Category Archives: Strength in Numbers

My Experience with Counting Circles #julychallenge Post 14

Standard

Still addressing 14 ways of thinking about good teaching from this post

2.  Plan goals for both the long term and the short term.

My number 1 goal is to help students grow – personally and academically.  My wish is that they leave my classroom believing in themselves, more self-confident than when they entered. 

Ideally, I do want every student to reach proficiency, but I am also a realist.  When students come to me with *ACT-PLAN scores in the 10-14 range, proficiency is not an immediate goal…growth is, pure and simple.  My class becomes the stepping stone to reach proficiency.  Students in this range generally have major gaps in number reasoning.  They are just now beginning to develop understanding and knowledge of assessed skills.

Last year, I wanted to use accessible tasks to begin each day…Counting Circles, Number Talks (pg 4 of link) and my post, Estimation180, and Visual Patterns were staples in my Algebra 2 classes.  Students in these classes ranging from ACTPLAN scores from 10 to 23-wide range of abilities and varied confidence levels.  These tasks were approachable for all students and I feel helped in developing number sense which allowed several students to make significant gains on thier ACT.

Counting Circles (Thanks to Sadie!) was very popular in both classes.  We literally got out of our desks to create a “circle” around the room. Yes, it seemed trivial at first, but I was able to see student confidence grow as they strengthened numeracy skills.

image

My Routine
We have a starting number and a number to count by.  In the beginning, I choose nice numbers, then some that required a little more thought.  Eventually, I allow students choose our counting number and starting point.  I would have expected them to take the easy route.  Not at all.  They like to challenge themselves.  We also countdown.  I like to write their responses on the board for them to visually see the patterns.  When a student makes a mistake, I try to not point it out, but rather, allow students to have opportunity to voice their concerns with a response, respectfully, of course.

After going so far around the circle, I stop and ask, What will _______ (a little further around the circle) say next? 

We usually get a couple of responses, so I allow them to explain their process then, as a class, they determine which one makes more sense.

Also, I like to ask…who will say ______ ?

Side note: Later in a functions unit, while looking at finite differences, a student explained, this is similar to what we were doing with Counting Circle the other day!

Our First Counting Circle – Count by 10
I began with couting by 10 on decade numbers, by -10 on decade numbers, then on numbers like 11 or 14, counting by 10 in both directions.  It was a great way to model the routine.  Students are comfortable with it.

Next week, we counted by 2s, up and down, starting on positive and then a negative.

Several students are all in – they’ve got this!

Then by 5s.  On 15, 70, -85 then numbers not ending in 0 or 5…. 37, 128, -89. Both up and down.

I began using single digit integers then a few double digits.

Next week we worked with decimals +3.7,  starting with an integer, then moving to devimals 11.2.  One student this particular day was quickly running through their numbers.  When I asked their strategy, they responded….its easy, add 4 then count .1 back 3 times.

We also use fraction expressions as well.

I already know my stronger numeracy students-those with “high status” in class (Ilana Horn).  So do their classmates.  What I love about counting circles is choosing different students to explain.  Struggling students pick up on numeracy techniques as explained by their peers.  They are able to see those high-status students’ thinking and realize, “I can do that too.”  Its a win-win.

Yes, at high school age, I have students who don’t want to participate, but with a bit of coaxing, they come around. It becomes a game.  Classmates encourage those who struggle.  We don’t laugh or make fun.  They celebrate when ‘that’ student experiences success.  Most of all, they smile.

Generally, it takes anywhere from 5-15 minutes depending on number choices, discussions, size of class, experience with the routine.

Suggestions:  pre-cal count around unit circle, elementary use money as a context, what others can you share?

Long term goals and planning changes with each group of students.  Having access to learning routines like these allow me to tailor toward each groups’ needs.

*In Kentucky, every student takes the PLAN during sophomore year and ACT during their junior year as part of our state accountability model.  To measure student growth from state data, students are grouped by their PLAN scores, then compared to others in this scoring band.  Once the ACT scores are available, they are given a percentile rank from within that initial grouping.  I, the teacher, can view this and whether they had high growth, expected growth or below expected growth.  The state assigns me an overall rating and this will eventually become 20% of our Certified Evaluation plan.  The other 80% is determined locally and by student growth and proficiency goals I personally set for my students early in the school year.

