Category Archives: online book chat

SMART goals #MTBoS30 Day 4


So, in Kentucky we are piloting PGES – Professional Growth and Effectiveness System.  Component are based on the Danielson Framework for Teaching.  I, personally believe it is an opportunity for major impact on student learning…

Back in the fall these are 2 goals I wrote for my classroom…  Wondering what feedback anyone could offer (please and thank you).  Do these follow the SMART goal format? What adjustments do I need to make?

I completely understand these should have been revised earlier in the year but it’s been a learning process for me. 

Goal 1:  Student Growth

Student Growth

My goal is for all Algebra 2 Learners and will be measured using Discovery Education Benchmarking Assessments.

My goal is for all students to improve their overall score by 15%  on the next Discovery Education Benchmark assessment.  If this is accomplished, 90% of my students would move up at least one proficiency level.  This is an achievable goal considering an average of 8% will move the class averages up one proficiency level.

Looking over commonly missed questions, I found there were gaps in the areas of Quantity and Functions for my students.  I plan to address these by:
• Using resources like Estimation180, 101 Questions, Visual Patterns as bell ringers for class discussions to build learner confidence and numeracy reasoning.
• Our most current unit is an Overview of Functions – through interactive, engaging instructional activities, learners will have an opportunity to talk about and discuss things they notice about different types of functions.  This will allow for conceptual development of learning targets.  Intentional formative assessments will allow me to adjust my plans daily. 

Goal 2: Professional Growth…

The Classroom Environment

I want to provide more meaningful problem solving opportunities for students to engage in discussion with their peers through activities that highlight and allow for students actively use the 8 Standards of Mathematical Practices.

3 goals for my administration/ peer observations:
Better questioning to draw out student ideas / strategies;
Provide quality tasks and structure the class time in a way that allows ALL students to be engaged in learning and discussion.
Develop a better culture of listening by lessening the amount of times I repeat what a student says – encouraging students to listen closely as their peers are talking.

I will read Powerful Problem Solving by Max Ray and participate in an online chat – then implement strategies discussed, reflecting, adjusting and sharing either through chat or blogging.
I will use suggestions from 5 Practices for Orchestrating Productive Mathematical Discussions by Smith & Stein to plan learning sequences that will impact student engagement and learning. 

Unit Organizer Update & Feedback Only Grading


Its been a good, very good, no, great start to the year.  Almost scary how smoothly it has begun.  But I will take it and be happy. Very happy.  I always have amazing kids.  They make me smile.  They make me think.  They make me love what I do.

I have read about comments only grading multiple times.  A colleague shared more research as part of an action research project last spring.  Reading and chatting Wilham’s Embedded Formative Assessment this summer convinced me I needed to give up grades on student work and offer feedback only.  So far, so good.  When I pass target quizzes back, I allow some time for students to mark on their organizers where they consider they are based on feedback I have offered.  I will definitely be sharing updates.

I shared a unit organizer here a couple of weeks ago.  It’s gone well, though I knew I wasn’t satisfied with it.  But this afternoon, Crazy Math Teacher Lady shared this


My thoughts are to modify my booklet style organizer to include this on the inside.  I appreciated the graph for each target.  This goes right along with some research from #efamath chat this summer.  It reminds me of something similar I had seen on @druinok’s block a while back.  I like how Lisa has a place for students to record multiple assessments.  This is a great layout!

I plan on keeping a vocabulary knowledge survey on the front as suggested by Math = Love.  Here is a sample of mine


And keeping the assessment grid on the back for personal reflection…


I re-intoduced an old assignment from a few years ago in my first units…students were asked to write their own unit assessment using our learning targets.  Most seemed to put good effort in to interpretting what each was asking.  Offering written feedback gave me a chance to address some of their misconceptions, mostly notational issues in diagrams they had included or clarifying some vocabulary.

My intentions were for them to go back through their INBs, notes, target quizzes.  A couple of times in class, I fielded specific questions they had.  Based on what I observed, I believe it was a useful task.

I am looking forward to my new organizers!  Thanks to Lisa, Sarah & @druinok for sharing such awesome ideas!

Summer Reading List






Embedded Formative Assessment Dylan Wiliam
Already completed an online chat with this book and looking forward to starting a face-to-face chat with colleagues from Science, World Languages and Family/Consumer Sciences this week!  Accountability is key and having these folks just down the hall as springboards for ideas, peer observations for accountability and encouragement when things don’t go exactly as expected…exciting! 

Practical ideas from years of research.  This book contains many, many doable techniques.  Chapter 1 explains how improving educational achievement impacts economic growth as well.  Chapter 2 sets the foundation, explaining what formative assessment is and is not.  I have read much about Formative Assessment the past 3 years and was already a believer, but this book offers great, practical techniques that I will be implementing next school year!

Teach Like A Pirate! Dave Burgess
The title itself is fun, but reading the reviews convinced me to put it on my summer list! Just flipping through and stopping at random spots…confirms this book will offer some fresh perspectives and ignite one’s teaching!
Join our chat #tlapmath or I believe there is a Monday evening #tlap chat as well!

