Category Archives: reflection on teaching

2017-2018 #GOALS #1TMCthing #SUNDAYFUNDAY

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NERVES. Anxious.

We have opening day for teachers and open house tomorrow night.  I am always nervous to meet new students and parents.  Scared.  Because I want to be great for them, I want to value their time.  I want them to learn and think and be challenged.  Somewhere in the mix, I want them to at least not *hate* math.

The past couple of years have been, well, not my best.  I chose to disconnect – because things were happening out of my control and I quickly became bitter.  So as not to spread that ugly, contagious monster at school, I added space between myself and most everyone in proximity at school.  I trusted no one.  I gave up.  I walked into my classroom and I left.  It was miserable.   This is not the work life I wanted, but it felt safe to isolate.  It seems selfish looking back now.  But I needed time to heal, forgive.  Sadly, my students did not get the best me and that breaks my heart.  I apologize.

megan

Last year in an effort to dig my way back, my friend and I read a book Choosing Joy (kindle is only $0.99 right now).  Its a 52-week devotional with a 4-page format.  Easy, but challenging.  I was reminded that no matter what, I get to choose.  I plan to pull the book out again this year for frequent reminders.

I almost didn’t attend TMC17.  Even being a veteran, the voices in my head – nearly convinced me I shouldn’t go.  I had submitted my proposal way back when – I wasn’t sure if anything I had to share would benefit anyone.  I have such respect for this community, I didn’t want to waste their time.  My friend, the book fairy said, “But you love math camp.  It re-energizes you.”  She was right.  Its what I needed.  A BIG, jumbo shot of mathy-filled joy to jumpstart this school year.

START

I had 2 things on my list I wanted to learn more about and experience #talkingpoints and #clotheslinemath.  I’ve dabbled in both, but never saw them completely through for what they can be.  So, my #1TMCthing will be these 2 actually.  I teach Algebra I – basically 3 levels CP using Springboard Curriculum, Algebra I – using our own resources, and Collaborative with Co-Teaching Model.  I am excited to see how each of these routines / tools will play out with all of my students.  My goal to implement each one time in each unit.

This may seem odd, I see both of these supporting my goal of intentional vocabulary / literacy strategies.  Several years ago, I worked hard at implementing ideas with this focus – I need to refine and focus on these as well.

STOP

I need to be very intentional about my self-care.  In order to be my best for my family and my students, I need to make better choices for my health and down time.  Ideas:

  • take a 5-10 min brain break to recharge somewhere in the middle of the school
  • read for pleasure throughout the school year.
  • journaling my food.
  • #FitBOS to work towards my activity goals. S/O here to @sarah3martin for always including me in fitbit weekly challenges.  Thank you.

So I will protect my self-care time by including it on my calendar, sadly this gives me permission to do it without guilt.

CONTINUE

I have worked very hard for several years learning about formative assessment, questioning and closure activities for reflection.  I intend to continue working to improve these and keep using some that I have found to be very beneficial to my students.  But improving and being more intentional with my follow-up tasks to the formative assessments.

I would also like to continue implementing some of the big ideas from our chat on #Makeitstick a couple of summers ago, that Anna does an amazing job of sharing in her posts and presentations.  Spaced practice, interleaving, being intentional and explicit about retrieval practice.

And I will continue life-lessons in my classroom – that’s what kids will take-a-way in the end.  (If you have questions about this poster, just ask.)

jim carey

here for the kids

When I was younger, I remember wanting to “Be a Barnabas” – yeah. That too.

 

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Better Questions Week 3 #MTBoS

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betterquestions

I’ve pondered this challenge for a couple of days.  So many options!  But a tweet from @mathymeg07 led me to a post from @MrAKHaines blog Math Pun Pending.

The post was celebrating a variety of strategies his students had use to answer the question:

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He wrote:  When I wrote the question, I had anticipated that students would use a couple of different strategies. What I didn’t know was that my 25 students would use a combined seven correct solution strategies to solve this problem.

Two parts to my post:  1. How can I make this an open question and 2. How can I use student samples to develop a better lesson in the future?

How can I make this an open question?

A.  Name a point that is NOT on this line.

B.  Name a point that this line passes through.

Thanks to @PIspeak‘s TMC14 session in Jenks, I urge students to “Support your claim with evidence/reasoning.  I want to see your thinking!”

How can I use student samples to develop a better lesson in the future for my classroom?

I appreciated the fact that he never explicitly taught “the teacher’s efficient strategy” but allowed group discussions and support to drive the lesson.  Students shared ideas.  The last paragraph  in his post says, “My students are acting like mathematicians, y’all. They’re using their toolkit of math ideas to solve problems flexibly. I couldn’t be happier.”

