# Think Puzzle Explore #makethinkvis

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I guess one can tell I taught geometry the first time I read this book.

I am grabbing this information from an Evidence File submitted for our Program Reviews…  formative assessment, student led questions, problem solving CTE, design-Art, communication, writing and exploration.

### Triangle Centers:

This task was presented as an introduction to the unit for discussion, then revisited after student investigations.  I actually used the Notice/Wonder routine, however, it could easily be modified to fit TPE.

Evidence:  After constructing special points of intersections in triangles with patty paper, students were asked to share what they noticed and wondered about the geometric figures.  A list of questions generated by students.  They were given the task of choosing a number of questions to explore using Geogebra software.  Following the investigations, students shared their findings and then used the software and what they had learned to answer a problem about location of an amusement park.  See list of questions below.

Triangle Centers Amusement Park modified from Georgia Department of Education.

What I love about the Amusement Park task is that there is no single correct answer.  There are multiple solutions, students were simply asked to share evidence of why they chose their particular location.  Students could either write a memo and/or present their findings to their classmates, which offer led to more questions of why? what? how?

# Making Thinking Visible, CH 3

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Our commissioner of education @DrSPruitt made a comment at TAC meeting that really rung true for me.  My paraphrase, in pre-service training, we “learn” a lot – hear a lot of theories, names – but its not until we are in a situation that we actually value that information,  that we truly understand – have a need for it when we may develop an appreciation for the idea.

I think I even heard him say Vygotsky in there somewhere – again, a name I heard many, many years ago – I was even assessed on his theories in EdPsych, but the name has popped up on my radar multiple times this summer – which makes me wonder if I go back and review – what ideas will I see that I should focus more on in my planning for learning opportunities?

Anyway, my point being – whether we call them literacy strategies, thinking routines or some other fancy label – the goal is the same.  We want students to dig below the surface, interact with the information, grapple with it, process and make sense in a way that connects to their world and gather an understanding on a level beyond the sit, get, assess and forget.

As I reviewed Chapter 3 – an Introduction to Thinking Routines, I realized some things I missed years ago.  The layout of the book was structured in such a way, one could utilize strategies from each section while planning for units.  They have been categorized to allow for thinking early in a unit, middle of the unit and finally, as a culminating task to help connect all of the learning.  I see this as a help for me – to use the chart, find a routine that will amplify the type of thinking I want my students to do and create an opportunity for students to interact with the information / skill development.

The analogy to use the routines to create an arc of learning rather than a single episode – will help me to focus on running a thread through the unit to better support continued learning and connections for my students.

I believe it may be an overwhelming task for teachers who are not yet in the mode of listening to their students and asking for support of their thinking as they begin to implement some of the strategies.  However, we can encourage one another by reminding “to go fast, go slow.” (Creating Cultures of Thinking, CHapter 10).  Choose 1 routine and work with it for a couple of weeks.  Reflect on your implementation, ask a peer to observe and share their evidence with you – What they see?  What they think?  What they wonder? from a spectator’s viewpoint.

One you’ve reflected and tried again, feel comfortable, then choose another routine.  Look at your students and decide what it is you want them to do – skim the routines and find one that fits and try it…slow and steady.  Give yourself time to try it.  Reflect.  Adjust.  Try again.  Ask students to reflect (CCoT) – tell them the name of the routine and ask them their thoughts – what worked well, what was difficult about it, suggestions for making it better.  I’ve met some teachers who refuse to get student feedback – “what can a 15 year old tell me that would help?” Well.  Their the person in your classroom everyday.  They can offer insight from the students point of view.  We sometimes forget what it is like to sit in their seats.

I’m a believer that when we ask for student input – and we share a summary, how you may try to adjust based on their feedback, we model value in their thinking.  This creates buy-in from them – to observe how we are trying to improve the classroom to have greater impact for them.

Chapter 3 also share how Thinking Routines are tools, structures and patterns for behavior.  I see this as a progressive model in the learning environment.  We help model, support the idea of the routines and how we can use them as tools.  Students begin to internalize the structures to lead their own discussions and eventually they become patterns of routine behavior for student thinking.  The author’s describe how routines become part of the fabric of our classrooms through repeated use.

