Saturday, January 10, 2015

Growing Your Fixed Mindsets Mid-Year!

Happy New Year Everyone!  

As we reach mid-January though, it really isn't our new year in education is it? For us, it is Happy Mid-Year! And our main task as we transition from one Semester (or term) to the next, is to ask, how are we doing, and what mid-course direction do we need to take to best improve and impact student learning?

I have often referenced Stanford professor Carol Dweck’s application of Fixed and Growth “Mindsets” of students in the classroom (2007), but now Dweck applies her mindset theory to us as teachers.  The critical question, it seems to me is this: If I have a fixed mindset about my ability as a teacher, is it possible for me to make mid-course directions and grow in my ability to teach over the rest of this 2014-2015 school year and beyond? Can I really have a “New” year?

The answer is good news: A Resounding YES!

The following excerpt (boxed in) is taken from the Marshall Memo – a weekly K-12 educational research brief I would encourage readers to check it out. The author – Kim Marshall – does a terrific job addressing a variety of educational research summaries each week.

Here is what he had to say about Dwecks’ recent article, Teachers’ Mindsets: Every Student Has Something to Teach Me in Educational Horizons, December 2014/January 2015 (Vol. 93, p. 10-14),

By the way, at the end of this blog, is a link to a mindset "test". Sixteen questions. See how you do!

In this article in Educational Horizons, Stanford professor Carol Dweck applies her “mindset” theory to the problem of teacher attrition – almost half of new teachers leave the classroom within five years. All too many teachers, she says, have a “fixed” mindset about the profession – either you’re born to be a great teacher or you’re not. Here are some of the agree/disagree statements Greg Gero of Claremont Graduate University used with teachers to ascertain their mindset:

The kind of teacher someone is, is something very basic about them and can’t be changed very much.

Teachers can change the way they teach in the classroom, but they can’t really change their true teaching ability.

Some teachers will be ineffective no matter how hard they try to improve.

No matter how much natural ability you may have, you can always find important ways to improve.

Every teacher, no matter who they are, can significantly improve their teaching ability.

The value of trying new teaching methods outweighs the risk of making a mistake.

I discuss problems in my classroom teaching with others in order to learn from them.

Teachers who agreed with the first three statements had a “fixed” mindset and often got discouraged when they encountered difficult students and learning problems in their early weeks in the classroom. “So,” says Dweck, “instead of rolling up their sleeves, using every resource at their disposal, and assuring themselves that they could only get better, they probably concluded that they didn’t really have the talent in the first place or that the kids were intractable – and fled.

Teachers who agreed with the last four statements had a “growth” mindset. They cared more about learning than about having a good reputation as a teacher. They didn’t believe that a perfect, error-free lesson defined them as a good teacher. These teachers behaved in strikingly different ways than those with a fixed mindset:

They engaged in more professional development, read more professional literature, and constantly picked up ideas and teaching techniques.

They observed other teachers and volunteered to have well-regarded teachers teach demonstration lessons with their students.

They confronted their teaching problems head-on and asked for feedback from supervisors and colleagues.

Teachers with a fixed mindset feared being judged negatively and were reluctant to be observed by others or collaborate with colleagues. They assumed it was their job to go it alone and that innate talent was the most important factor in success.

Dweck says that teachers stuck in the fixed mindset see underachieving, unmotivated, disruptive students as threats to their self-concept as good teachers. “But in a growth mindset, those students are challenges,” she says; “they’re opportunities to hone your skills, increase your understanding, and become a better teacher.” Growth mindset teachers believe, “Every student has something to teach me” and some even tell their students, “Every time you make a mistake, become confused, or struggle, you make me a better teacher.”

Is the fixed mindset fixed? No! says Dweck: “Research has shown that it’s never too late to develop a growth mindset about your abilities. The first step is to get in touch with your fixed mindset. We all have some of it tucked away somewhere, and it’s important to acknowledge that.” It says things like:

You’d be able to do this easily if you were a good teacher
You’ll never be as good as that teacher.
You’ll never be able to get these students to learn this.
If you take that risk and it doesn’t work out, you’ll lose your status/control/respect.
You see, you took a risk and failed; don’t try that again. Stick to what you know.
Why not face the facts; you’re just not cut out for this.

