Tag Archives: Nspire

Feedback a la positivity – examples

A colleague messaged me privately concerning the “positivity trip” I’m on in my posts.  While I don’t care for the word used, I’ll quote the question.

There you go again, Jill.  I’m gonna ask one more time. Aren’t you concerned about positivity and wussification of our students?

That’s not what I’m writing, talking, and thinking about.  I want to be better – intentional – about offering specific, actionable feedback.  The more I use and practice with I like…because…I wonder…, and What if… the more favorable the responses are.

I also wonder if we have a “no news is good news” attitude when marking papers. If we did a little data mining on the most recent set of graded papers or feedback comments, would we see descriptive positive comments? Or, it is habit to mark what is wrong or needs improvement? Do learners look at the whole of the assessment, or do they look for marks and comments? What is the positivity ratio of what they find?

Constantly scanning the world for the negative comes with a great cost. It undercuts our creativity, raises our stress levels, and lowers our motivation and ability to accomplish goals. (Achor, 91 pag.)

So, I’m curious… Is there anything wussifying <ick!> about the following feedback?

Example 1: Algebra I – I can evaluate an expression involving exponents that are integers.

Screen Shot 2013-12-29 at 4.29.52 PM


  • I like that you showed your work and thinking, because I can see that you do understand negative exponents. Questions 9 and 12 show that you have a solid understanding when asked to evaluate a negative exponent.
  • I like that your work in Question 10 is clear enough to show that you correctly evaluated the negative exponent. I wondered if you had trouble with fractions until I read your work in Questions 11 and 12.  Nice corrections, by the way. I like that you can see what you thought initially and what you now think, because it will help you when you review.
  • I wonder if you understand Question 11 even now. What if we meet for a few minutes to discuss your understanding of complex fractions and why a number raised to the zero power equals one?

Example 2: Leading Learners to Level Up formative assessment

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I like that Level 4 challenges learners to convert between different forms of a linear equation, because this will help with symbolic manipulation that is so important in 9th grade physics.

I wonder if the language will confuse learners.  As you can see from my work, I did not answer the question as you intended.  I read intercept form and used the slope-intercept form.  What if we ask for the equation written in two-intercept form? I wonder if the additional language will offer learners clarity.

Example 3: New Ask, Don’t Tell Art of Questioning document for Algebra II.

<Sam> What do you think?


  • I like it, because it is clear why each form has advantages, and that knowing all 3 forms is helpful.  I like it, because it is easy, using the slider bar, to navigate between the three forms.
  • I like that it is easy to see that the value of a is constant no matter the form.  I wonder how learners identify patterns in forms of hypotheses and then check.  I wonder if they will struggle with writing their hypotheses in words.
  • I wonder why the manipulatable points are so large.  I wonder why the user-added font is larger than the font of scale and values of the graphing window.
  •  I like that the value of a changes in fraction increments and that the functions are displayed with fraction coefficients rather than
  • decimals.  I wonder if learners will notice and document the pattern of the fractional coefficients when moving an x-intercept.
  •  I like that a double root is possible.  I wonder if learners will adjust the window to have the y-intercept in the graphing view. I wonder if learners will know to adjust and reset the viewing window.
  • What if the axis of symmetry is added to the graph?  I wonder if it would help or distract.
  • What if the background of the graphing window is graph paper? Would it help the visual process to be able to count?

<Sam> Thanks for the feedback.  Incorporated a few changes..  Font size is what it is.


  • I like the addition of the words: vertex form, factored form, standard form, because it provides clarity.  I wonder – I think – that it will offer learners language to document patterns and hypotheses in words.

What if we practice taking the time to offer positive, descriptive, and growth-oriented feedback? How might we change outlook, efficacy, and attitude? How might we learn to spot patterns of possibility?


Achor, Shawn (2010-09-14). The Happiness Advantage: The Seven Principles of Positive Psychology That Fuel Success and Performance at Work (Kindle Locations 1351-1353). Crown Publishing Group. Kindle Edition.

Ask; Don’t Tell: Listen to Learn and Assess – #nspiredatT3

At T³, Sam and I also facilitated a 90-minute session titled Ask, Don’t Tell: Listen to Learn and Assess.  Here’s the program description and our simple agenda.

Ask, Don’t Tell: Listen to Learn and Assess Can we merge diagnostic and formative assessment to lead learning? How will TI-Nspire™ CAS Handheld action-consequence documents combined with the TI-Nspire™ Navigator™ System allow us to leverage technology to focus on learning? What if we used the ideas of simplicity and restraint when developing and leading lessons? What can be learned if we question our way through an entire lesson? is it possible to allow students to steer the lesson through their questions? Will listening to student questions help us diagnose, assess and chart a course in real-time? Can we lead learning by following their thinking? Will you come to this session and plan to serve as a student, an observer, and a questioner?

