The Reflective Educator

Education ∪ Math ∪ Technology

Year: 2010 (page 13 of 20)

June 21, 2010 / 5 Comments

I don’t know how to use a fax machine

Today I had to ask for help using technology.  I know, I’m supposed to be embarrassed, I am the expert at my school on using technology, but really there are things I don’t know how to do.  I don’t know how to use a fax machine.  They were never a technology I considered useful, and in today’s world of email, I consider them somewhat archaic.

In any case, I had to send a fax today because it was the only way I could send this particular piece of information to a government ministry, don’t get me started on that.  I went to the front office and asked our really wonderful administrative assistant if she could help me.  Her jaw dropped, and the jaw of a colleague who was standing nearby dropped as well.  "You don’t know how to use a fax machine? But you’re like Mr. Technology! You should know this!"

My colleague patiently showed me how to send a fax, a skill I’m sure I’ll promptly forget.  It looks pretty easy but given that I have to send about 1 fax every year, it’s not a skill I get to practice often and I’ll probably have to ask again next year.  When my colleague finished showing me how to use our school’s photocopier, which I discovered doubles as a fax machine, I was happy and thanked her.  She did a fist-pump, exclaimed, "Yes! I showed Mr. Wees something with technology," and then went on to give the administrative assistant a high-five.  They were both excited that they got to show me something.

Now keep in mind, these are grown adults, and their reaction might not be the same as your students’ reaction, but let me ask the question: How do you think your kids would react if they got to teach you something?  Do you think that they would remember that experience? Would it be worth not looking like the expert for a couple of minutes?

June 21, 2010 / 2 Comments

The Relationship Between Accountability and Creativity

Imagine this graph represents the possible relationships between accountability and creativity.

Accountability vs Creativity graph

Where would you put the activities you do as a school?  Here are some examples of activities some school do, and where I think they lie on the accountability vs creativity scale.

Accountability vs Creativity with some ideas

What you may notice about this graph is that, for the most part, activities which hold schools and students highly accountability are not associated generally with creativity and that activities which are highly creative can fall short of being very accountable.  It’s not a perfect graph, and I think that some of the examples could be moved, but the idea I think is pretty clear: the more you increase accountability, the less flexible the activity, and hence the less ability for students to be creative while completing the activity.

Accountability in this sense means how the activity and the student’s performance of that activity, is shared with the student, the teachers, the school, and the wider community.  Standardized tests are considered a “highly accountability” activity simply because everyone has access to how well pretty much any school did, and educators within those schools generally have access to their individual marks, and of course students get feedback about how well they did.

Creative activities to me are generally areas where the student has a lot of choice on how the activity will be completed, and how they will complete the activity.  These are often the types of activities that I think students will actually be able to do once they finish their education, and according to Sir Ken Robinson, our schools fail to provide opportunities to students to do them.

There are a few activities which fall with higher accountability and decent ability for students to be creative, and we often find that these activities are not ones which are done by most schools.  Anyway, I’m sure the model I have up there is imperfect, so I invite you to follow this link to this collaborative Google drawing I’ve started, and we can add other activities to this chart.

June 17, 2010 / 0 Comments

Why you should give kids a second chance

Yesterday we had a community service day.  It worked wonderfully, and everyone who came participated really well.  The first thing that I noticed was how different the students looked when they were working in this different context.  The people who were normally stars of the classroom were not necessarily stars for the community service, and visa versa.  Some of the best and hardest workers were students who often do not work in the classroom well by themselves without lots of reinforcement.

The day was wonderfully productive and we accomplished a lot.  The volunteer organizer for the community garden begged us to come back because she said the amount of work we accomplished during the day was tremendous.  

This activity really built a lot of community spirit and brought us all closer together.  It was totally worth the effort we put into it as teachers organizing and showing leadership by modelling what types of behaviour we were expecting from the students.  In other words, all of the teachers involved worked hard too.

