Changing Math Attitudes

       I'm borrowing the title of a Facebook group to use as the title for this post.  The group called Changing Math Attitudes is composed of math teachers and other educators and (I suppose) other folks that seek to share experiences and expertise in the effort of helping students (and adults) to see mathematics as something beautiful, sensible, and doable by everyone.

       The first step in improving abilities in anything is to believe that you can do it.  We want students to understand that mathematics is not a secret code to which only a privileged few have access.  There is no "math brain".  Everyone can understand mathematics and it will take a group effort by many people in many circumstances to effectively change the view of mathematics that so many people hold.  This is the view that says "I'm not good at math."  (And so many people freely say this out loud when they would never say that they can't read or that they are bad at Science or History.

       I especially enjoy reading the posts from this group because they are generally politically agnostic.  It isn't a group that is pushing a political agenda one way or the other.  And this makes sense too because the "I'm bad at math." attitude is not coming from one group of people who members of any single political persuasion.  All sorts of people hold this view and so we are talking to all people when we say that we want to change attitudes about mathematics.

       Any math teacher will tell you that most of the students in their classes that struggle to understand the math would do so much better if they held the view that effort would lead to success; if they believed that getting the wrong answer doesn't mean that you are "dumb" but instead means that you've had a learning experience that can lead to better understanding.  If students can escape the Fixed Mindset that says "No amount of effort will lead to success.", then we know that we can help them to get to a point of better understanding.

       Attitude is everything.  Attitude determines the effort that students will put forth.  Attitude allows for a second try and a third try and a fourth try; or attitude gives permission to not try at all.  Attitude is the force that is stronger than caring adults.  Attitude shapes our views and ultimately shapes our destiny.  When our attitude tells us to give it a try, we are on our way to a world of opportunities.

Encouraging a Growth Mindset for your Students

       Growth Mindset is an understanding that you can learn and achieve anything if you are willing to work and practice and study and try.  A student's ability to learn is not predetermined from birth.


       This is an important concept for teachers who seem to always have some students who believe that they are not born with the skills necessary to learn.  A common saying among some students is, "I don't have a math brain.", meaning, "I don't have the ability to learn math regardless of the extent of my efforts."  We know now that this is not true.  But teachers are often faced with the prospects of needing to convince some of their students that this is not true.

       This chart is filled with suggestions for helping students to view their perceived obstacles in a different way.  Part of a teacher's job is to motivate their students to do their best everyday.  The more that we can convince students and then demonstrated to students that effort leads to (at least some level of) success, the more we are able to create a learning atmosphere in which students believe that they can learn.

       Growth Mindset is for weak and strong students alike.  We also have students who have been successful in the traditional school setting who don't have a growth mindset.  These students may have been praised for their "smarts" and they may be afraid to try something new for fear of not succeeding.  This limits their ability to grow.  Hence, encouraging a growth mindset is for all students and not just for a few.  Our best teachers have always been encouraging a growth mindset.  We have all had teachers who were able to convince us to try and to work hard in the belief that we would eventually succeed.  We need to see this occurring much more often in our classrooms.





Top Five Posts of 2015

       As I finish my second full year of blogging, I'd like to take a look back at 2015 and the five posts that got the biggest response from my readers.  But first I'd like to thank some of the many fellow bloggers that I've read and (sometimes) responded to over this year.  These professionals have caused me to pause and think about the various issues in public education that (perhaps) need to be changed; or that need to at least be debated.  I've also read many, many inspiring stories about teachers who work very hard--with little recognition--to help their students to succeed.

       Thank you to Alice Keeler, Starr Sackstein, Justin Tarte, Annie Murphy Paul, and Daisy Dyer Duerr.  I used to think that these were Super-Hero People who had some special gift or ability in the area of education.  But I've come to understand that they are just regular people like you and me who are eager to share their thoughts and ideas with the rest of us.  I, for one, am extremely grateful to include them among my professional learning community.  (And so are tens of thousands of other educators who follow these folks!)  I am continually inspired by your words; you keep me going and keep me writing.  Thank you.

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       Here are my top five posts from 2015:

#5) Open Letter to Teachers

       This was the second (and most popular) of a three-part series of Open Letters to the three most important stakeholders in our educational system: Students, Teachers, and Parents.  I wrote this "letter" to teachers on the eve of the 2015 - 2016 school year.  It was published on August 19th.  In it, I talked about how excited teachers are when a new school year begins--something, I bet, a lot of students don't realize.  I wrote about the tough job of teaching and I applauded the men and women who accept this responsibility.    Sometimes being a teacher involves difficult conversations with students about the need to continually struggle to learn something that isn't easy at first. Teachers shape the minds that shape the future of our country.  Teachers' influence over student achievement is well documented.  We always need great teachers.

