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.

Parents Like Their Children's Schools More Than They Like Education in America--Huh???

Question #1:  How satisfied are you with the quality of education of our your oldest child?
Question #2:  How satisfied are you with the quality of K-12 education that students receive in the United States today?

       How would you answer these two questions?  Gallup has asked these questions to Americans for years and the answers are always the same; paradoxical, but the same:

Answer #1: I like my child's school.  I think he/she is getting a good education.
Answer #2: I don't like education in America as much as I like the education in my child's school.

       What???  How can this be?  How is it that most parents are satisfied with their child's education, but not (generally) satisfied with the nation's schools?

       One possible reason is that parents live in the community that their child's school is located and they like their community.  Another reason could be that parents know their child's teachers; they've met them, talked to them, maybe are neighbors with them.  Their child's school is a place that they've visited many times and that they know pretty well.

       On the other hand, the quality of our nation's schools is heavily influenced by newspaper and media reports--which is generally negative.  (This is one of the reasons that I write this blog.)  Unfortunately, positive stories about public schools and American education are not told nearly as much as negative stories.

       Still, if so many people are happy with their child's school, then how can these same people be so negative about public schools in general?  Does this fall into the same category of, "Drivers around her are crazy, but I'm a good driver."?

       Our schools aren't perfect, and we certainly have challenges that need to be addressed.  I believe that these challenges can be better addressed when we have the support of the public that we serve.  Indeed we need all our collective "best thinking" to solve our most entrenched problems--such as the education of our poorest students.

       So cheer up American.  Maybe things aren't as bad you think--or should I say "As bad as you read in the press".

Graduation and Austin Cincotta

       A recent report from America's Promise Alliance on high school graduation rates reports that the United States High School Graduation Rate rose to 81.4% in 2013.  This represents a steady increase over the two prior years--a promising trend toward the (albeit, lofty) goal of a 90% high school graduation rate by 2020.  Ninety percent?? Maybe.   By 2020??  Not likely.

       About 3.3 million students are expected to graduate from high school this year according to the National Center for Educational Statistics. When we talk about millions of high school graduates and their collective prospects in the working world and the college world, it's easy to look at broad trends and predict likely outcomes.  But when we look at individuals, we move to the realm of real people with real concerns, real emotions, and real dreams for the their future.

       One of this year's high school graduates is my son, Austin Cincotta.  He was born in the waning years of the 20th century and grew up in the early years of the digital age.  He never used a rotary phone and he never changed a TV channel by turning a dial on the television.  He's loves his family, is a good friend, has been a boy scout since first grade, plays multiple instruments, and is interested in robotics and motion pictures.  He is excited about graduating from high school and moving on to the next phase of life.

       As for me, I am very excited for him and for the types of experiences that he will have over the next few years.  He will experience the freedoms and responsibilities of college while he thinks about his future endeavors.  He will be frustrated by meeting requirements that don't seem to have a direct link to his interests, and he will thrive in the areas that do.  He will have support from family and friends and (hopefully) from his school and his teachers.

     Our P-12 system along with family and community has done its best to prepare my son for his life after high school.  There will be ups and downs.  Ultimately his ability to make decisions, to meet goals, and achieve are up to him.  Still, I have the following hopes:

• I hope he is willing to ask questions when he doesn't understand something and he needs to understand it
• I hope he chooses right over wrong, even when right isn't comfortable
• I hope he understands the value of hard work and sees (or "imagines" if he can't see it) the benefits on the other side of hard work
• I hope he takes some chances that may be based on good criteria, but who's endpoint cannot always be known at the beginning.
• I hope he loves what he does

       When he was little, people always told me that I couldn't protect him from all of life's dangers.  I still can't.  I can try, but I can't do it all of the time.  It is his time to face the joys and dangers of life.

       Ladies and gentleman of the world, I present my son, Austin Cincotta--quite possibly the most precious and special high school graduate this year!

       Be nice to him.  He's still learning.

How Much Assessment is Too Much Assessment?

       So, here is how education is supposed to work...

1. The teacher teaches something.
2. The student learns it.
3. The teacher verifies that it has been learned.

Step #3 (above) is a very important step.  In the art of teaching, the actual "teaching" part is (indeed) only a part of what we do.  The far more important part is ensuring that learning is taking place.  If students aren't learning anything, then (one might say) we are not really teaching.  (Maybe we are just "presenting".)

       Sometimes we think that learning has taken place when it hasn't taken place.  Students nod their heads and smile and don't seem to have any questions; and it "looks like" they are understanding.  But unless our teachers are also psychics and are able to actually know what their students are thinking; some form of assessment is necessary for teachers and students (and parents) to verify that the "learning" really happened.  (After all, the goal of education isn't to get grades; the goal is to learn.)

       Outside of education, when people think about "assessment", they usually think about tests such as "Chapter Tests" and "Final Exams".  But educators know that there are many, many different ways to assess student understanding.  In fact, our best teachers incorporate some form of assessment into every lesson that they plan everyday.  This makes sense because how can a teacher know how or when to move on to the next topic unless they know how well their students understood the last topic?

       Assessment should be a part of every lesson.  It can take many varied forms.  Here is a list of ways to assess student understanding in the classroom from David Wees:

• 3 Things
• List 3 things that a fellow student might misunderstand about the topic
• Venn Diagram
• Have students compare and contrast a topic using a Venn diagram
• Write it down
• Have students write down an explanation of what they understand.
• My Favorite No
• Students complete a math problem and write their solution on an index card.  The teacher selects his/her favorite wrong answer and analyzes it with the class.

• Doodle It
• Have students draw what they understand rather then writing it.
• Chalkboard Splash
• Numerous students respond to a prompt/question on the chalkboard or whiteboard at the same time
• and 50 more to found here

       These many and varied forms of assessment could be graded or not graded.  But all of these assessments have the purpose of providing the teacher (and student) information about how well the students are learning.  Instead of assessment "of" learning, these include assessment "for" learning.

       So, How much assessment is too much assessment?  Assessment should take place frequently.  Some sort of assessment should occur with every lesson taught.  And we do this, the traditional, formal, summative assessments (like chapter tests) won't be such a big deal.

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.