Tag: The Reflective Educator (page 16 of 43)

The NCTM recently sent out survey asking their members how they feel about the timing of their major conference, normally held in April, asking them to consider alternate dates. I sent in my responses, and in the comment section proposed that another reason they may be seeing decline in their major conference (while seeing a simultaneous increase in their regional conferences) is that the money just isn’t in the US system anymore to support as many people attending an expensive conference in another city.

I had another proposal as well: what if the NCTM helped organize an online conference, much along the same lines as the very successful K-12 Online Conference.

I see the structure of the conference being much different than how a typical conference is structured. There could be pre-taped video presentations and keynotes as is typical but there could also be online workshops (in which participants are expected to actually participate and do something), sharing sessions, building sessions (wherein participants collaborate to build something for everyone’s classes), analysis of research sessions, mathematical problem solving sessions, and free-form discussions related to mathematics education (which would be excellent for that all so important opportunities for networking that conferences offer).

While the experience would not be the same, the cost would be so much less that many more people could potentially participate. With the NCTM as a supporting partner for such a conference, I suspect that many thousands of people would get involve. In fact, people from all over the world could attend the conference virtually!

Any thoughts?

Update: It occurred to me that a dedicated group could run this conference without the support of a major organization like the NCTM. Anyone interested in exploring this option with me?

I recommend watching this amazing video by Amy Burvall.
 

Thoughts?

If you are just getting started with technology integration in your mathematics class, then a sensible question is, where do I get started?

Here are four suggestions.

1. Introduce a graphing and geometry program into your classroom, like Geogebra or Geometer’s Sketchpad. These programs have the flexibility to allow you graph functions, explore geometry, and much more, all with the same program. Geogebra is a free install but your school may already have a license for Geometer’s Sketchpad. Both programs come with significant user communities and additional support resources.
    
2. Learn about student blogging. When I started it eight years ago with my students, I had one student each day summarize what happened in class, and I would rotate through students in the class. Other students were asked to comment on each other’s posts. This allowed my students to have an ongoing summary of the class (which they really appreciated for studying for assessments, and when they were absent from class), synthesize what they were learning in class, and when looking at each other’s posts they had another opportunity to see someone else’s perspective on the mathematics they were learning. Each year I used student blogging in my class the explanations students created became better. I left a school one year, and halfway through the following year, one of my former students tracked me down and asked me to put the blog back up so they could use it to study for their exams at the end of their two year course.
    
3. Use video recording in your classroom, either by recording experiments, having students create explanations, or act as hooks to problem solving tasks. With today’s video editors, learning how to edit video is relatively easy, and most video format compatibility problems are far less of an issue than they used to be.
    
4. Learn how to program a computer, with your students. First, you will learn a useful skill, and so will your students. Second, your students (and you!) will learn more about decomposing problems, debugging problems, and some potentially highly complex mathematical ideas. There are some excellent resources out there which make learning programming much easier than it used to be so do not feel intitimidated by this task. This is an excellent opportunity to model learning for your students.
    

What other technologies would you recommend math teachers learn how to use early in their technology integration journey?

Code.org has released a video of some big names in the programming world talking about their first experiences in computer programming, and why they think everyone should learn to code.

The reasons they give are that programming teaches you to think (via a quote from Steve Jobs), it helps you learn how to decompose problems into smaller steps, that learning how to program gives you power, and that it is a fundamental literacy in an age of ubiquitous computing.

I don’t see the "there will be lots of jobs available for you" reason that this video presents as a particularly good reason to learn how to program. What if the jobs that were required were jobs that did not give you power, or did not make you think? If everyone did know how to program, do you think that those offices would still look as cool?

Compare this first video to this video of Seymour Papert talking about computers and learning.

Notice that this video also presents the same reasons as in the first video (aside from future potential for jobs) but it gives agency for learning and presenting these reasons to children. I think that the second video is a more powerful as a result.

The video of Seymour Papert is from about 30 years ago and has a little over 9000 views on YouTube. The Code.org video is from a few days ago and already has more than 3 million views. It would be amazing if we could make this idea of Seymour’s – that computers give students agency in learning – a reality, and if we could give it as much coverage as the first video.

* If you are reading this in your email, you can view the videos online here.

Stephanie Glen shared with me this interesting project she is working on. The objective of the project is to produce a series of videos to get students excited about mathematics in much the same way that Bill Nye excites students about science. Here’s Stephanie talking about the project in her own words.

Right now Stephanie needs some money to produce a 5 minute promo to show to potential financial backers of the show. Help her out by donating to her Kickstarter page.

I’ve watched a lot of online webinars and presentations, and whenever there is a video of someone presenting at the front of the room, the audio quality is always horrible which makes the presentations hardly worth listening to. So that I don’t end up in the same situation when I end up having presentations recorded, I decided to look into getting an wireless microphone, but I quickly discovered that these are very expensive.

I thought about ways I could synchronize my iPhone audio recording with a video, when it occurred to me that there might be an application that allows my iPhone to act a wireless microphone, and sure enough, there is!

