The Reflective Educator

Education ∪ Math ∪ Technology

Menu Close

Month: September 2010 (page 2 of 3)

Resources for International Day of Peace

Here is a collection of resources I am building so my staff can talk about the International Day of Peace tomorrow. Hope they are useful.

5000 years of religion in 90 seconds (from here).

An interactive map which shows many of the conflicts between 1900 and 2004.

http://nobelprize.org/educational/peace/conflictmap/conflictmap.html

 

Lists of conflicts in recorded human history

http://en.wikipedia.org/wiki/Lists_of_wars

Note: You can add up the number of years we have been at war simply by taking the time to add up all of the wars listed on the previous page. This could be a great activity for your students.

 

Things you can do with your students

Check out this broadcast of events around the world celebrating world peace.

http://www.un.org/en/events/peaceday/2010/broadcast.shtml

Talk about the relationship between religion & conflict. Think of other reasons why conflict occurs. How could we be proactive in preventing some of these reasons from occurring.

 

Look at other activities you can do with your students here:

http://www.readwritethink.org/classroom-resources/calendar-activities/today-international-peace-20296.html

 

Sing along to Imagine by John Lennon

What is the minimum number of facts needed to memorize the multiplication table?

If you look at a 10 by 10 multiplication table, you’d think there were 100 facts that need to be memorized.

X 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100

1. First important fact is that the order we multiply numbers doesn’t change the answer. So let’s remove all of the unnecessary facts to memorize because we can just remember this rule instead.

X 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100

Now we only have 55 facts to memorize. That’s a lot less than 100. I’m willing to bet that most people know this already.

2. We should take advantage of the fact that one times anything is the anything. That will remove 10 more facts from the table.

X 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100

3. And of course we should note that ten times anything and you just add a zero (which in later years should be changed to move the decimal place once students are aware a decimal place exists).

X 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100

4. There is a great trick that is used in Stand and Deliver which can eliminate the nine times column. I couldn’t find the original clip from the movie, but here’s the same trick with a bit more explanation than he gave in the movie.

Let’s then cut out the nines times column from the table and look at what’s left.

X 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100

5, 6. The two times column and the five times column are just adding by twos and adding by fives, both of which are skills kids should have mastered by the time they are learning multiplication. If they haven’t mastered repeated addition, I would recommend pausing here and having them master it before learning multiplication.

X 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100

7, 8, 9, 10. We can also make multiplication by 6, 7, 8, and 9 much easier using the following tricks shown in the movie clip below. This works out to about 4 things to remember to be able to do this trick because of the complexity of this trick.

Now let’s look at what’s left to memorize. 

X 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100

So now students only have 3 multiplications to remember. Even better, all of these are fairly small numbers so that if they get stuck, they can just count it out using repeated addition. For those of you keeping track, this means we can reduce the entire multiplication table to just 13 total facts to remember. Not bad!

References:

http://www.dadsworksheets.com/v1/Strategies/eight_rules_of_multiplication.html

http://www.redshift.com/~bonajo/mmathmult.htm

Why I love my school

Last night I witnessed something which I really feel is a critical component of why our school works so well. 10 teachers sat around a table and ate together and openly discussed our recent MYP camp.

There were no accusations of blame or discussion of which teachers may have not pulled their weight; there was just an open discussion on how can we improve this camp. In about a 30 minute discussion, the group had outlined the successes of the camp and the failures of the camp. In about another 20 minutes, they had analyzed and categorized the successes and failures and come up with solutions to the problems that they saw.

They should have gone home to their families and rested, after all they were all tired. They could have decided to wait until later to discuss the issues. "Let’s hold off and wait until our meeting on Tuesday to discuss this," they could have said. Instead, they sat down in their dirty and smelly camp clothes and discussed improvements to the camp for an hour, almost immediately after the last child was safely on their way home with their parents.

It is this kind of commitment to our organization and to what we do which has made my school so much fun to work at. I love working with a group of people who are fully committed to what they do and in which everyone pulls their weight. 

What is a Learning Specialist in Technology?

This year I started a new job at my school. My official title is "Learning Specialist: Information Technology" which is a bit of a mouthful so I feel like I need to describe what I do in order to explain what the title means. I also have some freedom to write my job description because of how new the position is to my school.

My job involves multiple aspects, the most important of which is to turn our school into one which uses technology efficiently and effectively in our instruction and in our general organization of the school. So overall that means I’ll have multiple responsibilities within the school given the enormity of the task ahead of me.

First, I see my position as a professional development position. It is my job to help the staff improve their use of technology, to be thoughtful about how technology is used, and to incorporate technology more seamlessly into their practice. I’m going to do this through small group instruction, 1 on 1 tutoring sessions, training videos, sharing of resources & links, and occasionally whole group sessions. I’ll also share outside opportunities for my staff to learn how to use technology; this could take the form of webinars, tweet-ups, or conferences at other schools.

