Tag Archives: #makthinkvis

Zoom-In and STW #makthinkvis


April 2013

Following our unit pre-assessment, I used the following slides as part of an introduction to Similarity and Right Triangle Trig. while implementing Thinking Routines Zoom-In (page 64) and See-Think-Wonder (page 55) of Ritchhart, Church and Morrison’s Making Thinking Visible.  This was used as a hook for student engagement as we introduced the unit.

Moving left to right, then down, each time pausing and allow students to share their thinking STW.

These are snapshots from The Vietnam Veteran’s Memorial in Frankfort, Kentucky.  Avery Smith was my uncle.  A man I never knew, but every story I’ve heard was how selfless he was in everything he did.

vietnamsundial From the memorial website: The design concept is in the form of a large sundial. The stainless steel gnomon casts its shadow upon a granite plaza. There are 1,103 names of Kentuckians on the memorial, including 23 missing in action. Each name is engraved into the plaza, and placed so that the tip of the shadow touches his name on the anniversary of his death, thus giving each fallen veteran a personal Memorial Day.

The location of each name is fixed mathematically by the date of casualty, the geographic location of the memorial, the height of the gnomon and the physics of solar movement. The stones were then designed and cut to avoid dividing any individual name.

Students had several questions – wonderings about what type of math could be needed to design such an amazing memorial.

The follow-up was with random objects outside on the sidewalk at school.

We then utilized QFT Model for creating questions – you can read more details here.


We could easily refer back to their questions as we explored more in the unit.

Revisit of Making Thinking Visible, CH 1 #makthinkvis #eduread


This past week I finished reading Creating Cultures of Thinking.  Many great reminders of thinking routines and suggestions to challenge oneself to implement in the classroom.  While chatting with @druinok, she said she couldn’t wait to finish, so she could finally read Making Thinking Visible.  So, I thought I would revisit this summer.  Having chatted the book and implemented several routines over the past three years and reading the Cultures of Thinking – I thought it might provide an even more powerful opportunity for reflection.

Looks like @bridgetdunbar and @mary_dooms may join in on this round of chat too!

Ch 1 Unpacking Thinking

Things I’ve highlighted:

  • What kinds of mental activity are we trying to encourage in our students, colleagues, and friends?
  • What kinds of thinking do you value and want to promote in your classroom?
  • What kinds of thinking does that lesson force students to do?
    • These questions – stump me, too.
    • I must first make the various forms and processes of thinking visible to myself. 
    • CHALLENGE:  to ask myself these questions during my planning.
  • Careful noticing – because the mind is designed to detect patterns and make interpretations, slowing it down to fully notice and adjust describe can be extremely challenging.  
  • pg 7 ???  “we would do better to focus our attention on the levels or quality within a single type of thinking.”
  • ! understanding is not  a precursor to application, analysis, evaluating and creating, but a result of it (Wiske, 1997)
  • …we might consider understanding no to be a type of thinking but an outcome of thinking!
  • Compilation of several processes?
  • Work focused environment or Learning focused environment?
  • Tasks might be more fun than worksheets, but are they actually developing understanding?
  • Hands on =/= Minds on!!!
  • Mark Church:  Only then did I recognize that work and activity were not synonymous with learning.
  • This realization for me was around 2010…
  • page 10 exercise to try – to help me identify possible discrepancies.
  • A map of thinking involved in understanding – how closely are these connected to SMP?
    1. Observe closely and describe what’s there.
    2. Build explanations and interpretations.
    3. Reason with evidence.
    4. Make connections.
    5. Consider different viewpoints and perspectives.
    6. Capture the heart and form conclusions.
    7. Wonder and ask questions.
    8. Uncover complexity – go below surface learning.
  • Valuable to pause in class to discuss type of thinking that will be/was involved in the assignment.  Reflect on the routins (culture of thinking CH 7)
    • How do you feel it went?
    • Did it make discussion more productive and focused?
    • Do you feel you are coming away with a better understanding?
    • What was hard and what was easy about the routine?
    • What should we try to work on to improve next time?
  • Curiosity and Questions
  • “The questions we ask at the onset of our learning journey change, morph and develop as that journey moves forward…New questions reflect our depth of learning.”
  • How might we map this journey of curiosity?
  • Post and discuss initial essential questions, but have an anchor chart that we can record / build list of questions as we go deeper than surface learning.
  • Goals of Thinking?
    • Understanding
    • Solve Problems
    • Make Decisions
    • Form Judgments
  • What are other goals of thinking?  What are other types of thinking?
  • By being clearer in my own mind about the kinds of thinking I want my students to do, I can be more effective in my instructional planning. pg 15
  • Concept Map for Thinking:  What is thinking?  When you tell someone you are thinking, what kinds of things might actually be going on in your head?
  • How can I use this?
  • Week 1 of School – ask these questions.  Individual maps, small group discussion and combine.  Whole class.  Then use responses to create class wordle.  Print and put on display for first few weeks.

