New Year, New Mindset

After a very long hiatus, I have been drawn back to blogging by a challenge.  Though there are no prizes, Sam’s New Blogger Initiation was reason enough to jump back into this community.

Something new I have wanted to integrate into my classroom culture for several years is mindset coaching as developed by Carol Dweck.  The diagram below is a good summary of her work comparing students who have a fixed mindset to those who have a growth mindset.  The question is how can a teacher influence a student to change their mindset to a more growth oriented one?

My Berkeley colleague Marlo Warbuton developed a curriculum
based on Dweck’s book.

All of the documents below which I plan to use this fall were made by her.  During the first week of school, I’ll give the brainology survey and then allow students to share out their reactions.  After reading their responses that evening, I’ll share out my initial reactions and show them the fixed versus growth mindset diagram.  They’ll each get a copy to keep in their interactive notebooks (a place for both important class documents and math notes). For more on interactive notebooks, Sarah at Everyone is a Genius is the most organized crafty teacher I have ever come upon.

Then, once a week, we’ll spend 10 minutes discussing a quote.  These are quotes which Marlo compiled from Dweck’s book.  We’ll follow the same protocol each session:

Structure of the Coaching Lessons:

1.Students listen to the quotes of the day

2. Students think silently

3. Students share their thoughts in small groups

4. Students participate in a whole class discussion

5. Teacher shares her own personal response

 6. Students write a reflection

Last year, when Marlo did mindset coaching in her classroom, she used two quotes per session and tried to do it several times a week.  She found that it began to take up too much class time and has recommended to me that I do just one quote per class period, and one session per week.  I think that’s how I’ll start.

If you are familiar with Dweck’s work and have done similar mindset coaching with your students, I’d love to hear about it.  Also, I’m especially interested if anyone has done mindset coaching with adults.  I’m coaching my school’s math department this year and want to go through a very similar protocol each time we meet.  Not so that they’ll necessarily do this with their students, but so that my staff will begin to think about their own mindset in terms of how they approach teaching and their attitudes towards their students.  Now THAT is a work in progress…

Keeping Your Ears Open

My son, who is 2 1/2, often gets upset when a big truck that he has been watching abruptly drives away.  I’ve learned to eliminate the tears and disappointment by reminding him to, “Keep your ears open!” and frequently he moves onto the hunt for the next big vehicle.

Today in geometry, I was reminded about what can happen when you simply listen.

We were beginning the chapter on congruent triangles and I wanted to hear their intuition on what it means for two polygons to be congruent.  Their warm up was the following problem:

Imagine that this hexagon is made from 12 toothpicks.

1) How could 6 more toothpicks of the same size be used to divide the hexagon into 3 congruent regions?

2) Keeping two of the toothpicks from part 1 in the same place and moving four, use six toothpicks to divide the original hexagon into 2 congruent regions.

Although using manipulatives or GeoGebra was a natural approach to solving this problem, I didn’t have toothpicks on hand, nor the mobile computer lab.  I  figured that students would sketch out different diagrams to find a solution. After a few minutes, I looked over and saw that a student had taken out 12 Sharpies of equal length and had constructed a solution to the first question.A student creating a scale model of the problem that was over 2 feet wide felt like the proper time to have the rest of the class drop everything and come huddle around this student’s desk.  We gathered up, some on stools, some on desks so that all could have a clear areal view.  There was unanimous agreement that this was a correct solution to the first problem.

“How do you know that these 3 regions are congruent?” I asked.

While answers ranged from, “It just is.” to “You can measure it and see.” the most interesting one to me was the student who claimed that the 3 regions were congruent because each was equilateral and congruent figures had to be equilateral.  About a dozen students joined in the debate, I mostly just listened, so I could learn more about their intuition. The idea that congruent figures must be equilateral was a misconception that I hadn’t come up in previous years.  I’m glad my ears were open.

Expect the….Expected…but sometimes don’t

Algebra Scholars: A Pre-Algebra class of 8th graders who failed or did extremely poorly in 7th grade Pre-Algebra.

Algebra Readiness: The title or subtitle of numerous curricula directed at students with similar needs as my Algebra Scholars.  The “Algebra Readiness” subtitle is the only commonality among the three sets of curriculum I have reviewed: Holt’s Algebra Readiness, UCLA’s Introduction to Algebra, and MIND Research Institute’s A Blueprint for the Foundation of Algebra.

Two out of three of these texts do quite noteworthy job of providing opportunities for struggling students to learn the requisite skills for algebra in a variety of new ways.  I would happily follow them more or less by the book.

But why choose something different?  I mean if students are struggling with math using Holt in 6th and 7th grade, wouldn’t it make sense to purchase Holt’s Algebra Readiness program since it looks EXACTLY the same as their 6th, 7th and Algebra texts.  It’s comforting, right, to begin the school year being separated from your peers (all 8th graders take Algebra 1 except my 2 sections of Algebra Scholars), tracked into a class with other low-achieving students, and being handed a textbook which not only looks EXACTLY like your textbook from last year, but has the EXACT SAME CHAPTERS as your textbook from last year.  Bliss…

Someone drank the Kool-Aid and somehow expects that outcomes will change by using the exact same text taught in the exact same way (honestly…it takes a close eye to spot the differences between Holt’s Pre-Algebra and Algebra Readiness texts).  Worse, this flavor of Kool-Aid is being served straight up in far too many schools in this country.

