Tag Archives: TI-Nspire Navigator

LEARNing: Linear Functions Investigation – #AskDon’tTell

I used to think I needed to carefully scaffold each algebra learning experience into a series of steps so that each learner would learn.  Now I think I should listen more and talk less.  What if I practiced inquiry and student-directed learning? What if I lead by following the learners questions? How might I set up opportunities for learners to explore and think PRIOR to my show-and-tell show?

What if I gave my learners the following TI-Nspire document and asked them to explore it for 10 minutes? What if I asked them to jot down observations, patterns, and questions  that come to them as they play with this document? What would they learn? What would they ask me? What should I be prepared to ask instead of answering their questions? Can I spend an entire learning episode answering questions with questions to facilitate student learning?

Want to explore the investigation? Here’s how:

  • Clicking on the screenshot should enable you to download the TI-Nspire document and open it if you have the TI-Nspire software on your computer.
  • Clicking on the Launch Player button should open a player file where you can interact with the document without having TI-Nspire software. (Be patient; it is a little slow to launch.)

I would love to hear your thoughts and feedback.  Also, what questions would you ask, and what questions do you hope your learners ask?


Improving Confidence, Skills, and Implementation

On Monday, July 17, Westminster again hosted 100 math and science teachers teachers for summer institutes to learn to use the TI-Nspire to integrate technology into classroom learning episodes.  This summer, the following sessions were offered:

I facilitated the Getting Started with the TI-Nspire in Algebra.  This session included several teacher-learners who wanted to take Getting Started with the Middle Grades Math (but the course did not make).  I had the opportunity to practice my skills in differentiating to accommodate all sixteen learners.

We started with a quick write using the following prompts: Why are you here, and what do you want to learn?  Overwhelmingly, these sixteen teachers wrote and spoke about relationships and improving their ability to engage their students in the learning process.  “I want to feel more confident about using this technology to teach my students.” They discussed feeling overwhelmed by the technology and implementing lessons with students.

How often do students feel exactly the same way?  Aren’t students looking for a teacher who knows their strengths and struggles?  How often do students feel overwhelmed by the content and implementing new skills and idea?

The curriculum – a binder of materials and activities – had approximately 10 activities per day. So the question…Go deep into some of the lessons or cover all 10 activities each day.  I chose to be selective about the number of activities and spend time asking questions to deepening knowledge, skills, and understanding.

As the teacher, I feel guilty about what I did not cover from the materials.  What if they need something that I did not teach them?

Isn’t this the same decision classroom teachers have to make every year, every week, every day?  Should we cover all of the learning targets or identify what is essential and teach for mastery? Are we seeking to expose our students to many topics, or are we striving to help them learn and retain core material?

The time we have with learners is limited.  We have to make some very important decisions about how to use this time.

A Picture is Worth 1000 Words…

Can we use a photo to inspire learning and interdisciplinary studies? What if we start with photographs from our campus? Can we collaboratively design a lesson or series of lessons around something on our campus to implement together? How can we easily have learners contribute digital photos, ideas, and creativity? Can we will brainstorm and prototype together with photos to develop place-based learning lessons?

Lisa Nielson details how to share photos using Flickr in her post Using Flickr to Collect Images Captured on Cell Phones.  Using her advice, it is easy to set up a Flickr space for participants to share photos via email.

Bo and I use a Posterous space with our Synergy team to collect their observations and photographs.  We like Posterous because it offers our learners the opportunity to contribute images and video along with their questions about community issues.  Richard Byrne’s Try Posterous Spaces for Private Classroom Blogging will help you get started with Posterous if you are interested in collecting observations and questions along with images from your learners.

In our T³ International conference session today we started off with two photos from my campus. Details for these two photos can be found on Handicap Ramps: Connecting Ideas and Experiences to PBL – apply what you’ve learn and Connections: Questions, Photographs, Algebra Graphs, Perspectives, Environment.


Session Details:
Saturday, March 3, 11:15-12:45
90-Minute Hands-On • TI-Nspire™ CX Handheld, TI-Nspire™ CX CAS Handheld, TI-Nspire™ CX Navigator™ System

The Art of Questioning

“Questions are the way points on the path of wisdom.” ~ Grant Lichtman

Work on becoming a falconer…lead your learners through the art of questioning.

