speaker at our convention who talked about the importance of public education in society. His name was John Ralston Saul. I did not know him and did not know what to expect. Turns out the guy had given this topic some thought! His main point was that as people spend their money and resources on private education, less time and money will be available for public education. He warned about the increasing lack of social mobility in the U.S., a country founded on the idea that everyone can succeed and that there were no set social classes. (OK, so that was the theory anyway)

An emphasis on private education and kindergarten testing results in further stratification of society and the creation of ghetto schools. Would you want your children to go through this? Who is responsible for maintaining some balance in society and trying to make sure the poor have a shot?

I will never agree to the practice unveiled in this video. I find it quite alarming and sad. Have a look.

George Couras Top 100 Tech. Tools

George Couras has posted a cool slide show that gives the top 100 tech tools. You simply must follow the link to see his post. The top ten are:

1. Twitter


2. Youtube


3. Googledocs


4. Delicious


5. Slideshare


6. Skype


7. Google Reader


8. Word Press


9. Facebook


10. Moodle

How many of the 100 are you using? Could you use?

David Warlick on xtranormal

I got this video on a tweet from David Warlick, educational blogger and creator of classblogmeister. I have been following him for years as he was a keynote in Saskatoon. I also currently use classblogmeister to host my class's blog. I loved it that the person who introduced me to blogging has never used xtranormal, a program that creates cool animations with text to sound.

I point this out because in this 21st century world of education, it is hard to claim expertise on anything in particular. We are all learners and that is liberating and exciting. I can imagine my humble blog posts helping someone who is not as far along as me. If no one is interested in what I create, I still win as I learned in the process of creating something.

I also like the point he makes, that students need to be connected and information has to flow freely for them to learn freely. Our school boards need to hear this message many times over.

I am blogging and skyping with a class in Mexico. They just got a computer lab in the school and they decided to not install internet connections for the kids' computers in the lab. What the heck would they use them for? This kind of protectionism is amazing to me. I don't know how we could even think of stifling young learners curiousity in such a deliberate way, in the name of caring.

Nice job David. Keep having fun.

Twitter for Teachers and Students

I have just recently began using twitter to build my PLN. I love it, it is so fantastic to be connected to smart, motivated people. It is humbling that so many people are willing to share what they know and they find. I am going to introduce the idea to my class and I think it will benefit them immensely. One of our classroom goals is to build a learning network on-line and twitter will be a big part of this.

I found two posts (on twitter, there will be many) that may be helpful to other teachers breaking the same ground as me. One is The Ultimate Twitter Guide for Teachers from the blog Edudemic. It has many links and is an ample resource that you need to bookmark and share.

The other one is "5 Twitter Uses for School Leaders", from the blog Leaders On Line. This post gives five foundations for effective twitter use that is very helpful in guiding educator use and convincing staff to get on board.

Enjoy the resources!

http://leadersonline.wordpress.com/2009/10/21/5-twitter-uses-for-school-leaders/

One Grade 7 Student's 21st Century, or is it?

I found this on the cpchat daily blog. I saved it immediately and showed it to my class the next day. I thought it was a great example of a 21st century kid in a 21st century classroom.

As I watched it again I began to see it differently. It didn't seem to me to include the kind of rigor and heat Bernajean Porter calls for when technology is used. Our goal in our classroom is using higher level thinking, hopefully using technology! Does this video show signs of transformative learning and being a knowledge producer or is it using technology to be a knowledge consumer?

Watch it and let me know what you think!

Social Action Sites

I was tweeted the fantastic site "Invisible Children" the other day. It reminds me of how the internet brings great hope to our world. I was just at a presentation on violence prevention in school where we were shown a video comparing the world of the 80's with the world of 2010.

I was skeptical as to the point of the video. It seemed to be saying that the world of the 80's was a better, safer place. To me, the beauty of today's world is how there is something available for anyone, no matter what it is. I also think that anyone wanting to make a real positive difference has a greater chance to do so with instant, global communication and social networking.

I have used three main social action sites in my class, and plan on expanding how the students use them to build a better world. Have you seen or used these sites? How do you use them?

Taking it Global

Kiva

Me to We

"Meyer Math"

Professional Learning by Ryan Bretag

Ryan Bretag writes a great post in Metanoia entitled "Raise Your Hand". He talks about the imperative to learn and to share as extolled by the likes of Dean Shareski and Will Richardson. The traditional way for teachers to learn were PD days, convention and summer university courses. The opportunities for us to learn now are infinite. The same opportunities exist for our students and parents. The world is changing so fast it is imperative for teachers to adapt quickly to keep up.



When I talk to teachers about the many learning opportunities on-line, they almost always say that they don't have the time. Many say that schools will evolve into 21st century schools given small steps and time. David Warlick recently tweeted, "Small steps!" Do we (our children) really have that much time?"



