Attention to Precision #MTBoS

Recently we complete the Parallel Lines AB from Desmos.

As I was reading through the reflection slide and responses, I noticed several students had not actually answered the question.  Hmmmm.

Did they understand what it was asking?

I quickly began taking snapshots of their responses, the sorting them and presented them in groups by similarity.  My question to them – “What question do these answer?”  And this is where we began class the following day.

We discussed using pronouns and whether this was the best choice of words or not.  Then there was this set of responses.

This led to how we can review our responses to make sure we are answering the question being asked.

I remember when I taught geometry, students would often solve the problem, but they never actually used that solution to address the actual question being asked.  Calling their attention to this was often eye-opening and helped to remediate the issue quickly.

Attention to precision for me can be several things.  Accurate work, labeling our quantities, but also communicating our reasoning, answering a question thoroughly, supporting our responses with evidence.  Snapshots is a wonderful tool to bring things like this to light.

What are some ways you address attention to precision in your classroom?

Summer Reading 2019 Book 1 #hackingQs

Hacking Questions:  11 Answers That Create a Culture of Inquiry in Your Classroom by Connie Hamilton

What a great read!  So many thoughtful, practical tips that can impact my classroom tomorrow – except, its summer break, so I suppose impact my classroom next fall!

I always enjoy a lighter read to begin my summer learning and a chat with colleagues and friends to reflect on what we’ve read is always a good thing.  You can search up #eduread over that past few weeks for mine and @druinok’s take on this book.

One thing I loved about this book was the quotes to begin each hack.  I am thinking I will make mini posters, highlighting the word/focus: Engage, Think, Reflect, Listen, etc.  @druinok even stated at one point – the quotes alone could lead to some great PLC conversations.

My biggest take-a-way from the entire book is INTENTIONALITY.  There are such good suggestions, but preparation and being intentional with implementation of those ideas is the foundation of creating this culture.  Many of her strategies are simple moves on things a veteran teacher may already do – but why/how it impacts learning is very enlightening to me.  I walk away after each hack, feeling like I can do this.  I can make that work in our classroom.  There was really nothing in the book that overwhelmed me.  I never once felt I had to add to what I was already doing – but simply to adjust / make what I do better with her take on things.

A jot-down for each hack that I made…

• student feedback with new protocols, what worked, and how could we refine?
• IDK becomes a rise to action, not an end result.
• a punctuated lesson models responsibility, time management and goal setting – the student has a plan.
• teachers and students playing PINK PONG with questions – this gives a false sense of discussion.
• what impact will my questions have on triggering their thought?
• content questions alone are not enough – metacognitive…
• teachers include themselves in student learning – GET OUT of the way!
• answers are not transferable, logical thinking and reasoning are transferable.
• most difficult to master (for me) passing the baton back to them – accountability – who’s doing the thinking? “might”
• Very specific Questions trigger responses that expire.  we cannot without ownership of learning by asking all of the questions.
• Come to school to enjoy a day with your students.

These are just thoughts from the reading that made me pause or convicted me somehow to make improvements.  There are numerous structures offered within each hack.  I would like to add a few more posts and share my thoughts on how I see things going in my classroom.  The author does a beautiful job of helping us see how to walk in tomorrow and make a small adjustment;  she shares snapshots from real classrooms, offers ways to think about the pushbacks we may encounter and how to overcome them.

I am very appreciative of her sharing of ready to use resources on her website as well.

This book is great for any teacher at any grade level with any level of experience – young and veteran alike.  Get it. Read it. Talk about it.  Reflect on it.

Let me know how your changes impacted your students’ learning!

Something Old, Something New…

I used to keep a large poster up for our INBs table of contents.  For whatever reason, I got away from that last year and did not even do it last fall with those classes.  However, the poor attendance, numerous snow days have demanded I do it again…  to help students get / stay organized / catch up and for my own sanity!  When they ask…I can point to the poster…

Something new…  I am a believer in literacy strategies.  Students often are not taught how to take notes from what they read.  Most of us vomited highlighter all over our textbooks…  without discerning the needed, important information, we would just learn ALL of it.

