A question has been posed by Lisa Henry today about when and how guided instruction is used. I began musing over the question as soon as I read this, thinking back to when I first began teaching. Fortunately, it’s not as long ago as it might seem. While I am also an “old dog”, I have been teaching for only 11 years. Before that I was an ED RN, but I digress. When I first began teaching, I started with the idea that I wanted to create a room full of critical thinking and problem-solving. I really didn’t think this was so strange, seeing as I was a math major about to teach math. Isn’t that what math is? In my student teaching assignment I worked with teachers who had been trained at SLI at WestEd in bringing literacy into all subject area classrooms, and that was a natural fit for me. It was an extension of how I envisioned mathematics should be taught. I had not been taught that way, like so many of us I was lectured to, but I felt that there was a better way to engage and excite students about math. Part of it was I was so excited about math myself.
The reason for leading with all of that is to make clear why I feel the way I do about lecture, guided instruction, and inquiry. For the most part, I am an inquiry-based instructor. I push students to ask questions, and seek answers every day. I rarely lecture, and if I do, it is for short bursts, approximately 5 – 10 minutes at most. For the guided instruction part I am going to share a recent unit I covered with my geometry students.
We just finished a short unit on similarity and dilation of figures. I had really thought this out, starting with an activity to refresh them on proportion, moving to using proportion to compare two similar figures, then looking at perspective drawing to see how dilation works, and finally creating dilations themselves and being lead to look for patterns which would solidify the definition and allow them to extend their work to the general case. Things were going really well, until the general case portion. When the students saw all the variables, (x, y), (a, b) and scale factor k, they freaked. “What do we do with these?” “How am I supposed to know what this is?”, and many other such questions were heard all over the room. Try as I might to lead them, push their thinking with questioning, encourage them to back up and look closely at the work they had done previous with specific cases, they were filled with too much anxiety. I had them put it away and told them we would come back to it the next day. At this point I was very discouraged, they had clarified ratio, proportion, scale factor, dilation and comparing figures utilizing these ideas without much help at all, why were we suddenly experiencing high anxiety going from a specific case dilation to a general? Then it clicked, it was the algebra that was causing them anxiety. All year long I have had to scaffold and re-teach number sense and basic algebraic rules. It was time for another step back.
The next day I quickly walked through the initial steps of the activity, modeling the thought process I use to make sense of the material, giving them access to the algebra occurring in the specific cases that were leading to the general, then, I uncovered a problem on the board dilating a segment with coordinates that were all variables and a scale factor k, and began to walk them through the distance formula. Across the room, as I worked through it, asking for help at certain points along the way, stopping to “ponder” where I was, waiting for students to make suggestions and conjectures as I “thought” slowly they began to realize what was happening and became willing to become a part of the problem-solving process. Together we finished the general case, and relief swept through the room. “Is that all we were supposed to do?”
As I reflect on this lesson, and many others like it, I realize that to me, lecture and guided instruction are differentiating when the need arises. My listening to student discussions, monitoring their work and progress as they walked through these lessons and activities told me exactly when I needed to step in as a full leader, and just how much leading I needed to do.
I hope that answers Lisa’s questions. I’m sorry this is a long post, but I felt it was necessary to answer the questions that were posed, and for my own reflection and self-moderating. I’d also love to hear answers to Lisa’s questions from others, and would greatly appreciate a tweet or note here letting me know your thoughts or where I can read them. Keep pressing on, there are multiple rewards awaiting.