In his 2012 T³ International Conference keynote address, Dr. David Sousa challenged us to put the question first in problem-solving.  The brain will filter information and pick up what it needs if the question is known first.

“The real revolution in education and training, if it comes, will be overtly our priority from the skills of giving answers to the skills of finding new questions.” ~ Grant Lichtman

Technology offers our learners so many opportunities to tell us what they know and want to know.  The question really is

Can we break the habit of teaching
by the show-and-tell method? 

What if we guide learning through questions?  How will we practice?  What if we hear our learners questions and respond in the moment?  What if we facilitate discussions that prompt consensus building and collaboration?

Can we lead by following?  What can be learned if we listen to and question our learners?  How can we leverage technology to give every child a voice in class?  What do we do to make it safe for our learners to step up to the plate and ask their questions?  We want them think “swing even if you miss.”

The human brain is far too complex an organ to determine that x can’t be taught. ~ Frank Pajares during a discussion in EDS 771


The Falconer: What We Wish We Had Learned in School
by Grant Lichtman (May 24, 2010)

The Art of Questioning
60-Minute Hands-On
 Family of Handhelds, TI-Nspire™ CX Navigator™ System

Jill Gough, The Westminster Schools, Atlanta, GA, USA
Co-Presenter(s): Sam Gough

Stop, Collaborate, and Listen: inspiring non-graded formative assessment

On Monday, December 5, Jeff McCalla (St. Mary’s Episcopal School, Memphis, TN) and I co-facilitated a 2-hour session at Learning Forward.  The conference description said:

Learn to model practical classroom formative assessments. Hear stories and gain artifacts from National T3 instructors as they share their struggles and successes as well as the struggles and successes of their students in middle school and high school math. Develop processes and tools for creating formative assessments that integrate technology to motivate student collaboration.

While we planned our lesson, we also committed to modeling the techniques that we were promoting.  Our handout shows a linear path that we intended to take.

We started with a basic review of the traditional 4-point rubric.

Level 1 – Beginning
Level 2 – Progressing
Level 3 – Proficient
Level 4 – Exceptional

What do these descriptors “tell” a learner about their understanding?  Do these descriptors help a learner know where they are and how to get to the target level? So we reframed these ideas in different terms.

Level 1:  I’m getting my feet wet.
Level 2:  I’m comfortable with support.
Level 3:  I’m confident with the process.
Level 4:  I’m ready for the deep end.

Using the TI-Nspire Navigator system, we polled our participants to assess their disposition on formative assessment which caused us to change our plan on the fly.

We dropped all planned discussion of the theory of formative assessment and began to model and discuss how to create opportunities for collaboration.

We moved quickly to discuss how to develop formative assessments that offer opportunities to lead learners by following their progress and to help learners level up.

We feel that formative assessment should give all involved a different level of awareness.  How many times have we said “how can they not know this” when we are grading papers?  How many times have we heard our students proclaim “I thought I knew this, but what I studied was not on the test?”

“It is easy to miss something you’re not looking for.”

It is easy for a learner to feel and believe that they understand what is being learned.  But, do we offer them opportunities to calibrate their understanding with ours?  Leveled, non-graded formative assessment that offers learners the ability to calibrate their understanding with the teacher’s expectation and, at the same time, shows the path to the next level will improve learning and teaching.

Working from an identified area of strength and success offers learners the opportunity to stretch and grow.  Have students stop, collaborate, and listen to assess and report progress, to diagnose strengths and needs, and to communicate and collaborate with each other.

Stop, collaborate, and listen to your team.  Design leveled assessments to lead learners to the target level.  Intervene and enrich in one swoop with opportunities for all learners to self-assess, learn and grow.

Completing the Square / Leading by Following

On Saturday, September 17, Bo Adams and I were privileged to provide the keynote address for the 2011 Regional T³/MCTM Annual Conference.  Conference Director Jennifer Wilson facilitated a wonderfully effective learning opportunity for teachers, administrators, pre-service teachers, college professors, and others.

From the beginning, the program cover-art fascinated Bo and me. The conference theme was “Completing the Square,” and the image pictured a puzzle with a missing piece in the center. To build our keynote address, Bo and I imagined what that missing puzzle piece might be that would truly complete the square. Additionally, we threaded our talk with the idea of Leading by Following.