In the end, that’s what we all want – students thinking on their own, making sense and being confident enough to explore a problem with their own ideas.  So, how does this tie in with the Better Questions prompt?  My outline of the lesson feels a bit like those I’ve used from Formative Assessment Lessons, but I feel it lends itself to students doing the thinking, talking – I only provide the materials and support to make desired connections that will lead to the learning goal.

I’ve been following the #T3Learns chat from Wiliam’s book.  In chapter 3 of Embedding Formative Assessment, it suggests using student sample work. How might I structure a lesson, utilizing student samples of this question?  In Principles to Actions, MTP3 states Effective teaching engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

  1. Begin with the same question. Allow students to write a response. (3-5 min)
  2. Place students into small groups and allow them to share their approaches. (5-7)
  3. Allow groups to explore student samples, making note of different ideas, what they like/ways to improve, questions they’d like to ask the student. *maybe as a gallery walk? (15-20)
  4. Discuss their findings as a whole group. (10 in)
  5. Connections to/between the different mathematical representations. (5-10 min)
  6. Written reflection:  (3-5 min. possibly use as a start up / bell ringer to begin class with following day – providing an opportunity for retrieval of previous days information?)
    • my strategy was most like:____
    • the strategy I liked most was ____ because ___
    • the strategy I found most difficult to understand was ___ because ___
    • Which approach was most efficient?  Why?
    • What do you think was the BIG IDEA your teacher intended for you to learn/understand?
  7. Transfer…provide a few, different contextual problems that allow students to connect the mathematics to something tangible, maybe in a problem posing situation (should this be small group?  individual? ) (5-15, would this be better as follow-up the following day?)

Timing is often an issue for me.  I want to provide students with enough time to make sense/discuss, but not so much time it feels long and drawn out.  Are the times I have listed appropriate?

Please offer suggestions.  How have you used a similar approach successfully in your own classroom?

#MTBoS My Favorite: Open Questions & Level-Up Quiz

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Goodness.  I think this is where I fall apart.  I have so many favorite things I’ve used in my classroom, at times I cannot focus and choose one.  I become distracted, thinking I have to use EVERYTHING.  I have to pause, think about the learners in the classroom and what will be best, most effective for them.

Our second week back after Christmas break was very productive.  I chose to combine 2 ideas and focused my energy with them.  One goal I had set was to use open questions.  (Older posts – first attempt, more good questions – about strategy from Small / Lin).  Rather than giving students more inequalities and asking them to graph.  I gave them a point and asked them to create an inequality whose graph would “capture” the point.  Students had to think differently in order to create their response rather than following a procedural step by step or copying a classmate’s work.

The other was an idea someone had tweeted that caught my attention and I wanted to see how it would work in my classroom…level-up quizzes.  Since the target involved graphing inequalities, I gave each student a paper with 4 empty graphs and space in margins to write inequalities and verify.  Here is a sample of the criteria I gave them:

level up quiz

I told students I wanted everyone to be at level 3 by the end of the week – Level 4 was using multiple measures to verify their responses.  If students were at 3 or 4 early in the week, I posed a challenge to them to create two inequalities that would both capture the point.

This task accomplished several things for me.  It was obvious where students got stuck, it allowed me to give feedback or have a conversation about the symbols, which direction to shade, helped point out when/why to use the = if the point was on the boundary line or not, could quickly address issues with graphing key points of the line.  It allowed students to move on without waiting on their peers.

There were a couple of students in each class who continued to struggle-mostly students who had chosen NOT to put any time/effort into practice the prior week or who had been absent, but the rest of students made gains and improvements with this skill.  By the end of the week, majority of students were at or above the level 3.

The big thing with verifying I saw was students using (0,0) to test in their inequality algebraically as opposed to the actual point we picked.  I feel this was due to us graphing inequalities the prior week.  This year, I opted to encourage evidence of their claim by having them test a point to determine direction of shading as opposed to just saying above/below.

With only 1 response for every student each day, I was not overwhelmed, but able to give feedback.  I made notes of most common errors and addressed them as a whole class prior to passing the quiz back.  For many, I simply wrote a number corresponding to the Level-Up criteria.  Students knew the first couple of tries “didn’t count” but were opportunities to learn and level up by the end of the week.

My concerns after reading about Rubrics in Embedding Formative Assessment –  have I made it more of a skill-ckeck list?  By presenting it as an open question, is that enough to allow for student thinking?  Thoughts on how to improve are welcome!

Week 1 3-2-1 Sunday Summary #MTBoSchallenge

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My first week kicked my patootie.  I slept from 6 Friday night until 6 Saturday morning.

I was nervous, anxious about starting school with all of our continued renovation but all in all it was a very smooth start to the year.

3 good things…
Day 1 began with Notice & Wonder of Pascal’s or Sierpinski’s Triangles or some type of data collection activity in every class.  I feel it sets the tone for the year.  I addressed syllabus big ideas throughout the week.