Start talking back with growth-mindset thinking:

Nobody is good at this right away. It takes experience
I really admire that teacher. Maybe I can ask her to observe my class and give me feedback.
Maybe other teachers have some good ideas about how to teach this material more effectively.
Maybe I need to find some new strategies or set different goals.

Marshall then states: “Dweck suggests taking the mindset test to get a handle on the specific areas where you can change your thinking about growth and achievement.”

I would concur. It seems to me, that in a profession and a professional learning community culture, that asks your team to pursue ways to improve our work, the hope rests in the possibility we can all become Growth Mindset teachers and leaders.

Saturday, November 22, 2014

Nothing More At Thanksgiving!

We are how we treat each other and Nothing More
                                                                                                   —The Alternate Routes Band 

How is your endurance these days? Less than a week until Thanksgiving! Yikes! Are you ready? I bet you are. I know I am. I need a break from the intensity and the pace of events this fall as the 2014-2015 school season unfolds, and I need some down time with my family too.

As I have written before, this is my favorite holiday. For educators it seems to come at just the right time of the year, when we become just a bit edgy and weary from the pace, the life, the energy required to be a great teacher, social worker, counselor, administrator, nurse, school board member, coach – whatever your school role may be.

And it gives us a brief moment in our lives to stop, reflect on how we are actually “doing’ in this 2014-2015 season, and to notice and give thanks to those we love, to the grace of life, to the opportunities (won and lost) in our path, and to join the table of joy and sorrow in our personal journey with others this year.   

It is no secret: Teaching and leading and educating children well, is not an easy task.

At a gathering of neighbors and friends last night, a teaching colleague (who teaches 2nd grade in a low poverty neighborhood) mentioned to me how some days have been good and some not so much. There have been victories with the students, and there have been setbacks too. Some days, the students just do not treat each other very well.

Since I spend the majority of my days helping teachers learn math content to teach students, I asked her what she thought really mattered in her class. She said: “To accomplish anything, they just need to experience being loved. In the end if I can get them to learn how to treat each other with dignity, then deep learning can take place and it has been a good day”. As she shared her classroom experiences, she seemed really tired to me, and ready for that break next week. 

Her comments reminded me of a song originally written in 2012 by the group Alternate Routes in response to the school tragedy at Sandy Hook. The song went viral this past February when NBC played the song as part of their opening ceremony at the Socchi Olympics. The TV show NCIS also used it to end one of their episodes last season. The song, Nothing More has a simple message. As we reflect this Thanksgiving, as we take a close look at all the people in our influence circle, our lives boil down to:

We are how we treat each other, nothing more”

No matter how good or bad our teaching and leading story is today, we will be judged down the road, we will be remembered 5 or 10 years from now by how we treated our students and each other. We will be remembered by how we chose to impact others – for good or for bad. By how we worked to get better in our relationships with others – in order to learn and develop our knowledge together, despite the pain that it can cause sometimes.

Expect nothing more from your collaborative team

The paradigm of engaging interdependently with other adults around issues of improved student learning is not easy. I know. I have loved my colleagues and my students, and I have been at odds with them at times. In the end though, how we treat the others in our personal and professional lives is what really matters if as the song says we hope to achieve deep learning with endless possibilities. No acadmic ceilings for ourselves, our students or our colleagues.  

You can see and hear the song on utube and I have also listed the words here.