5 Practices for Orchestrating Productive Mathematical Discussions Smith & Stein
Again, joining in an online chat #5pracs with several across the country.  Short read with some powerful suggestions. 

Make Just One Change Rothstein & Santana
This was suggested by @jgough earlier in the spring but I just havn’t gotten around to reading it yet, but looking forward to learning how to get my students to ask their own questions!

My later on list…






Creating Innovators Wagner

Teach Like a Champion Lemov

The Lady Tasting Tea, Salsburg

Teaching Numeracy: 9 Habits to Ignite Mathematical Thinking, Pearse & Walton

The Falconer: What We Wished We Had Learned in School, Lichtman, Grant, Sunzi

Some excerpts from the John Van de Walle books

Some past favorites list:





Summer reading list, high school math

All Student Response Cards #made4math Monday


In reading Embedded Formative Assessment (Wiliam, 2011), there have been several practical techniques presented in each chapter.  While discussing chapter 4, @druinok suggested creating response cards this summer, based on the technique All Students Respond.

  I had seen a set made by an elementary teacher in my leadership network.  She had several cards labeled with letters, hole-punched and attached to a 3 inch ring that could be opened and placed around the metal frame on student desks. She explained students always had access to them.

I kept thinking about how to accomplish the same idea for my classroom.  I had a package of name badge holders I had picked up at our Mighty Dollar in town, but never found a use for them.  Basically, I put this example together quickly, to have something for #made4math today. Its not innovative, but for anyone who does not have a “clicker system” or devices to use with Poll-Everywhere, etc., its an option that I believe could prove as a useful tool.

My idea is to have a single card, with all responses.  I would need to ‘train’ students how to hold their cards allowing me to see their response clearly.  Mine is double sided, this could easily be accomplished with cardstock printed, then laminated if you didnt have the badge holders.  Each student could clip one into a pocket of their INB and have them on hand when its time to use them.  Or they could be clipped either to a hanging ribbon or the side of a magnetic cabinet, even placed in a basket if you only had one classroom set.


The first side includes a favorite of mine…always, sometimes, never…color coding green, yellow, red, respectively.  The student places their hand, so only the response they choose is visible and located at the top of the card when they hold it up for me to see.  I didn’t have the color circle stickers here at home, but I believe they may help in the visual for me to see.  By keeping responses color coded, I can quickly scan the room to see where students are, then make a decision as to what type of question follows or if we should procceed with discussion of why they responded as they did…supporting their claims with mathematical evidence, of course.

Notice, the QUESTION response.  A student may have a question or require some clarification, this choice doesn’t allow them to opt out, but provides a way to say, I need some help.


On the back side, there are simply color-coded (different from other side) multiple choice responses, again to allow a quick scan before deciding how to proceed.  If multiple answers are chosen, begin by asking students to give possible reasons why a student may have chosen A or D-the other answer, if I chose A, could I figure out how someone else would have chosen D?  I also like to ask, noone chose B or C, what is a possible reason why someone would not have chosen  ___?




Like I said, I plan to use color circle stickers which allow me to see student responsesmfrom across the room.  I am debating on howmto do true/false.  Would
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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.

Providing Students Time to Reflect #makthinkvis


Making Thinking Visible online chat has really challenged me to think differently this semester about my questioning, looking for opportunities for students to share their ideas but most importantly, giving them time to reflect.

To begin our unit on triangles, I used the Generate-Sort-Connect-Elaborate, with plans to elaborate towards the end of the unit. As a class, I simply went around the room, each student generating an idea/concept related to triangles and I added what they shared to the list.  I placed students in groups of 3 and asked them to sort the ideas any way they wanted and to connect each set of ideas to the triangle central theme.

Most had measuring, classifying/types, etc. However, several had made some connections back to our Day 1 activity with the Chaos game, Sierpinksi’s Triangle, Midsegments and their properties.

Today, in class, I asked them to flip back to INB page 47 and take a couple of minutes to do nothing but read through their original concept maps/webs. Before I could give them further instructions, one asked if they could add to it? Of course! That’s exactly what I want you to do! I’ll see if I can manage some before/after pics.  The following few minutes were great. Listening to them think and share outloud. One even said, “Man, I’ve sure learned a lot!”

The next task is one I read about inmy reader a few weeks ago. I apologize, if you blogged about this and I’ve forgotten your name, but I really, really liked it! I gave each student 4 sticky notes, directing them to place a + sign in the corner of one, ? on another, ! on the third and finally a student asked, “you’re not going to make me draw a lightbulb are you?!?”


I explained what each note would include:

+ One Improvement – this could be either an improvement they still needed to make OR an improvement I could make in teaching the unit. A student asked if it could be something they improved on during the unit..sure!


! What NOT to forget!


? A question they still have.


Lightbulb moment during the unit…


I gave them some time to flip back through their INBs, instructed them to place their notes on the board in the back of the room.  A few asked if they could bring theirs in tomorrow. 

