Maybe we need to think of it as teachnology rather than technology.

The time with our learners is limited.  We have to make some very important decisions about how to use this time.  We must consider the economics of our decisions based on the resources we have.  Is it cost effective, cognitively, to spend multiple days on a learning target to master something that a machine will do for us?   

 Is what we label as problem-solving and critical thinking really problem-solving and critical thinking or is it just harder stuff to deal with?  Can we teach problem-solving and critical thinking in the absence of context?

Do we have a common understanding of what good problem solvers and critical thinkers look like, sound like, and think like?  If we are teaching problem-solving, critical thinking, and creativity, shouldn’t we know what that means to us?  Shouldn’t we be able to describe it?

Does technology hamper or enhance a learner’s ability to problem solve and think critically?  I think I might be back to the struggle of using calculators to compute and a spell checker to write.  Do we even know enough to make a decision about technology until we experiment and learn by doing? 

If you have not read Can Texting Help Teens with Writing and Spelling? by Bill Ferriter, stop reading this right now to read Bill’s post.  It is a great example of leveraging technology to promote creativity and critical thinking using technology.  Read about having students write 25 word stories.  This is teachnology, not technology.  Tweet, text, type, write on paper – it doesn’t matter – unless you want to publish your work.  The technology, Twitter in this case, aids in the critical thinking; you are restricted to 140 characters.  The technology offers the learner a way to publish and see other published work. 

My ability to transport myself from place to place is actually enhanced and improved because of my truck.  I have no idea how my truck works other than gas goes in, step on the brake to stop, R means we are going to go in reverse, etc.  I do not need to understand the mechanics; I can have that done.  

I do not need to understand the mechanics; I can have that done.   I don’t need to know how to change the oil in my car.  I need to know that I need to have the oil changed in my car.  And, very important, I don’t need to learn this lesson by experience.  It is too expensive to learn experientially why I must have the oil changed in my car.

Isn’t it too expensive to spend 2-3 days on some topics that we traditionally teach?  Are we getting the biggest bang for our cognitive buck?  Often our learners can’t see the forest for the trees.  They never get to the why because of the how.  Don’t we need to learn when and how to use technology not only to engage our learners, but to increase our cognitive capital?

How can we learn to ask

  • Why are we learning this?  Is this essential?
  • Will technology do this for us so that we can learn more, deeper?
  • Does this have endurance, leverage, and relevance?
  • Shouldn’t we use technology to grapple with the mechanics so the learner shifts focus to the application, the why, the meaning?

Social Media Experiment: Day 6 – Student Interest

I spent my day with the Faculty Cohort working on understanding more about learning and the brain.  Part of the work of this experiment was developed from one of the practitioners corners from How the Brain Learnings by Dr. David Sousa.

Today there were over 45 tweets from more than 15 faculty and 7 students.

My favorite series of tweets involve faculty and students. 

Series 1 is from 8th grade French:

#20minwms@boadams1@jgough could the pilot be extended to one grade for a day? teachers can try a more integrated classroom+#of students up @TaraWestminster.

#20minwms@professeurb2 said yesterday she wished students could use phones in class but mentioned that going to lckr for them is a drag? @TaraWestminster.

This is my favorite for two reasons.  @TaraWestminster is a learner involved in Synergy 8 that @boadams1 and I facilitated first semester.  While our course is over and @TaraWestminster is now taking Writing Workshop, she is still engaged and invested in the community problem-solving issue her team addressed first semester.  These two tweets were launched at approximately 7:00 am before school.  She is invested in larger data collection for her team and advocating for @professeurb2’s wishes.  Learning continues beyond the classroom and the calendar.

Series 2 is from Calculus Concepts:

#20minwms Mram and trap better, width not always same, generic trap formula @sgough

@swgough #20minwms trapezoids rule, lrams drool. maritzas back #chewonki? @chrisreagn

#20minwms @swgough how do indefinite integrals actually calculate area under a curve? @mcaeser

This this may look like a foreign language, I know that @sgough is teaching Riemann sums and trapezoidal approximations for finding area under a curve.  Today, he is beginning to connect this idea to integrals.  @chrisreagn acknowledges that the trapezoidal approximation is more accurate than the left rectangular sum approximation while mcaeser asks how these approximations connect to the indefinite integral.  @mcaeser is asking how the theory connects to the context.  Isn’t this what we want?  We want our learners to ask us to help them get to the next level.  Outstanding!  It appears that the intended curriculum is being learned. 