#4) Learning vs. The Appearance of Learning

       Published on March 28th, this is an issue in which I feel very deeply.  The issue of the best way to measure learning and the problem (at times) of students appearing to be learning well (i.e. - getting good grades) but its only an appearance and it isn't real learning.
       I feel that P-12 education is the time when we have to be honest with students and their parents.  We don't want students to believe that they are achieving at a high level only to learn later in life (perhaps while sitting in a college class) that the grades they earned in high school did not represent their true ability.  The job of schools is to help students to learn.  We need to use multiple measures to get a true picture of their level of learning.  "Getting-a-good-grade" is not the job of schools.

#3) We Should Value Good Thinking More Than We Value Good Memorizing

       This post, from May 29th, quotes from Dr. Jo Boaler and Cathy Seeley.  In it, I talk about how our students'  thinking should be rewarded more than their ability to memorize math facts.  Sometimes elementary children who are very good at memorizing their multiplication facts (and recited them quickly) are viewed as being more able than students who cannot do this.  But we really don't students who can merely memorize facts.  What we really want is students who can think and reason and build on known facts to gain further knowledge.  Sometimes students memorize facts without knowing why the facts are true.  Later in their P-12 education they struggle because of this lack of understanding.  The goal isn't speed; the goal is learning.


#2)  No More Worksheets

       I began this post (from April 3rd) with a simple question:

Does you your child's mathematics teacher assign a lot of worksheets for homework and classwork?

If the answer is YES - Not a very effective teacher.
If the answer is NO - Likely to be a more effective teachers.


       Of course, this is an exaggeration, but the point is that this staple of P-12 education (the worksheet) should be a thing of the past.  They are boring; they are very un-engaging; and they de-emphasize thinking over mere "following steps".  They represent the opposite of what we want to see in our classrooms today.  Students should be spending class time reasoning and thinking and debating; they should be sharing ideas and thoughts.  They should hear from other students.  By the response I got from my readers, I'm thinking that this idea is not as radical as it may sound to some.

#1)  Growth Mindset Teachers

       This post had the most views of any post I've written since I started blogging more than two years ago (142 posts).  I talked about the idea of Growth Mindsets as created by Carol Dweck.  Specifically I talked about teachers who have the mindset that says anyone can learn.  These teachers help their students to understand that learning is always possible; productive struggle is a good thing; and their past negative learning experiences does not predict their future learning.

       Thank you to everyone who have shared this journey of learning and thinking with me in 2015.  The best of us are always trying to improve and to learn more.  Continue on and find your way to be the best educator you can be.

       All the best!

Peter Cincotta

Growth Mindset Parents

       I'm not sure if the idea of mindsets has broken out of the field of education and into the general public.  I hope it has.  Imagine if the parents of all of your students had a Growth Mindset and imagine if they helped their children (your students) to have a growth mindset.  That would be truly excellent scenario for any teacher!

       If you are not currently living this this ideal world, what can a teacher do to help her students' parents to understand the value of Growth Mindsets?

       Parents often ask teachers what they can do at home to help their children.  In the middle and high school years, sometimes the parents feel that they are not capable of helping their children because the content is beyond their ability.  This is an opportunity to talk about Growth Mindset with parents.  Here are some Growth Mindset suggestions that any parent can do:

1. Help your child to understand that effort yields results.  Read, study, practice, quiz yourself.  
2. Tell your child that true learning takes time.  You might not "get it" the first time.
3. Make sure your child understands that it is OK to make mistakes.  We all learn from our mistakes.
4. Praise your child for effort; don't praise your child for "being smart".  This seems counterproductive, but kids who are rewarded for "being smart" tend to take less chances for fear of losing the "smart" label.
5. Never, never, never, never tell your child that you were bad at math or science or anything else.  This gives children an excuse for not doing well, and it makes them believe that they have some sort of genetic deformity that predestines them to be bad at these subjects.

       So much of these suggestions go against the idea of "playing school"--looking smart, pretending to learn, memorizing stuff for the test, only caring about grades, and not caring about learning.  We want students to understand the value of hard work.  Learning faster isn't learning better.  It's OK to make mistakes.  When students hear this from their teachers and then hear it again at home, they will believe it.