So, here is what I did…  Students are 4 to a table, so I cut the review / summary notes into 4 sections.  I asked students to divide their pages into 4 sections with labels.

Each person at the table gets a different section of summary notes / examples.

This was over domain and range of continuous graphs.  With a snow day making a long weekend, I thought it was a great way to review.

1 minute to read.  1 minute to jot down important BIG ideas.

Rotate summary notes.

Repeat.

Some may think 1 minute was not enough time – but since this was a review of last week’s work, I felt it was fine.  If introducing new material, I may feel differently.

After the first round, I observed students writing during the reading time.  I shared my reasoning – the first time was to read – no worries about grabbing information to remember.  The second time was to skim / write big ideas… that way they were accessing the information at least twice.

After every student has read / written for all 4 sections.  They share out 1 BIG idea they wrote down with their table.

I asked for questions, but none.  So, I think next time I will have a post-it available to reflect…  something I learned, realized, was reminded of OR still have a question about…  they tend to ask when its written and anonymous.  I get that.

What summary, literacy, reading strategies do you use in math class?

 

w

Reflecting on Formative Assessments

Every Story has a Graph / Target Quiz

Earlier this week, I gave a short Target Quiz – just one big idea.Students were given three scenarios and asked to create a graph to model the situation.  Out of the class, there were 4 students I felt I needed to pull over to the side for some one on one time.  I found they were often drawing the “shape” of what was happening rather than comparing the distance from home to time.

The one most missed had Tom walking up a hill, quickly across the top, then ran down the other side.  Yes, most kids draw the shape of the hill.  As opposed to the distance continuing to increase as he ran down the other side.

Whiteboarding Examples / Non-examples

The second Target Quiz was on whiteboards – students had to create an example of a graph, set of ordered pairs and a table of values with a function and not a function in each example.

I laughed as one table was begging me to give “real quiz” and take a grade because they knew that they knew!!  As I walked around the room, observing, asking questions – there were 3 students with some minor mistakes and 3 who were really struggling.  Upon questioning, they were able to identify when the example was given, but unable to create examples on their own.  With some “funneling”  – they were able to get examples of each, but I have them * to keep an eye on and requiz next week.

Deltamath Practice – immediate feedback from tech;

Teacher observation & questioning

We had a very brief introduction to writing domain and range of graphs in interval notation.  We spent some time in the computer lab today practicing this on deltamath.com.   I appreciate the immediate feedback they are able to see if they miss the question.  Also, how he has programmed the many different options for defining domain and range.

Many misconceptions were cleared as we learned whether to use the endpoints or extreme values (if they were not the same).  There was discussion about the open circles and closed circles and which inequality symbols were correct to use and when.  And yes, a few realized they were mixing up the x and y for domain or range.  I look forward to practicing this skill Monday after their experiences today.

Desmos Activity – Inequalities on a Number Line – Matching Tasks

For my other class, we will be solving and graphing inequalities next week.  So while in the lab today, we worked on Desmos – Inequalities on a Number Line and Compound Inequalities.  The first task was a good review and learning opportunity for the direction of the symbols.  I still had some students exchanging those up.  Most were correct in open versus closed circles and what that meant in symbol terms.  Though I did not make it to all of the students in the second task – I was trying to catch students on the two sorting pages of the first activity as they were going through.  For some it was as simple as a brief discussion about why one was the correct choice and comparing it to their wrong match.  There are about 4 students still having troubles on the first task.  And several have not completed the last task.

I feel like looking at their responses, I can use their examples as discussion pieces while we are looking at our notes next week.

I almost feel like there were not as many issues in the second task.  However, I still have several that have not completed them yet.  But I feel like using live examples from their work and discussing maybe two stars and a wish they would have for each student – may help them steer away from making their own mistakes.

I love the real time feedback I get as a teacher and how I am able to grab kids before they move on too far and help erase some of their thinking and replaced it with correct ideas immediately.

Someday – I’ll get to have a classroom lab… I hope.  Until then, we will keep on doing what we can.