Series 3 is a connect between the Faculty Cohort and @abaconmoore.

#20minwms A Stroke of Insight Jill Bolte Taylor TED talk human brain function @jgough

#20minwms Cohort learning: interest in stroke recovery process. Did background knowledge help recovery? @jgough

#20minwms How can we help Ss find their nirvana? How can we help them find their we inside of them and choose? See A Stroke of Insight @jgough

#20minwms Can we teach Ss to drop fear to analyze the learning experience? How important is emotional support to recovery and success? @jgough

@jgough cohort talk on stroke sounds very cool. what kind of knowledge and recovery are you discussing? brain plasticity is amazing. @abaconmoore

@abaconmoore @jgough Role R & L Hemi. in Recovery of Function, Treat of Intention in Aphasia, ABM co-authored study, could she help cohort? @centerteach

@centerteach @jgough I would love to work with the cohort and talk about these brain-based issues. That stroke paper was a fun 1 2 write. @abaconmoore

This cohort of teachers got to experience how to connect their learning to the expertise and learning of another W faculty member.  They found a purpose of social medial for learning.

As always, you call follow our tweets on Twitter.  Here is a sample of todays learning.

Social Media Experiment: Day 5 – True Formative Assessment Begins!

Today’s update is all about formative assessment.  If you recall, when we started this experiment we wanted to integrate Dr. Sousa’s research about primacy-recency, formative assessment, and social media for learning.

Over the weekend @fnoschese tweeted:

We take this a positive formative assessment.  We have others, @Deacs84 and @mmhoward, tweeting encouragement and interest.  I don’t know @fnoschese other than he is a friend and colleague of @burkphysics1. We are learning together; playing together; communicating together.

From The Falconer: What we wish we had learned in schools, by our friend Grant Lichtman, we know that “Questions are waypoints on the path of wisdom.” (p. 35)

This week we hope to gain more information with our formative assessment.  We added a prompt to the quick write for our learners.  We now ask our learners to respond to

  • I have learned…
  • My question is…

My learners made me tweet twice at the 20 minute mark in Algebra I.  They were consistent as a whole group about what they learned, but their questions were split into to categories.

“We have learned to use spreadsheets and formulas for exponential growth. Our questions: Where does the exponent come from?”

“Learned to use spreadsheets and formulas for exponential growth. Our questions: Which is more efficient, spreadsheet or formula?”

I did not anticipate these questions.  Isn’t it great to know and answer our learners questions in real time rather than the next day or never?

Later in the day @epdobbs tweeted with her learners

“How do you find the mood more easily? What are subbordinating conjunctions? Are these all the uses of commas?”

 “I am going to answer these questions rather than move on, tomorrow. Yikes! My best laid plans aft gang aglay!”

In Inside the Black Box: Raising Standards Through Classroom Assessment Black and Wiliam say

For assessment to function formatively, the results have to be used to adjust teaching and learning; thus a significant aspect of any program will be the ways in which teachers make these adjustments.”

True formative assessment informs and causes shifts in planning, teaching, learning, and experiences.  I immediately answered all of my learners questions; I had their undivided attention, and they asked more questions.  @epdobbs had the same experience in English as I had in algebra.  We cannot move on if they have questions, if they have not learned.  Progress!

Learners working with @sgough are now tweeting with him.   How great for a teacher to read during the learning experience a tweet like the ones from @chrisreagan and @andrewwebb

“quick poll works! mass confusion ends with 100% accuracy” @chrisreagan

“everyone in the class might finally understand what a function is” @andrewwebb25

How great for our learners to read that their teacher sees their improvement.

“still trouble with tns file, better at diff ram methods, function notation improved”  @swgough

You can also read about the 4th Period PLC’s learning about social media in the series of tweets below.  As we learn together, we become more confident using the technology, implementing the primacy-recency practitioner’s corner, and trying a different type of formative assessment.

