Category Archives: Time

Time, accuracy, speed, & precision (TBT Remix)

It is critical that we take a moment to review the emerging evidence on the impact of timed testing and the ways in which it transforms children’s brains, leading to an inevitable path of math anxiety and low math achievement. (Boaler, Jo)

Her name was Mrs. Hughes.  I can still hear her:

F … F … J … J … F … F … J … J.

Time, accuracy, speed, and precision were ultimately important in the typing class I took my sophomore year of high school.  I am glad that I touch-type.  At typingtest.com, you can assess your typing speed and accuracy.  Here are my latest results:

Screen Shot 2014-12-06 at 11.31.17 AM

And, later in the day…

Screen Shot 2014-12-06 at 6.02.14 PM

There are plenty of people that do not touch type, some hunt-and-peck.  Is their work some how diminished because they may need more time than a touch typist?  If not witnessing the time and effort, would the reader of the product even know whether the author was speedy or not?

Are accuracy and precision when typing more important than speed and time?  Wouldn’t it be better to take more time and have an accurate product than to be quick with errors?

This has me thinking about assessment, testing, and time.  In a perfect world, we want both speed and accuracy.  What if we can’t have both?  What if a learner needs more time to demonstrate what they know?  Do we really expect all children to perform and produce at the same speed?  Are we sacrificing accuracy and precision for the sake of time?  Should it be the other way around? Are we assessing what our learners know and can show or how fast they can think and work?

How important is it to complete an assessment
within a fixed, pre-determined period of time?

How might we offer learners more time to demonstrate what they know and have learned?

Time is the variable; learning is the constant.


Time, accuracy, speed, & precision was first posted on April 30, 2012

Boaler, Jo. “Timed Tests and the Development of Math Anxiety.” Web log post. Jo Boaler. N.p., 06 July 2012. Web. 09 Nov. 2014.

 

Data collection from TSA…Can we transfer to school?

Here’s the final product right before the TSA representative collected it from me:

photo 3

So, there is an error. Could I use this picture to offer our learners an opportunity for error analysis? Could this picture be used to discuss communication and correct notation?

Screen Shot 2013-10-08 at 6.32.23 PM

Here’s what happened.  I arrived at the airport in Seattle for a 1:15 flight to Atlanta. Upon arriving at the security checkpoint, a TSA representative handed me a slip of paper (shown below) and asked me to hand it to the ticket checker.

photo 1

Fun! How might we use this type of data collection at school?

Screen Shot 2013-10-08 at 6.37.49 PM

What if we used this method to collect data about carpool? Having the time I arrived at security told me how long I had been standing in line.  I wonder if, when in a hurry, it feels like it takes longer to get through than it really takes.

The TSA agent checked my ID; I scanned my e-boarding pass, and she recorded the time.  Another opportunity for math.  How long did this portion of the process take?

photo 2

Only five minutes passed. A basic, everyday math problem. How often do we subtract times? How authentic are the questions on our assessments? Do they have context? Is this a (dreaded) word problem?

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There’s one more stop before passing through security.  My line – I always pick the slow one – stalled as the TSA representatives changed shifts.  Again, I wondered if this felt longer than it really was taking.  Holding the slip of paper allowed me to say to the nice but fidgety man in line ahead of me that we’d only been in line twelve minutes at this point.  He said “Twelve minutes; that’s not so bad.” Ahh…to have data.

I arrived at the security checkpoint, unloaded my MacBook, put my shoes and bags on the belt, and passed through the detector.  I handed over the slip and then asked if I could take one more picture.

photo 3

What was the total time I spent in line? How do we explain the error in the data collection? Could this type of data collection help us in our school community? Could our young learners use this type of data collection to find context and meaning for their learning?  Would we make different decision if we collected data and made data-driven decisions?

How might we show math in action?

In an “I can …” culture: Embracing “What if” and “Yet

My previous post, Spreading an “I can …” culture: Aware, Enable, Empower, has generated genuinely great questions.

  • What if they can’t, Jill? Really, what if they can’t say “I can…” at the end of the unit?
  • Math is so easy, Jill.  Can we do write “I can…” statement for other subjects, courses, or ideas?

Erin Paynter, @erinpaynter, published How Do You Help Student Reach Their Yet?  Can it be as simple as adding the word yet?  What if we repeat the questions with yet?

What if they can’t yet?  Really, what if they say “I can’t yet…” at the end of the unit?

From Erin Paynter:

“I find this one word to be a powerful tool to open a dialogue and to pause for reflection – on best instructional practices, on motivation, on student and parent engagement, and on teacher professional development plans.  It begins to wipe the slate clean so that we can work collaboratively on ways to engage our students in their learning by using more effective tools and strategies. It opens the dialogue to why and how – why aren’t they reaching their goals, and how can we get them there?”

Isn’t the answer now obvious?  We try again.  We collaborate to investigate other techniques, strategies, and opportunities.  We take action.  We send the message that “you can…” and we are going to work on it together until you can.  Learning is the constant; time is a variable.

Peyton Williams, @epdwilliams, answered the second question.  On her blog, Superfluous Thoughts, she published the essential learning “I can…” statements in her 5 Week Update for 8th Grade English post and in her 5 week update for Writing Workshop Enviro Writing post.

From Peyten Williams in an open letter to parents and students explaining her grading policy:

1) Letting a kid fail is not in my job description. I am supposed to teach, not judge. If it takes Johnny 17 times to understand where to put a comma between independent clauses, then so be it. I want him to learn commas, not learn that he can’t do them.

“I can…” instead of “I can’t…”  is teaching for learning.

I plan to use both sets of Peyten’s “I can…” statements to self-assess my writing and thinking.  I am thrilled to see that this “I can…” contagion can be both scalable and transferable.

