Category Archives: Questioning

January #MTBoSblog18 – Formative Assessment Strategies

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From Jennifer Fairbanks…

Happy Day – Our 1st one of 2018! Join us and blog today! Share anything you want! When you blog, tweet out the link.

Join us as we all blog on the same day – the 18th of each month!  Blog about anything.  Write at any time.  #Pushsend on the 18th.  Then, we will all have a plethora of good things to read.  We can use Twitter and the hashtag #MTBoSBlog18 to encourage and remind people to blog.  If you are interested, record your name and Twitter Handle, areas of interest/teaching/coaching, and a link to your blog’s website.  Don’t have a blog? 2018 is as good a time as any to start.  Take a risk and dive in! Or, read and add comments!

Hmmmm.  WElllll.  Okkkkkkk.  What do I blog about?  Here goes…

Our schoolwide focus this spring is on revisiting what we know about good formative assessment and putting it into practice.  Eventually, we will be encouraged to ensure we are utilizing the practice of PA on a daily basis – for those not already doing it.  After speaking with our SLC, we thought it would be a good use of time for our department virtual PLC – on our NTI (aka Snow Day) – to work on ensuring that each learning target in an upcoming unit has a quality FA in place.  And if not or if it really doesn’t measure what the target is intending, then plan a better one!

As we began building the document for Algebra I unit on Functions, I was reminded of so many great strategies  learned through the years and new strategies shared by others.  Most of these have been learned through trial and error, they didn’t “just happen.”  When trying new things, sometimes you need take NIKE’s advice and Just Do It!  See what happens, reflect and try it again!  So here is a list of a few things we ran across while working this morning:

  • Every Graph Has a Story

    When given a graph with no labels, numbers, etc. – can students devise a story that will related key features of the graph to the context of the story?

Here is @heather_kohn’s Ambiguous Sports Graph sports graph

  • Thumbs Up, Thumbs Down

Was reminded of this one by my colleague.  Basically, you can pose a question to the entire class, then ask for a Thumbs Up or Thumbs Down as to if it is true/false, example/noonexample, linear/nonlinear, function/not a function

  • Green Pens –

    I am super excited that my green pens arrived today!  I plan to use Amy’s idea for Bell Work, but integrate into independent practice time.  Students will have a brief practice page – when one finishes, I will check – if all good, they will receive a green pen and help me mark other papers.  After I have 3 or 4 Green Pen Helpers, I will have time to visit each table group for one-on-one help.

 

  • Give One, Get One –

    I believe the first time I ever used this was out of a Kagan book in Geometry.  In this unit, I plan to give students graphs of functions.  Before we begin, I will ask them to list 3 things they notice about the graph.  They will then have 4 or 5 True/False statements to respond to.  Here’s the GO-GO:  They will write one more True statement about the graph, then go visit someone else across the room, sharing / discussing their true statement, and receiving/discussing/recording their friend’s new statement.

 

  • White Boards & Summary Notes

    Individual to practice writing inverse function equations.  Nothing new here, I give them the function, they practice rewriting the inverse on the whiteboard, I walk around the room observing and noting…  Then I will address any common errors I see.  After reading this tweet:

debrief notes

and a discussion a few weeks ago with @druinok about student notes from the teacher – I was reminded…  we will discuss big ideas we noticed in our white boarding, then turn to our INBs and generate our own Summary Notes.  Since these are 9th graders, I will likely give them a few unworked Functions / Inverse examples to help them get started.  Once they have completed their Summary Notes, there will be some time later for independent practice.  Maybe even pull out those green pens again!

  •  Open Sort & Card Matching –

Years ago, I was taught about open sorts from a colleague who had attended John Antonetti training.  I plan to use this structure by giving students cards with several types of graphs, in the discussion with their noticing and sorting and support of reasoning – I am anticipating something coming up about dotted / point graphs and connected graphs.  In the debriefing of the sorting task, this will allow me to introduce / review the idea of discrete vs. continuous graphs.

The second part of this sort will be to place those cards inside the ziploc bag and get the other color cards out.  These cards will have various domains and ranges listed.  Again, in the discussion of their reasoning for their sorts and debriefing of the task,  I am anticipating someone sorting based on listed numbers vs. intervals, which will allow me to make the connection between the different notations for domain and range.

Finally, the matching task will be for students to match the correct domain and range to the correct function graph.  The best way for FA assessment to happen here – is to walk around, listen/observe and ask questions, never telling them, but helping them think on their own.