Believing in the powerful nature of stories, Bo and I told four stories to illuminate some puzzling issues facing educators today:

Puzzle 1: Why do we talk so much of teaching when it’s about LEARNING? Or… “How could they not know this?” [Assessment for Learning]

Puzzle 2: How can we make learning experiences more meaningful? Or… “When are we gonna use this?” [Contextual Learning]

Puzzle 3: Why are teachers and admin “US and THEM” when we all want our students to learn? Or… “You are a fool!” [Learning Partners]

Puzzle 4: Why is teaching an “egg crate culture” when we know learning is social? Or… “WE are smarter than ME.” [Learning Communities]

What do you think the missing piece might be? What completes the square? The following slide deck will lead you on the path that we explored during the keynote. We loved being in this community of learners at Brandon Middle School. It is always a privilege and pleasure to spend time learning with committed and curious educators.

Cross-posted with Bo Adams on his blog, It’s About Learning.

TI-Nspire Day 2 – Round Robin

We ventured off track from “the plan” for day two.  There are nine National T3 instructors facilitating learning at our site.  We decided to have our teacher-learners change classes so that they could work with and learn from four additional T3 instructors.

The Middle Grades teacher-learners had the following learning opportunites on day 2:

  • Investigating Computer Algebra Systems with Paul Alves
  • Creating Sliders with Josh Mize
  • Data Collection with the CBR with Margaret Bambrick
  • TI-Nspire Presentation View with Alicia Page

I had the opportunity to facilitate the following learning:

Here’s feedback from one of our teacher-learners:

“Hey y’all,

I am so excited!  I gave myself homework, which was to recreate the document that Josh (TI instructor) taught us how to do today, without looking at my notes or the previous document.  I did it!  Change the leg lengths by increasing or decreasing the sliders and the figure changes shape.  It also calculates c (hypotenuse) by measuring, but then look at the second page and you can see where the c value is calculated using c = square root of (a^2 + b^2) and the two columns (one measured and one calculated) match each other.  Too hard for 6th grade but useful in 7th and 8th.


I can also report an interesting story from Josh.  He says that he showed the Middle Grades teacher-learners several documents with sliders and then asked them which one they would like to create.  They said “none of them; it’s not what we teach.” So on the fly, he taught them to use sliders to illustrate the pythagorean theorem just as described above.  He was learning with his “students” to teach them what they wanted to learn.  Exciting!  Isn’t this how it is supposed to be?  Josh dropped his plan when it wasn’t going to work for his learners.  He taught how to use sliders to make math dynamic while meeting the needs of his learners.

When formatively assessed this morning, the Middle Grades teacher-learners could successfully work through the spiral activity showing they had acquired the essential skills of day 2 without marching through the standard curriculum.  Wow!

Age Estimation – Day One Lesson & Community Building

We want to try something different this year for the first day of Algebra I.  (We are hoping that other’s will join us too!)  Our learners will arrive with their new MacBooks. We want to use them immediately.  We think we are going to try the age estimation activity

The email request is shown below:

     We need you in pictures!  (and we need your permission to divulge your age to our students, if you’re game!)
     We are planning a multi-disciplinary/multi-grade lesson on graphing and numeracy that would help our students to start the year off using their new MacBooks.  We need volunteers who would be willing to tell us your true ages (as of August 11, 2011), knowing the students will discover these ages during implementation of the project. We will also be showing your picture; if you have a picture of yourself that you would like us to use, please email it to us.  If not, we will just use a photo on file.  We appreciate so much your willingness to participate, and we also appreciate your right to “pass on this one”.
     We usually use celebrities but thought it would be good community building to use our faces.  Jill piloted this activity with her 8th graders in May, and it was a big hit!  The kids suggested that we use faculty faces in August and the celebrities in May.  Think how great it would be for the kids to guess who we are (and how old we are – if they are smart, they will underestimate! – if not, what a teaching opportunity.)
     So, if you are game, please send us a photo and your age/date of birth.  Please?

Here is the presentation that we usually use:

In about 24 hours, we received 12 responses!  Enough to build the first lesson.  At the end of the week, 40% of the faculty responded to participate. Enough to build three lessons – one for 6th grade, one for 7th grade, and one for 8th grade.