Get to Know Your Students pt 2 #julychallenge Post 12

Standard

 Get to know your students, especially how they learn and think.

Taking my lead from this post, my intent is to consider how I can improve or implement the 14 ways discussed.  In my last post, I shared how important I feel it is to know our students as real people.  This one is to share #5things that impacted my classroom and helped me know how my students learn and think.

My 3 years with Kentucky Leadership Network and my experiences with #MTBoS have changed my mindset.  The work with KLN introduced me to a new set ideas and #MTBoS allowed me to explore with others and develop a new frame of reference as I seek to grow as an effective educator.

I cannot be grateful enough to all those who have challenged me and help me grow.  But as I think of the experiences that have opened my eyes to see better ways I can consider my students as learners, these are the ones that first come to my mind.  #5things for getting to know how my students think and learn…

Wait Time II
I learned about this routine from 75 Practical Strategies for Linking Assessment, Instruction and Learning (Keely, Tobey 2011).  A simple adjustment.  Yet it forced me to really listen to my students.  You can read more on a previous post, here.  Basically, it allows  the students AND teacher to process a student response.  We were all told in undergrad to wait 3 seconds after asking a question before calling on a student.  Some people actually think this deters the class flow.  I disagree. The idea with Wait Time II is to wait again, after the student response.  It allows the responder to consider what they said, the classmates to process what was said and the teacher to consider next steps, questions, etc.  A bit uncomfortable in the beginning, but once I explained the rationale to them, they got it, as did I.  Waiting and listening adds value to what students are saying.

What Makes You Say That?
Making Thinking Visible, (Ritchhart, Church, Morrison, 2011)
A chat with Liz Durkin challenged me to consider ways I could implement these routines into my high school math classroom.  It was the question “What makes you say that?”  that helped me begin drawing out student thinking.  What were they seeing? What evidence supported their statement?  With this routine, I began learning new ways of seeing problems myself.  Students’ ideas, strategies and approaches are way more intuitive than my own.

Notice and Wonder
I was first introduced to Notice & Wonder with Max Ray’s Ignite talk sharing The Math Forum’s simple, yet impactful strategy.  You can read more in Powerful Problem Solving (2013) as well.  When I pose a problem, scenario, graph, students may not readily know where to start.  But they can tell me what they notice.  Its a starting point.  Everyone can share something.  When we listen to what others are saying, that ignites other ideas as well.  And they begin sharing their “I wonders” which are great transitions to explore more.  Its great.  Its simple.

This routine carries over to standardized tests as well.  Students shared how they didn’t know how to approach certain problems on ACT or their EOCs, but they looked at it, thought about what they noticed, connected it to something they knew and was able to at least make an educated guess. 

Friendly Class Starters
After reading What’s Math Got to Do with It? and completing the Jo Boaler How to Learn Math course last summer, I knew I needed to find ways to invite students to think differently about math in my classroom.  Some major a-ha’s and sad realizations as to why so many kids are down on math.  I began with things like Number Talks she presnted during one session.  Amazing how many different ways students can see / approach a single problem.  When I invited them to share their thinking, they owned the math.  This past year, I implemented Counting Circles, Estimation 180, Visual Patterns as well.  These resources were primarily used as bell ringers to get students in math mode. However, there were days it lead to deeper, richer discussions and I was flexible enough to go with it.  My students’ confidence began to grow.  Their number sense was developing.  They were sharing their reasoning without me asking them to.  I saw some big gains on benchmarking and standardized testing for several students and I attribute them to these “friendly” and accessible resources.

Small Groups and Discussions
When I completed my initial National Board Certification in 2002, I quickly realized small group discussions provided a definite means to seeing student thinking.  It was a chat last summer, that made me realize I needed to quit butting-in.  I would hear a misconception and jump to add my 2 cents rather than allowing them to reason out if they were correct or needed to adjust.  I was stealing their learning opportunities! Yikes.  I began listening more-offering questions rather than telling them the direction they should go.  It was frustrsting for some students.  They despised me answering their questions with questions.