Community Service

Unfortunately some of our boys didn’t come for this day.  They apparently used Facebook and attempted to organize a mini-revolt and 7 of them did not attend the day at all.  They were noticeably missing, many of the students who attended the event complained about the fact that a group of the boys were missing.  Their decision not to come for the day certainly frustrated we teachers, and we decided that we had to come up with an appropriate way for the students to make restitution for what they had done.

Fortunately for us, all 7 of those students attended school the following day, hoping to participate in our afternoon party in the park.  First their homeroom teacher gave them a 20 minute lecture on how their lack of participation in the previous day’s event affected the entire school and then we put them straight to work, as the morning we had planned some school-wide service, working on our own community garden project.  

They got the least fun duty, which was shoveling the piles of manure.  They started working on it pretty diligently right away, and it was obvious that the speech from the homeroom teacher was pretty effective.  The rest of the students involved in the community garden were carting away the wheel-barrows full of manure, and these 7 boys worked tirelessly to fill the wheel-barrows.

We paused for a big spirit building activity, then everyone else in the school left for the community picnic at the park, and these 7 boys stayed back with me to continue the work from the morning.  First we had lunch, the same food planned for the picnic, then we started handing out flyers to the houses along the street.  It turned out that we had way more manure than we could actually use, so we offered some of it to residents of the houses on the nearby block.  One of the residents, was so impressed with the boys that she brought out a small treat for them.  The boys felt really uncomfortable accepting the gift, but it was clear from her insistence that they couldn’t say no.

Unexpected reward

After our brief stint handing out flyers, we got to work and moved several dozen wheel-barrows full of manure onto one of our small plots for our garden.  The work wasn’t glamorous but to their credit the boys worked really well.  About an hour and half into the work, they started recognizing that they were enjoying themselves, and I could tell that they were regretting their decision not to join in the work from the previous day, but for the right reasons.  They actually asked if they could continue the work we were doing tomorrow, as they wanted to finish the project.  They seemed to get it, that the work itself was enjoyable, especially in the company of their friends.  Really, everyone of these boys was a superstar that day and showed me just how hard they could work.  I was really impressed with their work ethic and diligence during the day and I let them know as much.  Tomorrow, when we finish our work, I plan on reflecting with them about the experience.  The objective of the reflection will be to find out if the really big lesson will be in fact learned: service in the context of a community is incredibly valuable.

The boys did a tremendous amount of work and taught me a lesson too.  Even a student who has made a big mistake can rectify it and should be given the opportunity to fix their mistake.  Every kid deserves a second chance, and these boys made the most of their second chance.  At the end of the day, we realized that they had move two thirds of the pile themselves, and they really looked like they felt good about themselves.

June 15, 2010 / 0 Comments

Learning specialist in technology

This morning I had a great discussion with the director of the IB Primary Years Program at my school.  We talked about my role for next year, and what ways I could help his staff become more comfortable using technology.  My title for next year is "Learning specialist: Technology" which is pretty broadly defined, and I have the luxury of writing my job description.  I may never again get this kind of opportunity to define my own role, so I’m making sure I do it right by involving the primary stake-holders in the process.

First, we both agreed that my role would be primarily helping teachers learn about the appropriate use of technology in their classrooms, and less about teaching students directly.  This would take the form of 1 on 1 instruction with the teacher, small group discussion, co-teaching topics, demoing lessons for teachers, but probably not as much whole faculty instruction.  We both agreed, whole faculty instruction is of limited use: really staff need to all have a direct need for whatever you are presenting for this type of instruction to be effective.

Another exciting aspect of my job next year will be observing teachers.  This may mean I offer pointers on ways they can improve their use of technology, or I may just give positive reinforcement for when lessons are obviously working well.  I will do a lot of observations in the beginning of the year so I can gather information about what is working well already for teachers, and where there are areas which could be improved.  I’ve observed a lot of my colleagues teach (I used to make a practice of watching everyone in my large math department teach), perhaps more than most teachers with my experience, but having this process be more formalized is exciting for me.  It means a move into a more administrative role.  One thing that the director and I both agreed on is that my observations would never be used for punitive measures or for evaluating teachers, only for helping teachers grow professionally.