After some practice and discussion, I feel like this might be another great spot to have students create their own Summary Notes of the ideas shared / discussed.

  • 2-Minute Assessment Grid

Goodness, this may be one of my favorite student reflections.  You can read about it here.  You can copy the grid and have students fill it in.  However, I like creating a large grid on my board and giving students 4 sticky notes on which to respond.  Basically Students are asked to tell ! Something they want to remember.  ? A question they still have.  @ An A-ah – lightbulb moment and + One improvement they can still make / need ot study.

  • Class Closer Reflection

An easy, quick one sentence reflection – have students choose one of these sentence starters and complete it…  Something I’ve learned,…, Something I realized….  OR Something was reminded was of…

Follow-Up Action is what matters most.

As with any FA – its not about the strategies – they only provide a vehicle for the information you get from student learning.  What happens next is very dependent on what information you receive.  In class strategies, you must be present, listening, allow yourself a few seconds to think through their responses / questions before responding to them with a question.  With reflections, exit tickets, target quizzes, we have the opportunity to filter through all of their responses, looking for commonalities and misconceptions – that will help us plan our next actions.  Do we need to address with the entire class?  Are there a handful we need to pull to the side while others are completing bellwork the next day?  Is everyone on the right track and ready to move forward?

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Generalizing Patterns: Tiling Tables

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Last fall after instructional rounds, one of the observers asked me if I would mind having some folks visit my classroom.  Sure.  They were most interested in questioning, interactions with students and use of Formative Assessment Lessons (FAL).

When they emailed to set up a date, we agreed on January 10.  Oh, wait.  This will be the beginning of a new semester with new students.  I won’t really know them.  They won’t really know me.  Great.  Now, I’m scared.  Oh well, let’s look at the positive – this will give me a chance to try out a new lesson.

I printed off 3 lessons to look at the evening before students returned to school.  I liked all three.  Building complex equations seemed perfect, so I began to prepare for it.  We were out for weather our second day back.  As I began looking over my lesson plans, it seemed the Tiling Tables was a better fit for the upcoming unit, so I switched gears.

I had done this lesson a couple of years ago, but never taught it in class.  As I began to revisit the task, I knew I liked it.  I knew it would offer some good discussion on ways to extend the patterns.  But wait.  These students barely know what a parabola is.  Would they have a clue as to how we would write an expression for a quadratic relationship?  Would I have a clue as to how to introduce it, this early in the semester?  No.

So I pondered for a while.  I would simply use the task as a way to say, we have the knowledge and tools to do parts A and B, but part C, well – that’s what we will be learning later in the semester.  It would give us a reason to learn it later, right?  Goodness.  What a canned comment.  By now, we had another snow day, so our visitors would be in our classroom on the 4th day of instruction.  I was stressing just a bit.  What was I thinking?  Starting off a new class with a FAL I had never used before?  We needed time to build some rapport.  Too late.  Let’s go with it.

I gave students the pre-assessment:

table tiles 1table tiles 2

The class was divided pretty much 3 ways – Those who doubled the number of tiles, after all – a side length of 20 is doubled to get 40, right?  The second group had sketched the designed on the the grid paper which had been provided, however, they wrote answers for the 30 cm table instead of the 40 cm.  And finally, several had the correct number of tiles by extending the pattern on the grid paper.  But I ask how efficient this strategy would be for, say 300 cm table?  Hmmm.

We began the lesson the following day by giving 3 samples of work.  Last school year, I figured out, I could save paper by having them use the shop ticket holder sleeves to hold the sample work – allowing them to draw, sketch, etc with dry erase.

These instructions would help their discussions:

samples discuss

The first sample was Leon:

leon

After some small group time, we shared our thinking with the whole class.  There was one student in particular who had confusion all over their face.  I encouraged them to ask the person sharing for clarification (using our starter stems).  I believe this is important to model and have them do early in the semester, so they become more comfortable with it.  Even with more explanation, they were still not seeing the pattern.  So another student shared.  Still no help.  Finally, a third students explained how they saw the pattern.  The confused student nodded and said, “Okay, I got it.”

Now, years ago, I would have said – great and moved on.  But I’ve learned…ask them to explain it to you.  They may say they’ve got it – just so you will move on, but how do you know they understand?   This student, however, could explain their thinking and were correct – they could even extend it to the next table size.