To be humble, to be kind.
It is the giving of the peace in your mind.
To a stranger, To a friend
To give in such a way that has no end.
We are Love
We are One
We are how we treat each other when the day is done.
We are Peace
We are War
We are how we treat each other and Nothing More
To be bold, to be brave.
It is the thinking that the heart can still be saved
And the darkness can come quick
The Dangers in the Anger and the hanging on to it.
We are Love
We are One
We are how we treat each other when the day is done.
We are Peace
We are War
We are how we treat each other and Nothing More
Tell me what it is that you see
A world that’s filled with endless possibilities?
Heroes don’t look like they used to, they look like you do.
We are Love
We are One
We are how we treat each other when the day is done.
We are Peace
We are War
We are how we treat each other and Nothing More

Long ago, my mentor, friend and colleague, Rick DuFour, taught me the importance of the ARTS for students and for our work with each other. Over the years, at the holiday season, I have placed together pictures and video from family events through that year. I usually set the “presentation” to a song that seems to create some emotions – laughter and tears - for our family, as we view the presentation. 

This year. I am choosing the song Nothing More (Because it is a surprise, I am hoping my family doesn't read this blog!). You should try it too. I dare you! Download the song (iTunes or some other place), get together 30-40 of your best pictures and then let the slideshow roll. See how it goes! If you are not sure how to do this on your computer, enlist a family member under the age of 30. They will know! Then play it for your family and friends and remind them of what is really important this holiday season…their heart! 

Happy Thanksgiving

Saturday, October 11, 2014

Integrating My Way Through The High School Mathematics Curriculum!

I suppose this blog entry is not for everyone. Yet, it is time for me to write it.

It is about mathematics. Moreover it is about High School mathematics. More moreover, it is about a fundamental scope and sequence shift in the high school mathematics curriculum caused by the natural shift of state expectations for a college and career ready high school curriculum. Super moreover, it is about teaching an integrated high school college prep mathematics curriculum for all students!

If you are still interested at this point, then read on!  Otherwise you might just want to wait for the next blog!

AGA or IMP? 

It has been tradition in the United States, to teach the expected standards of the high school mathematics curriculum via courses named Algebra, Geometry and Advanced Algebra (or sometimes named Algebra 2). Often referenced as the AGA sequence of courses, there was an aura and perception that the AGA sequence of isolated topics resulted in a lack of rigor in student learning, with an inappropriate emphasis on low level procedural knowledge and fluency (or computational fluency and drill), using memorized
algorithms for finding a “Math” problem answer (cross multiply and divide anyone?)

During the 1990’s (and a bit before) there was a niche middle school U.S. market referenced as Integrated Mathematics that had a few in-roads into high school math curricula, but not significant or widespread implementation success nationally. These programs were perceived to be better at increasing student conceptual understanding, but were often criticized for deserting computational fluency.

AGA was criticized as a curriculum that was a mile wide and an inch deep, with not much application or understanding. Integrated mathematics was criticized as a curriculum that was too deep, based on nice “Math” problems with not much connection to student proficiency on actual standards.

Of course neither extreme painting of these two seemingly opposite course pathways for the high school standards was completely accurate. There were many successful AGA and Integrated programs, and there were of course many non-successful examples as well. In reality much of the “success” of these programs – from a student learning point of view  - were not so much about the scope and sequence of topics within the program per se, as much as it was about the teacher or teacher team using the program.

In pursuit of AND

I have always thought that either of these extremes was not best. Why couldn’t students benefit from a high school mathematics curriculum – a teaching and assessing program- that was both? Why not have fewer standards, taught at a deeper level of complex reasoning for student understanding, AND develop the essential procedural knowledge and skills needed to demonstrate student learning via the route of higher-level cognitive demand tasks (Thus redefining what is meant by mathematical fluency)?

This was the real gift to the high school mathematics standards offered up by the CCSSM. And the efforts made by states such as Texas and Virginia to intentionally blend conceptual understanding standards with procedural fluency standards AND allow the former to influence student learning of the latter via a set of mathematical practice and process standards.

The CCSSM Conceptual Categories of standards in high school created the potential for an integrated theme around:   
            Number and Quantity
            Statistics and Probability
            With Modeling

These big idea categories and the 138 or so corresponding standards were not designed to be about any course per se. They were designed to help the reader understand the nature of the Coherence (Sense –making), Rigor (a balanced approach to understanding, procedural fluency, complexity of reasoning and applications) and Focus (Fewer standards).