All classes have their INBs set up and ready to go.  Several comments such as you really have thought this through, or do you really research your teaching that much?  Yes.  I have a plan and purpose for just about everything we will do.

Ending the week focused on 1 positive thing from their week was the best way I’ve ever ended week 1…

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2 goals for growing…
I downloaded a reflection packet for NCTM Practices to Standards and use it as I read throughout the semester.

Revisit previously read books…Making Thinking Visible and Embedded Formative Assessment.

1 goal for the week-
Get my bulletin boards completed…

A Good Start…

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Thanks to our GRIT team, this was my view as I waited in the turning lane this morning…

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And as students entered the building, the walkway was lined with faculty and staff cheering them on, welcoming them to a new school year.  High fives, smiles and laughter…a great way to start our Monday!

Every staff member had on safety yellow t-shirts with this logo…

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With traits we hope to instill in our students each day…

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As I looked through my rosters during prep, I was a little nervous.  Not many names I knew. 

My first class attended a school – wide session with our administration sharing their expectations for the year.

Our new principal spoke very direct to our students.  No fluff.  He shared how he used to look at our school and wonder what made us so great, thinking he’d love to work here some day.  He shared that settling was not acceptable.  Our students are passionate in their sports, band, vo-tech & SkillsUSA, FFA, jROTC as they compete at the highest levels – but that’s not enough, we must also be passionate about our academics.  We have a challenge to face, we work hard and practice because we want to win and be our best.

I left today feeling a bit defeated, like I had not connected with most of my students.  Though a few moments I saw twinkle in some eyes as they were thinking.  It was one class of students who have not been successful in math in recent years that what we did felt good and right.

After a few minutes with them, I changed my plans just a bit and went with Pascal’s Triangle and a Notice and Wonder (thanks, Max). 

Did they see all I wanted them to see? No.  But today was about letting their voices be heard, sharing their ideas (no matter how big or small), letting them experience ownership of their ideas.

After a silent (a difficult task for some of them) 2 minutes to simply look, they were given 2 minutes to jot down things they noticed.  Next we were up around the room for a quick, pair-share.  One student asked, “if I hear someone else’s idea and I like it better, can I add it to my list?” Sure!

As I began listing each notice, a student was worried someone else might steal their idea.  I asked, “What if I +1 with your initials beside it, so you can share the idea?”  And that’s what we did. 

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Everyone shared something.  I was very intentional to initial their ideas, write their thoughts, without judgement or approval.

We then took 2 minutes to wonder. I called time, and asked them to share.  As I turned to the class after writing the first wonder on the board…I saw nearly every student with hands in the air eager to share.

I smiled and thought…this is how it should be.. it’s going to be a good year.

Card Tossing & Spiraling Curriculum #tmc14

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Awesome session Mary and Alex!  Thank you. Thank you. Thank you.

The session focused on their experiences with Grade 10 Applied students ( Canada).  The entire course is activity based which allows students to not miss out on big ideas as they would in a traditional unit by unit aligned course.
Students have repeated opportunities to experience big ideas. The tasks are rich  with multiple entry points and different approaches to solving.  It’s a collaborative environment with accountable talk.  There are fewer disciplinary issues with increased engagement.

Each 6 weeks a mini – exam over entire course up to that point takes place.  Questions are in context and tied to activities they have completed.

We began with beads and pennies on our desks and this task… Cole has 2 smarties and 3 juju bed for $.18 while Noah has 4 smarties and 2 juju be for $.20.  They shared that systems are presented this way – no algebraic forms- for the first several weeks of class.  I, personally, can see how effective this strategy could be.

The next activity shared was Sum of Squares (he doesn’t refer to it as Pythagoras Theorem, yet – or did he say ever?)

Students are asked to cut all squares from side length 1 to side length 26.  Each square is labeled with side length, perimeter, area.  Then they build with them.

Basically students explore and eventually they focus on triangles formed with question, are there 3 you cannot make a triangle with?   Which combinations form different types of triangles. Begin looking at 3-4-5 triangle families, similar triangles (Kate suggested dilations here), discuss opposite side and adjacent sides, then give them a TRIG table and allow them to figure it out.

Compare side lengths with perimeter, or side length with areas.  The possibilities of math concepts are endless.
We ended the day with Card Tossing by collecting data, then using rates to make some predictions.

Video of Alex & Nathan picture below is only a screenshot.

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@AlexOverwijk downed by @nathankraft 75 to 72

Each person in the room completed several trials of tossing our cards for 20 seconds.  We found our average rate of success, then determined who we thought might beat King Card Tosser.

Alex asked us to predict how long they needed to toss if he gave Nathan a 35 (?) card advantage so it would be super close and exciting.  Our prediction 38 seconds about 75 cards. Many ways of making the predictions were possible. Not to shabby, huh?

This task was fun, exciting, engaging.  Definitely on the to-do list.

This approach is definitely something I would like to consider, if administration will allow it!