Here’s a wordle from three years ago, I located it in a draft for a post I never published.


My take-a-ways from Chapter 1:

  1. I need to think about and develop my own understanding of types of thinking beyond surface learning.
  2. I need to ask myself what type of thinking I want my students to do.
  3. Do the lessons/activities I have plan provide opportunities to develop understanding through the thinking I intend?


Creating Cultures of Thinking, Ritchhart #eduread bookchat


I’ve thoroughly enjoyed our June book chat with #eduread: Creating Cultures of Thinking:  The 8 Forces We Must Master to Truly Transform Our Schools.  So many ideas affirm things I already do.  But even more challenge me to think beyond my current stage in thinking as a teacher.  I look forward to wrapping this chat up and revisiting Making Thinking Visible to reviewing some great Routines and build my planning tool box!


Some links to archives on Storify for Chapater 4 – 9 are provided below:

Ch 1 Purpose & Promise

CH 2 Expectations


CH 3 Language

CH 4 Time

Ch 5 Modeling

CH 6 Opportunities

CH 7 Routines

CH 8 Interactions

CH 9 Environment

CH 10 Moving Toward Transformation

Trig Ratios – #made4math


Through the years, I’ve seen students struggling trying to remember which Trig Ratio is which.  I have a colleague who draws a big bucket with a toe dipped into the water.  She says she tells the students “Soak-a-Toe” to help them recall SOH-CAH-TOA.  Another has described the “Native American”  SOH-CAH-TOA tribe as the one who constructs their teepees using Right Triangles.  The most entertaining though is the rap from WCHS Math Department “Gettin’ Triggy Wit It” on youtube.

I wanted to use an inquiry activity to help them develop the definitions of the Trig Ratios.  Basically, they constructed 4 similar triangles, found the side measures, then recorded ratios of specific side lengths.  Next, I had them measure the acute angles, then we used the calculator to evaluate the sin, cos and tan for each angle measure.  Students were asked to compare each value to the ratios they had recorded in the table and determine which ratio was closest to their value.  Here’s the file https://www.dropbox.com/s/gfvhnictujfj2ik/similar%20triangles%20intro%20trig.docx?dl=0 Similar Triangles Trig Ratios.  Anyway, its not a perfect lesson, but a starting point.  If you use it, please comment to let me know how you modified it to make it a better learning experience for students.

In the past, students sometimes struggle trying to decide which ratio they need to use when solving a problem. I put together an activity adapted from a strategy called  Mix-Pair-Freeze I’ve used from my KaganCooperative Learning and Geometry book.  This book offers numerous, quality activities for engaging your students.

You can make copies of this file, Trig Ratio Cards File, then cut cards apart to use.

Trig Ratio Cards

Each student gets a card.  They figure out which Trig Ratio is illustrated on their card (& why).  They mix around the room (with some fun music would make it better), then pair up with someone.  Each person tells which Trig Ratio and why (can be peer assessment, if one is mistaken).  They swap cards, mix and pair with another classmate.  This continues for several minutes, allowing students to pair with several different people.

