The Power of "C" for Correct.

I have my students do “Check for Understanding” worksheets at the beginning of my flipped class.  These worksheets are typically 3 to 5 questions covering the basics of the lesson they watched before class.  Having students complete these problems provides many interactions between the students and me to make sure they do understand the material.  If they do not understand then I can work with them and help them learn the material.   For students who are shy or quiet these worksheets provide opportunities to really know what they understand.  

Students are expected to complete these problems and have me check their work before starting their normal assignment.  I am surprised at the power of me putting a “C” for correct on their problems even for my juniors and seniors in high school.  Many students won’t start their daily assignments until they have a “C” on each problem of their “Check for Understanding” worksheet even if I tell them that their problems are all correct.  They want that “C” on every problem. (see image)

Last spring I had some students whose goal was to get the “Big C” which was one big “C” on the whole page indicating that all the problems were correct.  (see image)

 

 

I surprised one of my students who often get the “Big C”.  One day I did not give him his normal “Big C”, I supersized it by taping eight more pieces of paper around his page making it a 3 by 3 big page then I put one “Mega C” on it.  (see image)  He loved it and took it home.  The “Mega C” has been hanging on his parents refrigerator for months.

Some of my students from this last fall heard about that students “Mega C”.  They decided that they wanted to beat that students “Mega C”.  So everyday they would do their “Check for Understanding” worksheets and they wanted me to check their work and answers but they did not allow me to put any “C’s” on their pages.  They had a plan to make a supersized “Mega C”.  At the end of the semester they taped all their worksheets together into a 12 by 12 page and had me paint one huge “C” on it.

 

I am surprised that something as simple as putting a “C” for correct on a problem for a student will motivate them to work hard.  Even a this simple “C” motivates my juniors and seniors to go above and beyond what is expected.  Look for ways you can motivate your students to succeed as you check for understanding or learning of your content.

Arithmetic and Algebra, are They Different?

I have not had a lot of time to reflect this year since I have an overload (classes all day and no prep period).  But last Thursday I was at a meeting were they were discussing number/math talks (Making Number Talks Matter).  One of our tasks was to solve a problem then try to think about all the different ways a student might solve a problem, like 55 – 17 of which I thought of four ways to solve it however doing this problem with students the presenter stated that there are eight common ways to solve it.

All this got me thinking about arithmetic and algebra.  I know that algebra is very powerful and more powerful than arithmetic but are there some similarities.  Are arithmetic and algebra really that different?  Consider the following parallel.

Model	Arithmetic	Algebra
Algorithm	12  X  14     4  8 1  2  0 1  6  8
Algorithm Expanded	10  +  2    X   10  +  4          40     8 100  20         .  100 + 60 + 8	a + 4       X  2a + 3           3a + 12 2a2 +  8a         . 2a2 + 11a + 12
Expanded “foil”	(10 + 2)(10 + 4) 100 + 40 + 20 + 8     100 + 60 + 8	(a + 4)(2a + 3) 2a2 + 3a + 8a + 12   2a2 + 11a + 12
Area	100 + 40 + 20 + 8	2a2 + 3a + 8a + 12
Summary	Pair each digit of one number with digit of the other number	Pair each term of one binomial with each term of the other binomial
Extending It	123 X 456     100 + 20 + 3 X 400 + 50 + 6 (100 + 20 + 3)(400 + 50 + 6) Pair each digit of one number with digit of the other number	a + 2c + 3 X 4a + 5c + 6 (a + 2c + 3)(4a + 2c + 6) Pair each term of one trinomial with each term of the other trinomial

“Algebra” is really doing the exact same processes with numbers that we do with variables, which shouldn’t surprise you considering the variables are representing numbers.  Drawing connections between our algebraic concepts to numerical calculations is important to our students understanding of mathematics.  Many times we as educators will need to redraw these connections as students get farther and farther into the algebra courses.

Student Teacher Relationships in Learning

My blog below was originally posted on Pearson Educations Research and Innovation site on July 6th, 2015.

Relationships in learning are important but it is only recently that I have realized how important these relationships are.  When I was lecturing – first 20 years of my teaching career – I thought I had a relationship with all students, but in reality I did not.  Yes, I interacted with students, but it was often me with the whole class. There was a whole class relationship but not many individual, personal relationships.  I normally only got to develop a real relationship with a student if they regularly came in before or after school to get help.

I started flipping my classroom in the fall of 2010, and I noticed a couple of things.  I loved not being the dispenser of information, and being out and about with the students, helping individuals or small groups of students.  Flipping allows me to have many individual conversations with the students on a daily basis since I am helping students one on one the whole class period.   I get to talk with each individual student.  I get to know them, their learning style, and their interests; I can talk about how mathematics applies to their interest.  Each student gets to know me on a personal level.  It was after I started flipping that I felt like I made many more personal connections with students and truly got to know individual students. 

Evidence of Relationships Mattering.  A former student teacher shared this with me a couple of months ago, “You taught me that at the heart of teaching is healthy relationships.  You made it a priority to get to know each and every one of our students personally and make them feel welcomed, respected, cherished, and challenged”

Just before Christmas, a student gave me a card that stated, “Merry Christmas!  I also want to say thank you for everything you do.  Even though I feel like I put a lot of time into Calculus, I know you put even more!  Also, just like you said that we impacted you, you definitely impact us too.  It’s nice to be able to know that there are teachers that genuinely care.   So thank you!  Anyway, I hope you and your family have a very Merry Christmas, and I will see you next year.  Thanks for dealing with me when I get frustrated.”

