So for those of you who know me, you know that I love coffee. Like, LOVE COFFEE. I don’t drink it black, even though I know I should. It needs a dash of sugar and a splash of 1/2 & 1/2 to reach perfection.
Why did I mention this? Well because my brain is dead and the title had 1/2 & 1/2 in it and I needed an intro. Let’s focus on the point: What 1/2 & 1/2 has to do with my classroom.
The other day I got into a convo on twitter here (oh and look at that. It starts with a GIF about coffee. So #onBrand and makes this into look planned) about why I like routines in my classroom. In particular how smaller routines fit into a larger routine that is the 1/2 and 1/2.
The Large Routine- a.k.a. The 1/2 &1/2:
I strive, for each period with my students, to spend 1/2 of the class period practicing math or actively doing math and 1/2 the class period learning new math. I teach on an hour block, and do have daily warm ups and, if my pacing/timings work out, a debrief/closing. Now here’s the “weird” part:
- First half of class: Practice from previous day(s) classes.
- Second half of class: New math learning. Either from a lecture or student exploration/discovery activity.
In 2018 I finally got the chance to make it to one of Anna Vance’s Make It Stick sessions at TMC18 in Cleveland where she presented alongside my now co-worker Alli George. Their presentation convinced me that if I wanted my students to actually learn the material in my classroom I needed to make sure that I structured the learning sequence in such a way that I am actively fighting the forgetting curve.
If the forgetting curve is new for you, its basically this pretty scary looking exponential decay function that represents the amount of knowledge retained (remembered) as a function of time assuming the content is taught only one time. Here’s a graph with an x-axis that does cause some concern for a math teacher given the non-linear nature of the x-axis…but let’s not focus on that right now as the visual still gets the point across: we forget stuff pretty quickly.
And if you don’t believe that curve. Ask someone for their phone number, don’t write it down, go think about something else for 10 minutes, and then try to remember the number. You probably won’t remember the number.
Interrupt the forgetting curve by: Lagging (delaying) practice from when the content is learned, come back to the content often, and mix up the content with other content so that students are seeing more than one topic at a time.
Now, if you are like me in 2017 when Anna first told me that, you’re thinking, “NO WAY! That sounds miserable as a learner! They’ll never get to get into a ‘groove’ of practicing problems and they’ll be frustrated!”
EXACTLY! THAT’S THE WHOLE POINT! If we allow students to semi-forget something, have them do practice that requires retrieving that stored information from their memory and use it over and over again they will be more likely to remember it!
Back to the phone call analogy. Remember the days of analog phones? Like the pre-speed dial phones connected to the wall but new enough to have push buttons. What’s was the phone number of your best friend from those days? Funny, I bet you remembered that one! Wanna know why? Because you had to think about recalling(reviewing) the number and dialing it every time you wanted to talk to them.
Have I convinced you? If not, seriously go read Make It Stick. It changed my life and I thank Anna and Alli for that.
So that is my long-winded way of saying “here’s why we practice old material first and then learn new material second in class.”
The Smaller Routines-a.k.a. The Instructional Routines:
While routines are wonderful in the sense that they make us comfortable by removing the unknown, doing the same thing over and over again can get boring. One of the things I find most amusing about myself, and I’m going to guess this is true for you all reading this blog as well, is that I despise change, but I also hate being in a rut.
The large routine of 1/2 & 1/2 stays the same, but I like to cycle through the routines that occupy each 1/2 so that we all get a bit of variety in our lives. Here’s what I used last year:
Practice Routines as First 1/2 of Class:
I like things where the answers are either given or can be self checked so that my time is spent with students who are stuck/struggling and not with students who just want me to check their work.
- Question Stacks: These can easily be made from existing worksheets or worksheets found online. Sarah Carter (@mathequalslove) has a blog post explaining how to make them here.
- Add ’em Ups: Where you take 4 problems and format them into quadrants on a piece of paper. Then in the center you place a circle with the SUM of the answers to the 4 problems. Students can check their work easily to know if they got all the answers correct. Groups have some pretty stellar convos about finding the errors together. Sara VanDerWerf has a blog about them here. (full disclosure I found that sometimes 4 problems can be a bit much when we get into some time-consuming content, so I will do 2 or 3 problems instead)
- Partner Problems: So these have a bunch of names, and I’m not sure what you may call them. But the idea is you make a handout with 2 columns where each row has a different problem BUT where the problem on each row has the same answer. I first read about them on this blog and in finding it again to cite it I noticed they have linked to Julie Ruelbach’s rather large google drive of existing problems (SCORE!)
- Two Truths and a Lie: which I heard about from Jon Orr here and are pretty much exactly what they sound like and can be morphed into different levels of sophistication for a task.
Note that I do not grade the practice. I even explicitly tell students that the goal is not necessarily for them to complete the entire activity in the 20-25 minutes we are working on this. We WILL see the activity again (because we spiral back with our practice) so don’t worry about working quickly, worry about working accurately.
Capstones As First 1/2 of Class:
Sometimes I want to collect work from students. Not just because I need to grade something from them (I’d love a day where I am not grading work…but today is not that day) but because I want the opportunity to give them thoughtful feedback on their work. I call these days “Capstone Days” because it means I’m going to give them slightly more time (30-40 mins) to work on a problem or a set of problems that synthesizes some learning from the previous week(s).
Sometimes I ask them to work with peers, other times its individual work. It really just depends on where we are in the learning process. If the capstone is on relatively new material I tend to let them work with a peer (but each in a different color pen) so they feel more relaxed. If the content has been around for a while I tend to have them work individually.
Here are two examples:
Note these are still just problems you could find on any existing worksheet but they’re more time-consuming so turning them into a Question Stack would just be too much. My goal for this year is to have one Capstone a week. I’ll keep you posted on my progress with that.
The Learning in the Second 1/2 of Class:
The learning part looks really different throughout the year. Sometimes it is a lecture via direct instruction. Sometimes it is a Desmos exploration activity with a debrief to make sure the whole class got the material we needed to see. Here’s an example of a geometry Activity Builder I’m really proud of that we did for quadrilateral properties to build off an activity from Michele Torres I edited for parallelograms.
Other activities that you’ve probably heard of that fit in this chunk nicely: 3 Act Math tasks,
Sometimes I have students do a Sometimes/Always/Never card sort which usually results in some nice mathematical arguments in class. We then debrief the sorts over the next day during the second 1/2 of class.
Here’s the thing I love about this structure: Let’s say you have an exploration that’s naturally a 2-part thing (when operating in 20-25 minute parts): You can do that activity over 2 days and then use the second day’s practice 1/2 to review OLDER material. It creates this natural space for older content review. Its so lovely.
This is the part where I admit that there is student push back to this structure over the first 3-4 weeks of class. Every year. The pushback is hard. Usually from both parents and students. I pushback with explaining cognitive science to students and to parents. This year I think I’m making an “Intro to Cognitive Science” letter to parents to send out the first week of school just to front load my reasonings. And here’s the thing. Every. Single. Parent who pushed back with me in those first few weeks, later takes it back. They see the growth in their child. The student starts to feel like the “get the math more” and begins to like the practice structures. They realize this works. And I’ll take 3-4 weeks of pushback if it means there is smooth sailing the rest of the year!
So this blog post wound up WAY longer than I had anticipated, but I hope it helps wrap your head around the 1/2 & 1/2 class structure and possibly convinces you that its a relatively simple instructional shift that yields some pretty good returns in student learning.