 

Look Back… formative assessment strategy

Not sure that this counts as a #MTBoS12days post since I actually returned to school today.  I appreciate having a day back before our students return.  It requires me to be in the building and I get a moment to refocus.

As I drove home this evening, what a beautiful moon!  So glad it was full on a day that we didn’t have students. ha.

Anyway, I pulled my Keeley & Tobey blue book over my shelf and began digging to see what strategies had I never tried – with the idea, I would pick a couple to try over the next couple of weeks.  Well, as I went down the table of contents, I realized I utilize many more of the strategies than I initially thought.

When I came across the “Look Back” approach – basically students account for what they learned over a given period of time.  They think of specific examples of things they know now and describe how they learned them.

I have used “brain dumps” before to list as many topics / ideas as they could about a given unit in a set amount of time – then they get up and meet with a partner for give-one, get one – but this basically just creates a review list of topics / skills.

However, what makes the look back strategy intriguing to me – having students to tell how they learned the concept.  This idea helps students think about their own learning.  It allows teachers to look at the sequence of their instructional plans and determine why students got the most out of certain aspects / activities.  Interesting.  Look back can also provide the teacher with ideas on how to plan differentiated learning in the future for specific students.

We must remember that this is allowing students to share what stood out to them in the learning cycle – but not necessarily how much they learned.

I look forward to using “Look Back” toward the end of a unit – maybe even use this feedback, compared with the unit assessment to see if students in fact showed proficiency on the concepts they listed.

Goals for Spring Semester #MTBoS12Days Post 4

Saw Elissa’s tweet and wondered… which lead to this conversation a couple of days ago…

• ---

  @misscalcul8 Dec 26

  Anyone want to share some professional goals they have/had? Feel like I “floated” through 2017 on the high of personal 2016 accomplishments. Want to be intentional about 2018 so I can look back on actual accomplishments this time next year.

  Replying to @misscalcul8

  Be intentional with planning formative assessments, develop and focus on vocab with roots-weekly system, and… more open questions in assignments & assessments. Are those measurable?

   @misscalcul8 Dec 27 I would say yes. Are you tracking your progress in any way?

   

  @pamjwilson Dec 27 Haven’t started yet. Replying to you, putting in black and white was a committment. Lol. Thought I might blog and come up w SMARTgoals and a plan before spring semester starts back.

   

  @misscalcul8 Dec 27 How will you measure intentionality? I think the other two could be measured with weekly checklists to hold yourself accountable for how often you’re doing them.

   

  @pamjwilson Dec 27 Maybe by including a form. Asst. Linked With each learning target in my lesson plans? And a quick reflection after the form. Asst with next steps?

   

  @misscalcul8 Dec 27  Is that something you can sustain?

   
   @pamjwilson Dec 27  I believe it would be much work first time around, but once it’s done, just needs refinement.

    

  @misscalcul8 Dec 27 All classes or just one to start?

  @pamjwilson Dec 27 Likely, one.

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So, what were those SMART goals again?

So, to take this…  Be intentional with planning formative assessments, develop and focus on vocab with roots-weekly system, and… more open questions in assignments & assessments. Are those measurable?

Elissa’s question – how do you measure intentionality?  Hmmmm.  If its a goal, I should be intentional with it right?  So, how do I measure that?  By asking someone to review my unit plans to ensure that I am including these in them?  By weekly self-accountability?

All of these things are related to my planning – I constantly use formative assessments, they are just not formally documented in my plans as they should be.  How do I know they are actually assessing the desired learning outcome?

At the beginning of each unit, I have a Words Worth Knowing Vocabulary Survey – that I modified from Sarah’s here.  I walk around the room and observe students’ assessments of their knowledge of these terms.  Towards the end of the unit, we revisit and they re-assess, hopefully being familiar and knowing more than they did in the beginning.

