PLN Tools; See end (use of cell phones in schools?)

Your PLN – what’s in it for ALL of us!
Event Creator:  Jo Hart
Event Type: Web Event
Name: Edublogs Fine Focus – Your PLN, what’s in it for all of us?
When: Aug 26 2010 – 4:00pm – 5:00pm-Aug 26 2010 , US/Pacific (GMT-08:00)*
Participant URL:

78% of us said we had a PLN.
Most imp aspect:
#1   help and support
#2  Social interaction

Jo Hart used a lot of multiple choice questions and other methods to encourage participation.

One key PLN tool for most participants:  Twitter
My answer:  email/intranet/shared drives at work  Suggested by participant.  Very similar to Twitter but more of a private network (?).

Moderator’s PLN:
RSS (Google Reader)
iGoogle (center of diagram – can get all the others from iGoogle
Twitter (Tweetdeck)

Jo showed us how to use a private area in Elluminate
We each created our lists and then pasted them to main screen.  Mine were:
Twitter (just started)
Jing (screencasts)
School network
Master’s program at school I am attending
PD classes at school
Teach for America people and resources

Someone suggested Merlot as a PLN tool.  For higher education.

Group talked about using Facebook and cell phones to connect with students.  I informed them that Facebook was blocked at my school and cell phones were prohibited.  Most of the others were higher ed teachers where it is a very effective communication tool.  You would think that could possibly work at a high school level too!

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Math Sophistication Values

I saw the value and modeling values here:

And I saw studying relations here:

Did anyone else find these math sophistification values rather pretentious the way they were presented in the pdf?  Not that it wasn’t valuable or even accurate, but I definitely this it was very mathcentric.  Like all the smart and important mathematicians met in private to tell everyone else how important they were🙂

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Math Anxiety

Math anxiety is the fear that one won’t be able to do the math or the fear that it’s too hard or the fear of failure which often stems from having a lack of confidence. For the most part, math anxiety is the fear about doing the math right, our minds draw a blank and we think we’ll fail and of course the more frustrated and anxious our minds become, the greater the chance for drawing blanks. Added pressure of having time limits on math tests and exams also cause the levels of anxiety grow for many students (from

This same site also suggests the following to overcome this anxiety:

1. A positive attitude will help. However, positive attitudes come with quality teaching for understanding which often isn’t the case with many traditional approaches to teaching mathematics.

2. Ask questions, be determined to ‘understand the math’. Don’t settle for anything less during instruction. Ask for clear illustrations and or demonstrations or simulations.

3. Practice regularly, especially when you’re having difficulty.

4. When total understanding escapes you, hire a tutor or work with peers that understand the math. You can do the math, sometimes it just take a different approach for you to understand some of the concepts.

5. Don’t just read over your notes – do the math. Practice the math and make sure you can honestly state that you understand what you are doing.

6. Be persistent and don’t over emphasize the fact that we all make mistakes. Remember, some of the most powerful learning stems from making a mistake.

Using this info, I made the following suggestions at other blogs:

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The Good and the Bad

Although I whined a bit in the beginning, the use of technology is what I thought was the highlight of this course.  There are probably several factors to that:  IT is my background, I am teaching a technology course this year, and I finally learned something about all these technologies I heard about (e.g. Twitter, Wikis) but never used.  Seriously, it takes time to understand these technologies AND learn how to apply them in a teacher’s setting.  This course allowed that.  Plus, our teacher was a great role model in her use of the technology and in her understanding of math.

The opportunities:  I would have introduced some of the technology at a slower pace in the beginning and replaced it with more assessment content.  Also, for some of the weeks I would have appreciated more background on the content before commenting on others or creating a mini-task myself. 

Since I took another course in Arcadia on assessment, I personally did not mind this course being light on assessment content.  In fact, I would even go so far as to change the name of this course to “Using technology to become a more effective teacher” and having that be the focus.

One last serious comment:  I was in a few online forums with our professor.  I was impressed and envious of her knowledge of math.  I certainly have some math apprehension as a teacher and am working to lessen it by learning more about math.