Today, there were over 80 tweets from 19 faculty members and 7 students that we know of.  Some of our students have protected their tweets and two of our colleagues are still struggling to have their tweets appear when we search on our hashtag.

About my goals for the week:

  • Our numbers are increasing so I can check that goal off my list.
  • @joeschmo81 has tweeted twice now, one more either @bcgymdad and @DownSouth300.  I have high hopes for more, but I’m not checking it as a success… yet.
  • Formative assessment of learning in a non-graded setting will impact classroom activities, planning, communication, confidence, and learning.  @epdobbs and I have crossed this mark.  Have others? Will others soon?
  • We want to have more tweets from our current team as well as tweets from others. I think we are making progress here too, but I’m greedy.  I want more.
  • There will be more pictures and less “eggs” (the default Twitter gravatar). There are more pictures and more eggs.  More new users are arriving; we’ve got to get rid of all those eggs!
  • More of our tweeters will understand the language of twitter. We are having a mini-lesson tomorrow before school on how and when to use @, #, RT, and HT.

It’s only Monday.  I thought my goals for this week were lofty.  I think my success now hangs on how many more of my colleagues will actually read the chapter on primacy-recency.  We’ll see…

As always, you can follow our work on Twitter.  Here is a sample of the tweets from today.


Is Efficiency Without Understanding Efficient?

Time and meaning.

How often do we hear the following? “I don’t have time to _____.”  “I can’t take the time to _____.” “If I do this, I won’t have time to _____.”  “I can’t believe they don’t understand _____.”  “It’s like they’ve never seen or heard _____.”

Time and meaning?

Time and meaning.  How often do we hear the following? “I don’t have time to spend 3 days on this section.”  “I can’t take the time to do a project.” “If I do this, I won’t have time to teach them everything they have to learn.”  “I can’t believe they don’t understand _____.”  “It’s like they’ve never seen or heard _____.”

Time and meaning…

How often do we hear the following? “I don’t have time to spend 3 days on exponential growth (slope, poetry, reconstruction).”  “I can’t take the time to do a project.” “If I do this, I won’t have time to teach them everything they have to learn.”  “I can’t believe they don’t understand exponential growth (slope, poetry, reconstruction).”  “It’s like they’ve never seen or heard of exponential growth (slope, poetry, reconstruction).”

Time and meaning!!!

We want our learners to be efficient.  We teach shortcuts, right?  I’ve been wondering about shortcuts for a while.  Is it a shortcut if I don’t know the long way?  We teach King Henry Died Monday Drinking Chocolate Milk to help learners become efficient about the order of prefixes in the metric system.  We teach Please Excuse My Dear Aunt Sally to help learners remember the order of operations.

Now, don’t get me wrong.  I LOVE mnemonic devices!  In How the Brain Learns Mathematics, How the Gifted Brain Learns, and How the Special-Needs brain learns Dr. Sousa gives evidence that process mnemonic devices are powerful for learners, particularly those with dyscalculia.

“Process mnemonics are so effective with students who have trouble with mathematics difficulties because they are powerful memory devices that actively engage the brain in processes fundamental to learning and memory.  They incorporate meaning through metaphors that are relevant to today’s students, they are attention-getting and motivating, and they use visualization techniques that help student link concrete associations with abstract symbols.”
How the Brain Learns Mathematics, David Sousa

How am I, how are we, helping students link concrete associations with abstract symbols?

Our current learning target in Algebra I involves exponential functions – exponential growth and decay.  We can just teach them the formula, but are we really teaching them if we do that?  Haven’t they been given the formula before?  How do we link concrete meaning to the abstract symbols in the formula?

My teammate, @bcgymdad, taught me how to do this a couple of years ago.  It takes more time to teach it – several days.  I’d like to describe it to you; you can decide about time and meaning and efficiency.  I’d LOVE to know what you think! Oh, and sorry for the pseudo-context. We had a sense of play; we had fun, and we learned. 