Yes, they are exposed to the terms within the unit, but do they have a deeper understanding of the words?  When I taught geometry, I did a lot with the etymology of the words.  I am wondering how I can develop a list of latin/greek roots, etc. relating to our intended vocabulary?  And someone develop a weekly system like my science colleague to help students truly build a foundational understanding.  I started a list just before Christmas Break, but have not spent much more time with this task.

I have included open questions often within a daily task, and tried to include in unit assessments.  But not at the level to truly elicit student thinking and frequency I would like.

The focus of these goals will all be one section of Algebra I.  My other Algebra I class uses the Springboard Curriculum – a completely different order of topics and pacing.

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For the Spring 2018 Semester, in my 4th block Algebra I class, I will increase (currently, I do not link them in my plans) my planning of formative assessments for each learning target listed / linked in my unit lesson plans.  Twice per week, I will take time to formally reflect (written) the student work and devise a plan for next steps.   Currently, I only informally reflect / plan next steps, without formal documentation in my plans.  I hope this work will lead to better quality formative assessments that are truly at the level and integrity of the standards.

Over the course of the Spring 2018 Semester, I will develop a list of common Latin / Greek roots as related to our content in Algebra I.  Through the collaboration of my colleague, I will develop and implement a weekly system to help students learn and make connections within the content to the roots, etc.   The list, weekly quiz results and study tools will be documented in lesson plans.  At the end of each month (January – April), I will reflect on our progress, analyze the impact on student learning and adjust, continue.  This list should grow throughout the semester.  List to students, implement study tool, report student progress.

I will revisit Small & Lin’s book More Good Questions for ideas on creating Open Questions.  As part of the formative assessment tools, I will begin to include these on a weekly basis in our lessons – for feedback only and incorporate on every unit assessment (after discussing with my content team teacher).

If I have a sheet in my planner for weekly reflection…  Suggestions?

 

 

Self-Care, #5Habits & #HEART! #blogitbingo #MTBoS

My past few weeks have been spent reading and chatting 5 Habits with a close friend.

Just last week, after a two day training with Dr. Kanold and a tweet from Casey, I decided to download HEART! for some reading with travel time on the road.

And this morning, I tried to get a walk in before the rains from storm Cindy set in while listening to Cult of Pedagogy.

Two things from the podcast…

If you want to know what your future life will be like, take a look at your life today. 

 I took this as, if my life right now doesn’t look how I want to see myself in the future, well, there are some choices I need to make.

This went right along with a quote Nicki Koziarz shared in 5 Habits: 

What you want most over what you want now.

And the beginning of our training with Dr. Kanold was about naming our vision and using it as the guide in our decisions.

Many will say, yes, Pam, this is common sense. Maybe. But apparently it’s a message I needed to hear at least 3 times before I actually heard it.  

The other thing that was shared in the podcast:

I dont like to think of myself as busy, but fruitful, productive, accomplished.

I would like to see myself as more efficient, intentional with my time.  

Anyway, just a quick reflection for myself of how 3 different resources are overlapping for me today.

Looking forward to this free webinar from Angela Watson, Teachers You are a Priority too! on June 28.

HEART! has been both convicting and motivating.  I have completed 80% of the book, finished Risk last night and beginning Thought today.  I am very excited to see how I will use what I’ve learned to have an impact on student learning in my school.  

I am sending myself a text for mid-September for accountabity.  Hopefully I will have a positive blog post for follow up.

What reading / resources / training have overlapped for you recently?

Stacking Cups… part 2 #MtbosBlogsplosion #myfavorite

I like big cups, I cannot lie.

We stacked cups in the first few days of school…

I’ve been stacking cups since…uh.  I think my first NCTM Navigating Through…  book was around 2002 or so.  Its been a while.  I have vivid memories of discussions in classes from room 125.  Yep.  It’s been while.  Long before there were songs about Solo cups.  My guess, a few of my sets of cups may be that old.

They’re a cheap resource.  Find a buddy or two, each buy some different sizes, split them up and you’ve got some varied sets of cups.  Hmmmm. What all can you do with cups?

I.  This past week, I began by displaying a single cup and asking students to generate as many questions as they can about said cup.  Set the timer.