Peyten’s posts also cause me to wonder what my “I can…” statements are for this semester.  By the end of this semester, I should be able to say “I can…” to the following.

  • I can embrace learning personally and professionally.
    • I can model that learning is process-oriented and ongoing.
    • I can use personal reflection to learn, grow, and challenge myself.
    • I can share my learning with others to garner feedback and to connect ideas.
  • I can use formative assessment to inform next steps in the learning process.
    • I can identify and acknowledge strengths, persistence, and challenges.
    • I can facilitate personalized goal setting and growth.
    • I can differentiate learning experiences based on the needs of each learner.

What if I share these “I can…” statements with my team?  How will they morph and improve? If “I can’t…” creeps into the thinking, will “yet” follow?

Time, accuracy, speed, & precision

Her name was Mrs. Hughes.  I can still hear her:

F … F … J … J … F … F … J … J.

Time, accuracy, speed, and precision were ultimately important in the typing class I took my sophomore year of high school.  I am glad that I touch type.  At typingtest.com, you can assess your typing speed and accuracy.  Here are my latest results:

There are plenty of people that do not touch type, some hunt-and-peck.  Is their work some how diminished because they may need more time than a touch typist?  If not witnessing the time and effort, would the reader of the product even know whether the author was speedy or not?

Are accuracy and precision when typing more important than speed and time?  Wouldn’t it be better to take more time and have an accurate product than to be quick with errors?

This has me thinking about assessment, testing, and time.  In a perfect world, we want both speed and accuracy.  What if we can’t have both?  What if a learner needs more time to demonstrate what they know?  Do we really expect all children to perform and produce at the same speed?  Are we sacrificing accuracy and precision for the sake of time?  Should it be the other way around? Are we assessing what our learners know and can show or how fast they can think and work?

How important is it to complete an assessment
within a fixed, pre-determined period of time?

How might we offer learners more time to demonstrate what they know and have learned?

Time is the variable; learning is the constant.

Right?

Wait, Listen, and Learn – edu180atl: jill gough 9.9.11

We all strive to seize the teachable moment.  How often are we successful?  Today, armed with day two of my lesson plan, I had a choice to continue with the plan or move out of the way to allow student-driven learning.  We started class by picking up where we left off from the previous lesson.  The first question launched was a high-order question.  This question sparked more questions and some rich thinking out loud.  I finally physically moved to the seat of a learner and joined the conversation as a co-learner.  At four separate moments in class, a learner turned to me and apologized for high-jacking “my lesson plan.”  The planned lesson did not occur; it could wait.  The lessons learned and the questions asked were richer in content and context.

Isn’t it interesting that the learners worried about my plan?  How conditioned are we?  How can we unlearn and relearn so that we listen carefully to questions?  How do we become a team of learners where the “teaching” responsibilities change quickly as the questions themselves?  How empowered to our learners feel to lead learning in a new or different direction?

What did I learn today?  Sometimes I should wait, listen, and learn.  I should facilitate learning by following their questions.

About the author: Jill Gough is a learner, challenged to teach and learn in our changing world. She risks, questions and seeks feedback to improve. You can follow her on Twitter at @jgough.

Image by Jill Gough.

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[This post was originally published as “edu180atl: jill gough 9.9.11.”]

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?

Is time a variable? Is learning a constant?

I think that I need some counseling – a reality check, if you will – about the meaning of: 

Time is the variable and learning is the constant. 

Is it true all of the time, some of the time, regularly with some exceptions, or only applicable to small children learning to walk and talk?

There are deadlines – we have an exam coming up that signifies the end of first semester.  So let’s take the idea of unlimited time off the table.  What, then, does “Time is the variable and learning is the constant” look like in practice, realistic on-the-ground, in-the-trenches, day-to-day practice?

A child performs poorly on a relatively high-stakes assessment; an assessment that carries a grade that some use to “define” this child.  Do we offer this child a mulligan?  Do we offer every child the same opportunity for said mulligan?  Do we require the “do-over” of this child?  Do we require the “do-over” of every child?

Let’s break these questions down with some details and more questions.  If we embrace “Time is the variable and learning is the constant”, then YES to the 2nd chance… or…are there more questions to be asked?

  • AG was sick the entire week prior to the assessment…mulligan?
  • DP is so nice, sweet and tries so hard…mulligan?
  • SM was irresponsible having no homework showing no effort…mulligan?
  • JH is disrespectful and disagreeable…mulligan?
  • RT is misplaced in this course (shh, she just can’t cut it here)…mulligan?  

If yes is the answer to any (or all) of the above, is the do-over optional or required?

What about an assessment?  Is time a variable?  Should AG, DD, SM, JH, and RT be able to (have to) express their learning, understanding, and growth in the same 55 minute time frame? 

  • AG is a visual leaner; she needs to draw and outline her thinking before documenting it formally.
  • DP is a memorizer; as long as there are no curve-balls on the assessment, she is great.
  • SM is unprepared but SMART; he can pull the information back, but it is slow going due to lack of practice.
  • JH checks his work on every question; he is determined not to make a mistake.
  • RT is carrying a heavy personal load at home and can’t concentrate; everything is a struggle.

Do we provide these students additional time to show and document their current level of ability, work, and understanding, or at the end of the period, is time up?  Does it matter which child you are? Does knowing more about why the additional time is needed change your feelings about providing additional time?  (What if you can’t know every child’s story?)

The two latest arguments being discussed within my team are that we were not preparing our students to take the SAT if we give them additional time and that something is wrong if you can’t do the work in the given time-frame.  I don’t wake up every morning planning to improve the future SAT scores of my 8th grade students; should I?  How will I know what is wrong if I can’t see this child’s work?  How will this child know what is wrong if they are not given the opportunity to “fall down”? What am I unintentionally teaching by providing or denying additional time?