The Reflective Educator

Education ∪ Math ∪ Technology

Tag: The Reflective Educator (page 12 of 43)

June 18, 2013 / 1 Comment

DIY Catapults!

Fork catapult - side view

One of my jobs at my current school is work on mathematics enrichment projects with three 4th grade students. For the past couple of weeks, in between their camps, my camp, and other end of year events, we have been working on looking into a mathematics modelling task, specifically, a fork catapult. The 4th grade boys and I completed this project over a series of 3 lessons with me, and 2 more lessons working on it independently between our sessions.

I built the fork catapult fairly quickly for the boys, mostly because we lacked a lot of time to work on this particular project, and partially because I wanted them to focus on the collection of data, not specifically the design of their catapult (As it turned out, the boys found time to create three more of their own designs anyway).

I set up the catapult, starting opening up the clip on the clipboard, and right away one of the boys asked, "I wonder how far it will go?"

Fork catapult - side view

So, we collected data. What we did was open up the clip part of the clipboard so that it was 1cm, 1.5cm, 2cm, 2.5cm, and 3cm open, and shot a mini-whiteboard eraser by releasing the clip, 10 times for each position of the clip. We then measured the distance (as accurately as we could) the eraser flew across the room. The initial prediction from the boys was that the wider the clip was open, the farther the eraser would fly, which the boys continued to believe, even once we had actually collected all of the data.

I showed the boys how to plot 1 or 2 points, and then I then asked them to carefully graph the rest of the data. This is what they produced (the red dots were added later).

Graph of results

Once the boys had their data graphed (do you see the small error in the graph above?), we looked at together to see what it meant. From the graph, the boys decided that it was clear that their initial hypothesis (they didn’t use this language, I did) was incorrect and that there was a maximum distance that the eraser could be launched. One of the boys had the insight that the problem was that when the clip was "open too wide" that too much of the energy went into throwing the clip up, and not enough went into catapulting the clip forward.

The boys also reasoned that the eraser would be shot the furthest when the clip was between 2cm and 2.5cm open. Our next step was to test their new hypothesis. As you can see from the red dots graphed above, their hypothesis was probably right, although in order for the boys to see that, we first had a discussion about finding average values from the graph.

At the end of the second class, we started cleaning up, and the boys asked me to photocopy their graph and data, and let them take home their other catapult designs. One of them said to the other boys, "Let’s keep working on this next year!"

There are a lot of ways one could go with this project, but one thing I really liked about it was that we created a mathematical investigation from some pretty basic supplies, that the data that results has enough experimental error that it makes it more obvious that collecting many trials is useful, and that the graph was clear enough that students could read the results from the graph fairly easily.
 

June 11, 2013 / 2 Comments

Bias in assessment

Every form of assessment of learning has bias. This bias may be hidden, or it may be quite obvious. As Cathy O’Neil points out, assessment is a proxy for what we want to measure – learning. We cannot measure the building of connections between neurons that is happening in the brain directly (or even potentially understand what that growth even means) so we use a proxy in the form of an assessment of the externally visible signs of learning.

One bias therefore is our tendency to forget that we are not actually measuring learning, we are measuring a proxy for learning.

Another bias is the language we use to do the assessment, whatever form that language takes. Language is necessarily a construct of our minds and no matter the appearance, it has deeply personal meaning based on our own experiences. As such, our use of language to communicate an assessment to a student contains an inherent bias based on our understanding of the language we have used.

The medium of the assessment also introduces bias. An assessment done on paper on pencil is limited to what can be collected in this form. As Dan Meyer and Dave Major are showing, digital assessments have different affordances (and different biases) that can change how students can interact with the assessment. Students who share their understanding verbally may have a very different explanation than if they write down their explanation.

There is further bias in the assessment based on our interpretation of the results of the assessment. If one knows the names (or race) of the people doing the assessment, is one sometimes more or less lenient? Look at this video of people assessing whether or not someone is stealing a bicycle. Do they exhibit any bias? Is it possible that teachers may experience similar bias (hopefully to a lesser degree!) when examining student work? How much of a difference to the student’s marks does it make if the work is messy or neat?

There are no doubt other biases in our assessments that I have not mentioned.

To combat bias, we must be first aware that it exists, and next that we should look at our assessments and ask ourselves, what bias is likely to exist in this form of this assessment? Can I address this bias? If not, can I use a second assessment in a different form and compare results?

June 7, 2013 / 0 Comments

Access to computers

President Obama recently unveiled a plan to have broadband Internet access in every school across the United States by 2018. There’s only one huge problem with that plan; according to the US government’s own research, as of 2006, there was only one computer for every four students, and many of those computers are old. Outfitting the rest of the students in the United States with a computer, and upgrading the existing ones to be useful, will come with a hefty price tag.

