Category Archives: teacher reflection

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

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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?

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Stacking Cups… part 2 #MtbosBlogsplosion #myfavorite

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I like big cups, I cannot lie.

We stacked cups in the first few days of school…

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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.

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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.

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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.

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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).

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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:

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  • 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

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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

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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!20160501_145551.jpg

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.) Look up mayday at Dictionary.comdistress 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]

 

Time. 8 Minutes…

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I’ve been pondering since Spring Break – why am I just now feeling really connected to my students?  Its bizarre-ishly late in the school year.  When I used to teach on 6-period day, It was early in December/January before I really felt my students trusted me – would take those learning risks I tried to encourage.  So why was it mid-March this year?

We had a debate in our school over scheduling earlier this semester, we have been on a 7-period schedule this year.  One teacher remarked the difference between a 6 and 7 period day was only 8 minutes per class and that we couldn’t gain much with 8 minutes.  But  I feel like my room is a revolving door, kids come in, kids leave, another group comes in, then leaves, etc.  My closing activities have dwindled to a little of nothing.  I am not effectively wrapping up the lessons.

So, I looked at the numbers – 8 minutes a class, 5 days a week, 34 weeks = 1,360 minutes divided by 55 minute class period is 24.7 class periods.  That’s nearly 5 weeks of instructional time.  Whew. No wonder I am so far behind in my units.  We also had 8 non-traditional instructional days – though students were not in the classroom, there were learning tasks completed.  But again, that’s 8 more instructional periods.  So I have missed between 6 and 7 weeks of instructional time with my students.

Wow.  Now, I see why it was mid-March rather than December / January to feel connected and trusted by my students.  I’m just now really able to see their thinking, predict their approach to a problem, getting them to step out on a limb and try – even if they aren’t sure.  Its only been recent weeks that some have gained the courage to ask the questions in their heads…without fear of judgement from classmates.

Sidebar thought – This is not a complaining session, but a reflection on the year so far… I’m not advocating for a 6 period, but grades 10-12 in our building had a modified-block schedule that was the best of both worlds.  Two yearlong periods, with 3 semester blocks. Ninth grade had its own wing and had 5 periods with a single semester block at the end of the day.  The debate was to go to a school wide modified – say 4 year long periods (minis) and 2 semester blocks for lab/hands-on learning/CTE/electives while still having an opportunity for year-long courses for core classes.  However, it was stated our faculty would be perceived as was not wanting to dig-in and do the hard work required on the 7 period.  I respectfully disagreed with this statement, no one in our faculty was trying to get out of work – only trying to find a solution that would support better opportunities for our learners.

How might I adjust for next school year?  What are things I can actively change in my classroom and approach that will allow me to make quicker connections with my learners?  And so now, I begin to think about summer reading, professional growth opportunities…

Reflecting on the Year #junechallenge 3

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As I begin to read through responses to class/teacher evaluation for Algebra 2, most are encouraging.

So much of distress I felt this year was due to outside circumstances – as much as it was within my reach, I tried to keep my classroom going.  But it was difficult and draining at times.

How can I continue to offer a classroom that’s inviting, open-to ideas and encourages students to work through challenging tasks?

1.  There must be a relationship established – I feel it takes several weeks, even months to establish this.  Students must trust that you are there for them.  You must reassure them they matter.  Your actions must confirm your words.

I think of a couple of students in particular this year who pushed back – often in the beginning of the year.  I continually had to remind them they were valued and help them see they were learning.  One in particular lashed out during class and refused to participate in a task they felt was not helpful.  The other refused to work in a group of students because that wasn’t “how she learned math.”

In the end, they both experienced success.  Maybe not at the level the state deems readiness, but such big strides moving their thinking forward and growing their confidence.  Each will experience success in life because they are hard workers and they have seen that failing at a difficult task does not define them as a person, but their response to that failure is what builds them.  It was rewarding to watch them pick up, look for ways to improve and after some more effort, smile at the final result, realizing how far they had traveled as a learner.

Taking time to listen to my learners and their ideas – allow them to know I value their thinking.  I need to consider this while building learning tasks and make sure to allow for time to do this.