(15 min) Introductions and Ignite talk on Assessment (40 min) Sam facilitates Quadratic_Roots.tns, 3-12-3 protocol for questioning, and QuadInvestForm.tns formative assessment (30 min) Jill facilitates Leveled Assessment discussion

I used the same Ignite slide deck from yesterday’s session since our participants were not the same group of people.  Interesting for me…I did not give the same talk, but I used the same images.

Sam then introduced the Ask; Don’t Tell idea by modeling a lesson on the discriminant using the TI-Nspire Quadratic_Roots.tns file and the 3-12-3 protocol.


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.)

Using the TI-Nspire document Quadratic_Roots.tns, facilitate a 3-12-3 protocol to generate student questions.

    • 3 minutes: Independent investigation of the Quadratic_Roots.tns file.
    • 12 minutes: Work with a partner to share questions, convert closed questions to open questions, and generate additional questions. Partners should identify their top 2-3 questions.
    • 3 minutes: Use the TI-Nspire Navigator to collect each student’s top question.

Facilitate the class discussion of the lesson by responding to student questions from students as well as the teacher.

Following his “lesson,” Sam check for understanding using the leveled QuadInvestForm.tns formative assessment.


Again, great discussion from our participants.  Sam received good feedback about his assessment.  Participants shared strategies they have used to debrief student responses while using the Navigator.  I thought it was great that Sam opened the discussion up by asking for ideas from the participants.

After experiencing a leveled assessment, I facilitated a discussion about the philosophy and strategies involved in using this type of formative assessment.  The summary of this discussion was captured by Sarah Bauguss (@SBauguss).

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I am grateful that Sarah took the time to tweet during the session.  Often I don’t really know what I conveyed. Having this series of tweets offers me another level of feedback.

For other examples of leveled assessments, see the following posts:

Leading Learners to Level Up – #LevelUpMath #LearnFwd12 – the details

Hello, I am Anne Conzemius, the host for your Learning Forward session.

Well, no pressure there, huh?  Actually, about 15 minutes prior to this quick introduction, I scanned the roster of participants and noticed Anne’s name on the list of our Learning Forward conference session..

My previous post, Leading Learners to Level Up – #LevelUpMath #LearnFwd12, was written prior to our presentation.  Here’s what we actually did after I got through the nervousness and shock of Anne’s presence.  (I used a quote from her book, The Power of SMART Goals: Using Goals to Improve Student Learning, in the slide deck for this conference session, in this blog post, to collaborate with Bo (@boadams1) on this rubric, and in many discussions with teachers.

To lead learners to level up – learners of any age – we want to find and highlight their bright spots.  We want learners working from a point of strength and climbing to the next level.  To introduce this idea, we used the YouTube video Dan Heath: How to Find Bright Spots, shown below.

I gave a 4-minute Ignite talk on the why we should lead learners to level up.

Jeff used the TI-Nspire Navigator for Networked Computers to assess our small audience so that we could adjust our plan to meet their needs.  We quickly learned that Algebra I could be our focus (whew!) and that teacher growth as well as student growth was important to our participants (yay!).

Jeff then shared the YouTube video Leah Alcala: My Favorite No, shown below, as a jumping off point for a discussion on turning mistakes into learning opportunities.  We then discussed how leveraging technology – we use TI-Nspire Navigator, but PollEverywhere, Google forms, and other tools could be used – to offer faster, more public feedback and discussion opportunities while redirecting the work to the learners.

Since Leah’s video was about multiplying polynomials, I shared our Algebra I leveled formative assessment to engage our group in a discussion about bright spot and strength finding.

How do we offer students voice to self-advocate for their learning?  The days of the negative self-talk “I don’t know nothing” must come to an end. Everyone needs to acknowledge what they know and what they want to know.  It is about empowerment – empowering the learner. It is about coaching.  How powerful for learner to approach the teacher and say: I can do XX; will you help me learn to YY?  I want to work in that environment, don’t you?

A question from our participants caused us to discuss our assessment plan. How did I handle summative assessments and what did my grade book look like?  I cannot post graded assessments here, because they might still be in play in Algebra I classrooms. I can, however, share How do we use the December exam as formative assessment? and the Google doc that we used to document progress on non-graded formative assessment work. (This is a copy; feel free to explore and “report” data to see how it feels. You can view the results here.)

Jeff asked amazing questions to facilitate the discussion.  Through his art of questioning, we talked about the philosophy of doing homework with deep practice, I can statements…, and leading by following.

My concluding remarks began with a quote from Anne Conzemius (and Jan O’Neill) which “outed” Anne as an assessment goddess to the rest of our participants.

“In order to engage in high-quality assessment, teachers need to first identify specific learning targets and then to know whether the targets are asking students to demonstrate their knowledge, reasoning skills, performance skills, or ability to create a quality product.