I’ll also need to continue my research about the use of technology. Twitter has been a great source of information in this regard, but I’m going to have to continue to expand my professional learning network and find other sources of information. I’m particularly interested in finding more people locally who use technologies in their schools so I can observe what they do in practice. I’ll also end up being the point person in my school when organizations want to talk to us about their products.

I’m going to explore technologies and look at what the market has to offer. We are currently looking into an eReader and pricing options for textbooks for example. I’m interested in accessories which could make some of our teacher’s lives easier. I won a free USB microscope which looks like it could be a great addition to our science department. I’m playing with the InFocus projector I won at ISTE. These technologies are something our school would otherwise not get to play without my involvement.

I still teach this year. I have two diploma program Math classes on my schedule. It is important that I use technology in my own practice with these students. Partially this is so I keep my practices current, partially it is so I can experiment with different ideas, and partially it is so I keep a connection to the students in the school. Some of the students don’t even know who I am, even in our small school, because I’m out of the classroom so much. The danger with me being pulled out of the classroom completely is that my teaching practice may stagnate and without some professional experience to draw upon, it will be hypocritical of me to be training staff in new technologies that I haven’t even used yet!

I’m looking forward to this year and I suspect that as the year goes on that what I do my modify and change. Perhaps the school will decide that their investment hasn’t been worthwhile, or perhaps I’ll be moved out of the classroom completely when our school expands to its full size. Who knows? In the meantime, I’m enjoying what I do.

 

Quizzes Should Mark Themselves

Quizzes should be used as part of formative assessment if you use them at all. They are a fast and simple way to get some feedback about what lower level skills your students know. However, my recommendation is that if you are going to use a quiz, use one that marks itself.

http://thatquiz.org and http://assistments.org both offer a free quiz platform which provide feedback to the students. Feedback is a critical part of the learning process, and the sooner is offered to the students, the more effective it is. Why not offer it immediately after the students complete the quiz?

The feedback from Thatquiz is pretty basic, essentially is your answer right or wrong and then a list of the correct answers at the end. You can customize the options a bit with Thatquiz and its strength is the ability to create custom quizzes, and you can even create questions with some interactivity.

Assistments on the other hand allows you to create extremely high quality assessments which can actually be part of the learning process. They provide the opportunity to create a really useful formative assessment. Students can be working on a problem (in math) and ask for a hint on a problem, and based on the work the student has done to date, the hint changes. The backend for the teachers provides a lot of useful information, including whether or not a student has asked for a hint on any particular question.

Either way, if you are going to use an online quiz, make sure it provides immediate feedback to the students.

What is Wolfram Alpha?

These are just some brief notes on the Wolfram Alpha presentation I attended today. Here’s the entire presentation if you want to download it (no audio, just slides) and here if you want to view it online.

  • Search engine layered on top of Mathematica
  • Computation driven so much different than Google
  • App for Smartphones, very useful as a mobile device
  • Widget builder (Beta phase, launch in October?)
  • Wolfram Alpha API (used in Bing for example)
  • Uses in education:
    1. Visual aid
    2. Walk students through solution
    3. Compare, combine, correlate data
    4. Focus students on a particular concept using widgets
    5. Promotes Socratic learning
    6. Interdiscplinary lessons are easier because of internal mapping to other disciplines
    7. See examples here: http://www.wolframalpha.com/examples/
    8. Chemistry, biology, geography, every discipline has an example query in Wolfram Alpha.

Wolfram Alpha is going to change how we teach mathematics as it gains wide spread adoption. We won’t be able to ask questions at lower order thinking when students have access to it because students will be able to query the Wolfram Alpha computational database and have the complete solutions to the problems given to them. We will need to focus on higher order thinking skills instead.

 

Using Glass in Education

Update: It looks like Glass has been discontinued.

 

Glass is a new web service which is opening up by invite only at this point. I just discovered it today, and I’m thrilled with the possibilities. Think of Glass as social bookmarking combined with a discussion forum embedded on every website you visit. You can share text comments, links to other websites, even videos on any web page.

Glass also allows you to create groups of users, and share a particular resource with a group. These groups could be useful as you could create a group of your students, and share a discussion about an online resource with an entire group of students.

The potential for collaboration and discussion using Glass is amazing. I wouldn’t use it to replace discussions that you can easily have in person, but it could be a great homework assignment. It can also be a way for students to ask questions with you about a website, and the comments themselves can be embedded within the context of the page as you can specify the location on the page you want the comment to be.

Teachers could use this to evaluate common resources and discuss ideas they have around a particular piece of content available on the web. Students could work in groups and comment on videos in a more private fashion as each comment is available only to the person that is part of the group.

It only works in Google Chrome or Firefox. Check out this video below for more details and here’s another post that discusses Glass in more detail.

Revamping Mathematics Curriculum

What if we revamped the mathematics curriculum to match the style of teaching Dan Meyer recommends? What would that look like? Watch the @ddmeyer video below from his TED talk, and then let’s look at how we can make specific changes to our own teaching practice, and talk about whether or not these are changes worth making.