Just remember – for students who have never been asked to think this way – we cannot give up, only support and encourage them to continue.  For teachers who have never been asked to think this way or teach this way – we cannot give up.  We must keep challenging ourselves, support one another and encourage to keep reflect, adjust, try again.

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Sharing an idea today that reminds me of my Ice Cube Gum container that became my paperclip holder in my teacher bag, an idea I shared on my 3rd #made4math post ever.

I still use it today! And I have another I use to store random dice.

This spring I noticed students with these fancy gum containers.

Empty…..

Are perfect to store card sort, flashcards, matching activity.  Cards are about an 8th of a sheet of standard paper, so smaller than standard index cards.  But one could easily print 8 cards to a page.

I asked students to donate the empty gum containers to their favorite math teacher. And several did.  I actually bought a pack today.  \$1.98 for 35 pieces of gum and a super cool container vs. \$0.96 for 15 pieces in a throw-a-way package.  In my opinion, a no-brainer bargain!

What other ideas for these cute containers?

# Zoom-In and STW #makthinkvis

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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.

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

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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.
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
• METACOGNITION
• 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

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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

# Math Teacher in Wood Shop

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So the past couple of days this math teacher spent some time in the wood shop (aka Dad’s garage).

Last year, my friend Melanie posted pictures of chairs she’d painted for her mom.  She has this crazy, talented vision for seeing beautiful things.  But I remember thinking, these chairs are beautiful, even when unfinished.

A few weeks before school was out I told my dad I wanted his help building a pair of Adirondack Chairs this summer and he said sure he’d help me.  My dad’s worked with wood as long as I can remember.  He’s retired now, but no one holds a light to his knowledge and understanding of sewing machines – such a mechanical mind – always tinkering.  I remember my Granny laughing about how he’d take apart the telephone or some other item to see how it worked when he was growing up.  The smell of cut wood has always brought about happy memories for me.  When I was young, one year for Christmas, he built doll bunk beds for me – we actually refinished them a few years ago for my daughter.

He and mom borrowed a chair from some friends at church to pattern from.  We estimated how much wood we’d need.  My husband and I picked up the wood and screws this past weekend.  Tuesday morning I dropped my daughter off for 4-H camp and stopped by their house to fill my day with lots of sawdust.

Dad handed me pieces of the pattern and I’d trace, then cut after some instruction on the saw I would use.  So many different tools and saws.  I know that my least favorite was the jigsaw.  He blamed it on the type of blade that was in it.  Anyway, we got all the pieces cut, routered (?) the edges and was ready for assembly.

Wednesday morning we began working on the puzzle.  There were some angles we had to adjust.  I loved listening to his thinking out loud.  I’d ask questions – knowing he knew what was going on, but I was wondering – why’d we do it that way from a mathematical point of view.  So many different ways of measuring to ensure we had just the right angles.  Making sure we measured from the same level/point of reference.  A 16th or 32nd is not that big of a deal for a small measure, but when extended, something is not going to line up just right, so yes, we had to re-cut a few pieces.  When everything must line up… measurement matters.  We adjusted often as we constructed the first chair.  The second chair was much quicker than the first.  They sit perfectly.  A little bit of finishing touches to sand some rough edges, but they are ready for our front porch or back yard and hours of conversation and sipping on iced tea.

If you’ll notice in the pictures above, I’ve included a “center finder” – two of them actually.  I told my husband last night, I know how to read them, but when reading to the left, I paused and questioned myself.  No troubles when reading to the right.  But I wondered, is there something in the way I was taught that causes me to process differently when reading measurements to the left?  Is there a connection to students’ struggle when looking at signed numbers?  Some of the Exeter problems I’ve been looking at and a tie-in to the clothesline discussions will definitely show up in our classroom this fall.

As I used this tool the first time, I kept seeing a connection to absolute value.  How might I use this when introducing and working with absolute value equations / functions?  Anyone ever used this tool within this context in math class?  If I created some out of card stock and laminated, would that be sufficient?  Of having an actually tool in hand, would that make it more real for students?