Question 1:

I need to hire two of you. You can pick up some quick spending money.  Volunteers?  Great!  The job is to clean windows for 20 days.  DG, I want to hire you and I’ll pay you $40 per day; does that sound fair? <Yes, ma’am>  GW, I also want to hire you, but your payment plan is different, okay?  I will pay you $0.01 today, tomorrow $0.02, $0.04 the next day, and so on. Not a new problem to me, but apparently a new problem for the learners.  I took a quick poll of the class.  Whose payment plan would be best for your if you intend to complete all 20 days?  The vote was great; it split right down the middle.

Big questions:  If both workers complete the 20 days, how much will they each be paid?  Instantly, everyone knew DG would be paid $800.  <Yeah, baby!>  How much would GW be paid?  They just sat there.  Really!  Waiting for me to tell them; they are so conditioned that even after 4+ months with me, they waited.  I had to say “Don’t you have a calculator? Figure it out?”  Then my favorite question “is it okay if we work together?”  AHHRRRGGGG!!!!!!!  Are you kidding me?  YES!

Not one learner, not one, thought to use a spreadsheet.  Never occurred to them; they didn’t know how.  We stopped; we took the time to learn. 

Stage 1:  Simple spreadsheet formulas – make the spreadsheet work and why to use a spreadsheet.


 DG is feeling “ripped-off”.  So let’s change his daily rate to $100.  BOOM! The power of spreadsheets.


The question…will the time taken to do this work numerically connect meaning to the abstract symbols?  The first meaningful connection popped up immediately.  Again the question…How much was GW paid for her 20 days of window washing? 

My learners who speak before they think belted out “$5242.88!”  KC, profoundly quiet reserved KC, said loudly with a great frustrated voice: “No she did not!  That’s how much she was paid on day 20!”  Meaning!  This led them to ask me how to find the total.  I love it, love, love, love it when they ask me to teach them something. 


We graphed the data.  Look how much can be learned graphically. Now we can visualize the difference in constant rate and exponential rate.  Then we wrote equations.  It made sense to them that the equation for GW was y = 0.01(2)^x.  Interestingly, they had a little trouble getting to DG’s equation y = 40.  Sigh…so much work to do to connect ideas.   


While my learners could not solve for the day DG and GW would be paid the same wage algebraically, they can all tell me when looking at the graph.  Are we letting the analytic algebra, the efficient way, hamper learning and understanding?

Question 2:

ES has $1500 and invests it at 8.5% interest compounded yearly.  In 10 years, he will be 24 and, hopefully, graduating with his masters degree. How much money will he have at the end of 10 years if he just makes this initial deposit?

Can you apply what we just did with spreadsheets to answer this question? Oh, if you know the formula, just use it.  It is more efficient.  Does anyone know the formula?  Nope.  They know there is a formula, but they don’t know it.  And that is OK. 

Without direct instruction from the adult in the room, one learner realized that you had to have a year zero.  This rumor then spread throughout the community very quickly.  Oh sure, there were questions about getting the spreadsheet to work, but they were confident about their math/arithmetic.  Well, oops, some had to remember that 8.5% is not 8.5; it is 0.085.  But they learned it experientially and from each other; they were not told.  They learned from the data; it did not make sense. 


Again, the power of the spreadsheet.  8.5% is not at all realistic for 2011.  What happens if we change the interest rate to 1.5%? 


How long will it take ES’s money to double?  The spreadsheet is not efficient.  Using a graph is much more efficient.  This is why we need to understand the formula, but not before we understand the problem.


Do you think the spreadsheet work will help learners understand?  Does taking the time to work with the numbers help students understand the problem?  Will it help students interpret the graph?

Time and meaning…If we take the time to teach multiple representations of the same idea will we increase the opportunities for students to find meaning and understanding?

February is Black History Month. A request…

I aspire to be interdisciplinary, relevant, and informed.  Will you help me learn? 

February is Black History Month.  I coach young learners through algebra.  I facilitate experiences for adult learners engaged in conversations concerning pedagogy and technology. 