When I call “Freeze!” Students are to go to a corner of the room which is designated Sin, Cos or Tan.  Within the group in each corner, students double check one-another’s card to determine if they are at the right location.  Again, peer assessment, if someone is wrong, they coach to explain why, then help them determine where they belong.

Students swap cards, mix-pair-freeze again.

I like this activity for several reasons:

  • 1. Students are out of their seats and active.
  • 2.  Students are talking about math.
  • 3.  It allows them to both self-peer assess in a low-stress situation.
  • 4.  I can listen to their descriptions and address any misconceptions as a whole-class as a follow-up.


To clarify, the intent of this activity is for students to determine what information they are given in relation to a given angle, then decide which ratio it illustrates. It is meant to help students who struggle deciphering what information is given.

Quadrilateral Diagonals Properties


Over spring break, I was surfing online resources, searching for ideas and suggestions on how to plan and be more purposeful with the Mathematical Standards, which I have realized this year just how key these are to the success of CCSS. As I looked through Inside Mathematics , I ran across some PD training materials. I watched clips from Cathy Humphrey’s class. The Kite Task, an investigation of quadrilateral properties from seemed like a great activity to ease back on day 1 when we returned.

The task in short is for a kite company, who wishes to launch a new line of kites consisting of all types of qudrilaterals. The students are asked to devise a plan for how to cut/assemble the braces for each type of kite. They are only working with the diagonals in the investigation.

Rather than running copies and cutting out, I used my paper cutter to cut 1″ strips one color card-stock lengthwise and 1″strips width wise of a different collor (I didn’t realize how helpful this would be until later on). I created a strip to use as a guide on each strip, placed 7 holes equally spaced. Odd amount is best since they will be looking at bisectors some.
Each student would receive 2 of one color and 1 of another color.

Here are some snapshots of possible braces built.

For anyone who is having trouble visualizing, I’ve added some “sides” to the diagonals:

As we began the 2nd day of class, a few groups needed just a bit more time to wrap up their investigation. Using fist to five, I asked how many they still needed to determine. Most groups only 2 or 3, so I set the timer to keep us on track. I love days like this to walk around and just listen.

As I was questioning one of the groups, trying to ensure an absent student was on track, I asked the group’s members to “fill an order” – pick 2 sticks and construct the diagonals needed to brace…kite that was a rhombus, then another shape, etc to quiz them for understanding. AHA! Why couldn’t I use this as a formative assessment for the entire class?!?! Perfect.

When all groups had completed and debriefed a bit, I placed orders for kites and the students had to build the braces and pop up to show me for a quick assessment.


These pics were actually a geometrically defined kite. If you look closely, you can see a few wrong repsonses. To address these, I used extra sets of sticks to build a correct example and an incorrect example. To ask for suggestions why one was and the other was not correct. Why was one example actually a rhombus, allowing them to really compare/contrast the two figures.

Another great mistake I saw…when asked to create a rectangle, the top sketch is what I saw from about 6 students. Of course, my initial thought was, they dont understand the diagonals must be congruent.

Then I saw a student trace their shape in the air…second sketch. I literally saw their thinking. They had not used the sticks as diagonals. Clarified and corrected!

A post-it note quiz today, I built the braces, they had to tell me the quadrilateral name. A stop-light self assess, revealed most were confident, of the 10 yellows, 7 got all parts correct. The others missed 1, 2 or 3. All green students had each part correct.

We did a little speed dating to use properties to solve problems. As I listened to their approaches, most everyone seemed on track. Overall, I was very pleased with the results of the lesson.

Chalk Talk part 2 #makthinkvis


Another task I presented students in the form of a Chalk Talk

We had previously used a patty paper lesson to construct our kites. image

Simply enough, we constructed the kite by first creating an obtuse angle, with different side lengths. Folding along AC, tracing original obtuse angle using a straightedge to form the kite. Immediately students made comments about the line of symmetry. They were given time to investigate side lengths, angles, diagonals, etc. forming ideas and testing them to prove properties.

Their Chalk Talk task was to devise a plan to calculate the area of a kite.