Here are my take-a-ways from the past two days:

• There are a lot of different types, sizes and qualities of wood.
• There are just as many different types, sizes and qualities of screws.
• Who knew so many different saws would be needed for a “simple” project?
• Measure twice and cut once is a real thing.
• The tools I use in math class are only the surface of what can be done.  I should build a literal classroom toolbox that enables students to see real-life angle finders, measuring devices and their uses.  “When Am I Ever Gonna Use This?” would be long gone if I taught math in this context.
• As a math teacher, I have no clue.  I need to spend more time in shop class to develop a true understanding of applications of several of the concepts I teach.  Although on at least 3 different occasions I’ve been told no or ignored when I asked to attend Geometry in Construction – knowing it would provide purposeful curriculum for students to learn and see meaningful use of the math.
• I can see why folks would enjoy woodworking.  It was a great learning experience.  Relaxing too.
• I have a pair of treasures we created that will be around for years to come.
• Time with my parents.  My mom kept our tumblers full of iced sun tea and just observed our work.  Priceless.  Especially with all the tragic events this past week in Orlando.  A split second changes our lives – before we even have a chance to think.  I am grateful to have invested time with my mom and dad these past couple of days.  I am saddened for those who no longer have this opportunity.

But even more saddened by those who choose not to take advantage of the opportunity.  Let’s lay off of social media, celebrate with one another in real life.  Do without a few less material items, work a few less hours so you can invest in time with one another – its worth far more than something that will only fade with time.

# #mathphoto16 and #symmetry Week 1

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I wondered a few weeks ago about the #mathphoto16 challenge.  It was fun last summer, looking for math around me.

Here are some things I noticed on my walk this morning.

The first picture I’ve noticed many times as I walk past my neighbor’s house.  The parabolic shape in the shadows is what first caught my eye.  What causes it to look like a parabolic curve?  Wondering… the symmetry of the parabolic shape I notice with the vertex on the line of symmetry.  But as I thought more, could I consider each shadow as a translation, then scale of the one before it?

The second picture of a black-eyed susie with some rotational symmetry.

I’m not sure I ever paid attention to the three types of leaves a Sassafras tree has until my daughter created a leaf collection as a 4H project recently.  Looking at the various leaves she picked along our road, I was reminded of the beautiful patterns we often overlook in nature.  I enjoyed listening to her compare the types of Maple leaves she found, looking at the leaf guides trying to decipher which tree each came from.

We learned some new terms as she searched for the names – was the arrangement opposite or alternate?  I see some reflection but also translational symmetry with those. Were the lobes pinnately or palmately arranged?  Again, translation / glide-reflection or a semi-rotational.  I see some good opportunities for rotational vs. point symmetry with pictures I’ve seen posted in #mathphoto16.

It was when she began inking the backs of the leaves to create prints that the true beauty became evident – so many details we never even saw before.

She has already begun looking at other trees – since next year, she will need to create a collection of 20 native trees different than the 10 submitted this year.

# A New Open Educational Resource Platform

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I’ve kind of been out of the loop the past few days, but I have seen a few posts concerning sharing of resources – ideas – lessons – curriculum.  I’ll be honest, this is where I sometimes get overwhelmed – so many resources and my math teacher ADHD takes over, then I get nothing accomplished.
A few weeks ago, I placed my name on a wait list (& you can too!) for a new open-ed platform.  You can read the press release from last fall here and a list of #goopen states and districts here.  I was excited when I received an invitation to be a private beta participant.  However, with the last days of school looming, I had to focus on the job at hand and get the year wrapped up.  Now that I’ve had a few days away, I’m excited to begin exploring this new tool.
What little time I’ve spent perusing this evening, it seems you can search uploaded K12 materials tagged grade level, subject, standards, target audience, resource type, time to complete, format, PD options, DoK, even type of license.  As a user, I can rate materials and write a review.
So far, the platform seems user friendly, easy to search. What I hope to find are quality lessons and resources that will enhance what I already do in the classroom.  I look forward to sharing more as I explore!