Bretag writes:



"How would we react to students if they told us they didn’t have time to learn? they didn’t have time to improve upon their skill set? they didn’t need to know that? they didn’t need to try anything new, challenge their current ideas, or push beyond the norm? Would terms like prioritize, organize, time management, etc. be part of our discussion? Many students have so many demands outside of the school day that if we as educators are demanding their learning be 24/7, shouldn’t we be practicing what we preach?"

I love the learning collaborative, social networking sites allow. I can hardly stand it when I am unable to learn in that way for too long. I too get a bit frustrated with staff who appear to not care about changing the way the classroom works. I find it hard to understand why people are reluctant to see the opportunities to learn in amazing ways in an incredible world.

Bretag makes recommendations fo teachers:

1. Dedicate a portion of your day to honing your professional practice both locally and digitally

2. Establish a professional learning network

3. Establish and maintain a virtual professional learning space that fosters shared knowledge and resources

4. Make professional reflection, scholarly work, and learning a priority and make it public.

5. Model professional learning for colleagues, students, and parents

6. Take a risk, rethink your norm, challenge your assumptions, and embrace the idea of being disturbed.

I think it is great advice. The challenge of building PLC's and becoming twenty first century learners and teachers is too important to wait another moment!

12 videos posted by Scott McLeod: Dangerously Irrelevant

I just read a post in Dangerously Irrelevant by Scott McLeod entitled "12 Videos to Spark Educators Thinking". The videos listed on this post are just exceptional for teachers' educational journeys. I would sugggest that you look at each of them and possibly use them for staff PD opportunities! I have included a TED talk by Jeff Jarvis, the author of "What Would Google Do?"
For ease of access, even though I didn't collate the list, I have shown it below:

Sir Ken Robinson, Changing education paradigms (11 minutes)
Sugatra Mitra, The child-driven education (17 minutes)
Clay Shirky, How cognitive surplus will change the world (13 minutes)
Chris Anderson, How web video powers global innovation (19 minutes)
Dean Shareski, Sharing: The moral imperative (25 minutes)
Henry Jenkins, TEDxNYED (18 minutes)
Daniel Pink, Drive: The surprising truth about what motivates us (11 minutes)
Dan Meyer, Math class needs a makeover (12 minutes)
Jeff Jarvis, TEDxNYED (17 minutes)
Lisa Nielsen, Response to principal who bans social media (4 minutes)
New Brunswick Department of Education, 21st century education in New Brunswick (6 minutes)
Charles Leadbeter, On innovation (19 minutes)

Higher Order Thinking

In a post by Joe Bower entitled "Poor pedagogy + Technology = Accelerated Malpractice", he responds to comments he received when he criticised a teacher who posted about using google docs to create tests.

The debate is quite lively and Joe really digs deep to defend his point that creating google docs tests is not a twenty first century idea. According to Joe, true-false content tests are just another example of out-dated assessment tactics in a teacher centered classroom (my words).

He tells the story from a Kohn book where a surgeon from a century ago visits a modern operating room and would feel quite confused. A teacher from 1oo years ago visiting a modern classroom would feel right at home. Bower makes the point that it is our job to speak out and to recognize the old and tired from the new. He quotes Kohn:

"all that is necessary for the triumph of damaging educational policies is that good educators keep silent"

And Gerald Bracey:

"There is a growing technology of testing that permits us now to do in nanoseconds things that we shouldn't be doing at all."

At our school, we have just come up with a goal for our technology initiative. We came up with the following:

"students will develop and practise higher order thinking skills (will be knowledge producers)"

We are quite proud of our goal as it is student centered, pedagogically based, as old as Piaget and 21st century as well. Notice that it doesn't even mention technology?!

Creating tests with google docs is a great idea. Does it change the classroom?

How about using microsoft publisher, web 2.0, blogging, web pages, e-books?

What is your school's goal with technology?

Nokia gives it's two cents worth

Alan November appears in this video. I'm going to look for dissenting viewpoints! I'll let you know where to find them!

Introduction to Technology and 21st Century Learning from New Learning Institute on Vimeo.

Tinkering School

Check this out on TED talks. Wouldn't you like to have gone to tinkering school?

University courses on-line and exams using google

I love it that M.I.T. offers all of their courses on-line for free. This is such a great idea that announces loud and clear that sharing is the way of the present and future. The New York Times published a post on M.I.T. and others' open, on-line courses. They offer over 2000 courses that anyone can audit for free. Have a look and enjoy!

In another great example of 21st century learning, Danish students are able to use google when writing exams. This seems incredibly simple to do and very practical if you are interested in assessing higher order thinking and not retention of data.

The BBC article goes on to say:

"The internet is indispensible, including in the exam situation. I'm sure that is would be a matter of very few years when most European countries will be on the same line."

In my class, I am using a math curriculum posted on-line by Dan Meyer for my advanced students and I will use the internet for many exams from now on. It is amazing how many useful innovations are available from people sharing on-line. Hope you find it as fun as I do.