2.  There must be variety – routines are important but continuing the exact routines all year long becomes mundane and boring.  For example, I like students having a task to begin class – but I also know that changing some of these up every few weeks keeps their interest peaked a bit.  I’m not sure I will have every single thing listed here, but some of my favorites:

Estimation 180, Counting Circles, Visual Patterns, Would You Rather?, Krypto, Math Dice, Flashbacks, Time-Distance Graphs, StatRat from USAtoday.

We were supposed to implement Leader in Me this past year.  Again, one of those things that could have a huge impact, yet, if no follow through, it sizzles out.  Which makes me sad.  One quarter, I used Make a Difference Monday.  I copied articles from What Do You Stand for? (Barbara Lewis) – students read, then on a post-it would respond briefly to a prompt I had on the board pertaining to the article, but relating back to their life / choices.

Test-Prep Tuesday was essentially flashbacks to pre-algebra and geometric concepts – intended to help students study for upcoming ACT.

Fast-Five Friday was a flashback of big ideas from the previous week.

Some ideas I want to add for next year:

Graphical Data is presented, but students create the questions.  Understanding data displays is so important – so I hope to build a file of examples to use here.  Now I need a cool, catchy name for this structure.

Function Junction – using the NAGS format, I will give students one of the models, they must fill-in / create the other 3.  Possibly even use a railroad/train format in graphics that connect each model: Numerical/table of values, Algebraic / Equation, Graphical, Sentence / Context description.

Literacy and Vocabulary strategies are important to me.  I feel several of my students struggle with reading and comprehension, so I am hoping to build a structure to help them link new terms to prior knowledge.

3.  Communication with home is vital, yet I continue to fail at doing a good job.  I start with good intentions.  Do parents even know who I am?  Do they know my views on education?  Do they feel I am approachable?  Again, it will be a goal to make positive strides to utilize home as a resource and support.

Painting a Bridge

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In my Algebra I, we are looking at parent functions. Students said this week was quite easy, they felt they were doing 3rd grade work.  But I assured them
recognizing the parent equation and making connections to the parent graphs may seem easy, but it’s a lead-in to more intense math!

We’ve done several data collections throughout the semester, mostly linear, a few quadratic and exponential.   But today we took a look at rational with Painting the Bridge, which is embedded in a MARS lesson. 

Students are asked to sketch the relationship x:# workers and y: # hours each works to complete the given job.

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Those are a good overview of what we saw.  I allowed students to ask questions about things they wondered about others’ graphs.  At first glance, a couple of the graphs may look odd, but given the chance to share thwir thimking, student reasoning made perfect sense in the real world.

Though I didn’t have an actual student create this graph, I included it on the board.

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I followed the suggested questioning in the MARS lesson, which led most students to some A-ha moments.  What does point Q mean? Points S? Does it make more sense for the graph be solid or dotted? Why?

As a data collection to follow up this discussion, we picked up erasers. One student held a cup in their dominant hand and picked up one eraser at a time and placed it in the cup, we timed.  Then another student helped.  Continued adding workers and it eventually became too crowded, they were dropping erasers and slowed them down.

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We compared the shape of our scatter plot and decided maybe exponential or quadrant 1 of a rational (inverse) function.

The calculator power regression resulted in
y =76x^-1.  Which gave us a chance to discuss that -1 exponent.  How it meant the inverse of multiplying by x, which was to divide by x.  So we graphed y=76/x. Nice. They were seeing the connection to our Painting the bridge discussion. 

Oh wait, how many erasers were we picking up? 78. Not bad, huh?

My goal is to give them a concrete data collection for which they can access and connect back to the math.

To end the day, they asked if they could draw a graph on the board and everyone guess the parent function name.  Sure.   They were on task and engaged so I was fine with it.
They began graphing the endpoints of their graphs,  so their classmates were finishing the graph and naming the function. It was humorous. But again, they were engaged.

I love these kids.  They were my favorites today.  It’s been a tough semester at times, but I want to end these last weeks strong. I want them to leave our classroom having grown in confidence and changed their attitude toward math.  That’s my goal.