Most every group approached the problem by dissecting the kite into right triangles, then combining areas. Several approached dissection as top triangle/bottom triangle, but would have to adjust their thinking when I asked them test their idea with specific total diagonal lengths. Some even extended the kite to create a rectangle. In the end, our discussion centered around 3 statements/procedures for finding area of a kite.

1/2(d1*d2) (d1*d2)/2 d1*d2

Allow them to determine which will /will not work and share evidence as to their conclusions. (Hello! MP3 critique reasoning of others.)

Sure, it would have been quicker to say here’s the formula, here’s a worksheet, practice, learn it. But its so much more fun “listening” to their Chalk Talk. Again, the end discussion is key-allowing them to think / work through each group’s findings, address any misconceptions and finally coming to a concensus as a class.

Chalk Talk part 1 #makthinkvis


I have wanted to try Chalk Talk, a strategy from our #makthinkvis bookchat, for several weeks.  However, I wanted it to be an authentic learning experience rather than a contrived activity just to say we did it.  This past 2 weeks, I found myself able to use it in 2 very different contexts.  Chalk Talk requires students to communicate written dialogue, no verbal.

The first was at the end of a unit of study.  I used the “2 Minute Assessment Grid” discussed here,


as a reflection tool for my students a couple of days before the unit assessment.  At the end of the previous post, I wondered how to address student questions/misconceptions.  I chose to recopy the questions onto a post it, placed in the middle of a dry erase poster.  Students were curious as they entered the room that afternoon and saw the posters hanging around.

Students took a dry erase marker and were instructed to respond without verbally talking, to suggest, explain, give examples or ask questions on the posters. 







Notice 2 posters were red.  I explained to students that red flags went up for me as I read the statements from their classmates post-it note reflection on the 2MAG. 

After students had opportunities to respond on each poster, we carouselled around to read responses.  I’ll be honest, I was hoping for more guidance, in depth statements from them.  There were some good examples, but majority were point-blank, straight forward surface statements without in depth explanations.  However, as we discussed the posters, I felt the thoughtful ideas came through.  “Here’s how I remember this…”, “If you can think of it this way…”

Which shows most of them can verbally give ideas, explanations but written is not as strong.  How do we assess them? High stakes testing is almost always written.  Another reason I am not am not a fan.  It just seems unfair we judge students and even teachers based on written, mc tests that don’t allow opportunity to showcase strengths of all students.

Overall, I feel like this task gave students a chance to address those ideas they were still fuzzy on, gaining suggestions from classmates, whether written in the Chalk Talk or our wrap up discussion.  On our unit assessment, questions that targeted the concepts from Chalk Talk, students performed very well on.  I do feel the opportunity to discuss/process verbally as the follow-up is key. A wrap upmdiscussion gave me opportunity to address any unclear / incorrect comments as well.

I look forward to finding more opportunities to use Chalk Talk to move learning forward and make thinking visible.

Environment – Shaping a Culture of Thinking #makthinkvis


This semester I have been participating in an online chat #makthinkvis with @lizdk and others addressing the book Making Thinking Visible by Ritchart, Church, et al.  Its been very challenging at times-pushing me think outisde my norm for ways to integrate these thinking routines into my instruction.  As well as causing me to step outside my comfort zone as I attempt to put them into action.

I had intended to blog about my experiences and reflections as I’ve tried these thinking routines, however, time seems to  evade me.  Hopefully, I can find time here and there before the end of the semester to get a few things shared.

As we finished up chapter 7 this past week, one idea from page 243 keeps coming to mind.  A key force that shapes the culture of thinking is the environment.  Sure, we all come in our classrooms, organizing, putting some thought into the layout, neat desk (maybe on open house night, but definitely not now for me), where/how papers are turned in, supplies, flow of the room, etc.

But if someone walked in my classroom, after hours, empty of students, no teacher around, what would serve as evidence of learning/thinking?  How much could you discern about the thinking and learning that goes on in my classroom just by stepping inside?

Sure, they may see an agenda and “I can” statements posted daily – but is that evidence of student thinking/learning?

