Wednesday, August 26, 2015

Making a Plan to Make It Stick

My summer was filled with a variety of professional reading, including:

In addition to reading this book, I took an online course in blended learning.  This book showed me that many models fall under the umbrella of blended learning.  The most powerful blended learning models involve making a school from the ground up and leveraging technology as a tool for teaching and individualizing instruction.  Little did I realize that “flipping the classroom” (something I started doing 4 years ago from time to time) is a blended model. 

I first heard about Carol Dweck’s book when I took a Stanford MOOC course by Jo Boaler called “How to Learn Math” in the summer of 2014.  People with fixed mindsets think their ability to do math is based on their intelligence or innate ability - that they are born with it.  These people get frustrated when learning doesn’t come quickly to them.  Failure or risk of failure leads them to take an easier path. Growth mindset people see failure as a part of learning and the effort needed to reach success makes them smarter.  Great ideas, even though the reading felt like a stream of consciousness at times.

This book looked at innovators in several areas – social innovators, entrepreneurial innovators and innovators in education.  Allowing children time to play and experiment was seen as important.  Letting them work together to fail and learn from their failures was necessary. The book looked at several college and grade school programs that do this successfully.  The short video clips were interesting, but were a repeat of what could be read within the body of the text.  

This was actually my daughter’s summer reading book.  She did not like it at all, but I told her I would read it and I did.  If I did plan on writing a memoir, it would have been a very helpful book.  A list of suggested memoirs found at the end of the book looked interesting.  Perhaps I will read one or two of these memoirs next summer.

But the most powerful and practical book was...

Make It Stick: The Science of Successful Learning by Peter C. Brown, Henry L. Roediger III and Mark A. McDaniel.  Thanks to Daren Starnes (AP statistics teacher and super math presenter) for sharing this book during Best Practices Night at the AP Statistics Reading this past summer. Daren's presentation can be found at  It is the fifth presentation in the list.

If you are not familiar with this book, click on the stack of books shown below to go to a video by Cathy DeHart which provides a good summary of the ideas from the book. Plus there are practical ways to implement those ideas to improve your learning and the learning of your students.  My students will be watching this video for homework on the first night of school and I will be using EDPuzzle to embed questions within the video. This will model the same type of self-quizzing students should be doing as they learn new material.

My Plan to Make It Stick

Learning that is easy is stagnant and most likely boring.  Think about it.  What makes a student stay up late playing video games?  It is the challenge of learning the strategy needed to make it to the next level that produces zombie-eyed students in our classes.  "Making mistakes and correcting them build the bridge to advanced learning." (Make It Stick, pg. 7)  Students get this for video games, because there is low-risk in playing the game.  Your character dies, no problem.  You have another life or you can always try again.  The student wants to persevere.  Unfortunately, students (and their parents) don't see mistakes in school as "the bridge to advanced learning".  Applying the concepts from the book will hopefully change that a bit.

1) Quiz and Quiz Often - Research shows that frequent low-stakes quizzes produce bigger gains in retention.  So, I am going to have quizzes every week on our scheduled lab day for the class.  With about 12 quizzes in a semester, I will be able to drop a quiz or two.  This means students won't have to make up a quiz when they are absent.  In addition, quizzes will count for 50% of my grade for the class, graded homework sets 30% and tests 20%.  With each quiz only counting about 5% of the student's grade, they will be low stakes.  Plus, tests counted 50% of the students grade in the past and now they are worth less.  In the end, I will probably be asking the same total number of questions, but just asking the questions more frequently.

2) Interleaved Practicing - Why do students do poorly on cumulative tests?  It is because the concepts are mixed up.  However, practice is rarely mixed up.  Students do all of one type of problem and then another type of problem.  They don't have practice with recognizing the concept in a mixed up set of problems.  Sure, my students will hate "mixed" practice. ("But Blah-Blah-Blah was in the last chapter, Mrs. Nataro.")  But in the long run, they will do better.  Plus, reviewing for the AP exam will really be review and not relearning everything from the fall semester.

3) Write to Learn/Explain to Learn - Although math has a beauty in the efficiency of its communication and its notation, there is much to be learned by explaining something to others and in writing about it. (Hmmm...I am writing now and learning now.)  My students do a fair amount of verbal explaining in Geometry and much written explaining in AP Stat.  I need to add more of the written explaining in Geometry and the verbal explaining in Stat.  I am not quite sure how this will pan out yet.  Perhaps by incorporating formal exit tickets from time to time in Geometry and doing a "think-pair-share" verbal class opener from time to time in AP Stat.

4) Give It a Try First - When I was a math student in high school, I didn't want to give things a try first.  My motto was "Just show me what to do and I'll do it."  But that type of learning is not long lasting.  "When you're asked to struggle with solving a problem before being shown how to solve it, the subsequent solution is better learned and more durably remembered." (Make It Stick, pg. 86) Having students attempt to solve a problem before I show them how to do it will be challenging for me.  It is hard to see students struggle and we want them to be successful.  How much struggling is productive? I am not sure how I am going to make this part of my plan a reality...not yet.

5) Reflect and Learn - For many adults, this seems obvious.  But how many times have you seen a student look at a grade on a test/quiz/assignment and then crumple it into a ball.  I want to scream at the top of my lungs "It took me 10 minutes to grade your paper and write comments to you.  The least you could do is look at them and try to learn something from your mistakes." OK, so screaming probably won't be good for my blood pressure.  But I could have students completing the following sentence after every quiz. "I need to get a better understanding of BLANK."  Then, they will describe what they will do to get a better understanding (such as, work through 5 examples of that type of problem and check their answer) or describe the conceptual error they made (such as, I thought the hypotenuse could be adjacent because it was next to the angle, but the hypotenuse is always across from the right angle.  Adjacent sides must be one of the legs.)  

