It is impossible to be an educator today and not have heard of George Couros' Innovator's Mindset. I first read it this summer and when I returned to school, our assistant superintendent announced that this book would be the first of two book studies we have the option of participating in this school year. Although I already read the book, I wanted to be part of the conversation, so I read it again, and again, and again. Yes, that is a total of 4 times. Each time I read this book, I learn something new. It's as if George hid little Easter eggs all over his book to be found each time you read.
There are so many takeaways from this book, my favorite being "Change is the opportunity to do something amazing." ~ George Couros
As I have mentioned in my previous post, I never gave up that new teacher "want to save the world" desire when it came to the type of classroom I wanted to provide for my students. Well, three years ago, I took the biggest risk of my career and made a huge change to the way I teach math. I have to say it was truly amazing. The method I hope to describe in today became so much more than a way to keep all kids learning and engaged in math class, it has transformed they way I think about teaching and learning. In many ways, the changes I have made help students engage in the 8 Characteristics of the Innovator's Mindset.
Let's dive in! The graphic below illustrating the 8 Characteristics will be guiding my discussion of the Quadrant System over my next few posts. (This is not a one-post system.)
Empathetic Teacher
Would you want to be a learner in your own classroom?
~ George Couros, Innovator's Mindset
I teach in a very unique district. 60% of our students are state identified as gifted. We know that traditional schools are particularly challenging for these students as they do not typically learn best in this setting. As a matter of fact, many gifted students do not finish high school. We see a lot of our gifted kiddos under performing. Many teachers do not understand this is a form of perfectionism and needs to be addressed.
Others become super students and refuse to think outside the box. These students want to know how to find an answer then replicate that process over and over until they receive 100% on the unit test. This type of student is over worked, over stressed, self critical, and under imaginative. It is not that they have no imagination, rather, they are afraid to use it for fear they will be "wrong". The important thing to remember is that students who are gifted in mathematics only need a few repetitions to master a skill. When this happens, these students can often cause disruptions in class. This brings up a whole new discussion on homework that I will not explore in this post. There just isn't time.
Still, there is a third type of student in my school that is not gifted. We have been focusing so much of our effort this year exploring ways to empower our gifted students, that this group seems to be overshadowed. These students can sometimes be very good at doing math or they can struggle. It may take longer for these students to learn math and it always bothered me that they didn't get the time in class to fully practice and explore concepts before moving on. I saw how this was contributing to poor attitudes towards math. It is also important to mention that Jo Boaler, author of my favorite book on teaching math, Mathematical Mindsets, reminds us that professional mathematicians are the slowest workers. Think about it. A mathematician can spend her entire career working on one problem, yet we expect our students to learn mathematical concepts in a prescribed amount of time. This is not to say I let my students spend the entire school year learning how to divide fractions and nothing else, but it has helped me to be more mindful that students learn a different rates.
I share this mantra with my students, It's not when you learned 6th grade math, it's that you learned 6th grade math.
The Innovator's Mindset encourages teachers to ask themselves the most difficult question: Would I like to be a learner in my own classroom?
I think it is easy to answer "yes" to this question because most teachers run their class in the way they learn best. But what about the other students? What about the creatively gifted that often remind us of everyone's favorite creative student from Hogwarts, Luna Lovegood? What about the student that does not enter your class with the same love of your content as you? What about the fast learners? What about the slow learners? Would they want to be learners in your classroom?
Three years ago, my answer was no. I had students that finished their work quickly and accurately. Nothing I gave them keep them "busy" so I could work with the students that really needed me.
So, here's what I did:
I have created a Four Quadrant learning system. I took all of the content I wanted to teach my students and broke it down into related topics, using "I Can" statements to break up the content. I put all of the information and resources the students would need to be successful working with the content on a unit guide. Please refer to the Decimals Unit Guide I use at the beginning of the year to introduce the quadrant system to my students. The content in this guide is basically activities and materials I have used in a traditional setting. Please note that some of the materials in the unit guide are taken from our textbook that our district has paid for us to use with our students only.