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Expert Ways of Seeing Accessible to Novices

Dr. Bruce Kirchoff
Department of Biology
UNC Greensboro

Recording at

Let me start off by saying that I was not the best student during this session.  In fact, I fell asleep about 45 minutes in!  The stuff was extremely interesting, but I have to admit, a lot of it was over my head.  I think this is partly due to my immediate concern of getting lesson plans ready for my students next week and not having enough sleep.  Regardless, below are the notes I took.

Botany is Kirchoff’s specialty.
Cognitive difficulty:  recognizing something like flowers but not being able to explain it to others.
Concept:  something is easy to identify for someone who has the experience, but it is difficult for that person to train others to do this.
This is especially true if what you are trying to learn something with a lot of variation.  Still, repetition was the way to teach.

Can we do this in math?  For example, when you look at graphs, you might be able to quickly discern that a linear equation does not go with a parabola.  Is there a way to learn from this and maybe even make it quicker?

Peter Horn asked about more basic tasks.  Bruce said that he is proposing this as an addition.  He is saying this is complementary and additive.  Still need to do some basic education.

Two types of perception
Analytical: used by non-experts.  Dog owner can’t see a winner.  Students learning to identify plants.  Part based.  Is reportable.
Configural or Holistic: dog judge immediately sees winner.  Is configuration based.  Is not reportable.  Gestalt.  Used to perceive faces.  Easy to perceive a face, difficult to describe to someone else.

Different parts of brain are used for these two types of perception.  This is proof that there are two modes and that they are different.

Quick Reflection:  Amazed how a botanist is being holistic and looking at how these two types of cognitive perception could be helpful for math teachers.

Hung in for 40 minutes, but needed to leave.  Picked it up next day by reviewing the last section…

Showed Kolb’s experiential learning model.  Concrete experience to observation to hypothesis to testing back to experience.
Look at graph
Figure out graph
Hypothesis of graph
Type into computer and get feedback

Bruce suggests doing this repetitively and it is effective since it is using all parts of the brain.

Someone asked where is the creative aspect of this?  Bruce likened this to learning to walk.  Child gets up, falls down.  Repeatedly.  Its not flashy, but it is a significant learning (to walk).

Bruce views this as math skills training.  He believes that creativity could be included but hasn’t gotten that far.
Experts have the ability to see the whole AND the ability to break it down into its parts.  Novices can break up the parts but don’t have the experience or knowledge to fully process it.

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Analyzing Textbook Examples for Blooms

First, I used this site to help refresh my memory for math verbs in the context of Bloom’s Taxonomy:

Second, I used the attached example (page322.jpg) from the Algebra 1 textbook that was used in the School District of Philadelphia last year.  This is the last example in the graphing systems of equations section.  The solution is broken into the following steps, after which I have “labeled” using Blooms:

Organize:  Level 4 (Analysis)
Write:  Level 1 (Knowledge)
Solve: Level 3 (Application)
Graph:  Level 3 (Application)

Obviously, these tasks are not properly scaffolded according to Blooms.  In fact, as the solution is presented, the highest order of thinking is expected first!  Also, and perhaps more alarmingly,  there are no high-level tasks that are required.  The student is not asked to do any synthesis or evaluation in this problem.
Although I applaud this problems connection to a real-life situation, it could have gone a bit further.  For example, the student could have been asked to create a similar problem using sports.  Or, the student could have been asked to predict what might happen to the solution if the birds of prey are worth only 10 points each.

page 322

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Keith Devlin

The following is a comment I left at the Math Forum @ Drexel
My comment has not yet been “moderated” but here is the thread:

Although I am a very new teacher, I’m not sure I understand the controversy here.  I see two continuums here: one about process and one about content.  Devlin talks about traditional versus progressive ways to teach.  I think many math teachers would not argue with using a more traditional approach to introduce concepts and then move towards a progressive approach for the students to practice and learn the concept.  (Dy/Dan might be the exception, but one could argue that his students do need some underlying concepts to figure out the volume of water being filled.  Or, he is showing a teaser that then some concepts have to be taught in order to proceed).
The second continuum is around content.  Again, I don’t think there would be many math teachers who would argue against real-life application of the content.  And, as with most continuums, it can be somewhat problematic to be at either extreme.  Let’s let the teacher make that call depending on the lesson.  I would suggest that lower order tasks could be done with less real-life application whereas high level order of thinking would be better accomplished with real-life application.

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