The Value of Reasoning in an Era of Fake News and Alternative Facts

       What do you believe?  Why do you believe it?  How do you decide what you believe?  Is there a difference between your perception of something and the actual truth?  Have you ever thought something was true for a long time only to discover what you thought was true (for months or years) turned out to be false the whole time?

       The old adage is "Don't believe everything you read."  This is valuable advice today just as much as it was in the past.  The Information Age not only increased the volume of information coming at us on a daily basis, it also increased the sources that create and publish this information.  Ordinary individuals can write blogs (case in point: me [!]) as easily as large institutions.  Information may or may not be vetted and fact-checked before being published.

       Another common source of information is friends and family; people you trust.  But what if your circle of friends and family is composed of lots of people that are just like you?  They look like you; they talk like you; they think like you.  You go through your life talking to these people and hearing the same things all of the time and eventually you believe that all people believe this.  But when you reference "all people", what you really mean is "all of the people that I know"--which is probably a subset of (say) all of the people in your town or all of the people in your country.  This phenomenon is knows as the Echo Chamber.

       Wikipedia defines Echo Chamber as a metaphorical description of a situation in which information, ideas, or beliefs are amplified or reinforced by communication and repetition inside a defined system.  Although the free flow of ideas via the internet might have lessened this effect, some have found that the internet has only amplified the Echo Chamber effect.

       Hence, we now live in an age in which the ability to weed out truth and facts may be harder than ever before.  Students, perhaps particularly teenagers, can become easy victims of believing in partial truths, fake news, and so called alternative facts.  This is why we need to teach students to question the things they read; to consider the source of their information; and to seek other points of views or at least other sources to confirm or to deny what they hear, see, or read.  Reasoning (the action of thinking about something in a logical, sensible way) is a skill that is more important today than ever before.  Our openness to consider other views influences our openness to people, places, foods, and experiences.

       We can't move forward and solve problems as a people or as a country, if we aren't able to fully understand the issues that we face.  Reasoning is a valuable skill.  Like any other skill, reasoning requires opportunities for practice to get good at it.  Schools should be able to provide these opportunities.

When Students are Thinking, Students are Learning

       I was recently introduced to a fantastic list of 100 questions that teachers can ask in mathematics class that will encourage students to think and reason and share their thoughts with each other.  A portion of these 100 questions are in the graphics in this post.  The rest can be found here.

       The questions are separated into categories that help students to:

1. Work together to make sense of mathematics.
2. Rely more on themselves to determine if something is mathematically correct.
3. To reason mathematically.
4. Evaluate their own processes and engage in productive peer interaction.
5. Gain a better understanding with problem comprehension.
6. Learn to conjecture, invent, and solve problems.
7. Learn to connect mathematics, its ideas, and its applications.
8. Persevere.
9. Focus on the mathematics from activities.

       Every parent that has ever received the unimaginative response of "Fine." to the question, "How was school today." understands the frustration of trying encourage a dialogue with young people who are either unable or unwilling to do so.  Teachers face this dilemma every day.  Except, for teachers, their are tasked with making sure that the students are actually learning the content that they are teaching.  Teachers don't have the luxury of dismissing an uninformed, mono-syllabic response.  Hence teachers do their best to use strategies that will encourage students to share their thinking.  These questions help teachers to achieve this goal.

       Here is a sampling of some of these great, discourse-encouraging questions:

How would you explain _________ to someone who missed class today?

How did you reach that conclusion?

Can you think of a case where that wouldn't work?

Could you reword that in simpler terms?

How is your solution method the same as or different from (student)'s method?

How does this relate to ____________ ?

       These questions help students to understand that mathematics is not just a bunch of rules that lead to a single number answer.  We want students who are able to understand the reasoning behind the rules.  We want students to think and reason and discuss and struggle and fail and try again.  We want students to have strategies for finding solutions beyond just asking the teacher.  We want students to learn from each other, to recall past lessons, and to know how to check their own work.

       These questions are a great resource to our teachers.  When students are thinking, students are learning.

A Tale of Two Classrooms -- Solve Problems

This is the seventh in a ten-part series based on the poster: A Tale of Two Classrooms.

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Solve Problems

       School used to be:

• Read the book
• Memorize the facts
• Recite what you've memorized

over and over and over again.  

       What are the capitals of the states in the United States?

       What year did World War 1 begin?

       What is the formula for finding the area of a triangle?