During the Age Estimation lesson on Super Saturday, an idea popped into my head and out of my mouth.  February is Black History Month.  The age estimation activity is a great engaging math lesson for statistics and numeracy.  Could we combine the two?  Could we compile photos and birthdates of famous living people that our students should know? I suppose I’m trying for current events rather than history. 

I mentioned this twist to the age estimation lesson as a possibility with the dedicated Super Saturday teachers and they agreed.  That was going to be it for me.  I dropped a seed; would it grow?  Well, yes…I want to “grow” it.  I woke up this morning wondering how I could at least get this lesson started for my learners, my 13-14 year-olds and the adult learners I worked with on Super Saturday.

How many of our learners have heard Nelson Mandela speakMaya Angelou?

In 1998 I had the privilege of hearing an astrophysicist speak on why Pluto should not be a planet at the PAESMT dinner.  He said that there were only 3000 astrophysicists and he was the only black astrophysicist at that time.  He challenged us to consider the probability of being in the room with him that night.  In an interesting turn of events, the next morning I flew from Washington D.C. to Minneapolis in the seat next to his on our Delta flight.  As we deplaned, I turned and asked him what he thought the probability was of my having dinner with him the night before and being assigned the seat next to him this morning.  Cool, huh?  Yes, but I don’t remember his name. 

I want my students to know more than I know.

So here’s where you can help.  

  • Will you help us find the name, birth date, and link to a photo of a living person to be celebrated during Black History month. 
  • To enhance the lesson, we could also benefit from a link to a biography and/or a video. 
  • The math part of the lesson works best for algebra if there is a wide age range.

If you are willing to help, will you please contribute to the shared Black History Month Age Estimation Google Spreadsheet?  If you contribute, would you leave contact information, either your Twitter handle or an email address?

I should say that while we welcome sports figures, musicians, and actors, I am hoping for other contributions too.  For example, I selected John Hope Bryant.

I will organize the images and birth dates on a Google presentation or PowerPoint presentation and share.  My thought is that as we facilitate the age estimation lesson we could have our learners journal anything they know about these people.  Then every day we could take a few minutes in class to show part of a video or a biography.   

Do you think we could find other teachers of our learners that might extend this activity into their lessons?  What could our colleagues teaching our learners English, history, science do with this lesson or a modification of this lesson?

Will the power of sharing information through social media enhance and improve learning for all?

Super Saturday for Atlanta Public Schools – TI-Nspire Learning

I spent today, Saturday, January 22, 2011 learning with 25 teachers from the Atlanta Public Schools.  Today was Super Saturday. 

From the flyer:

Atlanta Public Schools
High School Mathematics and Professional Learning
Super Saturday

High School Mathematics teachers are invited to attend an Inspire graphing calculator training delivered by Texas Instrument trainers. This session will include ‘just in time’ useful activities to be used within the classroom utilizing these calculators. Each teacher will receive a class set of TI-Nspire calculators to use within their school. Calculators will remain property of Atlanta Public Schools.

Mathematics teachers interested in attending can register for the Super Saturday- Learning Experience Academy. Interested teachers should complete online registration by Friday, January 7, 2011.

So, there are a couple of really important things you should know.  There were 25 seats in the workshop.  Within 48 hours of the flyer being released the session was full and had a waiting list of 22 teachers.  These dedicated teachers were not paid a stipend.  They volunteered to come to learn to use this technology.  They gave their time and energy on a Saturday to acquire technology for their learners, the children in their charge.  They sacrificed their family and free time to provide new and different learning experiences for their young learners.

It was awesome!  I do not usually enjoy one-day workshops; there is not enough time to build community and to get to know each other.  I will repeat; it was awesome!  They were a warm group.  They wanted collaborative learning.  They wanted to experiment and investigate instead of being directed.  They wanted to think and process. 

Usually I have to fight off comments and questions like “do you have this written down, step-by-step?”  No one – repeat – No one asked me that question on Super Saturday.  It was a first for me, and I’ve been facilitating workshops on handheld technology since 1990.  Wow!

We worked together to learn.  We discussed technology to support learning, formative assessment, Bloom’s Taxonomy, the language of mathematics, lessons with endurance and leverage, differentiation, and many other best practices.  The agenda below looks simple.  The learning was complex.  Pedagogy, assessment, math knowledge, and technology skills were weaved together to form the tapestry of our common experience.