The next student sample was Gianna:

gianna

So many more of the students picked right up on Gianna’s approach.  The confused student – smiled stating they liked / could see this one better.  For me, it was listening and watching the students discussing – that brought me an a-ha!  This is the example we will use to generate the quadratic expression I was worried about!  The total whole tiles would equal (step x step) + (step – 1)x(step-1)  Yay!

Finally, we had Ava’s sample:

ava

Many of the students could not make the connection with the side lengths on Ava’s sketches in the beginning.  Then they began going back and looking at their own sketches to verify the numbers Ava recorded in the table.  They noticed the same patterns and agreed with them.

After this final discussion – we went back to see if each student had answered the task fully.  We quickly realized though there was some good, correct thinking going on in their work – they had not addressed the questions completely.  The class agreed that Ava’s was the most complete with her table.  And it was interesting to hear their discussions of how they would explain to the other students how they could expand their responses to be better and more thorough.   One student even brought up it was challenging trying to figure out their thinking since there was no written explanations of what they were doing.  (I thought – yes, this is what I feel like sometimes too.)

As we continued discussing having thorough answers – I shared Ava’s data in a graph…  they were quick to see the quarter tiles always remained four and the half tiles being linear, a focus from 8th grade.  But what about the total tiles.  How can we write an expression to model that data?  And I took them back to the slide with Gianna’s work to look for patterns between the table size/step number and the total whole tiles.  We test our thinking with different sizes and it worked.  We tested our expression in Desmos…and what?  It hit all of the data points!

desmos-graph tiling tables

They had some experiences with the visual patterns – and good feedback to me about liking them, but still having to think.  This task reinforced some of those ideas.  IN their reflections – though many may have preferred someone else’s sample work – they “saw” how Gianna’s work led us to a more efficient expression or even Ava’s approach to orgaznizing the data in a table was pretty helpful to see the patterns so we could find describe the expressions.

Total Tiles = 4 quarter tiles+ 4(n-1) half tiles + n^2 + (n-1)^2  whole tiles.

I will definitely be using this lesson in my future.  It brought just enough confusion, but great opportunity for sharing and discussion.  And the observations were great.  Students were not shy.  At the end of the day – I was amazed we had only been together for 3 or 4 days… wow, this is going to be an outstanding semester!

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.

 

I Still Have a Question About…

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We did not get through all I intended today to allow some students who wanted to watch the inauguration that opportunity.  But we did address a couple of more questions from the 2-minute reflection students had completed.  You can look back to the previous post to see the original task.

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We addressed the two blue questions in the after lunch class.  Why can’t you multiply the numbers by each other?  Well, lets see.  Again, as I did with another class, I asked them to add two numbers that would give us 18.  We graphed our responses, then graphed the equations x+y=18.  And likewise, give me two numbers that would multiply to give us 18.  We graphed our responses along with xy=18.

When we added the equation to the product set, students were caught off guard with what they saw.  WHY is there a graph in the third quadrant?  Will that red curve ever cross the y-axis?  Doesn’t it eventually get to the axis?  Again, just attempting to address their question, by looking at a couple of horizontal translations and introducing them to that boundary line called an asymptote, led to even more wonderings.  Which is what math class should be about.  As long as they were on task, I continued to go with their questions.  Only 3 students were not interested, who would likely have been off task no matter what I chose to do, so I made the decision to keep going with the majority’s curiosities.

Another student asked about our statement “x cannot be in the denominator” but yet when we find rate of change with a table of values, we compare y over x. Hmmmm.  Good question.  So I gave a table of values, asked the student to talk me through finding rate of change.  When we wrote our ratios, what values did we use?  Not the actual y and x values, but the change in y over the change in x.

The entire class really reminded me that we can say something with an intent, but what our students hear is something else…how important communication is, how important is it that we allow some time to process and clarify their misunderstandings.

Finally, we addressed the question, we’ve been told x’s exponent must be 1 in the linear function.  We’ve seen greater than 1, but if it is less than 1, can it still be linear?  Let’s see.  Go to y=, type in x and choose an exponent less than 1.  What do you see.  Share with your neighbors.  So, how would you respond to this question, students?

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To me, this was one of the most productive two days I’ve had in this class.  Students were engaged because we were addressing their questions.  I’m not sure I actually answered their questions, but I provided them with some examples that allowed them to answer their own questions.

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?