       Today's learners need so much more than mere memorization skills.  They need to know how to use these facts to make predictions, to see connections, and to find solutions.  The classrooms we need today require students to think and reason and discuss and hypothesize.  We need students who can be presented with a problem and know the tools they need to address the issues involved in the problem; and to find a way to solve the problem.

       Problem solving prepares students for the real world they will encounter beyond high school; be it college or career or relationships or buying a car or choosing a route to a destination.  We need problem solvers.  And the classroom is the ideal place to practice problem solving skills.  It isn't enough to have students who are only good at memorizing procedures or memorizes mere facts.  Anyone can find facts with the click of a mouse today.  Schools have to push students to do more.

       As with any other skill, problem solving takes practice.  Students need to hear from other students in addition to hearing from a teacher.  They need to be presented with problems that are (perhaps) a little bit beyond their reach, yet close enough to their abilities so that they can have ideas on where to begin.  Classroom need to have an atmosphere that respects effort and ideas so that students are free to offer their suggestions.  And we need to understand that problem solving is a slow process.  The quickest answer isn't always the correct answer.  Taking time to think is important.

       We need more and better problem solvers.

Soft Skills Education

       Our public schools' biggest offering is opportunity.  Students learn from qualified professionals and from a long list of course offerings--probably the longest at the high school level.  But we are not just teaching our students the R's, we are preparing them for the adult world.  This means that we are also tasked with teaching our students the so-called "soft skills".  Here is a short list of some of these skills:

• Listening 
• Presentation Skills 
• Giving Feedback 
• Decision Making 
• Inspiring 
• Persuasion 
•  Interpersonal Relationships 
• Dealing with Difficult People 
• Conflict Resolution 
• Self Confidence 
• Resilience 
• Assertiveness 
• Friendliness 
• Empathy 
  
• Problem Solving 
• Critical Thinking 
• Organization 
• Planning 
• Scheduling 
• Time Management

       Employers tell us that high school and college graduates who have these soft skills are much more likely to be successful employees than those who don't.  Students aren't "graded" on these skills in school, however many of these skills are incorporated into classrooms as rules of behavior (friendliness, conflict resolution, planning), suggested steps in completing assignments (decision making, resilience, organization), and learning strategies (problem solving, critical thinking, giving feedback).

       Students who are successful and confident usually possess these skills at a high level.  Students who are only concerned with the "book work" of school may possess the knowledge needed for their future, but they may also struggle with relationships with their co-workers.  This "soft-skills" education is an important part of our school system.  The ability of our students to get along with other students and to organize their thoughts, ideas, and lives is all a part of growing up and being responsible.  

       And everyone gets to receive this education for free in our public schools.  

Why Do You Teach?

       The school year ended four days ago and I am thinking about welcoming my teachers to the next school year.  (Wow.  That was a short summer vacation.)

       Every year in our school district the teachers return to school one week before the students return.  On one of the days of that first-week-back, all of the secondary teachers in the district meet in their subject areas for a full day of professional development before the school year begins.  This is a time to learn about new resources, to network with other teachers in other schools, and to energize teachers to get excited about the new school year.

       We know that an effective teaching strategy for student understanding is to ask a lot of questions that encourage students to think about what they are learning.  If students can explain what they are doing and why they are doing it, they must understand it pretty well.  It also reinforces the idea that we want students to understand underlining concepts and not just to get-the-right-answer.

       In that vein, I am going to ask our teachers some questions in an effort to encourage them to think about what they do and why they do it.  These question will challenge the teachers to consider different possibilities.  They will be questions that defy simple answers.

       I'm in the beginning stages of preparing this presentation and I am certainly open to suggestions.  Feel free share (in the comment section below) other questions that you feel would be good questions for teachers in the beginning of the school year.

Questions:
(1) Why do you teach?
(2) What are your goals this year?
(3) What will you do differently this year?
(4) How will you make a difference?
(5) What do you want to learn this year?
(6) Why is mathematics difficult for some of your students?
(7) How will you help students who don't ask questions?
(8) How will you engage your students in their learning this year?
(9) How do you help your students to value "learning" over "getting-grades"?
(10) Why do you teach?

       We ask (or should be asking) our students difficult questions every day.  As such, we need to ask ourselves difficult questions.  Teaching students who are willing and able and ready to learn is easy.  But trying to reach the unwilling, the struggling, and the distracted student takes time and effort and expertise.

       Why do you teach?

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.

Thinking about Thinking

       There has been a lot of talk recently about the need for schools to teach students how to think.  Actually, the need to build thinking skills has always been a big part of schooling, but our changing world seems to have added to the value of thinking skills.