I’m sure we are all guilty of creating problems for our students which are too well defined. I know I have. I’m trying to change how I do my own teaching practice, but it is always helpful to do this with a team of other people. Does anyone want to jump in and help take a set of math curriculum and turn it into something which is more useful for our students’ learning? Let’s create a problem forming curriculum instead of a strict problem solving curriculum?

I’m putting the call out to collaborators here (or for anyone to point me at a similar project with which I can join efforts). Please check out http://mathtransformation.wikispaces.com/ and ask for an invite to the wiki if you are interested in helping with the mathematics curriculum revamp.

The Public Education Monopoly

Currently public education holds a virtual monopoly in most countries around the world. The problem is that each school district is the sole provider for education for all students who cannot afford much more expensive private education. Worse, students are often forced to go to the school which is geographically closest to them which often forces them into bad schools. This kind of monopoly is exactly what we try to avoid in business, and many high profile cases have happened over the past decade have demonstrated how concerned our judicial systems are with breaking up monopolies.

This argument has been used to allow other types of schools to open, like charter schools for example. Charter schools are examples of public funding being used to open a different kind of school and provide some choice for public school students. They don’t seem to be having much success in actually boosting scores of students however and recent studies have shown that charter schools are no more or less capable of educating our kids.

Some school districts have tried to allow vouchers so that students can use their tax dollars (or a portion of them) and send them to whatever school they choose to attend. This would allow some measure of choice for the students, and the hope is that this would force the schools in question to improve, or potentially close because of a "lack of clients".

Neither of these alternatives to public education has shown signs of success. Charter school results have been ambivalent and most of the voucher systems have been failures. In fact, almost all education reform efforts have made very little progress in improving graduation rates and recent improvements in some large school districts (think NYC) have been shown to be false progress.

So what is the problem then if allowing more choice for schools hasn’t worked in improving the quality of education? The issue lies in the fact that almost all of these solutions have been subject to the ultimate authority, that of standardized tests meant to measure the success of the schools. We haven’t actually been offering more choice when we require schools to fall within a small set of standard norms. Some charter schools have been exempt from standardized testing, but of course the progress of these schools have been so difficult to measure that we do not know yet if just exempting a school from standardized testing has any impact on the student learning in those buildings.

So long as we require every school to meet a set of standard norms and tie their funding to their success in meeting these norms, then we should expect all schools to become more similar to each other. This negates the effect of more choice when all schools have to meet the same objectives, and generally rely on the same flawed learning methods to achieve their goals.

The solution is to throw away the cheap standardized tests as measures of school success and look at more expensive measures. There are lots of other options to standardized tests, including portfolio assessment, individual education plans for every student, or community assessment of schools. None of these options is as cheap as standardized tests, but one could argue that in a continual "band-aid" approach to the real problem of the educational monopoly, we have spent far more money.

There are actual examples of schools around the world where real learning is taking place. If you examine these school districts, you’ll often find that they lack the myopic focus on a standardized test that have spread across Canada, the UK, the US, and Australia. In other words, by ignoring the standardized test and focusing on student learning, they have managed to offer a much improved education for their students. We should be looking at these examples and finding ways to diversify the ways in which we measure the success of our students and be willing to fund the costs of these alternate measures.

Let’s Prepare Students for Life

What types of things are actually going to happen with any frequency in our student’s lives? Is there anything obvious for which we are not preparing them? I know a lot of current effort is being put into preparing students for events which are unlikely to happen, but what about the common things?

Here’s a list of things practically everyone will have happen in their lives.

  • Serious illness
  • A car accident
  • Death of a family member or close friend
  • Paying taxes 
  • Find a life partner

Here’s a list of things that will happen to a significant portion of people (25% or more) at some point in their lives.

I argue that schools actively work to discuss the issues in the second group much more than things in the first group. How many schools have a grief program? How many schools teach kids how and when to fill out their tax forms? What to do if you become seriously ill?

I think schools tend to leave these things which happen to practically everyone as a job for the family of the students to teach and then we cover these other activities which happen more than they should, but not to everyone. I’m not sure why we do that. One could easily argue that a serious illness is as difficult to deal with as anything on the second list, especially if that illness becomes chronic. Why don’t we talk about this in schools? I’m not saying that we need to have an exhaustive discussion of everything that could happen in life, but some preparation for the bigger events of life is pretty important in my opinion.

Some schools do talk about everything on this list. Some schools bring in grief counselors after a major incident related to the school community. Some schools teaching nothing on either lists, which I think should be criminal.

Our job is to prepare students for life. We can’t teach them absolutely everything they need to know or completely take over the job of parents to prepare their kids for life, but we should recognize that not every family has the same ability to talk about these important issues. We must claw back some of the time we spend preparing students for tests for the more important discussion of life.