II.  Turn to your groups and share your questions.  Then say whether it was mathematical in nature or not.  Each group shares out 1 question with the whole class.  Then if anyone had a question they wanted to share that had not been included.

Yes, we actually looked at the etymology of cup…wondering where the name originated.

III.  a.  I went with “Why am I stacking cups?” as my transition to the task.  You guys are engineers today.  Packaging designers, specifically.  Design a box to ship a stack of 50 cups.  They needed tools, so I gave each group 4 – 7 cups (did I mention some of these cups may actually be older than some students?), each group with a different size/brand of cup and a measuring device.  Set the timer 5-7 minutes depending on class.

III b.  As I monitor their work, I usually here a few moving in the wrong direction.  I pause the timer and their discussions…attention at the board:

I need some help.  One group has a stack of 5 cups measuring 14 cm, and their height for a stack of 50 cups would be 140 cm.  Do you agree or disagree with their response?  Turn to your group and discuss.  Set the timer.

I have some varied responses usually.  When I get to someone who disagrees, I ask how tall they think the box should be and they come to the board to explain their reasoning.

III. c. Yes, believe.  You will sometimes have a class where no one disagrees with the 140 cm response.  Have them to create a table of values to record their measures for 1 cup, 2 cups, 3 cups, etc.  Set timer.  Usually during this time you will hear the a-ha’s.  Bring the class back together to discuss / share their thinking.  Modeling how the cups would be stacked.

Okay, so moving on now.

IV.  Once we feel fairly confident in our expressions. I ask them to find the height of a stack of ____ cups for their group.

V.  Well, what if I had a box that was 80 cm tall, what is the largest amount of cups could I ship in that box?

VI.  At that point, we share our expressions we’ve created for each type of cup.  I put all cups on display and ask groups if they can match the cup with its expression for  total height (cm).

This leads to some light bulb moments for a few students.  They can now see how different parts of the expression represents different physical parts of the cup.  I always thought it would be fun to list the expressions on cards and they have to match to the cups and play the Race Game from The Price is Right.

VII.  For other practice, we use the expressions:

• simplify expression
• find the total height of 50 cups
• how many cups to make a stack of 80 cm?

VIII.  Closer choices

• What’s one take-a-way from today’s task?
• Something I learned… realized… or was reminded of…
• How are the expressions alike?  different?
• Which two expressions are most alike?  Explain.  Which two are most different? Explain.

IX.   Systems

Next, have students compare their cup stack to another groups stack of cups.  When will the two stacks be equal heights?  Just using my groups’ expressions above, they get at least 6 practice problems.  You can leave it as an open task – students can choose tables of values, creating equations to solve or even solve graphically.  The key component is to ensure they interpret their solutions (x, y) = (cups, stack height) within the context of the scenario.

A Light Bulb Moment #MTBoS30

Here’s a shameful post – one of those things I knew it happened, and wanted to believe I knew WHY it happened, but in reality…I was struggling.  Until yesterday…  in after school, tutoring a student for upcoming comprehensive final.

I know how manipulating an equation will transform the graph of the function.  I can predict it quite efficiently.  I know and my students even recognize that y=a (x-h)^2 +k will translate left / right… “opposite” of what the sign / operation is in the parentheses with the h.  But why?

So one day, as I heard myself describing the transformation to a student, I thought…that sounds so stupid.  I mean, hello.  No wonder it doesn’t stick.  It makes no sense (what I had just said).  In my mind, I heard Pam, the student, asking why do we change the sign of the h, but not the k?  Why does the h move opposite, but the k translates direction of the operation?

I started really making more sense to myself when I focused on function transformations in Algebra 2 and transformations for plane figures in Geometry the past couple of years.  But I was definitely not satisfied with what I was saying.  I believe our work with equations of circles related to slope and pythagorean theorem is what started chipping away my lack of true understanding.  Because I began to explore, ask questions.  I was curious.

When I started having students create tables of values, seeing how the values changed with each transformation helped, but not to the level I’d like.