Include with the plan (linked above) is this statement: 

In addition to connecting America’s students, ConnectED harnesses the ingenuity of the American private sector get new technologies into students’ hands and support digital learning content.

I read this as, "We will use public money to buy computers for students via private companies" and very likely, those private companies will make enormous profits, given the size of the US education market.

Here’s a more creative solution: develop open-source hardware for schools, like the Raspberry Pi. Not only will the costs be lower in the long run (since the US government can then mass-produce the hardware for schools at cost), it will create jobs within the United States, and allow for innovation in the field through end-user adaptation.

There are a couple of arguments against this idea.

First, one thing that brings down the price of computers is production in mass scale. To this I say, the number of students in the US school system is more than sufficient to allow economy of scale to bring down prices to reasonable levels.

The second argument is that competition between different manufacturers of computers reduces prices, which to some extend is true. However, technology companies also artificially increase their profits in a variety of ways, including delaying new features for their computers to force turn-over of their devices when they introduce these features, and continuing to build their hardware for planned obselescence rather durability and life-span.

While I think that there are tremendous benefits to technology in schools, I also think that schools should use public money wisely. The United States certainly has the technical capability of developing high-quality, durable, open-source hardware. The question is, why aren’t they using it?

June 6, 2013 / 0 Comments

What did you learn in school today?

I’m grateful that I work in a school where I do not believe that any of these (updated) lyrics by Pikku Myy apply. Via the Blue Skunk blog.

 

What did you learn in school today, dear little boy of mine?
What did you learn in school today, dear little boy of mine?
I learned that I must pass a test
To sort the learners from the rest
That winners win and losers lose
And TAKS test scores is how they choose
And that’s what I learned in school today
That’s what I learned in school

What did you learn in school today, dear little girl of mine?
What did you learn in school today, dear little girl of mine?
It matters what my parents earn
I’ll get better grades with cash to burn
If I don’t speak English I can’t be smart
And no more music and no more art
And that’s what I learned in school today
That’s what I learned in school

What did you learn in school today, dear little boy of mine?
What did you learn in school today, dear little boy of mine?
Teachers fill my empty mind
So that I won’t be left behind
I’m learning how to play the game
And all right answers look the same
And that’s what I learned in school today
That’s what I learned in school

What did you learn in school today, dear little girl of mine?
What did you learn in school today, dear little girl of mine?
Learning’s just a job I do
From seven thirty til half-past two
And all my interests have to wait
‘Til I drop out or graduate
And that’s what I learned in school today
That’s what I learned in school

 

If they apply in your school, what are you going to do about it?

June 4, 2013 / 5 Comments

Things I did not learn in teacher college

The best leaders are the best learners

 

These are some things I wish I learned in my teacher training:

  • The goal is not classroom management, the goal is effective student learning. It may be that a well-behaved class is an excellent environment for learning, but the means by which you end up with that well-behaved class matter.
     
  • Most of your early lessons are going to be awful. Remember the ones that aren’t and build on your successes.
     
  • Connect with other educators as much as you can. You are each other’s best lines of support.
     
  • You are always in charge of your professional development. Any experiences which other people require you to do are training, not professional development.
     
  • Never stop learning. You should continue to explore your own subject area, because a teacher who is inspired by what they teach is more able to inspire others. Always take time to learn more about teaching, because what you learned in college is only part of the story.

 

Note: It may be that this advice was given to me during my time in teacher college, but I didn’t learn it then, and I sure wish I did.

June 3, 2013 / 5 Comments

How first aid training is like mathematics education

Entranced
(Image credit: drewleavy)

I talked to someone recently about first aid training, and they expressed their frustration at how ineffective first aid training usually is.

Unfortunately, according to my friend, many people who teach first aid actually have very little practical experience using first aid. As a result, the agencies that are responsible for first aid certification give their instructors "idiot-proof, deadly boring, text-filled presentations" to use in their training so that every first aid course is at least minimally useful. According to my friend, instructors are expressly prohibited from using their real life experience and telling stories of themselves actually using first aid, and also from explaining the reasons behind the protocols used in first aid. Further, most people taking first aid training have little to no interest in first aid themselves, they are almost certainly required to take a first aid course as part of retaining certification in their line of employment.

It occurred to me that this situation is remarkably similar to the position that we find ourselves in mathematics education, at least in the k to 12 level. Mathematics teachers often lack experience either making mathematical discoveries, or even applying mathematics as might an engineer or physicist. Consequently, curriculum is packaged in such a way so that nearly anyone can follow the text and make sure the students get at least a minimally effective mathematics background. We aren’t prohibited from using stories to relay our experience in mathematics, but we often have pretty frustrating limitations on what mathematics we can teach, and at the end of their k-12 program, how our students will be assessed. Finally, almost none of our students is really interested in mathematics; most of them are in our courses because they are required to be there.