Students Making Sense of Quadratics

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I realize some folks will bash me for sharing this from an Algebra 2 class, but based on benchmarks, most of my students have major gaps in quadratics. 

I began with reviewing multiplying 2 binomials on our whiteboards.  I shared the box/area model and several smiles celebrated because they “saw it” and were doing it correctly!

Last week, I pulled out a box of Algebra Tiles.  We literally explored building squares.  I wish I had taken pictures because some of their squares were like a grandmother’s beautiful quilt blocks.  I began tying it back to our box/area models -I’d rather think of it as leading (not forcing) their thinking – but they were quickly picking up the patterns. 

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We then began looking at the algebraic equivalents, again, with a sketch along side allowing them to “see” the process.

Our next step was to find the missing value without tiles/picture models…and then I asked them to review their multuplying with 5 expressions alongside.

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“What? You think they’re the same thing?!?” I asked,  “Prove it to me. Well, by-golly-jee. You are on to something!”

The following day in class, I made a HUGE ordeal of different ways to write zero.

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I explained our next few minutes were a process. But we talked about it, step by step, completing the square, adding ‘that zero’ in our expression, the separating the trinomial and 2 constants.  Rewriting our trinomial as a binomial squared.

Ok. Why in the world would anyone want to do this?  I told them we were finding hidden information.

As they arrived at this form (x+4)^2 – 9, I paused, reminding them to think back on our function transformations before Christmas break.  How would this function y= (x+4)^2 – 9 move on our graph from this one y=x^2?  Quiet. “Move left 4 and down 9!” Someone exclaimed.  Really? Are you sure? We graphed the two and yes, it did just that.  So what does this tell me about my parabola?  They didn’t say vertex. Or minimum.  They said it shows us how the graph was transformed. 

I will take that.

I then asked them to move left 4 and down 9 from the origin.  What have you found? The lowest point.  The vertex. The minimum. All their responses, not my statements.

We set our expression equal to zero and solved the equation, using our inverse operations.  They made the connections with the x-value of the vertex being the “center line” of the parabola.  They realized the +- 5 were steps in either direction from the center line.

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I most appreciated the questions they asked on #3, 4 and 7.  Several chose #7 thinking it was shorter, thus less work. Snafoo. No middle term. What happens? 

I suggested they look at it from a transformations point of view.  Someone shared-It doesn’t slide left or right, only down.  Another student said-well, that’s the easiest equation to solve! (Yep.)

Why did #4 bother some? The middle term had an odd coefficient.  But once they shared their thinking, ok. Got that one too!

#3 was what we math folks recognize as perfect square trinomial.  But for the students, it was an a-ha.  Again, using the transformations context, we moved right 5, but not up or down.

L: But I thought all quadratics intersected x-axis twice?  I asked – did this one? No.

What about y=x^2 + 3?  It moves up 3. Ok. How many times did it intersect the x-axis? It doesn’t.   Hmmm.

A student who is rarely engaged then asked, if you can make a parabola that doesn’t intersect the x-axis, can you find one that doesn’t intersect either axis?  Me: Can we? What would it look like? S: Noooo. As its going up, increasing, it would be increasing outward, too!  More discussion, between them. Me not included. I was smiling.

And their questions were what drove our lesson today.   And I was so excited, telling them their questions make me think! And when they’re asking questions, their brains are processing the information – making it their own.

It was a good day.

SMART goals #MTBoS30 Day 4

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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. 

No jumping in, silent/listening, no repeating & my win for the day #ppschat

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Our #ppschats the past few weeks have brought some a-has and good reminders for me.  Here are a few adjustments I am trying to mindful of:

1. When students are working in small groups, I have often jumped in to their conversation when I heard them going in the wrong direction.  Of course, my intentions may have been to redirect them. 
 
Needed adjustment:  Be silent and listen.  Giving them space to muddle through their own thinking without jumping in and telling them what I think they should think.  A key for me may be to keep my tablet, clipboard, post-its to jot down notes of their conversation.  Key points to reference back to later.  Jot down questions I might like to ask.  Not sure when to ask /share, maybe as a quick revisit before the end of class?

2. In my efforts to “value” what a student shares, I often find myself repeating. Afterall, those softspoken students need to be heard, so I repeat it so classmates across the room “hear” them.  Oh, no.

Needed adjustment: Ask student to speak up so others can hear.  If they are intimidated, offer an encouraging word, let them know you like it, find it interesting or you want others to hear it.  When I repeat, I am causing others to not listen because they know I’m going to repeat.  Oh, my.  Guilty.  Who knew?  What are ways you create a listening community of students? 