Overall, I want to do less spoon-feeding and I want to provide my students with more opportunities for failure, because growing from failure = learning.  Ideally the corrective feedback I give to students on their mistakes will lead them to recognizing and correcting their own errors.

Evaluating the Plan and Reapplying the Glue to Make It Stick

In the past my blogs have mostly been reflections on my teaching in general or some specific lesson I did in my classroom.  That meant I only wrote when I felt like it and I didn't have a need to formally write and reflect all the time.  Now I have a need to track the progress of my plan and blog about the reapplying of glue (or tape or velcro) needed to "Make It Stick".  And in the process, I will be applying "The Science of Successful Learning" to my own teaching.

Additional Resources from Some Other Cool Teachers

As I was working on writing this blog, I came across some ideas from some other teachers that helped me refine my ideas and they may provide you with some useful ideas, too.

Julie Reulbach @jruelbach 

Global Math Department 
Attend their sessions weekly at 9 PM EST.  Even if you have already begun your school year, you can still use some of the ideas in this recording of the Global Math Dept. webinar.

Meg Craig @mathymeg07  
Her Make It Stick: Student Brochure is at

Friday, February 13, 2015

When Are We Ever Going to Use This???

Are you an adult who has been out in the work world for many years??  

Quick: State the quadratic formula. Bonus points if you are not a teacher.  

Question 2: If you are not a teacher, when did you last use the quadratic formula in your job? 

"When are I ever going to use this?? I am not going to become a math teacher." This is something that my 14-year old daughter is stating these days.  And now I find myself asking  a similar question when it comes to the computational, algorithmic hoops we expect students to jump through.  For example, simplifying complex fractions.  Why do we need to spend multiple days on this topic?  To say we need to do it, because it is needed for the next course or because it is needed on the SAT doesn't sit well with me anymore.

Any job in the real-world involving complex computations is going to involve a computer to do it.  And as for the SAT, a solid background of the basics in algebra, geometry, probability and statistics with a growth mindset will allow a student to be successful.

I used to recite the arguments that many teachers have said relative to "When are we ever going to use this?"  I can hear myself now saying something like, "We live in a democracy and that allows you to make choices later in life.  You can be want you want to be when you grow up, if you have a broad background.  Learning this will allow you to have more options."  Although that is still true, what skills are really needed in the real-world?  Companies say they want students with more math skills, but what does that really mean??  I highly doubt that means doing a question like #24, shown above.  

What really matters in math is the need to have kids learn to ask their own questions and find their own answers.  For example, yesterday we were looking an a traditional angle of depression problem and we figured out that the plane was about 100 miles from the airport.  Do planes really start descending 100 miles from the airport?  Does that seem reasonable?  How long would that take?
The students had no idea how to answer these questions.  One student told me he had only been in a plane once and didn't have any idea how fast a plane goes or how long it would take for a plane to travel 100 miles.  I told the class, "Take out your phones and find the answer." After a brief discussion on website validity and a little metal estimation, we had our answers.

If you have never watched either of these TED Talks, you should.  I am familiar with Dan Meyer's talk, but had not heard of Conrad Wolfram's talk.  In fact, the filming date of July 2010 for Wolfram's talk makes me wonder where I have been for the past 5 years.

How can we makeover our math classes?  How can we get teach real math in our classrooms? I don't have the answers, but I do know that it requires systemic change for it to be lasting change.  Changes involving culture. Changes involving parents. Changes involving colleagues and changes involving myself.  For now, I will work on myself and what I can change within the walls of my classroom.

Note: Moody's Mega Math Challenge is one way to get students involved in doing real-math.  This is an applied math modeling competition for Juniors and Seniors.  I am excited to have a team of 5 students participating from my school this year. To find out more about the challenge, go to

Monday, January 12, 2015

We're Too Cool to Function!

You know that your students are enjoying doing challenging math problems when:

A) They show up 45 minutes before the school day starts.
B) They cheer and give each other "High Fives" when getting a question right.
C) They draw all over your board after the contest is over to discuss how to solve a problem.
D) They design a math t-shirt that says "We're too cool to f(x)."
E) All of the above.

The correct answer is E.  All of these things happened when my students participated in MAA's Math Madness competition.  There are several things that make this competition great.

Math Shirt Designed by Moravian Academy's Math Madness Team

First, students compete as a team against another school.  The team score is made of the top scores, like in a cross-country meet.  The top scoring students varied from week to week and sometimes even included freshmen.

Second, students compete against themselves.  They see their previous personal best on their computer screen and try to get a new personal best.  The problems are varied - some of the problems are multiple choice and some are short answer.  Some involve traditional topics in algebra or geometry.  Others involve graph theory or probability.  But no matter what there is always something every student can answer and they get immediate feedback about their answer being right or wrong.  Here is a sample problem.  Can you figure out the correct answer?

Third, after the bracket round of competition was over, we could still arrange for competitions against other schools and my students wanted to continue to compete!  The 7:20 AM meeting time was not a deterrent!

Finally, the cost was reasonable at $12.50 per student for the entire fall season.

What is the next step for my team?  I have found a set of videos at MAA's Curriculum Inspirations website to help my students develop some new strategies to attack challenging problems.  We are also going to watch the Who Wants to Be a Mathematician Competition from January 12, 2015.  

MAA's Curriculum Inspirations