What is hanging on my walls? And who put it there?

What does the room arrangement say about student interactions?

Where is my desk? Can this indicate anything about our learning environment?

If there is nothing on my walls, what does that communicate?

If you knew nothing about me, but you walked in my classroom – I wonder…

What you would see?  What would you notice?
What do you think is going on?
What does it make you wonder? What questions do you want to ask?

What does it say about about me as a teacher, about the learning opportunities I provide my students?

I wonder what evidence of thinking and learning you might find…

Pictures to come later…I invite you back to step inside my classroom soon!

See, Think, Wonder #makthinkvis


For our next Making Thinking Visible chat, we were asked to read Chapter 3 and implement the first routine presented – See Think Wonder (STW) pg 55.  I realized late Wednesday evening students were scheduled off for a staff PD day on Friday.  I scrambled wondering how I could incorporate this strategy in a meaningful way.  We had worked with parallel lines / transversals and the angle relationships created.  My goal was for students to look for ways to prove lines parallel.  How could I use STW to get this accomplished?

When I searched for images of parallel lines in architecture, I ran across a picture of a building in Australia and a picture of the Illusion as well.  You can find more here Cafe Wall Illusion.

My plan was to use the optical illusion – the placement of the black and white blocks causes one to think the lines are getting closer / farther apart.  However, as I flipped through my book, I saw the routine of Zoom In and wondered if I could combine the 2 somehow.  And here is what I did:

Zoom In – Ask Students what they see, pretty standard – black rectangle.  So many ideas (some silly) of what this could actually be part of…


Slide 2 was a little more interesting, alternating black / white rectangles with several things they thought it could be a part of – keyboard, referee’s shirt, prisoner uniform, zebra…


Slide 3 eliminated some of their predictions…I did have a person actually state a building. Hmm.  I think they must have seen it before.


When I revealed the final picture – it was fun listening to their comments.  One was very perplexed “Why would anyone want their building to look that way?”  It is found in Melbourne, Australia.


After a few moments of sharing / discussion – students were comfortable.  As I shared with students that we were going to do a thinking routine called See Think Wonder – I tried to explain each step.  This is the slide I shared with students:


I went through each step, allowing time for students to record what they saw, what they thought and anything they wonder (a question they could investigate/answer).    We then shared our responses.  After the first 2 statements, I paused and revisited what we were to do for each step.  We agreed the statements would actually go to “Think.”  Here were responses:


After sharing, students were given a copy of the Cafe Wall Illusion – but not allowed to use rulers/protractors to measure anything.  You can see from the snapshots, several chose to use patty paper.

Student A traced the lines to show they were actually straight, then translated the copied lines over the originals to show they were parallel.


Student B traced the edges of the rectangles, then translated to different levels to show the lines were equidistant at all parts, thus parallel.


Student C over-layed tape, traced edges at 2 different levels, then peeled the tape and matched them up…IMG01093

One student used the pink line on the notebook paper and overlaid it to show the lines were actually straight and several traced the rectangles onto patty paper and translated to others to show congruence.

It felt a bit contrived – I’m not sure what level of thinking was achieved, but I will use See Think Wonder again.  It was a good start to model the 3 steps of the routine.  Following the activity, students could be asked – if I only had 2 lines – how could I prove they are parallel?

In discussion some responses:

  • to extend the lines to see if they ever intersect (student knows the definition);
  • measure the distant between the lines at different points (again, student understands they are equidistant;
  • draw a line perpendicular to one line, extend it, if its perpendicular to the other line, then the 2 lines are parallel (yep a student came up with that one)
  • and finally, cut both lines with a transversal, measure/compare the angles to see if the relationships exist (the understand converses/working backwards to prove).

What I appreciated about STW – I didn’t tell students what question to answer or even how to answer it.  They created their own question and chose a way to answer it.  The only problem with this – they may not wonder/choose “the question” I’m wanted them to investigate/answer.  In the end, if you can get students to make a connection with the content, give them opportunities to notice/wonder, allow them to come up with their own questions – they’ll be interested in finding the answer…