Use Backward Planning to Promote Student Responsibility Success in Mathematics

During my years as the director of mathematics and science at Stevenson HSD 125, outside Chicago, Illinois, I noticed a strange teacher mindset shift about student work (and the student doing of mathematics assignments) at the fifth- to sixth-grade levels. At first I thought this mindset was a “You are not 11 years old anymore” type of perspective, as in a “You need to grow up and be more responsible” message to our middle-school students.

Once our students entered middle and high school, I noticed other mindsets among many high school mathematics teachers that baffled me: “If your work is not done on time, then you cannot turn it in,” and “Now that you are 16 years old, it is my job to prepare you for the real world.”

For the most part, our K-5 teachers somehow did not have these same mindsets. Perhaps the problem of students not doing their assigned work could have been connected to the age of the students; the K-5 students were just too young to know it could be a choice to not do their work. Maybe this mindset was connected to the decline in parent involvement in mathematics as their children moved into middle school. Or it could be that high school students take on too many extracurricular activities and responsibilities that compete with their assigned work outside of class.

At Stevenson, we decided as a mathematics department to address the challenging problem of expecting and supporting all of our students to accept the responsibility for doing their assigned work. To do this, we knew we needed to become much more measured in terms of the nature of assigned work. In other words, this meant we would:

  1. Be very purposeful about limiting the number of mathematics tasks assigned for student work and the test preparation necessary outside of class.
  2. Be intentional about limiting the time required to do the assigned work outside of class (including the preparation for a major unit assessment).
  3. Teach all of our students in grades 6–12 how to plan and organize their time to achieve the assigned work outside of class.
  4. Expect students to do their assigned work on time, and require them to do the work, whether on time or not.

You are not misreading our collective commitment in number four. Every mathematics teacher honored this agreement. We knew that assigning students a zero and refusing to accept their makeup work was damaging and unwise. If we actually taught our middle school and high school students to become more responsible, then we could not let them make the choice to be irresponsible—agreed?

The Lawn Mower Metaphor

Rick DuFour of PLC At Work™ and I worked together for 35 years. One of his favorite stories was one I now use frequently. Some of you have most likely heard me reveal the “lawn mower” story in order to make this point about teaching students to be more responsible.  Here it is:

If I tell my son when I get home on Friday night that he needs to have the lawn mowed, only to get home to discover he has not done his assignment, my response to him would not be “You will never have to mow the lawn again! We need to move on to other lawns.”

In fact, my response would be, “You will mow the lawn, and you will mow it to my satisfaction. And until you get that assignment done, there will be no car, no going out, no life, and no privileges of any kind!”

Rick’s point was that we do not teach children to become responsible by allowing them to engage in irresponsible behaviors (not doing their work), including those in which we cannot accurately measure what a student does or does not know (because the student is allowed by us to make the bad choice of not trying). Taking away privileges at school, and engaging students in a “required doing” of our carefully measured mathematics assignments is a good start but still places much of our energy on the back end of the initial assignment and required effort by the student.

Rather than place our energy into an end-of-the-line punishment (the negative effects of taking away privileges), our math teaching energy should be directed at front-of-the-line behavior changes—that is, what can we teach our students that may better help them engage in the necessary work we assign? Can we help them to get the lawn mowed—for that matter, mowed well—and on time?

Planning Ahead—and Backwards

It turns out a recent study led by University of Iowa professor William Hedgcock and his co-authors—marketing professors Jooyoung Park of Peking University and Fang-Chi Lu from Korea University—provides insight into how we can help our mathematics students plan for their assigned work, prepare for unit assessments, and get it done on time.

The researchers note that some students make a plan of attack in chronological order. The students note the steps they'll take first, next, and so on. For example, forward-planning students preparing for a major unit assessment may plan tasks to accomplish along the way and then end with a final review before the unit assessment.

Other students might plan backward starting with a visualization of the end goal—for example, passing the test—then tracing in reverse the steps (using a timeline of sorts) to get there. According to the study, backward planners are more likely to stay engaged in their assignments longer and successfully be prepared on time for the assignment or assessment.

As an example, according to the study, in one experiment 53 U.S. undergraduate students planned for a class exam. Each participant was provided with 15 activities they could do to study for the test. One group of students was instructed to arrange the activities by working backward from their goal. The other students had to plan the activities in chronological order, starting from the first day of studying. Those who planned backward (reverse chronological order) tended to exert more effort than the forward planners (chronological order) to achieve their desired grades. Backward planning allowed students to think of the tasks and small steps required to reach the completion of assignments or preparation for an assessment more clearly.

So, Which Type of Planner Are You?

Forward or backward? Do you tend to plan to meet your assigned deadlines using chronological or reverse chronological planning? I was glad to discover I am more of a backward planner. The sample of research from Hedgcock and his colleagues seemed to validate my current approach to assignments. It doesn’t mean I am always perfect at hitting those work-life deadlines in front of me (as some of my colleagues will attest to), and it doesn’t mean I can take a zero, either. I am still responsible for getting those assignments done, even if they are sometimes a bit late. I am glad, however, to know it is at least a good idea to backward plan the way I do.

Now, I just need to teach my math students to be backward planners for all of their assignments for 2018-2019. Or perhaps I could help them just start with a plan period, and then take action on that backward mapped plan.

Hmm, my end of first semester goal is... To get there by Thanksgiving I need to… To get there by Halloween I need to… To get there by Labor Day I need to…

Yikes, I need to start planning! Have a great 2018-2019 school year. What a great plan that would be! 


Learn more about HMH’s new learning programs for K-12 students, including Into Math.