Fortunately, first aid training is occasionally successful. My friend suggested that about 80% of the time, people who have first aid training are more useful in an emergency situation than people without the training. At my school, a 6th grade student, learned the Heimlich maneuver during a recent first aid training, and then used it to save the life of his mother two weeks later (An aside: according to my friend, the correct response when someone is choking, after encouraging them to cough, is 5 sharp blows to their back with the heel of your hand, right in the middle of their shoulder blades, followed by abdominal thrusts, then CPR if they fall unconscious). Not teaching first aid is obviously not an option, even when the programs are usually limited in effectiveness, but I wonder, what would happen if we let people who were highly experienced in using first aid have a bit more flexibility in how it was taught?

In the same way, our mathematics education is not a complete disaster. Many people go on from their subpar mathematics education to be able to use mathematics in a meaningful way, and some of those people even make new mathematical discoveries. However, the surest proof I have that our system is less than adequate is the enormous number of people I have met who will happily admit that they were terrible at mathematics, hated it, and now never use it.

The question that I think defines my career as a mathematics educator is, what can we do about this issue? It is of limited use to complain about a problem, especially one as well discussed as mathematics education, without proposing some sort of solution.

What if mathematics educators who had actually used mathematics to solve problems, or had developed new areas of mathematics, had more freedom in how they were able to help their students learn mathematics? If someone has significant experience in topology, number theory, mathematical modelling or any other area of mathematics, why not let them teach this area of mathematics to their students, perhaps leaving out some other area of our curriculum so that they would have time to do so. What if we taught mathematics in such a way that our primary goal was to inspire our students into further study of mathematics?

 

May 28, 2013 / 2 Comments

Poverty

1.6 Million Homeless American Children

 

Whenever John (not his real name) entered my class, we had to open the windows. He smelled really bad, most of the time. He also wasn’t in class very often, and I never knew when he would be school, and when he wouldn’t be in school. There seemed to be no rhyme or reason to his attendance.

When John did attend class, he had to be given a new pencil and book in order to write down any notes or work any math problems. Eventually, I just kept a pencil and a notebook in class for him since he never did any homework.

He was an attentive and bright student, but he missed so many classes that he struggled to keep up. In fact, "keeping up" became impossible for John. When he wrote tests, he would do the questions nearly flawlessly that he had seen in class, but there were rarely enough of these kinds of problems for John to demonstrate mastery of the curriculum.

In about February of the year, John stopped coming to class, and I never found out what happened to him. I was talking to one of my colleagues about John, and she mentioned he was homeless, and I felt completely embarrassed that I never realized.

John is not alone. There were 1.6 million children in the United States in the year 2011 who experienced homelessness for at least part of the year. Many of these children struggle in school because of issues similar to what John experienced, and then continue to suffer throughout their lives in the vicious circle that is poverty.

I suggested to someone recently that we should build schools, especially in areas likely to be high risk, to be more like community centres, with access to health-care, food services, emergency shelters, social services, and after school care programs all under the same roof. Services for children could then be managed centrally by the school and the odds that a child could slip through the cracks and not get what they needed would be diminished. It would also be a lot less expensive than the current emergency-room health care system in the United States. The response of the person was basically along the lines of "It’s the parent’s fault. They need to be more involved."

To this I respond, we should not punish children for the periodic inability of their parents to make their lives work. If we are to be a humane society, then all children in our society should be cared for, whether or not their parents are always able to provide this care.

May 22, 2013 / 0 Comments

Host your own services

When you rely on a service, particularly a "free" (ad-supported services aren’t really free) service, you always run the risk that whomever is maintaining and controlling the service will shut it down, or strip it of functionality so as to make it less useful (or even useless) for you. This happened to Google Reader, it almost happened to Delicious, it happened to Posterous; this list will continue to grow over time.

The lesson for me here is not to rely on these third party servives, but take the time to maintain and control my own services. Right now, I maintain my own blog, my own online bookmarking site, and my own RSS reader. Running these services myself has been very easy as I have had minimal interruptions in the service of my website, and the code-base for these services is also under my control (so I can modify them as I need) since they are all open-source projects.

When OX Text is released, I am considering increasing the investment I put into my website (currently about $150 a year) so that I can consolodate all of the various projects I am maintaining onto one site, and migrate away from Google Docs. I just found Roundcube, which looks like it has the functionality I need to replace my current Gmail webmail. 

I would like to migrate completely away from all services that are maintained by third party organizations because these organizations have a history of misusing the data I provide to them, and suspending support for products that do not meet the organization’s goals, regardless of the popularity of the product with their customers.

What other alternatives do you know about for popular services?

« Older posts Newer posts »

Archived posts

Calendar

January 2025
M T W T F S S
 12345
6789101112
13141516171819
20212223242526
2728293031