The name of the application is Pocket Audio, and it costs $1.99 (provided you already have an iPhone) which is obviously much more affordable than the three hundred dollars one can potentially spend on a good wireless microphone,.

To get the application working, you have to first download a copy of the server software for your computer (both Mac and a PC versions available) and install it on your computer. You may need to adjust your default sound options after doing this, as it seems that Pocket Audio wants to make itself the default audio input and output for your computer. You will also need to ensure that the firewall on your computer allows communication from Pocket Audio with the rest of your network. Now run the Pocket Audio server (called PocketControl) on your computer.

Next, you download the client software to your iPhone and start it up. It should automatically search for and connect to your Pocket audio server, and presumably if there is more than one available on your network, it should allow you to select which one you want to use.

Now whenever you use any program on your computer that has an option to select a microphone, you should be able to select your iPhone (called Senstic PocketAudio in the options) as an option. See an example of what this looks like below in the audio settings for Skype.

The audio quality was excellent, but there is a small delay, depending on your network. This is because instead of the audio being fed directly into your computer from an attached device, it needs to travel over your network. Still the small delay may be worth it to greatly increase your audio quality, and anything would be better than some of the sound quality I’ve seen in some recorded presentations.

Here’s a very short sample of the audio in a screen-recording I did. Note that I actually walked about 15 metres away from my computer, which is obviously not visible in the webcam embedded in the video below.

* This post was not paid for by anyone. I am just offering a solution to a problem that I had, and this seems like the best (and cheapest) option for me. I’m recording this solution here so that I remember it, should I need to use it again soon.

Bon Crowder shared this very interesting TED talk about some of the mathematics in movement and dance. I recommend reading her post to see some more resources on the mathematics of dance and movement.

Erik and Karl show some ways in which one can explore combinatorics, topology, symmetry, patterns in numbers, and fractions through movement.

An obvious question I have is, where else could we embed movement into mathematics?

• Students could count their steps while they move from classroom to classroom, or count steps as they climb them.
• A teacher could put a giant number line (or cartesian plane) on the floor of their classroom and students could practice arithmetic visually.
• Students could verify the Pythagorean theorem by counting steps as they walk along the legs and hypotenus of a large right-angled triangle on a playing field.
• When students all dance in a group, they could create tesselation patterns as they move across the dance floor in a group. They may need to see a video (shot from above) of themselves moving to see why this is interesting.

What are some other ways in which we could use movement activities to explore mathematical ideas?

I watched this video, and I was reminded of the primary reason I became a teacher. As a bullied youth, I wanted to try and help prevent this from happening to other children. I cannot see how I have been remotely successful in this goal.

I spend so much of my energy focusing on improving how my passion, mathematics, is taught, but not enough time thinking about and helping the kids who are my charges. I know that there are kids at my school who feel alone, and while they may not experience the intensity of the bullying that I did as a child, I’m sure their spirits are no less wounded than mine used to be.

Bullying is a complex problem. There are no simple solutions. That being said, children spend about 8 of their 16 waking hours involved in school in some fashion, and if at the end of this time they still feel isolated, alone, and broken, then we have failed utterly as an institution.

No one else has much time to influence their lives as we do. We need to make more of a difference.

Unfortunately we spend so much of our time and energy as an institution focusing on stuff which is almost trivial compared to some of the needs of our most vulnerable students. We know about Maslow’s hierarchy of needs, and while we cannot prove empirically that it has validity, we know from our experience that children cannot learn effectively unless they feel loved and love themselves.

• Schools should feel like communities where everyone knows everone else by name. It should not be possible for children to pass through our hallways and classrooms without talking to a single soul during the day,
   
• We should reframe the problem in the positive. Instead of "don’t be a bully" we should model and teach empathy and compassion,
   
• We need to start modeling empathy and compassion within our wider communities. We will never end bullying in schools while we accept it in the world outside of school,
   
• Compassion often develops from experience with the other. Instead of separating kids by age, we need to find ways to form connections between kids of different ages. This way younger children always have an older ally, even when they scared to talk to adults. We need inclusive classrooms, not just because it results in better outcomes for the children with special needs, but because it will help all of the children learn about their colleagues more deeply,
   
• We need to treat social interactions as a skill to be learned. When kids interact poorly, it is an opportunity for learning, and when kids are struggling, we should scaffold the skills they need both to cope and to understand their peers. One of my biggest problems growing up was that I did not understand the motivations and actions of the people around me, and so I often reacted poorly to even the smallest bit of negative attention. My nickname was Spaz instead of Porkchop.

Thank you, Shane, for reminding me of why I became an educator in the first place.

It is my experience that the more deeply I learn about a domain, the more questions I have. Similarly, when I know very little about something, I have lots of questions as well (although these are usually much different questions than the questions I have as I gain expertise). In the middle somewhere, the number of questions I have drops off as I mistakenly believe that I understand the domain better than I actually do.

Being able to ask questions about a domain is one of the ways one learns about it. So this diagram implies that a challenge in becoming an expert in a domain of knowledge is that eventually you know too much, and you run out of questions to ask, making learning more in that domain more challenging.

How can we encourage people to continue to ask questions as their expertise grows?