     So this leads to the obvious question, How do you teach students how to think?  How do teachers create a learning environment in their classrooms that encourage students to think and to reason and to build on past knowledge?

       It is clear that there are times in a typical student's day when they are merely doing what they are told to do.  "Copy the notes,"  "Read this passage."  "Answer the questions."  Very little thinking is needed to complete these tasks.  Quite possibly, no thinking is needed to complete some of these tasks.

       So, once again, How do you teach students to think?  Or maybe I should ask, How do teachers encourage students to think?  One way to do this is to present students with problems to be solved.  We may suggest certain tools to solve the problem, but we do not tell them how to solve the problem.  The "problem" could be lots of things.  Here is a short list of problems to consider:

1. x+27=51
2. Run a mile in at least 30 seconds less time than you did at the beginning of the school year.
3. Learn to drive a car.
4. What can you do at your school to encourage students to be more friendly with each other?"

       The first "problem" could require thinking or it could require very little or no thinking.  If a tells a students to "subtract 27 from both sides of the equation", the student only needs to do-what-he's-told.  No thinking required.  If, instead, the teacher asks the question, "What number added to 27 is 51?", the student needs to do some thinking.  Of course we want the students to get the right answer, but the more important skill that we (eventually) want is for the student to know how to get the right answer.  We want to know what the student did to get the right answer--or the wrong answer.  We want the student to understand what is being asked and to devise a path to a solution.  (Lots of thinking!)

     The second "problem" is a physical problem.  Let's say that this student ran as fast as she could the first time she ran the mile, and now she is asked to run the same mile in at least 30 seconds less (later in the school year).  Let's also assume that this student has the desire to solve this problem.  She has to think, How can this be done?  What can I possibly do to run faster than my fastest running speed?

       The third problem requires a lot of procedural knowledge and a lot of rules to know.  Before students learn to drive, they often have a great deal of experience riding in a vehicle and (perhaps) observing someone driving.  This is knowledge that can help them when they are learning to drive.  They also (probably) have to learn things that they could not learn via mere observation.  Driving requires a lot of decision making which requires thinking.  Eventually experience with driving lessens the need for most of these thinking opportunities.  But in the beginning, driving requires a lot of thinking.  Considering that so many young people are able to acquire a driver's license, it must be true that even difficult problems that require a lot of thinking can be accomplished when we are sufficiently motivated to accomplish them.

     Finally the last "problem" is a social problem that is not (usually) solved through the learning of simple and procedural steps.  Indeed, this is the sort of problem that tests our abilities to think.  There is certainly more than one answer to this problem, yet these multiple answers may be very difficult to discover.

       Who knows how many difficult problems our students will face during high school, after high school, and well into their adult years?  The ability to think and to reason is a necessary asset in our lives.  Thinking can be taught and thinking can be practiced in our schools.  But thinking must be encouraged.  We cannot allow our students to go through the entire school day--everyday--and never ask them a difficult question that requires thinking.  We cannot allow them to spend all day in school merely doing-what-they-are-told.

       Students need opportunities to struggle with a problem in a classroom learning environment that provides encouragement.  The joy of thinking through a difficult problem and finding a possible solution is an experience that we want our students to have on a regular basis.  Thinking requires practice.

Problems Seen and Problems Solved

          American public schools can be described in some very large numbers:

100,000 schools

3,700,000 teachers

55,000,000 students

700,000,000,000 dollars

       Yipes!  Those are certainly huge numbers.  Of course, the United States is a big county of over 300 million people.  When we talk about any "system" in the United States, we are going to use some very big numbers.  And sometimes big numbers can make it seem as if the problems with our educational system are too big for us to solve.  But there is no such thing as a problem that is too big to solve.

       At one time in America it seemed ridiculous that women would ever get the right to vote.  At one time it seemed impossible that man would ever walk on the moon.  Separating our garbage into plastic and paper items in one spot and everything else in another spot was unheard of.  Smoking cigarettes used to be common in restaurants and offices.  And in our schools, it used to be practically impossible for students receiving Special Education services to sit in regular "mainstream" classrooms.

       All of these problems weren't even viewed as problems by most of our society at one point.  But then we recognized the problems and we changed public opinion about the problems and we took steps to address the problems.

       Our public schools take steps to improve the lives of all of our students everyday.  We all play a large part in our large system by finding ways to solve problems one student at a time; one problem at a time; one school at a time.

       Nothing is impossible.  Every problem has a solution.  Strong, dedicated professionals in our schools are problem solvers--everyday.

       Be a problem solver!