The teacher must also understand what it will take for students to become masters of the learning targets…

Equally as important, the teacher must share these learning targets and strategies with the students in language that they understand. It is not enough that the teacher knows where students are headed; the students must also know where they are headed, and both the teacher and the students must be moving in the same direction.” (Conzemius, O’Neill,  66 pag.)

To end the session, we quoted CL – an 8th grader in my care while beginning her journey to learn Algebra:

“I truly believe the formative assessments are helpful for using as study guides for tests. I use them as study guides and I learn from my mistakes through them.

I do like the fact that they are not graded because it takes the pressure off of taking them and makes me believe it is okay if you do not know the material at first. They are really helpful for going back and looking at what I missed, and then ask you for help on those questions.

Having the four levels really helps because I know what levels I need to work on so that I can keep moving up to a higher level.”

Notice her last sentence: … I can keep moving up to a higher level.

Lead learners to level up by empowering them to ask their own questions.


Conzemius, Anne; O’Neill, Jan. The Power of SMART Goals: Using Goals to Improve Student Learning. Bloomington, IN: Solution Tree, 2006. Print.

2010-11 was the last year I taught Algebra I, but if you want to see the day-by-day plan for the entire 2010-11 year in Algebra I, it is still online as a resource.

Practice seeking questions – #AskDon’tTell

Do you create carefully crafted worksheets to guide student learning?  I did for years.  I wanted my learners to be successful, and I thought it was my job to step them through the problem-solving process.  It would foster confidence and success, right?  Year after year, the next teacher of my learners would ask me if I taught X, Y, and Z topics.  Even when the learners in my care did everything I asked of them, they were not always successful at retaining what needed to be learned.

Do these carefully crafted worksheets really promote learn in the long run? Are we teaching perseverance, critical thinking, and problem solving when the path is so carefully crafted? Does having a step-by-step roadmap create opportunities to learn or handicap a creative process?

What if we offered our learners more opportunities to chart their own path from where they are to the target? Is the path they take as important as the learning they acquire?  How can we create investigations that prompt students to make observations and ask their own questions?

In writing LEARNing: Linear Functions Investigation – #AskDon’tTell and LEARNing: Quadratic Functions Investigation Zeros and Roots – #AskDon’tTell, I’ve been trying to work out an idea for prompting student investigation and questioning using dynamic investigations without much scaffolding.  I continue to reflect and ponder Steve Arnold’s great comment on the  LEARNing: Linear Functions Investigation – #AskDon’tTell post.  Here’s a snippet if you missed Steve’s comment:

My own experience is that “free orientation” (to use van Hiele’s terminology) tends to occupy kids for between 20 seconds and 2 minutes tops. It helps them a lot to be given some goal or curious thing or something to get them started… but I could well imagine that, in the right hands (i.e. yours) a class could be trained to be curious and capable of exploring.

Hmm…Could I help young learners learn to be curious and capable of exploring?  Are there protocols that I could employ while I am practicing the art of questioning?  I think I already engage in the art of questioning regularly with learners, but I am asked often about how to teach other teachers to “do what I do.”  I want to continue to hone this craft, to learn more, to become masterful.

So, what do I do to continue to learn?

  1. Read, read, read…Currently high on my list:
    1. Grant Lichtman‘s The Falconer: What We Wish We Had Learned in School,
    2. John Barell’s Developing More Curious Minds, and
    3. Dan Rothstein’s Make Just One Change: Teach Students to Ask Their Own Questions.
  2. Practice, practice, practice…Remove the scaffolding:
    1. Watch Dan Meyer: Math class needs a makeover and try it.
    2. Stop creating slideuments.  If your TI-Nspire document, your PowerPoint presentation, or your worksheet has multiple pages, slides, or steps, eliminate lots! Create space for questions, investigation, and thinking.
    3. Use Gamestorming games to develop techniques for learning to ask questions. I like Brainwriting, 3-12-3, and others.
  3. Risk, reflect, revise:
    1. Try it – more than once. One trial does not make an experiment.  Celebrate even small successes.
    2. Have strong wait time, and have questions in your “back pocket” if prompting is needed.
    3. Seek feedback from a trusted colleague. Engage in peer observations to help you see from another perspective.


LEARNing: Quadratic Functions Investigation Zeros and Roots – #AskDon’tTell

What questions could we ask to help our learners investigate and “discover the rules” for the number of roots or zeros of a quadratic function?

Should we start by questioning their understanding vocabulary?  Can we questions our learners to connect roots, x-intercepts, and zeros?  Can we listen to the learners’ questions to take their path instead of our carefully scaffolded plan?

What questions should be asked to lead our learners to move them identifying no real roots,  1 real root, and 2 real roots graphically to identifying the number of roots using the equation and the discriminant?

Remember, we ask questions; we do not tell rules or definitions.  The art of questioning must be practiced and honed.

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?


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.

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!

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.