3.  I may ask for volunteers and the same 8 people are sharing.  Spread the love.

Needed adjustment:  I tried to be very purposeful in sharing this week.  In geometry, I picked a problem several seemed to have trouble with.  I structured the task with Know: what information is given, Notice: what do I notice about the diagram? Other information I can use to move me further?  Wonder: What other measures can I determine? How can I justify my reasoning? 

Students took couple of minutes individually, to jot down a couple of things in each bullet, then in their groups of 3 to discuss.  I asked each group to pick 1 thing they felt was important to share.  Yep.  Good ol’ Think-Pair-Share.  As I went around to groups, I arrived at one who said…they already shared ours, so I used the suggestion from PPS to +1 on the board.  It seemed that others were really listening to what was being said.

A win in class today as I gave students a diagram with no questions.  They noticed/wondered and it was a statement from a student that 2 chords were congruent.  When I asked them to convinece me…their statement was quite fuzzy ending with “it just seems like they would be.” I challenged the others to prove or dispute the statement… 

“Oh yea” high fives, “we got it!” & “you’re genius!”  Students celebrating something they hadn’t seen before. 

What was even better, the way they justified their reasoning…all different, not one that I had seen myself.  And that is why I don’t care for the answer key as the answer key. Students sharing their strategy and each confirming the others.  Hearing them say ‘that’s cool’ to another student’s strategy.  Engaged while looking at a different approach.  I truly feel the take aways from a single problem approached this way is valuable.  It was a productive day.

Student Reflection on HW

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When I get back from a conference, I have the best intentions of sharing, but its nearly 3 weeks later and I am just starting to get caught up…only to realize there are less than 3 weeks of instructional time before Christmas break. 

Starting to stress in my Geometry blocks classes…similarity (although I tied in some with our congruence unit and they used dilations in our transformations unit…) right triangles and circles…then a super dooper quick approach to modeling via 3-d problems.  Anyone have an amazing project that ties circles and right triangles together?  Anyway, a bit off topic, because the stress causes me not to focus.

  I attended a session led by @ottensam sharing different approaches to ensure we are integrating the SMPs in our instruction.  He was very engaging and shared some simple, research-based strategies.

A great idea he shared was to change up the way we approach homework.  One simple suggestion was to ask students to eflect on the problems…which were most alike? Most different?  Why? Which one did you think was easiest? Most difficult, why?  I had students to do a quick write using this idea this past week.  Once they were finished, they had to meet with someone they did not sit next to and share their responses.  Finally, I called on students, asking them to share -not what they had written- but something they had heard. 

I am always amazed at student responses when I use startegies similar to this and could kick myself for not being more intentional, more often.  Several shared exact similar/different pairings but for totally different reasons.  I love it, being able to see and hear their ideas and thinking. 

Happy Birthday #Made4Math !!! Formative Assessmemt Reminder Cards

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First, just let me say a big THANK YOU to @druinok for beginning #made4math and to all of the generous folks who have openingly shared their classroom ideas, lessons, tips over the past year.  I was overwhelmed with how quickly it took off!  Still, today, I am amazed at the generosity of this community.  I have learned so much and my classroom was definitelh impacted by your awesome ideas!

My share for today was initially a result of a convo with @rachelrosales and @druinok, brainstorming ways to organize reminders for the numerous formative assessment techniques…something simple, at your finger tips. 

I loved @druinok’s post today and her Student Engagement Flipchart.  Very.Nice.  It will definitely be on my to-do list for a future project.  However, I am choosing to share a similar idea, just a bit different format.  I cut down index cards to fit sports card pages… pack of 10 for $1.  I am able to display up to 90 of these reminders ranging from formative assessment techniques to various strategies for student engagement, reflection, etc. 

Front side of card has title, with some information…

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Back side of cards has description, suggestions, reminders…

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I have placed the pages in a small 3 ring binder which can easily hold more pages.  Currently, I am trying to include summaries/reminders of techniques I have used or see being easily modified for math class.

Looking forward to learning and sharing more FA techniques with my amazing PLN!!!

Pam Wilson, NBCT
Currently Reading
5 Practices for Orchestrating Productive Mathematical Discussions, Smith & Stein
Teach Like  a Pirate, Dave Burgess
From Ashes to Honor, Loree Lough