       Learning isn't a competition.  Students with a fixed mindset toward any particular subject can change to a growth mindset if they have supportive teachers and parents that encourage a growth mindset.

       Learning real does take a village--a Growth Mindset village would be a pretty good place to live!

Growth Mindset Teachers

       Have you heard about Mindsets?  In my school district, I am hard-pressed to meet a supervisor or a principal or a teacher who hasn't heard about it.  Here's a quick video that defines Growth and Fixed mindsets:

       Teachers who understand the Growth Mindset are able to help their students to understand that effort yields results and mistakes are the building blocks of true learning.  These teachers don't encourage their students to get good grades, they encourage questioning and curiousity.

       Students with a growth mindset believe that their is nothing that they can't do.  They don't mind making mistakes because they don't view them as mistakes.  Instead they view mistakes as an important part of the journey toward learning and true understanding.

       Teachers can help students to develop a growth mindset by praising their thinking and their effort, rather than praising that they simply got the right answer.  In fact, if students are constantly told that they are smart, research tells us that they tend to avoid making mistakes and they will hide the things that they can't do because they fear that they will lose the label of "being smart".

       This is (yet) another reason why we have to end this school culture of over-valuing grades.  School is supposed to be about learning and we want our students to understand that learning requires effort.  Effort requires trying new things and taking chances and not getting it right the first time.  This is not only "OK", it is necessary for true learning to take place.

       We love our growth mindset teachers that produce our growth mindset students.  Learning can be hard work.  We want our students to value this hard work and to recognize that there is always a prize waiting to reward them for this hard work.

Open Letter to Teachers

 This is the second of a three-part series of open letters to the three most important stakeholders in our educational system: students, teachers, and parents.  All three of these groups play a vital role in the education of our children.

Dear Teachers,

       If students only knew how excited and anxious and thrilled and nervous and ... all teachers are as the first day of school approaches.  The first impression, the first lesson, the first assignment, the first words that a teacher utters on the first day of school--every second is precious.

       A teacher's role in the education of our nation's children is the most vital and influential component of our educational system. As a teacher, your abilities have more of an impact on student achievement than any other factor.  All of this importance (I know) puts a lot of pressure on you to do the best job possible everyday.


       And to add to these pressures--as you already know--teaching is a very difficult job.  Different students with different learning styles; some having good days and some having bad days ON THE SAME DAY; building positive relationships and teaching to the highest standards.  The demands on you are many.

       I want you to know how much I appreciate the work that you do.  The best of you strive to improve all of the time.  Teaching is the sort of profession that's hard to master.  There is always something more that you can do; more students that you can reach; better strategies that are more effective for more students.

       You also, at times, have to be the one who tells a student that he isn't reaching his potential--and I thank you for that too. We have to be honest with our students and we don't want them to have a false sense of accomplishment only to discover (perhaps in college) that they real do not have the abilities that they were told they had.

       I hope you will be a warm demander as a teacher this year.  That is, be the teacher with high standards who insists that students do their best everyday, and at the same time your students know that you care for them and will do everything you can to help them to achieve.  Students appreciate teachers who believe that they can be successful with difficult material.  Students don't want teachers who make everything easy and demand very little from them. This only tells the students that they aren't worth the effort to teach.  Help your students to engage in productive struggle in the classroom.

       To all of our great teachers, I hope you have the best school year ever!  We often say that our students are our future.  If this is true, than it is true that our teachers are the ones who shape our future.

Somebody Has To Tell Them

       Nobody likes to hear bad news.  And nobody wants to be the person to give the bad news.

       In our public schools, we (sometimes) have the following problem...a student is not achieving at an acceptable level.  He tries to do well; he does some things well; but overall his achievement is too low for his grade or age level.  Public schools have lots of ways of helping students to raise their level of achievement and (indeed) it is our job and moral responsibility to do so.

       The problem is that someone has to tell the student and his parents that he is achieving below grade level.  That is a hard conversation to have.  No teacher wants to tell their students' parents this news.  No parent wants to hear this news.  But someone has to do it because we don't want to allow students to go through school thinking that they are doing fine (academically) when, in fact, they are below grade level.

       Sometimes we try to give this news through grades on report cards or via standardized testing grades, but the message doesn't always get through.  Sometimes students get a few good grades on minor assignments and parents "hang on" to those grades and seem to ignore the poor grades on the more major assignments.