 Just as Number and Quantity, Functions, and Modeling are not separate courses students take, neither should the Algebra standards, Geometry standards or Statistics standards be thought of as completely separate courses that isolate topics and standards within a given year.

We can call the courses students are to take in their first three years of high school mathematics whatever we want, but even if you chose to call it algebra – it has been forever changed for 2015 and beyond.


First, we don't really write mathematics textbooks anymore. We write mathematics content for which the textbook is just one format. Students and teachers can access the content online, on their ipad, or iphone or other web-sourced/app device, and they can “experience” the content in a more dynamic way via video resources, games, and other forms of digital intervention and formative support.

Second, the modern day high school Algebra 1 course and all high school courses are now more integrated, regardless of the course title. The 1st, 2nd, and 3rd year of high school mathematics a college and career ready student learns is now built on a foundation of progressions and themes within each course and across the three courses.  So, which is better for high school students? An AGA sequence or an Integrated sequence? I am asked this question almost every week!

The answer is

It is not the names of the high school courses that ultimately will impact student learning. It is not whether you call a high school math course Algebra 1 or Mathematics I.  Geometry or Mathematics II. What matters above all else, are the quality, design and nature of your lessons and assessments every day.  

And yet, there are some great benefits to teaching these high school standards within a scope and sequence that takes advantage of expanded ways of student thinking, if the content progressions are to adhere to certain rhythms for student learning. These choices though are not dependent on the claim of AGA or IMP. These scope and sequence integrated shifts should occur no matter what you choose to call your courses as student learning experiences are based on a natural progression of topics. As one example, consider the role of:

Functions: Notice that in this more modern day view of the high school curriculum, students do not write a linear equation, rather they build a linear function, an exponential function, a quadratic function, a logarithmic function, etc… Building functions, interpreting functions, and analyzing functions are a major aspect of the high school curriculum now - generated from within and by a modeling context. This work, from a standards progression point of view should  be placed in advance of the equation solving aspect of the curriculum.

At the risk of getting just a bit specific in a blog entry, imagine a yearlong progression for the standard: I can build a function that models a relationship between two quantities.

This progression would begin with arithmetic sequences (constant rate of change) in Unit 2, move to linear functions (Unit 3) and then linear statistics (Unit 4), followed later by geometric sequences (constant percent rate of change) and more statistics in Unit 6, exponential functions (Unit 6 or 7) and eventually quadratic and polynomial functions  (Units 9 and 10). Thus, the standard has a logical progression for student learning built within the course – across multiple conceptual categories.

Equations:  A correct sequence to follow out of the building and interpreting of functions is to extend function development to include the topic of equations as the equivalence of two functions. This opens the door for students to solve linear, exponential, quadratic and other types of equations using three representations: Numerical (or table), visual (or graphical) and analytical (algebraic). What happens in your class, when students are asked to demonstrate fluency on a mathematical task such as:  

                                                Solve: x^2 + 2x = -3x -7 
If students have first experienced standards on how to build and interpret linear and quadratic functions, then multiple solution pathways become available or a lower level cognitive demand task such as this. In an AGA course sequence this standard would be taught in the spring of ninth grade. In an Integrated course sequence this standard would occur sometime in the fall of tenth grade, but the progression for building functions, then equations would still hold true. 

In this simple example, it is not about the course, as much as it is about your commitment to integrate student work with functions as a precursor to equation solving, and of course choosing a balance of higher and lower cognitive demand tasks in the process of building student fluency and understanding.

There are many more integrated topics and progression of standards to explore and discuss..., but not in this blog. However, one of the more elegant aspects of the geometry clusters is the use of transformations  (functions) as one of three ways to explore, justify and reason within the geometry standards. Thus, functions play a deeply embedded role throughout all three years of high school mathematics. 

For deeper insight I invite you examine our recently released high school mathematics series. We have also given the integrated question and series a lot of deep thought over the past 2.5 years as well.  We hope this will help you in your high school standard mapping journey - whatever integrated path you might choose!