11 Mar

I co-presented a power session at the T3 International Conference Sunday morning, and I’ve posted the stories that I shared of Running around a Track I and Running around a Track II. I have also posted Running around a Track III during which I processed the feedback we received during and after the sessions.

Several participants asked about the time that rich tasks take, and so I thought it might be helpful to think about making time for tasks in this separate post. I enjoy teaching on a block schedule. I know I don’t feel as rushed as I would otherwise. But a friend asked me how often we do these types of tasks in our classes.

How often do you do this type of rich task?

There are some tasks through which the math content can be initially and naturally be learned. I think of Placing a Fire Hydrant (and last year’s notes here) and Locating a Warehouse (with last year’s notes here). There are some that are more culminating tasks for a unit, especially the modeling tasks. A typical unit for us lasts about 8 days. (See some of the Unit Student Reflections posts to know more about how we organize content: Special Right Triangles, Dilations.) We do the culminating performance type tasks 1-2 of those days towards the end of the unit. On the other days, we are learning the content using practices such as look for and make use of structure and look for and express regularity in repeated reasoning, but not always through tasks.

For example, when our learning goal is

G-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

I find that exploring the relationships using technology first, verifying conjectures using formative assessment questions (more skill-based practice), and then moving towards why works best for my students. If you know of a good task for learning G-C.A.2, I would love to know. But for now, at least, we end this unit with a few culminating tasks instead of beginning the unit with them. The culminating tasks are Circles in TrianglesInscribing and Circumscribing Right TrianglesTemple Geometry. I will note that while we didn’t actually do the tasks until the end of the unit, I did show students one of the diagrams from the beginning so that they could keep in mind throughout the unit where we were heading.

So now that you know that I don’t give a rich task every day, let’s think about what steps we might take to reduce the class time for the tasks. [These questions and comments will make more sense if you have looked at how the lessons for Running around a Track I and Running around a Track II played out with my students.] One of the participants in our Sunday session wondered what would have happened if I had given the students a teaser of what was to come the day before this lesson. What if I had shown them the picture and asked what they wondered then? Or sent a link to a Google form for them to submit their question outside of class?

Or what if I actually showed them the tasks and questions (blacking out information in I that would give away II or vice versa) just so students could begin the process of thinking about the structure of the track before they did any calculations in class? I think these are great ideas – having students spend the “alone” time for processing the questions being asked could definitely make the time spent on the task take less class time.

Another question that tied into the idea of planning lessons with rich tasks was whether we use a textbook. I think of the textbook as a source of information and practice problems for students. We don’t have our units arranged like our textbook, but I do reference page numbers for each lesson on the student syllabus so that they will know where to look for extra help and practice. (Our textbook isn’t CCSS at this point, and I’m not convinced that the new ones have geometry written in the spirit of CCSS. When I’m reviewing a new textbook, I first look at the Table of Contents. When transformations is still the topic of chapter 8, I find myself skeptical.)

Someone else asked about how rich tasks complement some of the skills practice that students need. We don’t get to every practice problem that we include on our student handouts, but I have finally had the time to work through them, and so I post the worked handouts online for students to check problems they do outside of class for additional practice. We also give online practice assignments with two chances to students through Canvas so that they can get immediate feedback on what they know and don’t know. We are trying to teach our students how to use formative assessment.

[I’ve been reading Transformative Assessment and Transformative Assessment in Action, both by James Popham. According to Popham, the first level of formative assessment is when it is used by the teacher to make instructional adjustments as needed to further student learning. The second level of formative assessment is when it is used by the student to make learning adjustments as needed to further learning. The third level of formative assessment is when it is used by the class as a whole to help all students meet the learning goals of the lesson, and the fourth level of formative assessment is a transformation of the school – all teachers are learning about formative assessment in school wide PD and practicing it in their classrooms.]

My students and I have explicitly discussed in class that if you take the online practice assignment and miss every problem, you should make a learning adjustment before trying again.

So if I don’t use a textbook, how do I plan my lessons?

The top three sites that I use are Illustrative Mathematics, the Mathematics Assessment Project, and the Math Nspired lessons at TI’s site. I also follow a lot of bloggers. It helps that I’ve taught geometry for 20 years, and it helps that I’ve been making an effort for students to learn by doing for at least 17 of those years. (I owe a huge apology to all of the students I had the first 3 years.)

But it does take time. I am lucky to work with a great team of geometry teachers who are willing to help and try tasks and use formative assessment with their students. We taught our CCSS Geometry course last year for the first time, and our administrator worked it out so we could have 4 teachers and 30 students in our first block class together. We worked through the lessons together with the students and each other, and then the other 3 teachers had a planning block after that class so that they could correct everything we had done wrong the first time before they taught it in their own classrooms the rest of the day. This year, we have a team of Algebra 2 teachers doing the same thing, and next year, our Algebra 1 teachers will teach one class together. I didn’t know what my administrator would say when I proposed this idea to him, but I’ve learned it doesn’t hurt to ask. It was a total scheduling pain, and some of our other classes were more crowded, but that was worth the sacrifice for what we learned teaching the first class together.

I’ve just told you what works for us in our efforts to include more rich tasks, but it’s only one perspective. What works for you? What additional sites do you use to find rich tasks? Do you start with them more often than end with them? We’d love to learn more from you as the journey continues … easing the hurry syndrome, one task at a time.