Some of the GREAT replies include:

  • “I love the people I get to work with.”
  • “I will be 55 just like the speed limit!  If some kids says, “is that all??!!” feel free to smack ’em.”
  • “Well…a lady never tells…but I liked Gloria Steinum’s comment when she turned 60, “This is what 60 looks like.”  So, you can tell the kiddies that I am (almost) XX,  if you don’t think you will scare them to death.  :-)”
  • “I guess we cannot use that picture of Darlene if it is for student use, huh?!?!  I will send a picture for sure!  How much time do I have to go to glamor shots????”

And the pictures are great.  Can you image the face of a JH student when they see their principal like this?  How fun!

So, what’s the activity?

We are going to show you a series of photos, and you are to estimate each person’s age.  We want to know “Who is the best estimator (and who is the worst)?”   All you have to do is estimate the age of each person and enter it in the spreadsheet.  The learners guess the age of each person in the slideshow.

We think that we will use our teachers instead of the celebrities.  My 8th graders reported that they did not always know all of their teachers on the first day of school.  We hope that this lesson will help our learners connect with their teachers and build our community.

What about the math?

How will we determine the best estimator? the worst?  We will decide as a class.  Let the learners collaboratively develop their criteria to determine the best and the worst.

Usually, the first comment is to find the difference in the estimate and the actual age and sum the differences us – a great first thought.  The sign of the difference has meaning.

Did you over estimate or under estimate?  How does the sign of the difference help you decide if you over or under estimated? If your sum is the closest to zero, are you the best estimator?

How can we find how far off the estimates are but eliminate the direction of “off-ness?”   If we find the absolute value of the difference in the estimate and the actual age, will we find the best and worst estimators?

What would a graph of this data look like?  Which variable would be acceptable for the independent variable? Does it matter?

Why is there a positive correlation in the plot of the data?  What would be the line of best fit?  How do you know?

Can you determine from the graph if you over or under estimated?

What else can be learned?

There are several spreadsheet skills to introduce with this lesson.  The learners will generate a scatter plot and graph a function.  Mental math will be used.

From experience, this lesson creates a loud conversational classroom.  Shock and awe at some of the ages and estimates!  Lots of laughter mixed with learning.  In May, the entire activity took approximately 30 minutes.  We hope that we can use the first 55 minute class period to learn and laugh together as we discuss our community while doing a little math.

Handicap Ramps: Connecting Ideas and Experiences to PBL – apply what you learn

I don’t often have the question “When are we going to use this?” launched at me.  Sometimes I wonder why?  Why aren’t my learners asking this question?  I often ask myself “When are they ever going to use this really?” when teaching Algebra I.  How can I better show our learners that algebra is used for many real purposes, not just on a test?

On September 14, 2010, I had the privilege of attending TEDxAtl where I heard Logan Smalley talk about creating a movement with Movement Turned Movie.  Logan introduced us to Darius Weems and his story Darius Goes West.  In the spring, Darius joined our 8th graders for their retreat – an amazing experience for all.

On July 19, we will host approximately 170 teachers from nine different states for a summer learning experience.  We’ve done this summer camp for teachers for several years.  Each year there is a teacher or two who will struggle to navigate our campus.  There are stairs everywhere.  We do have elevators, but they are not always in the most convenient places.

In Synergy, we problem-find and attempt to problem-solve based on observations of our environment and community.  Logan’s advocacy for wheelchair accessible spaces combined with accommodating teacher-learners with mobility problems has caused me to want to learn more about our campus and the ease of access to our spaces.

Where are our ramps and elevators?  What are the requirements and specifications for these ramps?  Are the requirements based on the angle of elevation or the ratio of the length of the ramp to the height of the ramp?  Is the angle of elevation connected to the ratio of length to height?  Isn’t this rise over run?

What can be learned by investigating the ramps on our campus? Does our learning have to be restricted to our campus?