Luckily, my summer drink of choice is Prosecco with lavender honey.  I have created 4 goals for my class and will interweave them into my warm ups, classwork, assessments, and homework each week.  Call me crazy, but I think that students’ poor performance in math class has as much (if not more) to do with their attitudes about school and math as it does with their perceived lack of knowledge and practice on computational algorithms.

In no particular order (and all of equal importance):


* Fostering mathematical curiosity and improving number sense.

* Struggling and ultimately gaining confidence and strategies for mathematical problem solving.

* Identifying your strengths and weaknesses in computational skills and improving on         them.

* Learning, practicing, and being proud of what it takes to be successful in school.

I have made an extensive list of what each of these goals will look like in practice and made a lovely Google-Calendar of the school year, color coded with each goal and general topics/resources I’ll use.  If you were going to be these students’ 9th grade Algebra 1 teacher, what would be on your wish list for what they would know or be able to do when they arrived in your class?  How would you fill  in the content for each of these goals? Would your goals be significantly different?

My Google-Calendar started as a spreadsheet.  Here’s a sketch of September with the H# referring to the chapter of Holt which will be lightly stirred, not shaken into the mix.

I’m still not sure what a typical class period will look like, whether we’ll interweave each goal into a single class period, or over the course of the week.

Will integers only be taught via Holt?  Heck no.  As I always explain to student teachers during the first week of school, a textbook is no more than a list of problems.  It doesn’t tell you HOW to teach..that’s where your craft comes in.  But since each student will have a textbook, I may as well send it home and use it for homework when we need to practice stuff.

Will integers only be taught in September?  Well, if you drank the Kool-Aid, then you’d be led to believe (by the teacher’s guide) that 3 weeks is all you’ll need for integer operation mastery.  You’d also be led to believe that you should wait to teach integers until chapter 14 (i.e. sometime in March). If this is really a course to prepare students for success in algebra, it seems to be that we should start with integers since they are such a stumbling block for students who struggle in algebra.  That way we have the whole year to think about them in a variety of contexts, not 3 weeks of practice which somehow leads to mastery.

Why memorization as a focus and why start with perfect squares? There are some things which deserve automaticity.  Times tables are a big one.  Unfortunately, while teachers expect memorization of times tables beginning around 3rd grade, no grade level seems to be willing to say, “The buck stops here.” So, struggling 8th graders don’t know their times tables and no one in 5th-7th has been willing to take time to ensure that they do.  In Algebra Scholars, the buck stops here.  BUT…if I were to expect students to memorize their times tables in September of 8th grade, they’d refuse.  “This class is for babies,” or “I already KNOW them,” or “I’m switching out of this class,” would be the more polite of the commonly overheard phrases.  So we need to start with something new. Something cool.  Something no one has asked them to memorize before.  But it also has to be relevant to where they’re going in math.  Memorizing perfect squares is just right for September and just right for struggling students.

And we need to reward their progress…And no, I didn’t think of this on my own. 

Got 2 more weeks to ponder…

Shifting Paradigms

A colleague at my school attended the AVID teacher-training conference this summer and shared this video with us.  She suggested that we watch and discuss it at our upcoming retreat as a springboard for conversations about how to increase collaboration among our students and shifting some of our goals for ourselves as educators.

Not a bad idea…

Finding a New Lense

Mr. Benson, my high school math teacher from whom I had the honor of learning geometry, BC Calculus, MV calculus, and some dabbling into linear algebra, had a replica of “The Thinker,” by French sculptor Rodin.  When a student in our class made an especially insightful comment, connection, or creative solution, Mr. Benson would gleefully take down the sculpture and place it on your desk.  There it would stay for the remainder of the period.  Earning it was an honor which didn’t happen often.  From my recollection, it was not much more than a few times a year.   This summer I attended my 20th high school reunion and I strayed from the school tour to peek in Mr. Benson’s old classroom door.  I could show you exactly where I was sitting the one time I was awarded this honor.

I struggled to find a way to replicate this tradition, yet make it my own.  A few summers ago, while touring the Leonardo Da Vinci museum in Florence, Italy, I stumbled upon this bib and knew it was the perfect item for my classroom.  When a student has a ‘moment of brilliance’ they get to sign their name on the bib and keep it with them for the remainder of the period.  I’m sure this won’t surprise many of you, but yes, most of the students who have been honored with this prestigious prize HAVE worn it for at least some of the class period.

As the beginning of the school year approaches, I have been thinking about how to introduce this coveted bib to my new group of students.  Today in the car, I had an idea.

While at first I enjoyed the unique sounds of Adele’s “Rolling in the Deep,” I tired of it after its umpteenth playing on the radio.  But after watching this video go viral on Facebook, I now hear her original version with new ears (speaking of which, it has over 2 million views on You Tube which is quite astounding to me).

I’m wondering if showing this video during the first week of school could naturally lead into a conversation about problem solving strategies.  After I saw Mike Tompkins’ version of “Rolling in the Deep” not only did I hear Adele’s version in a whole new way, but I actually enjoy hearing her song again.  Maybe I’m grasping at straws, but it reminds me of how students’ often try to replicate the same problem solving strategy as they have seen in a textbook or that their parents taught them.  In doing this, there’s rarely any creativity or deep thinking involved.  But when you see someone take that same problem and solve it in a truly unique way, you gain more insights into your original method, often understanding it far better than you originally did.  Is this a theme worth pursuing with these contrasting versions of the same song?  I’ll keep mulling it over.