I'm really good at the 4th wall. Probably because I majored in theatre in college. People can walk into my room, and I can just keep on teaching like they were never in my room. This habit/talent has come in very handy for the math studio! We have all sorts of people pop in our rooms- peers, administrators, instructional coaches, and visitors from other school districts. It has become part of my practise to be open about the way I teach. I have learned to value the debriefing after some of the observations because I get kind, gentle, insightful feedback on what I do really well and what I need to reflect on in my practises.
Growth can not happen on it's own- it takes personal reflection and caring colleagues to direct the growth. It has been especially valuable to have our grade level PLC (Planned Learning Communities) be on math this year. It gave us devoted time to analyze our tasks and planned for success and failure! I am looking forward to next year when I can sit down with my team and do more of the lesson planning. I think in another 2 years we will have all of the Bridges lessons with the 1) Math goal 2) aligned to the Common Core Standards,and 3) the cognitive demand either clarified or upped.
It's all about the mathematical task and what it demands of the students and the teachers. Research shows us the higher the cognitive demand the more learning occurs in the classroom.
" ...mathematical tasks is built on the idea that the tasks used in the classroom form the basis for student's learning." (Doyle, 1988)
Lower level demands include memorization and procedures without connections. The article has a nice visual showing example of each level of demand. Memorization:
"What are the decimal and percentage equivalencies for the fractions 1/2 and 1/4?"
1/2=0.5= 50%
Procedures without connections are the students doing the math without understanding why they are doing it. They plug in a formula, work it, and walk away.
One of the pivotal changes in my classroom has been moving away from the "worksheet". Bridges really does not have that many worksheets in the lessons. It is always making some kind of model, whether it is manipulative based or pictorial based, A teacher can observe and question the student to check understanding. It feels strange to give a worksheet to a student now. The best use of a worksheet may be as an exit test, and even then I want to be walking around the room observing how they work.
The most difficult part I run into is explaining to parents and after school programs why I don't send home packets of worksheets for homework. Besides the tediousness of the task, focusing on how many minutes and hours are spent on a worksheet is not "the best bang " for my buck. Real learning comes from students being able to perform the mathematical task showing how they are connecting to it to make sense of the math. It is not about me grading a work sheet but about me listening into students talking to make sense of the math and watching them work with uni fix cubes, or playing the math games in math stations. Guess which one is harder work?
Higher level demand tasks demand the student be able to explain and defend their work or reflect and change their mind about their work. One example:
"Procedures with Connections"
Using a 10 X10 grid, identify the decimal and percent equivalents of 3/5,
Even better
"Doing the Math"
Shade 6 small squares in a 4 X 10 rectangle. Using the rectangle, explain how to determine each of the following:(a) the percent of the area that is shaded. (b) the decimal part of the area that is shaded, and (c) the fractional part of the area that is shaded.
This is a great way to set up a task but also part of our teacher tool box is also thinking about student management problems, how much time is given for the task, and holding students responsible for their learning. A good teacher has management set up and implemented, taking into account the behaviors in the classroom every year. Time is always a problem in our schools anymore. The constant interruptions of the office buzzing in, birthday card invitations being handed out in the hallway, or cupcakes brought in for birthdays, pullouts for non academic reasons can strangle a lesson for certain students and frustrate a teacher when they lose 3/4 of the class's attention with each interruption. (In first grade that means at least 10 minutes to get them back to thinking and being on task.)
I have found it valuable in our PLC' s to line the lessons up to our first grade CCSS to determine how much time to spend on a lesson. It is the only way to determine what gets the most class time. I do not advocate throwing out a lesson because it is not in my first grade CCSS. It is always important to look at the trajectory for upper grades. For example: Money is not included in the CCSS for First grade. It is a standard in Second Grade. (2MD.C.8) Therefore I do spend some time teaching money.
Using the Task analysis alone or with teams focuses the task on the learning for the student. We cannot operate behind closed doors anymore. It is risky and scary to be observed by our peers and other people. It is a risk well worth taking because it is about the student and me becoming the best I can be in my vocation as a teacher! Bring on the 4th wall!
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