  • Algebra?  (I think there must be slope, geometry, and right triangle trig at a minimum.)
  • Science? (I think mechanical advantage might come in to play here.)
  • Writing workshop?  (Do we need more ramps? Are there areas where a ramp is needed? How can we advocate for others?)
  • History?  (When and why did the Americans with Disabilities Act (ADA) become law?)
Here is a photo we took today at the entrance to Pressley where most of us enter to go to the dining hall.  If you look closely, you will see a meter stick on the ground near AS’s feet.  
In the latest version of the TI-Nspire CX operating system you can analyze a digital photograph.  It is a great way to use ratios and proportions along with unit conversion.  Can you predict how tall AS is based on the measurements and the scale?  (I was less than an inch off.)  Does our ramp fall within the ADA’s specifications?  
Let’s make sure the variables and measurements are defined clearly.  m=3.83 cm is the measurement of the meter stick on the screen of the Nspire.  rl=23.3 cm and rh=1.91 cm are the screen measurements for the ramp length and the ramp height, respectively.  ah=4.64 cm corresponds to AS’s height on the screen. 
Can you think of ways to use your environment to teach?  We should not be restricting learning to the four walls of our classrooms.  Can we find ways to show our young learners how their learning connects to their community and beyond?

Connections: Questions, Photographs, Algebra Graphs, Perspective, Environment

Several of my tribe are participating in the 3six5 project (365 days, 365 points of view) which has caused us to wonder about this experience for education.  Here’s the invitation I received:

Dear Ms. Gough, Tara, Sarah, and Whit:

There are many stories to tell in the world of education and many voices that need to be heard.  We have started a new project, edu180atl, designed to share stories of learning and highlight voices from the Atlanta community.  During the 2011-2012 school year, we hope to have 180 different learners (students, parents, educators, etc.) participate in this project.  The purpose of edu180atl is to nurture and encourage the spirits of those who love to learn, to connect learners across disciplines and settings, and to deepen the national conversation about education by enabling parents, students, and educators to share stories of what they are learning every day.  In order to test the feasibility of such a project, we will be piloting a similar experience (edu180atlbeta) during the month of April.

We would like to invite you to be one of the founding writers for this project.

If you are interested in participating, please complete our beta signup form (link: http://bit.ly/edu180altsignup) and select two Monday-Friday dates (your first and second choice) during the moth of April when you will be able to submit a reflection based on the prompt:  what did you learn today? We will respond with a confirmation of the date and further instructions for submitting your reflection.  We ask that your reflection be no more than 250 words (1 typewritten page), and if you choose, you may also submit a photograph or a short video (no more than 90 seconds) to go along with your submission.

We look forward to this project and how you will consider participating.

**  Due to a limited number of days in April, we may not be able to accomodate every learner who wishes to participate.

One of our Synergy 8 team, Whit Weinmann (aka @runningwitty), started us off on April 1 with a challenge to realize connections.  In Synergy 8 we believe in the value of prototyping and the power of feedback.

I spent the weekend working with my writing team in Dallas planning a professional development experience for teacher-learners.  I thought I might practice answering the question: what did you learn today?  I also want to ask for your feedback while I practice and prepare for my edu180atlbeta day on April 11.


The theme of the day has been the art of questioning. My learning revolves around trying to ask better questions, questions that are open-ended enough to promote risk-taking, differentiation, and finding connections.

How can we leverage the technology in our hands help learners apply what we are teaching and see the beauty of the world through their learning?

Imagine learning about linear functions, perspective, design, and environment simultaneously.  Do we think helping our learners see that the patterns we teach actually model things they see will help them find relevance and pique their interest?  For our artists, would it be fun to insert their art into our technology and model the shapes and structures that exist in our community?

Can we take a photograph of the bridge to the Summer Camp and find the algebra in the photo?  What can we learn?  Do we need a lesson on perspective to gain an understanding of why these lines are not parallel in the photo but are in reality?

Can there be an entire theme for integrated learning around our bridge and the environment where it sits?  Who comprises the team that would spend just even one day using this bridge as the catalyst for learning?

Where are our resources to integrate and blend curriculum to support learning? How can we model lifelong learning side-by-side with the young learners in our care?  Will we?

I learned I am willing to try. It is worth the risk.  Will you join me?



It is interesting to me that I could write about what I learned today in 250 words, but I’m having trouble describing myself in 140 characters.  I think it is good to know this today while I have time to think and revise.

I’d love your thoughts and feedback.