       And so, sometimes students go through elementary and middle school thinking that they are doing fine and then they get to high school and struggle with their academic course work.  Even worse, sometimes these struggling students even go through high school with no one in authority ever telling them that they are below grade level.  These are the students that go on to college and (only) then are finally told that they do not have the ability that they thought they had--no one ever told them.

       Our job is to help students to learn.  Part of that job is telling students how well they are learning.  We don't help our students by letting them think that all is fine when it isn't.  Someone will tell them at some point, so it might as well be sooner rather than later.  It doesn't have to be an argumentative conversation.  Teachers and schools will help students to do better--that's our job.

       One way to communicate this message is to have a grading policy that rewards high academic achievement and discourages mere compliance with school and classroom rules.  While we certainly want students to behave in school, what we really want is for students to learn in school.  Teachers who have high expectations for their students and are very clear about those expectations tend to have students who reach those expectations.

       It's OK to tell students that they have not achieved the goal yet.  It doesn't mean that they will never get there, but it does tell them that where they are (academically) is not acceptable and they have to do more, try more, and achieve more.

       Somebody has to tell them.  Be brave and be the one who cares the most about your students.  Be clear about your expectations and tell students when they have and haven't met these expectations.

We Should Value Good Thinking More Than We Value Good Memorizing

       Stanford professor, Dr. Jo Boaler, recently published an article titled, "Memorizers are the lowest achievers...".  In it she makes the point that some students are really good at memorizing math facts and memorizing math procedures, but (sometimes) these same students are very poor at understanding the concepts connected to these math procedures.  To those who believe that "mathematics" is nothing more than adding and multiplying, it may seem odd that we (educators) view this issue of memorizing as a bad thing.  It may also seem untrue that these memorizers are low achievers.

       Dr. Boaler goes on say that here in the United States, we (often times) reward students for being good at memorizing math facts, but offer very few compliments and rewards for being good thinkers and reasoners.  She says that, "We need students who can ask good questions, map out pathways, reason about complex solutions, set up models, and communicate in different forms."  These are the skills that help students to be good and successful learners, as well as helping them to understand the abstract, higher-math skills taught in upper Algebra classes and Calculus.

       The same thinking that favors memorization (often) also believes that students who are able to come up with answers quickly must be smarter than those who are slower to answer questions.  This, too, is not true but (sadly) is often the message that is given to students in school.  Former NCTM (National Council of Teachers of Mathematics) President, Cathy Seeley, wrote a great book titled, Faster Is Not Smarter.  In this book, Ms. Seeley stresses the importance of teaching mathematics for understanding and not just for "getting the right answer".

       High school mathematics teachers will tell you that it is a common situation to have students in (say) an Algebra 2 class or a Pre-Calculus class that were consider great "math students" in elementary and (maybe) in middle school, but then suddenly began to struggle in mathematics in high school because they never really "learned" and understood the mathematics; instead, they just did their best to memorize facts and procedures.  This sort of "learning" is not permanent.  The basic skills of (say) operations with fractions and integers (positive and negative numbers) are quickly forgotten because they were never really learned in the first place.

       But this situation can be changed.  For some it is a huge change from the way we were taught and from the trainers we received as teachers.  For others, it is a very welcome change to the way mathematics teaching needs to be.

       It isn't about grades.  It's about learning.  We need to have a good balance between procedural knowledge and conceptual knowledge.  If we intend to truly prepare our students the best we can for their futures, we need to equip them with the tools to success.  It isn't fair to give students (and their parents) the false impression that they are highly-able just because they are good at memorizing or getting the answers fast.

Attitude Trumps Ability

       Remember when you left for school as a child and your mother said, "Do your best"?  It turns out, that was pretty good advice.

       Most students who don't succeed in their school subjects have plenty of ability but instead lack the desire to do their best.  Maybe they believe that they don't have the natural, genetic, brainpower to succeed (read Mindsets by Carol Dweck).  Maybe they have problems at home that make their schoolwork seem very unimportant.  Maybe they have a fear of failure.  I contend that most of the time, it isn't ability that is holding them back.

     Here is the most common teacher phone call to parents:

Teacher: Hello Ms. Thompson.
Parent: Hello Ms. Salero.  Is there a problem with my son, Donald, in your class?
Teacher: Donald has lots of ability; he just needs to put in the effort.

       Every teacher knows that their job is two-fold:

       (1) Teach
       (2) Encourage students to learn  

If learning isn't taking place, the best teachers with the best lesson plans won't make any difference in the lives of their students.  Hence, teachers spend a lot of time thinking and experimenting with the best ways to motivate students to do their best.

