From the start of the semester until last Thursday, my students were working with systems in some form.
A month and a half of teaching, practicing, assessing, reteaching, practicing, assessing, teaching, practicing, assessing, reteaching… you get the idea.
Linear systems was probably one of the most difficult concepts I’ve taught this year. The ideas and methods involved literally pull together all of the algebra and rational number skills students learned in 6th and 7th grade. There’s so many ways a minor mistake can derail a train of thought. There’s also the concepts of variable, maintaining equality, substitution, and representing situations with algebra. Even after so much time working with systems, I’m still not certain some students truly understand that substitution is just swapping out a variable for something of equal value or that we need to create an equivalent equation with one type of variable to be able to solve the system.
Without surprise, I found myself using a variety of questions throughout my lessons to help students make sense of a system. As we got deeper and deeper into the content, I found practice activities devolved from productive group work to people attempting to do the same thing without regard for the problem or throwing up hands and declaring, “I need help.”
While recognizing that help is needed is a good starting point, later in the unit the process became exhausting. A hand goes up from a student looking for help. I ask the questions. Students answer correctly or incorrectly. I tweak my approach if students were incorrect or move onto another question if the student was correct. Rinse and repeat. Later in the unit, my questions were pretty much the same and were able to guide students:
- Can you read the system/problem aloud for me?
- What are the variables in the situation?
- How could we represent the word problem with equations? Why do we need two equations?
- Does either equation have a variable that’s isolated?
- Do you see any opposite coefficients between the equations?
- Looking at the system, which method (substitution or elimination) would require less work/algebra? How do you know?
- Have we created an equation with only one type of variable?
- We ended up with a nonsense equation? What does that mean?
- We ended up with an equation that’s always true? What does that mean?
- Do we have the whole solution to the system?
- How can we find the value of x/y that we know the value of y/x?
- Have we answered the question?
The interesting part about my questions is that most students were able to correctly answer them and got used to the routine. Nevertheless, students did not adopt these questions for themselves even with repeated reminders from me.
In some respects, I felt like I was getting trapped in a cycle I experienced during my first year of teaching. I was somehow becoming the sole questioner in the class. Naturally, I started to get down on myself about this development. What was I doing or not doing that was causing students to avoid questioning themselves? Was it the difficulty of the content that was driving students to only seek help from me? Was it my explanation of concepts and examples? Was it my progression of concepts? Was it my pace? Did the behaviors I was seeing reflecting a deeper problem that never got resolved earlier in the year? Was I not explicit enough in directing students to self-question? In a year that continues to make me doubt my abilities as a teacher, you can imagine that I was rapidly falling down the rabbit hole as I asked myself these questions about students not asking themselves questions.
After a week of what felt like nonstop questioning on my part and very little productive practice, I finally reached my breaking point. I declared to my classes, “I can’t be the person asking all of the questions. Time after time, people stare at a problem and call me over claiming they need help. Every time I do help, I always ask the same handful of questions every single time. Every single time. Every single time. Curiously, people are usually able to answer these questions every single time. Every single time. Every single time. At what point do people stop asking me for help and start asking themselves the questions they already know I’m going to ask? Since day one, I’ve told you to ask yourself questions. What’s been happening here is exactly why I’ve told you to engage in this process. You do know. You can make sense of the problem. Even if you’re uncertain, you know something you can always do to help you reason with a problem.”
At this point, the class was dead silent and I continued on for another couple minutes acknowledging that the content might not directly to the lives of my students, but the thinking they engage in as they work with systems builds the reasoning skills they will use later in life. I ended my speech by reiterating the need for students to ask themselves questions. In my later class, I wrote my questions on the board and stated I expected to hear and see students using these questions during the next practice activity.
Whether it was my delivery of my message or its content, students worked incredibly hard during the remainder of class. When hands went up and I assisted students, the nature of the exchanges were different. Everyone had something on their paper that they referred to as they spoke to me. In some cases, students just wanted to check if they were on the right track. In other cases, students were uncertain, but they at least used phrases like, “I tried… I noticed… Here’s the part that continues to confuse me…” Students were purposeful in the help they were seeking. I could tell people were questioning themselves and my help was to confirm their questioning. Basically, it was the type of interactions I had been missing out on for a long time.
I’m sharing this post because I’m wondering how I can make students continue to self-question. Does anyone have any activities, strategies, or routines besides constant verbal reminders that they use to promote self-questioning? How do I teach and structure my classroom so that students are intentional with how they seek help? How do I get students to move away from saying, “I need help. I don’t get this,” and start having specific questions planned when they seek help? Once again, what can I do besides verbal reminders and modeling?