The quadrants are set up to increase in complexity. The first quadrant provides acquisition of the skill. The second quadrant allows for further practice or problem solving. Next, students enter the third quadrant which allows them to apply the skill through problem solving practice or performance assessment. (My favorite place to find my P.A. is on the Georgia DOE website.) Finally, quadrant 4 is an extension of the skills. Only a few students actually complete quadrant 4 as it is not required in order to move on. This is particularly for my gifted students that need additional challenges. I also use their work on this quadrant to collect data for their Written Education Plans. However, I occasionally get students that are not mathematically gifted try these quadrants to extend their knowledge on particular content.
While the students can work at their own pace, they are given deadlines for completing the quadrants, which is usually the day before a quiz. On the flip side, students are not slowed down for working faster. They can continue through the unit without having to wait for their peers to catch up. Students that complete an entire unit of study, have the opportunity to complete a set of extension quadrants which introduce 7th grade skills.
This system allows the students to move through a unit at a pace that is appropriate for them. I use a coordinate plane, yes, they are also learning math through the very set up of the system. That was not an accident. On my boards, I have several coordinate planes with a magnet for each student.
Most students begin in the first set of quadrants in quadrant 1. However, based on pre-testing (or progress on our online assessment system), some students already have the basic skill and can skip this quadrant and possibly even the second quadrant. Our district has purchased a subscription to ALEKS which delivers another layer of differentiation. In a nutshell, students work to complete their "Pie" which includes all 6th grade standards. Because the students are always working on this system and periodically take "Knowledge Checks", I know what skills they have mastered. If I am not confident that the students have mastered a skill, I can assign assessments to gain information on their progress.
As students complete one quadrant, they move directly on to the next. Periodically, they are required to stop and get a mini-lesson or small group discussion before moving on. Although they are moving at their own pace, they can not move their name until their work has been checked off by me. I assign specific problems and allow the students to choose a set number of problems they think will challenge them in quadrants 1 and 2.
What I love about this system is that I am forced to make individual time for each student. I discuss the math with each child at least one time per class period, often more. Students can work with each other, independently, or with me to master the content. As a result, I have a very clear understanding of my students' strengths and struggles. It has been very exciting to see a huge increase in my students' attitudes towards math. Students that begin the year stating that math is their lease favorite subject, often leave at the end of the year sharing that math is now their favorite class of the day. Does this mean more students enjoy being learners in my classroom?
Most importantly, I am building relationships with my students through this process. Because I am sitting down with my students everyday, they feel more comfortable sharing stories about themselves with me. I am also finding that I truly love all of my students!
There is so much to say about quadrants and this brief overview does not even begin to encompass all that can be achieved through this system. Since I have started this, I have presented the quadrant system at several conferences. Feel free to access the presentation my intervention specialist (and biggest cheerleader for quadrant work), Amy Smart, and I used this past summer at a conference. At my school, science teachers and our ESOL teacher have modified this system to use in their content areas with much success. Can you use this system in your class?
What do you think? Please leave a comment below with suggestions or methods you have found successful in your class.
Thanks for reading! Have a fantastic day.
Note: You will notice on the unit guide that several of the quadrants have a video lesson aspect. I utilize a flipped classroom in several ways. Most students use the videos to preview a concept that we will discuss in class. Others use it as their instruction for the content. Some students never watch some of the videos and get their instruction directly from me. In every case, the students are required to discuss the content with me individually or, more likely, in a small group. Each video has a summary component, 3-4 questions to answer in their composition books, and a work session which allows them to practice the skills presented. Most videos ask students to pause the video and complete a few problems then continue the video to go over the answers. I also require all students to ask a question, even if they think they've go the concepts down. This lets me know, to what extent do they understand the content. Some students will ask a question that will extend their learning beyond the basic skills, those are my favorites.
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