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.

 

Social Media Experiment: Day 3 – Connections!

The tweet from @boadams1 while at the ropes course with our young learners connected to my learning and work in every hour of today.

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

THE most powerful learning for me today was the connections between Dr. Sousa’s research on the 20 minute learning episode (primacy-recency), formative assessment, and social media.  In the JH History PLT today, we paused the discussion about essential learnings for students studying the Civil War.  I asked these adult learners to summarize what they were learning.  @JenLalley called on one of the adult learners.  His reply was honest and direct.  “I’m not learning anything; I don’t teach this course.  I’m not actually paying attention.” 

I was THRILLED with his honesty, candor, trust, and assessment.  Isn’t it better to know  at the 20 minute mark than to get to the end of the class period and realize (or not) that a learner was left out?  @JenLalley used her solid facilitator skills to deflect attention from this adult learner to others to summarize our learning.  We tweeted.  Then the magic happened.  The team began to connect the essential learning work of the Civil War to essential learning work for World Cultures.  It engaged this left-out learner.  He enthusiastically participated in the work and conversation after the 25 minute mark.  His contribution was valuable.

Formative assessment at 20 minutes, at any time, informs all learners.  It allows us to make on-the-fly adjustments to accomodate and include all learners.  Notice that the team made the adjustment; the learners adjusted to have inclusion.  It was an unspoken community decision.  Powerful!

Today, day 3, we had 13 faculty members and 4 students directly tweeting at the 20 minute mark.  The tweets using #20minwms has an 11 hour span today.  Eleven hours of tweets on learning from our learners.  Eleven hours! 

Of course you can follow this work on Twitter, but again here are examples. This list is longer than normal because we can start to see connections between classes.  Connections made by teachers and by students.  I think it is so great and very interesting to see the summary of learning posted by the teacher and the student.  (Note:  I always use learner rather student but in this case, we are all learners.  I am using teacher and student to differentiate the age of the learners.)

Isn’t this great?  One of my young learners said in class today that Coach Jones was teaching them about spreadsheets in science today too.  Connection!  You can read my tweet above and @aatmuri1’s tweet.  @aatmuri1 does not sit with me to learn algebra but has Coach Jones.  This confirmed that my learners were accurate in their assessment of what they were learning and the connection between two of their classes.  Progress!

Look at the tweets from @epdobbs and @runningwitty about songs and poetry.  See @aatmuri1’s tweet today connected to @senor206’s tweets yesterday about reading in Spanish.  Nice!  @kplomgren, @TaraWestminster, and @boadams1 all gave perspectives about learning from the ropes course.  Our students, our young learners, can see our learning too.  Read @JenLalley and @jgough’s tweets about the History PLC. 

@abaconmoore is using formative assessment and self-assessment and is reporting results of learning.  @occam98 is on leave this week and is still participating.  This is his second day of tweeting with our virtual colleagues about our learning, formative assessment, and social media. 

@sgough asked today if his learners could directly tweet.  Could they tweet with him so that multiple voices and perpectives could be recorded?  Wow!  Yes, yes, yes!

The most powerful tweet, for me, of the day comes from @boadams1 while at the ropes course with our young learners.  If you didn’t know he was at the ropes course, you could assume that he was with us in the History PLT.  If you didn’t know he was at the ropes course, you could assume that he was with us in the Algebra I.  If you didn’t know he was at the ropes course, you could assume that he was with us in English. We are pulling together. 

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

Social Media Experiment: #20minwms Day 2

A quick report on our progress.  Today 12 faculty members and 3 students participated in our social media, learning and the brain, formative assessment project.  Actually 13 faculty members tweeted; we think that the missing tweets are from a faculty member with protected tweets; more problem solving tomorrow.  The BEST thing is that this faculty member wants her learners’ tweets to be “on the record.” 

The research from Dr. Sousa is being discussed with our learners, their parents, and our colleagues.  While you can follow us on Twitter, here are some samples:

High school students engaged with tweets from across our campus to learn what is happening at school.  Most are intrigued that their Junior High principal @boadams1 knows how to and actually tweets.   We know that he is practicing walk-through observations to better understand our learners (of any age). 

Two of our virtual colleagues are dreaming and envisioning this work and learning at their schools.  I’m close enough and want to drive over and talk to faculty and learners about the experiment for one.  If you decide to try this with your colleagues and learners, will you let us know your hashtag?  We want to watch our learning grow.   

Today we have a snapshot of what is happening in the high school and the junior high.  Our conversation today took a turn from “how do I do this on Twitter” to “I saw your tweet; I have a question.” “Your learners are using spreadsheets to connect to formulas; what was your approach?” We are not wondering what is being learned in our building; we are reading about it, asking questions, and learning.

Think of the possibilities for learning if we can make connections, if our learners make connections. 

It’s about learning for all!

Social Media Experiment: #20minwms Day 1

On Friday, January 7, 2011, my colleagues and I ran a practice round for an experiment that combines tweeting and social media with formative assessment and some of Dr. Souza’s brain research on primacy-recency.  I left school that afternoon with a strong sense of play-for-learning with my colleagues.  You can read about this practice round in the following blogs:

Experiments in Learning by Doing:  Social Media Experiment: Brain & Learning; Formative Assessment
It’s about Learning:  Achievement-Action: #20minwms
Quantum Progress:  20 minute pulse checks!  
¡Inglés fatal!:  The School as a PLC  

While we were all set to start on Monday, January 10, we were thwarted by Mother Nature.  Today, January 18, has been our next school day.  I was worried that we had lost our momentum.   In fact, I missed the 20 minute mark in my 8:00 class.  My learners thought it was hilarious!  (I did redeem myself during the rest of the day.)

More than 40 tweets from 11 faculty members went out over the course of the school day.  While you can follow us on Twitter, here are some samples:

¡Inglés fatal! posted My 20-minute learning which documents his students’ behavior as well as his learning.  He writes:

“My 20 minute learning for today: when the student has ownership of the activity, the impulse to abandon it is not nearly as strong as when they’re simply “carrying my luggage.”

Beautiful!

@boadams1 and I co-facilitate Synergy 8.  The Mobile Technology Team (aka the Synergy 8 cell phone team) has requested to participate along with the 5 HS, 12 JH, and 2 ES teachers in our Social Media, Formative Assessment, Learning and the Brain Experiment this week.  In order to make this easier for his classmates, one of the MTT team leaders setup a backchannel using TodaysMeet for students not on Twitter.

Four faculty members sought me out today to ask for a lesson on Twitter and tweeting.  This was no easy task because I spent the majority of my day off campus with my learners at Georgia Tech’s ropes course.  We are going to have a Q&A session or a mini-lesson for new tweeters Friday morning.

@sgough reported being taught his learners.  It started because he had the hashtag mixed up.  He used #20wmsmin instead of #20minwms.  “So then I had to learn how to delete.  They had me resend.”  Several of his students and former students are now following him.   

Are we learning together?  Are we integrating research about primacy-recency for our learners?  Is there potential for learning, discovery, and connections?

To follow ¡Inglés fatal!’s example: 

My 20 minute learning for today:  I have a lot to learn from all members of our community regardless of their age or level of formal education. 

The most profound comment of the day comes from my learners when emerging from the ropes.

“Take risks and trust your teammates. Reach out a hand to help. The first step is the scariest.”

 

 

Seeking brightspots and dollups of feedback about learning and growth.

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