Our Basic Agenda

Since we are into multiple representations, I also submit our agenda in images from the TI-Nspire.

  • Basic calculator work


  • Tangent to a Curve



  • Circles, analytically and geometrically

Dedicated teachers volunteering their time to learn, to acquire technology, to improve learning experiences for children…Now that is a news story!

It was a Super Saturday.

Social Media Experiment: Day 4 – Integrating Ideas!

“Was initially worried about #20minwms impact on class time/flow, but it has been a big hit.  Love it! Not disruptive at all.” ~ @valerieste

How great is that?  @valerieste’s tweet summarizes the initial teacher concern and hesitation.  Her tweet challenges us to try, to experiment rather than assume.   

The two tweets above are from our young learners.  In addition to working on retention (primacy-recency) we were hoping that we would find connections between our courses.  Our young learners are noticing.  Are we? It is worth repeating.

“Science and math are really related;  curriculum bleed into each other” ~ @TaraWestminster 

“I noticed that too, starting to see how twitter can be used as a tool, collaboration.” ~ @fencersz

As always, you can follow the conversation on Twitter using our hashtag, but here is a sample of what we are learning. 

Imagine starting your school day as a 14-year-old to see a tweet from your principal that many of your classmates and teachers can read that says

“You are doing a great job contributing to #20minwms.  Keep up the effort!”

Bravo to our principal, @boadams1.  Bravo and brava to the faculty members participating in this experiment.  Model learning for all! 

Today, Friday, January 21, there were more than 53 tweets by at least 14 faculty and 5 students where 4 are from our junior high and one is from the high school. @swgough wants his high school learners to directly participate so that he can have documentation of the formative assessment to reflect on as he plans for the next lesson.   

Our friend and colleague, @Deacs84, took the time to tweet from across the creek.  It means a lot to many of our tweeters that she is watching, reading, and encouraging from afar.

We are experiencing a few problems and struggles.  If you have problem-solving ideas, we would love to hear them.

  • Yesterday, we did not get any results when we searched on our #20minwms hashtag.  This is problematic if you are looking for connections between classrooms, teachers, and learners.  After several hours of communication with our fabulous IT department, we learned that ads were the cause of the problem.  We have resolved this internally with great support from our IT guys.  (Thanks, again.)
  • When we search on the #20minwms hashtag, some tweets with this hashtag do not appear.  It seems to skip a tweet or two from time to time.  This is very frustrating to the tweeter and to the data collector. 
  • One adult-learner’s tweets using #20minwms have never appeared during the search.  We have already changed her tweets from protected to not protected.  We can see her tweets in our timeline, but they don’t appear when we search.  It is frustrating.  She wonders what she is doing wrong when she isn’t doing anything wrong.  It is maddening.

This past week we have been tweeting responses to the question “What have you learned?” or the prompt “I have learned…”  Next week those continuing to participate will be asked to tweet answer to “My question is …” or “I still need…”

We have had more faculty discussing Dr. Sousa’s research about retention and primacy-recency.  A few more have read the research.  My goals for this week:

  • Our #20minwms team will grow in number, in confidence, and in learning. 
  • There will be more pictures and less “eggs” (the default Twitter gravatar).
  • More of our tweeters will understand the language of twitter. 
    • Specifically, more understanding of @, #, RT, HT as well as when/why to use them.
  • More of our colleagues will read the article from Dr. Sousa to be more informed about why we are trying this experiment. 
  • Formative assessment of learning in a non-graded setting will impact classroom activities, planning, communication, confidence, and learning.
  • We want to have more tweets from our current team as well as tweets from others.
  • I want @bcgymdad and @joeschmo81 to tweet or to know that @DownSouth300 is ahead of them.  (Yes, according to the data collection, @DownSouth300 is much more “with it” than these two!)

Remember @boadams1’s tweet from the ropes course on Thursday:

When we don’t pull TOGETHER as a team, we can get stuck. In sync, we can move forward.


Seeking brightspots and dollups of feedback about learning and growth.

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