A great idea that the director had was helping teachers build action research goals for the following year.  Essentially this would look like teachers setting goals individually, or with consultation with me, and then helping the teacher plan their way through the meeting of the goal.  This could take an entire school year, or it could be completed within a few months.  During the year, I would be available as a mentor, or as a training resource as necessary.  What is important about this process to me is that it puts the teachers in charge of their learning in this area, and it is the kind of training which is sustainable.

One of the ways we are going to support goal setting is by having teachers complete a self-assessment form for their use and understanding of technology.  Our self-assessment is planned to focus on use in the classroom, as well as administrative use outside of the classroom.  Part of the form I plan to have them fill out will include will include some specific goals for the teachers to work toward.  This form will be submitted as part of our end of year staff meetings, and then we can revisit the personal goals of the teachers at the beginning of the year.  Here is a sample of the self-assessment form, which is still a work in progress.  This way we can start the year with some positive action the teachers can take, and hopefully focus each teacher’s learning on what they want to work on.

I’m excited about next year: it promises to be a learning experience for myself and for our school.

May 31, 2010 / 4 Comments

End of Year Experiential Assessments

I’m very excited as this will be my first year using experiential assessments as an end of year task.  Every year before this I have been required to produce a "final exam" for each of my subjects, while for the past three years at least I have known the futility of measuring students ability accurately with a single exam.   The school I work at is still in the early stages of adopting experiential exams, but they have had them running for at least one year with success.

The basic idea is, the students get given a final task to complete, which is a cross-disciplinary assessment of what the students have learned how to do this year.  The objective is that a few subjects get together and find a common guiding question for their assessment.  Teachers from these subjects work together to create a task which can be assessed using their own criteria from each subject.  We’ve chosen to break the task into pieces for each subject, but ideally there should be one complete task for the student to do.

Here are some examples, which I can finally share because the students have been introduced to the tasks themselves (and so they are no longer a secret).  I have to tell you, I have been waiting to write this blog post for more than a month!  Note that the students will have several hours to complete these tasks, broken up into 4 or sometimes 5 blocks of time.

In the 9th grade, our guiding question is, "How as Imperialism affected our society?" and we are looking a specific focus of Central and South America and the colonization of those parts of the world.  In Mathematics, my task was, "Determine how much sugar could a galleon carry?" which was relevant because sugar is an example of a trade resource upon which the colonies depended.  Here is the task sheet I provided to the students.  You can see that the task is open-ended, that there is no one specific solution, and that what I will be grading the students on is the process they will be going through.  The task also involves a wide variety of mathematics from the year, and I can generally assume that if the students are unsure about how to include a specific piece of mathematics, then they didn’t really get it.

This is also the kind of task that students might actually find interesting.  In the creation of their diagrams to help explain themselves, there is a large amount of creative license which can be applied.  When the students decide on their assumptions, which they have to justify, they can have all sorts of wild assumptions, provided there is some reasonable basis for their assumption.

Galleons are also pretty cool.  They have been popularized  by movies like Pirates of the Caribbean, so the students are very likely to have some personal idea of what they are like.  The photo shown here is from the Wikipedia article about Galleons, and is licensed under a Creative Commons license.

This type of task also lends itself well to differentiation, as the students who wish to present more of their knowledge and understanding can take into account more factors which could affect the amount of sugar these Galleons could hold.  For example, the sugar to be transported would almost certainly be done so in as water-tight barrels as the merchants could find.

In the 10th grade, our guiding question is, "How do we best get our voice heard? Is it through Science, Math, or Language?"  We start by gathering evidence in all three subjects, specifically on the environmental effect of large multinational organization policies can have on small impoverished countries.  We complete our week with a trial, in which students will present their scientific or mathematical evidence to their teachers.  They will also role-play either French speaking or Spanish speaking people’s of said countries (we originally said that this case was a comparison of the Dominican Republic and Haiti) who have been affected by the multinational organization.