So, here it is folks… when we’re looking at the y=a(x-h)^2 + k…the h is actually NOT the x-coordinate of the vertex.  The h is the transformation back to zero (origin).  Can we look at it that way?  Does that even make sense?  The x-value is where we moved from the origin.  The h will return us back to the origin.  I know its not where I need to be yet.  But I’m open to listening to other’s ideas here.  I’m not satisfied with “it moves just opposite of what we think.”

My next failure as a teacher saga…I don’t do a good job of helping students differentiate between linear functions and arithmetic sequences.  I’m starting to muddle an understanding.  At a moment in time, they are comfortable with each idea, but they continue to mix up when its a first term, n=1 OR an initial value n=0.  The best I can do for now, verify your equation works for the values…

May Day, May Day #MTBoS30 #5pracs

Thursday night, I printed off a packet of handouts from a session I’d led at KCM conference in 2012, simply because there was a data collection activity “Look Out Below!” I wanted to use in class on Friday.  As I flipped through the pages, I was taken back by what I used to do.  And it made me sad.  I walked in Friday morning, straight over to a colleague’s room and asked for accountability these last few weeks of school.

Multiple times the past several months  I have been directed back to 5 Practices for Orchestrating Productive Mathematics Discussions, Smith and Stein 2011. I read the in book even participated in a chat.  The following school year, I implemented a few lessons purposefully using this structure.  I found that the FALs from Mathshell often followed the same format.  It led to great discussions, thinking and sharing in my classroom.  So, what happened?  A rut.  I still used the structure, but not intentionally planning NEW lessons, just recycling the ones I’d become comfortable with.

Last November, I attended an ACT Boot Camp sponsored by@UKPIMSER, one of the strategies shared was the 5 practices!  This winter, we had 8 Non-Traditional Instructional Days in our district- where students / teachers participated in learning tasks during Snow Days.  Our department used NCTMs Principles to Actions book, focusing on the 8 Mathematics Teaching Practices, one of which was promoting whole class discourse, and using Smith & Stein’s outline.  This spring, I have come across several chats mentioning the 5Practices for discourse.

Just today, I read @marybourassa’s post Day 80 Ropes and Systems, that described how she used a chart to track observations and conversations inspired by this book.  I also read @bridgetdunbar’s Teach Math as a Story post as well as watched @gfletchy’s Ignite Talk on becoming an 83%er – one who is asking questions to effectively engage students… We must focus on task planning – better questions (Frank’s hot sauce!) in order to listen to our students rather than for their responses.  (S/O @maxmathforum 2>4 Ignite!).

As soon as I arrived home, I grabbed a box from the shelf to get out my #5pracs for a revisit.  And all these treasures were there with it!

As I flipped through my book, I found these notes…penned on the last day of summer break, on a final trip to the water park, I’m assuming 2012…reading while my daughter and her friend splashed in the wave pool.

I was preparing for the first few days / unit of Algebra 2…

So, here’s my goal for the #MTBoS30 challenge: to revisit #5pracs and plan a couple of intentional lessons, ask better questions, monitor observations and conversations – maybe even record with my phone in pocket and see if  can accomplish some of the “Try This” Smith & Stein have outlined in their book.

I’m asking for accountability, MTBoS.  Mayday! Mayday!

The title, I thought was fitting, rather than sink these last few weeks – which normally kick my butt, I am determined to finish strong in an effort to leave a great impression with my budding, almost 10th graders – allowing them to see that math is more than just math.

from etymonline:

mayday (interj.) distress call, 1923, apparently an Englished spelling of French m’aider, shortening of venez m’aider “come help me!” But possibly a random coinage with coincidental resemblance:

“May Day” Is Airplane SOS
ENGLISH aviators who use radio telephone transmitting sets on their planes, instead of telegraph sets, have been puzzling over the problem of choosing a distress call for transmission by voice. The letters SOS wouldn’t do, and just plain “help!” was not liked, and so “May Day” was chosen. This was thought particularly fitting since it sounds very much like the French m’aidez, which means “help me.” [“The Wireless Age,” June 1923]