Thursday, July 7, 2016

Rethinking Mathematics Instruction

Throughout my teaching career I have seen so many students enter my high school math classes with a firm belief in their ability (or lack thereof) to do math.  I can’t count the number of parents who have sat down at conferences and opened with, “Well, I wasn’t any good at math, so it makes sense my child struggles.”  I have always been saddened by this attitude and felt the negative self-fulfilling prophecy was undermining students’ learning.  I tried in vague and individual ways to address this, but never took it to a formalized, systematic level to maximize the impact.

I have also always struggled with the apathy many students feel toward mathematics.  It is often something “to get through” on their way to something bigger and better.  I think part of this is how students have felt about mathematics, but I also believe it is about the disconnect of classroom mathematics to the real world.  While I have always felt my mathematical Achilles heel is practical application, I know my students need it both to engage deeply with the content and to improve their attitudes and overall learning.  Again, I wanted to make changes, but never felt successful in my attempts.

After reading Carol Dweck’s Mindset:  The New Psychology of Success (2007), I found myself nodding a lot and agreeing with her research.  I had always felt many of her findings, but never really articulated them.  However, I still didn’t really see the immediate application to my math concerns.  I was just stronger in my beliefs but no closer to a significant change in my classroom.  However, when I read Jo Boaler’s Mathematical Mindsets (2016), I began to see ways to change my instruction to be explicit and systematic about improving my students’ learning and attitudes about mathematics.
One key moment for me was when Boaler described how math is perceived as a performance subject with right and wrong answers.  This was a stop-point for me-it made so much sense to me but I had never thought of math in that way.  Yet, I believe this perception is the key to addressing both of my concerns.  If I can turn math back into a collaborative, logical, inquiry experience with multiple paths to solutions, I might be able to change some of my students’ minds and re-open doors for their future that they felt were closed because they “weren’t any good in math.”

This was the moment where I finally saw some tangible ideas that showed me how the changes I wanted to make might look and gave me some ideas how those changes could truly impact learning.  This is where my genius hour project finally took shape.  I hope to create inquiry tasks for each unit in order to cultivate more positive attitudes about mathematics and deepen the learning of the concepts.   I have several articles and research studies to read on deep learning that I hope will also give me ideas and insight into how to improve my instruction.

I still worry about my own lack of knowledge with real world applications, but I am willing to set that aside to move forward.  I have decided that I have been willing to incorporate technologies that I didn’t fully feel comfortable with and learned along with the students, so this will be the same.  I can’t ask my students to be uncomfortable and take risks if I am not willing to do so myself and model it openly.  Standford University’s will be one source I turn to for ideas, as well as the wealth of teaching ideas available on

The additional element in all this research and change is a new look at grading and assessment.  After attending the three day FIRST institute conference this summer which focused on grading and assessment, I believe we have to look different at how, when, and why we assess kids.  Boaler also addresses this assessment issue as being overwhelmingly negative and not motivating for most students.  Our math department has made some change in assessment by moving to mastery with retesting options and clearly identified standards, yet students still equate the scale scores with a letter grade.  I hope to work with my department on ways to continue to move away from scores which demotivate and move toward constructive feedback.  I could envision a system where students track their own progress through the objectives and control their own paths to learning.  After a summative exam, I want students to reflect on their learning process and progress.  I think so many of our students consider themselves powerless in education-they have fixed mindsets about what they can do (and have done) to improve their learning.  If they are empowered to choose learning paths on their own, they may begin to see their own success as a direct outcome.  However, I need to always be sure to emphasize growth and progress or this will all just be another grade chase with no real change beyond some superficial elements.

I am still struggling with the exact “product” of my genius hour project.  I have two or three different ideas that I want to implement, so I need to decide if I am going to phase in the changes (measuring success as I go) or if I am going to make a major, multi-faceted change.  As I start to work out the actual details, I think the best plan will appear.  I also will be sitting down with my department to talk about what they plan to do in response to Boaler’s book as we read it at as a summer book study.  We may choose a department approach that will address some of my ideas which will improve impact both in scope and design (more heads are better than 1!)

Tuesday, July 5, 2016


Creating an engaging classroom and motivating students are top concerns for most educators.  They are topics of blogs, PD sessions, books, and staff lunch tables.  My question has always been what happens between those beautiful elementary years when students are curious and excited to learn and my high school classroom where compliance, apathy, and grade chasing rule the day?
I believe a few things are at play.  One-we have “taught” students who is “good” at school and who isn’t.  The current system values such a narrow band of learning that by high school, many students are disenfranchised and have a fixed mindset about what they can and cannot do.  Two-our curriculum and assessments are often disengaged from any tangible, real application or skill students see as relevant.

There are likely many other factors, but I think we could address, system-wide, these two factors, dramatic changes would be seen.  If students were taught and coached with growth mindset philosophies, given opportunities to have successful failure and learn through a variety of paths, by high school we might see more resilient, open-minded learners, ready for the challenging course work of the 21st century.  We could foster the types of critical thinking we all say we want in our classes but are frustrated when it doesn’t happen.  We could move from (re)teaching basics (which are important) and repetitive topics to deeper thinking, application, critical tasks in each content area.  If we can change the way we assess students and report on those assessments, I think we will be one giant leap forward in changing our students’ perceptions and experiences in school.

Don’t get me wrong, I am a purist in many ways.  I think all students should be exposed to some ideas like Shakespeare, economics, mathematics, and chemistry.  I think self-direction and autonomy are great, but if you have parented a toddler, you know that kids like what is familiar.  If left to their own devices, chicken nuggets would be the main stay of most toddlers’ diets.  As parents, it is our obligation to expose our children to new experiences, even when they don’t like it or think they want it.  Often, that one forced bite of something new (which they would not do willingly) becomes next week’s favorite food.  Maybe it’s the 12th bite that gets them, or maybe they never acquire a taste for broccoli, but the point is we must push them beyond their comfort zone.  Put them on the bike, promise to hold on, knowing we will break that promise for their own good.

I think education is the same.  We should absolutely honor and encourage students’ interests and talents, but we also have an obligation to open new doors to them, introduce them to new skills and topics, even if they might not “willingly” choose them.  I had no idea as a HS student that I would end up as a teacher.  I took classes I liked and did well in because it made me feel good about myself and steered clear (when I could) of those that I didn’t like and struggled with because who likes that feeling?  I think this is part of our disengagement problem, students and our system have created fixed mindsets and roles for students which have closed doors.  We do not encourage curiosity and open-mindedness, risk-taking and exploration.  Will anyone every TRULY need Shakespeare?  (No, unless you are English teacher J).  Does that mean reading his work is an archaic tradition which has no merit in today’s world?  No.  Yet, some students will approach it with the mindset “I won’t ever need this.”  We need to change both the way we teach these concepts and the attitudes students bring to the content.  We don’t know what kids will or won’t need in their future because the world is changing too rapidly.  We need to foster a love of learning because we do know they will have to be able to keep up with rapid change.  We need to foster critical thinking because in a world of too much information, they will need to be able to filter and sort through the rubbish to find the golden nuggets.  We need to cultivate open-mindedness to look beyond the familiar and comfortable because that is where the true answers for our world’s problems are going to be found.