       When parents ask, "What can I do at home to help my child?", the best answer is to encourage your child to do their best everyday.

       Students need to understand that learning takes time and learning is hard and learning requires struggle.  But a lack of understanding after the first try does not mean that you are unable to learn.  In fact, it's the struggle that helps your brain to make more connections and to retain what you are learning.  Stanford educator, Jo Boaler, talks about this all of the time (see video).  Students need to understand the value in making mistakes--it isn't an excuse to give up.  In fact, mistakes are excellent learning opportunities.

       Some students are anxious to learn and don't mind making mistakes.  But others are so focused on "getting-the-right-answer" and "winning" that they are quick to give up when they don't understand something the first time.  We need students to understand the value of productive struggle.

       Keep trying; keep struggling; keep making mistakes; and keep learning.

The Challenge of Educating Poor Students - Part 2

       American Public Schools face many and varied challenges.  Funding, equity, and public support to name a few.  On the top of this list of challenges, I would include: The Achievement of Poor Students.

       It is easy to understand the underpinnings of this problem, and yet it is extremely complex to succeed in overcoming this problem.  The problem stems from two indisputable facts:

1. Poor students consistently demonstrate lower achievement than their non-poor peers.
2. The proportion of poor students in our nation's public schools is over 50% and is growing.

       I will examine this challenge from three perspectives:

1. Poor students who have succeeded in our schools
2. Understanding the special and different needs of poor students 
3. Expert advice on successfully educating poor students

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The Challenge of Educating Poor Students - Part 2

Understanding the Special and Different Needs of Poor Students

       People who grow up in a middle class (or higher) home environment may take for granted simple life experiences that poor students and their families never experience.  Well-meaning teachers may have never experienced living in a poor environment and working with poor people until their first year in the classroom.  Particularly since school teachers must have a college degree and it is rare for poor people to earn a college degree, teachers are generally from a middle class (or higher) background.  

       Here is a short list of challenges for most poor students:

1) Regular, quality medical care

       

       Middle class families generally have a regular doctor for their children.  When children are sick, they go to the doctor and they get better in a couple of days.  When poor students get sick, they don't have access to a doctor or to medicine; this makes them sicker.  When they are too sick to come to school, they generally miss more school days because it takes them longer to get better.  And if they come to school when they are sick, it is harder for them to concentrate on their school work.       

      A lack of medical care leads to other issues that are more prevalent among the poor such as untreated ear infections and hearing loss issues, greater exposure to lead, and a higher incidence of asthma (source).  All of these health issue contribute to higher absenteeism and lower engagement with class lessons at school.

2) Small vocabulary when they start school

       Students from poor households hear and use considerably less words than students from middle class households.  This puts poor students at an academic disadvantage from their first day of kindergarten.  Students who are less able to use words to express their feelings and to explain their thinking because frustrated and soon shy away from activities that involve reading because they don't want to appear less able than their peers.

      Opportunities to increase each students' personal vocabulary must be of primary importance for poor students.  We know from multiple studies that students who are not reading on grade level (or above) by third grade have a reduced chance of graduating from high school. (source)  This is a significant risk factor for poor students.  In 2013, the overall national high school graduation rate was 81.4%  but the rate for poor students was only 73.3%.

3) Fixed vs. Growth Mindset

       Stanford psychologist, Carol Dweck, and her book Mindset has taken the education world by storm over the past few years.  And so it should.  She has proved that students who believe that they are not smart will refuse to try to succeed.  This is the belief of the "Fixed" mindset; the one that says, "I have a fixed capacity for learning and no matter how hard I try I won't get any smarter."  In fact, nobody has a brain that isn't capable of learning more.

       But poor students are more likely to believe in the Fixed Mindset because they are less likely to see the many opportunities that will be offered to them in the future beyond high school and college graduation.  Poor students need to be praised for their effort and teachers need to point out when their thinking has led to a great solution to a problem.  Students with Fixed Mindsets believe that they just got lucky whenever they get a good test grade.  They need to understand that it is their effort and their learning that led to that good test grade.

       Teachers at every level (elementary, middle, and high school) can help poor students to succeed.  But we have to understand the deficiencies that they bring to school and we cannot label every lack of effort as "laziness".  Some poor students do succeed; they are the lucky ones.  They probably had great teachers and caring parents or caring authority figures at home.  Overcoming these deficiencies is a very difficult job for our public schools; but understanding the problem is certainly the first step.

       All teachers should receive some training in the education of poor students.