A couple of my students wrote a blog post “Student Perspective of Flipped Learning”.  Here is part of the post that discusses the student teacher relationship.  “The relationship that we’ve all developed with our math teacher is something that none of us would ever trade.  Not only has Flipped Classroom helped us to know him in a professional setting, but it has also allowed us to know him on a more personal level.  Even during the parts of the school year when we’re not involved in one of his classes, he still finds the time to check in with all of us.  Be it through email, during passing time in the halls, or even around the lunch table, he is always there to make sure we are doing well.”

I received a couple of notes at the end of school from students and I have shared parts of the notes that deal with  the student teacher relationship. 

·         One student wrote “Mr. Faulkner, I don’t know where to begin, other than thank you.  You have not only touched my life academically, but in every other aspect as well.  You’ve taught me so much that I can’t even begin to explain how much you’ve impacted my life.  It seems so minuscule to send an email that says “thanks a ton”, but unfortunately I don’t know what else to give.  There are no words to describe how much you’ve changed my life.  Starting high school was a tough time for me, but you were always there to help.  Every conversation with you is a blessing.  You’ve given me opportunities that I never thought I would have. … You care about your students and you truly listen.  THAT is what makes you a great teacher and even better person.  You give so much and ask nothing in return.  You’ve changed my life in so many ways, and that’s all for the better.  I look forward to continuing to communicate with you in the future for advice, math help, or merely for a friend.  Thank you for all that you do and God bless.”

·         Another student, “Mr. Faulkner, You are someone that I am unbelievably thankful for.  You really opened me up and helped me realize my full potential.  Not only in math but also in life.  You work so hard and I respect that and hope to be just like that.  Lastly thank you for taking me in and being such a great mentor and friend to me.”

·         Three students wrote, “Words cannot express how grateful we are for having you as our teacher.  From Algebra 2 to Calculus, you’ve helped us grow not just as students, but ultimately has people.  You’ve shown us that without hard work and dedication, our goals are much harder to reach.  You’ve show us that sometimes you have to put your nose to the grindstone and get the job done (with laughs and espresso beans along the way).  You’ve shown us that there are no such things as stupid questions and that questions are how we become lifelong learners.  We’re proud to call you our teacher, but even more proud to call you our friend.  Thanks for all those life lessons and some math along the way.  THANKS AGAIN FOR EVERYTHING and for helping those three quiet kids in the back of Calculus class!!  Sincerely your lifelong friends the ‘Back Table Crew’.”

I tried flipping my classroom hoping that it would improve learning but I think it is the combination of flipping and an increase personal one on one connections with students that improved the student learning in my classroom.  (See https://goo.gl/hnWX0y for data on how student learning has increased in my classroom and “Positive Impact of Peer Instruction Flipped Learning” for more information about student teacher relationships in learning.)

So whether you flip or not develop those personal relationships with students, their lives and yours will be richer because of it; plus students will know that you really care about them and learning will likely increase as a result.

Visit http://troyfaulkner.com/  or my blog at http://troyfaulkner.blogspot.com/ for more information.

Reflection

             Reflection is necessary and very beneficial, but hard to do.

Why is reflection hard to do?  Time and Screens 

Many times as a teacher, husband, and father I either do not take the time to reflect or simply do not have the time.  As a teacher, I am often busy grading papers, entering grades, preparing lessons, working with students, teaching with an overload, or working on preparing a presentation.  This means I do not always have the time to ponder on what is going on.  I have no time to ask myself “How is each class going?” or “How can I improve the student learning in my classes?” Once in a while I have time to reflect at school but I often choose to talk with a colleague or go hang out with students instead of reflecting.  Both of these are important.  Positive relationships with fellow teachers are helpful and encouraging, while relationships with students can often be enjoyable, as well as educational.  Outside of school I have family responsibilities with kids’ activities, household duties, and the never ending “to do” list.

So why would I say “screens” keep me from reflecting?  When I am at school and have time I may check my email, the weather, or Twitter for interesting educational ideas.  All of these activities and apps take place within a screen.  When I am at home and have time to reflect, I may hang out with my family or just want some down time, so I turn to a screen (TV with Netflix) to relax.  All this can be good but it keeps my mind occupied so I can’t reflect.  When I am sitting waiting for my son to get done with soccer practice, I pull out my phone to check email instead of just sitting there and reflecting on my teaching or personal life.

Why is reflection important?

When you reflect you are able to see what is going well, what is going okay but could be improved upon, and what is going poorly, definitely needing to be changed and improved.  I recently had the pleasure of having some time to reflect.  I was at a conference and took the advantage of spare time to reflect with colleagues.  Conferences are normally great times to network and learn new things, but at this conference I had the joy of reflecting with two of my co-workers.  I had the pleasure of driving three and a half hours to this conference with one colleague which was a great time to talk.  For us, that meant discussing our classrooms and our schools.  Talking about what is going well, what we are doing, why, what we would like to change in our classrooms, as well as many other topics.  After three and a half hours we arrived and joined a third colleague.  The three of us continued to reflect on how things are going for a couple more hours.  We normally meet and talk one hour a week during our PLC (Professional Learning Community) but having multiple hours to just talk and reflect was wonderfully energizing.   The next night we had more time to talk and reflect over food after attending multiple breakout sessions.

Reflection is hard to do but I would encourage you to find the time or make the time, to do so.  This can be done by removing screens at least once a week for the purpose of reflection.  This time spent in thought will give you a new, fresh perspective.   It will help you see how blessed you are, and help you see the important instead of just the urgent. Having the chance to reflect for multiple hours with a colleague or friend is of great benefit as well.