Image on the right is of the island of Hispaniola and is from a Wikipedia article about said island.  It is also licensed under a Creative Commons license.

I’ve collected some data sources, through my contacts on Facebook actually, and will share these sources with the 10th grade students as a starting place.  The best part is, most of the data is largely unprocessed, which means the students will have to do this themselves!  In mathematics, the objective is to analyze the data and depending on whether they side with the multinational or the local population, build a case to present in the trial.  Here is a copy of the task sheet we provided.

The day after the trial, students reflect on their contribution in each subject and we wrap up the trial with some conclusions.  It will be really interesting to see what results.

I’m pretty pleased with the design of our experiential exams this year, and I’ll talk more about how well they went after I’ve finished this week, which looks like it will be extremely busy.

May 29, 2010 / 0 Comments

Introducing Probability Using Settlers

This past week I was looking for a way to introduce probability to my 9th grade students.  One of the problems students have when they are first learning probability is developing some intuition about what to expect.

I decided that one of the best ways to develop intuition about probability is to have some strong emotions associated with the results of their initial probability experiments, so I decided to teach my 9th grade students how to play Settlers of Catan.  I didn’t give them any information about best strategies to play the game, I just taught them the basic rules and set them loose.  Here are some rules for your reference.

Settlers Map

The basic idea is, each hexagon produces resources, but only when the number shown on the hexagon is rolled as the total of 2 six-sided dice.  If you have a settlement located at one of the vertexes of a hexagon which has just produced resources, you gain 1 of those resources.  You can then save up these resources, trade them with other players, or then use them to buy more settlements, cities, etc… Essentially if you gain enough resources of the right type before your opponent, and you win.

The actual system we used to play is called JSettlers, and it is an open source Settlers of Catan server.  I hosted it on my laptop with no difficulty and shared the link to my students to play it.  This way I didn’t have to pay for a class set of expensive Settlers of Catan games.

It only took about 10 or 15 minutes of playing for the kids to realize when they had made poor choices, or when someone had an obvious advantage.  The question I had once we had played for enough time that they had gathered some data (I required them to keep track of what was rolled as they played), which starting settlements were poorly placed, and which were in the best locations.  Students looked at the following situation and decided that this intersection of hexagons was a good place to put a settlement.

Good choice of settlement

They looked at an intersection like the following and decided that this was a poor place to put a settlement.

Poor settlement location

I asked them why they liked the first spot and didn’t like the second?  One of them said it perfectly, "well, the numbers 8,9, and 10 are WAY more likely to come up than 2, 4, and 11."

We followed with a discussion of why each number was not equally likely to come up using a typically sample space table, and then we kept playing, having both put some context on the probability we were learning, and developing some intuition about which numbers were more likely to come up.  I was able to extend their thinking quite a bit, as there were several different games being played, none of which had exactly the same set of numbers rolled.  It really worked well, and I’ll continue to use an example like this in my practice.

May 28, 2010 / 5 Comments

Teaching Chi squared test

I tried something new this when I taught the Chi squared test.  Instead of focusing on the formal procedure that one must follow in order to use the test correctly, I focused on what we were actually DOING when we were doing the test.  As a result my students understood the test much more easily, and I had far fewer questions about how to actually use the test.

First, we talked about the expected values, starting with the sums of the expected values.  See the following table.  Here the "Yes" and "No" refer to whether or the particular person being surveyed watches the TV show Glee.

  Yes, I watch Glee No, I do not watch Glee
Male      100
Female      100
   120  80  200

Essentially this backwards from where I started normally, with the observed values table, because I wanted students to understand how we construct this table, rather than relying on rote memorization of the formulas for the expected values.  I started with this fact, that we have 50%  males and females in our data.  Hence, I said, if gender is independent of our question about Glee, how many males should we expect to answer Yes to the question about Glee?  Students pretty easily came up with 60 males, reasoning that 50% of 120 is 60.  I focused their attention on how what they did to get this answer, and then we filled in the rest of the table.

