One challenge for math teaching today is the breadth and depth of material we have to cover in one year. This long list of standards, each of which could be taught for a month or more alone, is difficult to cover with 360 minutes a week times about 36 weeks in the school year for a total of 216 hours of study in a year.
Yet that's the charge and we navigate it as well as we can with a variety of teaching/learning strategies including explicit teaching and mathematical conversations.
This week, I'll lead a number of explicit teaching lessons which I hope will be give-and-take conversations with my students. I'd like to stretch this teaching out for a month or more so that we could partake in more project based learning, but I simply don't have the time given the expectations of the curriculum. One reason I'm not totally frustrated by this is that our students overall do very well in math throughout the grades and by the end of high school generally meet high levels of math knowledge so I have some trust in the expectations set.
What will this week's focus on explicit teaching look like?
First, I'll tell students that we're going to walk through a number of points related to the behavior of numbers and multiplication. We'll essentially look at and try out multiplication in many ways as we think deeply about numbers and how they behave. This study began last week with a review of order of operations, the associative, distributive, and commutative properties of multiplication. Next we'll revisit how numbers increase when we multiply by the positive powers of ten, the area model for multiplication with whole numbers and decimals, traditional algorithms for multiplication, and using that knowledge as well as visualization and systematic strategies for problem solving. Each of these lessons could easily become a week of exploration, practice, discussion, and more, but time prohibits that at this time and to a large degree this is review of past teaching students had in earlier grades.
Once I explain the focus of these explicit lessons. I'll discuss with students what helps children the most during lessons like these. Typically finding a good seat where they can easily see the board and not get distracted is a first priority. Then having a table, clipboard, or notebook to write on helps. Writing questions and taking notes on the study packet can help to keep them focused and participating without fear of getting something wrong or asking an obvious question is also important. Throughout the teaching I'll ask lots of questions and make time for student questioning too.
These old-time explicit lessons, in my opinion, still have a place in the math teaching/learning program. I remember back to a time when I took a course in a new subject that was completely open-ended. I learned almost nothing because I had no background information to attach the learning to so I wandered down investigative paths that were totally off track. The course was a waste of time. Good teaching and learning demands choreography that responds to where students are at, what they need, and what the program expectations are.
This is one reason, in general, that I am not a fan of walk-throughs. In many cases, at walk-throughs or rounds, the people assessing the classroom program are distanced from what is really going on. They haven't had a conversation with the educator about why he/she is making the teaching choices they are making or how they are choreographing the program to meet the needs of the children. Instead a walk-through only gives a glimpse of classroom life at a given moment. It's too shallow for true study and depth. The book, Intentional Interruption, describes this well.
Instead when stakeholders are working together with full-circle approaches to creating, teaching, and assessing learning programs, that's when we get the kind of assessment and feedback that's meaningful and forward moving.
I still hold there's room for explicit teaching in a math program, but that kind of teaching can't be the mainstay of the curriculum and it has to be done with care and good focus. Onward.