5 Practices for Orchestrating Productive Mathematics Discussions (Smith & Stein, 2011) is a quick read that offers samples to incorporate into your classroom. The 5 practice provide structure to help you develop discussion based tasks rather than step-by-step inquiry lessons.

Another valuable resource for me are the Formative Assessment Lessons provided by Mathematics Assessment Project.  Most lessons follow a similar format to the #5pracs.  I used to struggle offering questions that would move learners forward.  Though some disagree with scripted lessons, this resource supported me with sample questions for specific student misconceptions.  As a rssult, I began asking better questions on my own.

Another aspect of the FALs is the way they suggest grouping students, not by ability, but similar thinking – whether it be similar misconceptions or approaches to a problem.  This supports what I have been reading this summer with Ilana Horn’s Strength in Numbers (2012).  She presents how social status in the classroom may actually hinder student learning and achievment.  I believe grouping students homogenously by approach and thinking puts them on equal playing fields to share and build their ideas. 

By observing student responses and listening to their discussion, I am able to select and sequence ideas for them to share that will allow more engagement from the class as a whole.  Students are able to listen and view strategies similar to their own, but also consider new approaches which in turn builds their own skill set and toolbox for thinking.

image

The common thread is to not to do all of the talking, but to sincerely listen to my students and their thinking.

Strength in Numbers

Standard

As mentioned in an earlier post, I started reading Ilana Seidel Horn’s Strength in Numbers just as the last month of school began. But as we all know, the end of the year takes over…EOCs, Finals, Prom, Graduation, closing days, packed up 1/2 of an entire school and stored it in our gymnasium for major renovations this summer.  Yep, my book went to the back burner.

Finally, today, I found time to jump in and start reading again…

…at the pool.  A friend’s mom jokingly asked, “Are you studying over there? Don’t rush it, school will be here soon enough.”  My reply, “Yep, reading a book I’ve been looking forward to for several weeks.  And yes, its mathy, I love me some math.”

Again, proof only my online PLN actually get me and my hunger to learn more.  And that’s okay.

Only 2 chapters completed between snacks, reapplying suncreen, having to leave for a camp meeting…but oh, my, so much to think about.

Some of my highlights…

Positive behavior comes from students’ engagement in the subject matter.

Four Principles for Equitable Mathematics Teaching:
   1. Learning is not the same as achievement. (So.true.  Never thought about it quite like this).
        Every student has something mathematically to contribute.
   2. Achievement gaps often reflect gaps in opportunities to learn.  (This one made me sad).
         “Instead of the blame game that begins when we view our students as low-achieving, we can think about how to re-create our classrooms and departments in ways that will increase the opportunities for students across achievement levels to learn by thinking mathematically.” Yes! Pg 14
    3. All students can be pushed to learn mathematics more deeply . (Sad. Again.  We fail to challenge them and provide interesting, engaging tasks).
        ” opportunity gaps affect all students.  A key characterisitic of an equitqble classroom is that ALL students are supported to substantially participate in each phase of instruction…”
   4. Students need to see themselves in mathematics. ( hmmm.  Ready to read more on this one for sure).
       “Mathematics as a subject , has a reputation for being interesting to a narrow group of people… students often feel mathematics allows no room for questioning… in didactic teaching situations, students feel their job is to receive preexisting knowledge.”

I am excited to continue Strength in Numbers.  Already, its challenged me and given me some things to think about…how I can recognize the difference in learning and achievement, how I can look for ways for every student to engage everyday…

…that I am providing opportunities for my highest achieving to learn and move forward just the same as my middle of the road learners and those who struggle as well.  An email this spring from a parent proved this point, ” in 12 years of school, I have not once had a teacher contact me…”  This is a gifted, creative learner who achieves above their peers.  However, I was not seeing growth for them as I had seen in their peers.  Yes, this student was above proficiency, but that didn’t mean my job was finished.  They needed to grow too.  And I was concerned…was it something in my teaching that I needed to adjust?  In order to help every one of my students, I must constantly reflect on my practices and adjust…

So I will continue reading and thinking on these 4 principles-how they are supported or need to be considered in my own classroom.