  Yes, I watch Glee No, I do not watch Glee
Male  60  40  100
Female  60  40  100
   120  80  200

I then set up an observed values table, and filled in the table used way different numbers. I made sure students understand that the previous table represented the expected survey results if Gender wasn’t a factor in people choosing to watch Glee, but that the following table represented our actual survey results.

  Yes, I watch Glee No, I do not watch Glee
Male  25  75  100
Female  95  5  100
   120  80  200

Right away, one of the students said that this second table obviously meant that there was a relationship between Gender and choosing to watch Glee?  The reason he gave, "Well those numbers are way off the expected values."  

I then asked a really important question.  "How much different do they have to be before the results are significantly different than our expected results?"

Students realized that we’d probably want to start by subtracting our two sets of information like so.

O E O – E
25 60 -35
75 40 35
95 60 35
5 40 -35

I pointed out that we don’t really care if the difference is positive or negative, since either way the results are "way off" if the difference is big.  So we squared the observed minus the expected values to make the answer positive. Note that we haven’t really done much work with absolute value, so I chose to ignore it for this example, which helped make my case for the calculation, but probably needs some discussion.

O E O – E (O – E)2
25 60 -35 1225
75 40 35 1225
95 60 35 1225
5 40 -35 1225

Next I pointed out that the numbers were too big, and that I wanted to be able to make a comparison between the size of the difference between observed and expected values in one chart with the size of the same type of difference in another chart.  Normalization (which is not a word I used with the students) is a useful way to do this, and hence we want to divide by the expected values.

O E O – E (O – E)2 (O – E)2/E
25 60 -35 1225 20.42
75 40 35 1225 30.63
95 60 35 1225 20.42
5 40 -35 1225 30.63

Someone noticed that this was a bunch of different numbers and that it would be more useful if we had a single number, so I suggested adding up all of these normalized differences.  This number, I labelled as Χ2calculated and we had our result.  Note that my objective here was not to formalize the calculation, but more to justify the calculation informally, so that the students would feel like the understood what they were doing.

From there the rest of the lesson was relatively easy, we had a discussion about how to compare Χ2 results which led to the table of critical values, and with this table I introduced the notion of degrees of freedom.  I didn’t try to explain why the critical values tend to increase with the degrees of freedom or with the significance level, but the students were okay with these additional steps because the initial calculation, and reasons for the calculation made a lot more sense.  I was able to talk about the test at a deeper level than I had before, and when the students came time to actually practicing the calculation themselves, they had a lot fewer difficulties than I had anticipated.

One observation a student had was, "Using those list operations you taught us on the calculator sure would make this a lot easier," and a bunch of the students had an "Aha!" moment as they realized why I bothered to show them how to do the list operations on their calculator.

The essential difference in teaching here was using a conceptual framework versus my old method of rote memorization of the process.  I think I know which way I’ll try in the future, even with something which seems so mechanical in nature.

May 27, 2010 / 0 Comments

Museum of Math

An organization called the Museum of Math is having a contest to promote how Mathematics can be fun and exciting.  As per their website:

"Mathematics illuminates the patterns and structures all around us. Our dynamic exhibits and programs will stimulate inquiry, spark curiosity, and reveal the wonders of mathematics."

The idea of an organization which is dedicated to spreading the word about how mathematics is evident in the real world is fascinating to me, because this is a question I always have to answer.  Every single one of my classes, every year that I teach, asks me why they are learning math.  The relevance of mathematics for the typical high school student to the real world is really hard to see, especially if one is is learning the material in the more traditional way mathematics can be taught.

They are having a contest to promote both their organization and the love of mathematics.  From their website again:

Enter our Twitter contest and tell the world why you love math! The best tweet with hashtag #MathIsFun will win a free iPad. Contest ends June 1, 2010.

 

« Older posts Newer posts »

Archived posts

Calendar

December 2024
M T W T F S S
 1
2345678
9101112131415
16171819202122
23242526272829
3031