A quick glance showed that many still are not comfortable with proofs, a few are having trouble with the ‘names’ of triangle centers. I am more concerend they know/understand each of the centers’ special properties for problem solving. There were a variety of lightbulb moments.  And even a few misconceptions are obvious in some of their responses.

My plan is to address common questions as whole class.  I had originally thought I would respond to the individual questions/misconceptions by using different color sticky notes up on the board.  However, now, I’m thinking I may recopy some of the misconceptions onto dry erase boards and use them in a chalk talk carousel activity. 

To begin, have a variety of comments, some I agree with and others I am concerned with.  Give students red, yellow, green stickers – they carousel through the statements, placing green on those they agree with, yellow or red on those they have questions about.  Would this or the chalk talk be more beneificial here? 

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…

#75FACTS week 4 – #24 I used to think… but now I know…


This week we’ve been off from school for fall break – a road trip down south to visit Winter the Dolphin in Clearwater and a few days of warm sunshine on the beach has me somewhat re-energized.  I’ll be honest, my book is still at school.  The directions for this week were to use one of the FACTS #1-10 but I haven’t been in class to do this. (Sorry)  Before leaving school last week, I chose FACT #24 I used to think…, but now I know…  as a left-hand page assignment for my Geometry students’ INB.

#24 I used to think… Now, I know…

Eight Standards for Mathematical Practices

Practice 1 Make sense of problems and persevere in solving them.  This FACT allowed students to reflect on their learning, an opportunity to share what they used to think and what they now know after working with the concept.  Students responded to this prompt after exploring in small group investigations, pair-share processing, independent practice and finally whole class discussions/questions over Triangle Congruence.  I used to think… but now I know gave students the chance to make sense of the ideas they have been working with in class.

Facts and Teaching Goals

The goal of the lesson sequence was to allow students to recognize and determine which side-angle combos were appropriate and would guarantee triangle congruencies and finally applying those ideas with informal proofs.  By allowing them to respond in writing, I was made aware of their initial misconceptions – but also able to see they had in fact realized on their own how to prove trianlges congruent with a limited amount of given information.
I learned that the AAA and HL were the two students had struggled with most but they wrote about how the activities / discussion helped them realize specifically what was needed with each combo.  Another common error they pointed out in their reflections were that order of the included sides/angles did matter with situations of AAS and ASA.

Planning to Use and Implement Facts

One reason I chose this FACT was because I am looking to implement more literacy strategies into my instruction.  This FACT provided students with the opportunity to reflect on their learning in written format – a different type of processing that just talking/telling what they’ve learned.  By the time the prompt was given, students had explored in small groups, shared verbally with a partner, practiced individually.  The writing component seemed to complete the various types of literacy strategies.  By giving students a chance to respond to this prompt, I was able to see in-depth their full understanding of the intended concepts.

Small Steps

Were your students engaged?  Yes, I was very pleased observing students as they wrote their responses.  Most students took their time to share insightful reflections.  There were a few who tried to skim by with very vague responses, I gave them written feedback and asked they resubmit their responses.  Based on their new responses, I expect those few will give their best effort first time around next time given this prompt. 
Were you confident and excited about using the FACT?   I felt it was a good opporutnity to have students share their learning in writing.  I was not as excited about the FACT until after I actually started reading their responses…
How did use of the FACT affect the student-to-student or student-teacher dynamic?  Student to teacher – I felt they were honest in their responses – and most were insightful – I was encouraged to use this FACT again because it allowed me to see into their thinking.
Was the information gained from the FACT useful to youYes,  however, I don’t think I will change my approach to the lesson in the future – students were able to adjust their thinking because of the lesson format.  The FACT let me see this as a successful sequence – what a good formative assessment strategy should do!
Would you have gotten the same information without using the FACT?  I’m not sure I would have given students the opportunity to reflect had I not used the FACT.
What added value did the FACT bring to teaching and learning? Based on student responses – I believe most appreciated having the opportunity to think about their learning – it “tied up loose ends” for them in the end.
Did using the FACT cause you to do something differently or think differently about teaching and learning?   It made me realize I’ve failed to provide students with good opportunities to refelct on their learning between lessons / practice and before “official assessment” occurs.  This is something I plan to implement more for my students!  It was quick, little/no prep and offered me the chance to really see what students thought about their learning.
Would you use this FACT again?  Yes.
Are there modifications you could make to this FACT to improve its usefulness?   I believe next time I will plan more time for students to share out their responses – maybe within a pair-share then as a whole class, possibly using the ‘Around the Clock’ appointment cards idea from Global Math Department.

Using Data from FACTs

Most students realized that AAA could only guarantee similarity amond the triangles.  There were several misunderstandings about HL I was not aware of until after I read student reflections.  I will be more puposeful in defining the included parts in the various combos, for example I shared examples with students and asked how AAS and ASA are alike / different because this was one that a few still had struggle with.  During this discussion / sharing – it was obvious some a-ha! moments occurred.