Blended Learning Thoughts

As we all ponder what August looks like for schools, I find that my thoughts keep landing on the blended learning option. I imagine that half of the students in my high school would be in the building on Monday/Tuesday, the other half on Thursday/Friday. While at home, students would do additional school work online. Wednesdays are a bonus day with many options. 

Disclaimer 1: I do not have recommendations from my state or school district yet. I have no insider information. This is just my brain doing what it wants to do. It could all be for nothing, and that’s fine. Maybe my thoughts will be helpful to someone else considering this option?

Disclaimer 2: My thoughts are mostly isolated to my own high school math class.

Two Days at Home: Virtual learning. 

·     Students would watch a video. I’d like to try using Edpuzzle for tracking, accountability, and asking thoughtful questions. I’m intrigued by the opportunity to get responses from all students. 

·     Students would practice a new skill. I like Delta math for this. I’m thinking I could condense my list of skills to 36 (by eliminating a few and combining some) so that the focus is 1 skill/week.

·     Students would record themselves working out one problem, describing what they are doing, so I can actually see the math that they are doing. I’m considering flipgrid as a platform for this. 

Two Days in School: We do all the things that we missed during distance learning.

·     Short (15 min?) assessments weekly. Assess a combination of new & retention skills.

·     Focus on applying new and old skills to non-standard problems. I want to focus on the skill students practiced at home but ask questions differently than delta math. 

·     This is the time for open middles, desmos activities, 3 act tasks, and more.

·     Spiral through some skills for retention.

·      I would like to do some additional skill practice so that I can watch what students are doing and look for common errors, but I suspect I’m out of class time by now. I’m hoping skill practice can be done mainly at home or doing intervention times.

Bonus Day: All weeks with five days should have an extra day.

·     This day is an opportunity to be creative.

·     Ideally, it would include some extra teacher planning time. All of this reinventing the wheel is going to require it.

·     What if we could “invite” specific students to attend in person, even for half of this day? Bring me the handful of students who haven’t mastered this weeks’ skill or are having trouble keeping up with the online portion at home. 

·     If face to face isn’t possible, individual and small group tutoring could happen via zoom.

My Brain's Off Switch is Broken

I saw this picture on social media recently, and I feel this so much! 

I told myself that I would not spend my summer worrying about what the fall looks like.

For the most part, I haven't worried. I am confident in my state, school district, administrators, and colleagues' ability to figure it out. I even feel ready to embrace whatever changes are necessary to keep everyone safe.

But that doesn't mean I don't think about it. Every. Day.

At supper tonight, my daughter said "Mom, you keep saying that you don't want to talk about school in the fall and then you keep talking about school in the fall!" She's right. I can't turn it off.

It occurred to me that I have this long-neglected blog, and that this would be a good place for me to tap out my thoughts and clear my head. 

What's New

While I've been busy not blogging the last couple of years, there have been quite a few changes in my classroom . . . 

Integrated Math: Two years ago we stopped teaching the traditional progression of Algebra 1, Geometry, Algebra 2 and replaced it with Math 1, Math 2, and Math 3. I think this was one of the BEST decisions our math department has ever made. We saw a huge jump in our students' state assessment scores as well as their ability to retain concepts year to year (also due to some other things we're doing). Now I teach Math 2 & Math 3 (and continue to have one Calculus and one Physics class). I now teach some geometry for the first time in my career and I'm not mad about it.

1:1 Chromebooks: This year our school put a chromebook in the hands of every student. I have loved students having consistent access to google classroom where I share all of our class materials and information for absent students. I've loved that I don't have to track down a cart of devices every time I want to do a Desmos activity. I was less excited when my Principal said "think about how you can use these to eliminate the use of paper".


Less Paper: We started the school year trying to use a chromebook the same way we would use a worksheet. We converted our sheets of notes and practice problems to PDFs and taught students to use Kami to write on them. I won't detail all the issues, but it didn't go well. Students were frustrated. Parents called. We knew we needed a plan B.


Changing Up Daily Practice: After lots of conversations with my colleagues and trying a bunch of different things, I've mostly settled in to having students do the bulk of their daily practice on individual white boards. I either project the problems for all to see, or I will print a single page per 4-person group. Along the way (and also inspired by the book Make It Stick), I started learning that students don't need to do as many reps of a particular problem as I once thought. If they get a concept after five practice problems, then they don't need to do twenty. What they do need is to revisit that concept in the future to help them remember. Each day we spend part of the class period practicing something new, and the rest of the time on spiral review.


Spiral, Spiral, Spiral: Possibly the biggest change of the past two years has been my commitment to spiraling. Almost daily, my students practice something new as well something they learned yesterday, last week, last month, and/or last semester. Every assessment has 3(ish) "retention" problems where any topic from the year is fair game (I do make sure they've seen these as part of their spiral practice within the week of the assessment).


No More Homework: A completely unintended result of all these above things is realizing that, if my students could get a good 48 minutes of working on math each day, they really didn't need to practice something 20 more times at home. I've assigned almost no homework all year in Math 2 or Math 3. My Calculus and Physics classes still have homework, although it has decreased there too.


Less Talking:  The only way to make more time for in-class practice is to spend less time telling students what to do and more time just letting them do it. I introduce a new topic with just enough information to get students started. When questions or obstacles come up, we figure them out as we go. It is really a pretty big philosophical change that doesn't happen overnight. I've had this "less talking" goal for years, but it has taken time and pressure from these other factors to get there. It turns out my students do just fine (better even) with fewer of my words!

Exponent Puzzles

The other day I spent the teeny-tiniest time on twitter. Fortunately, I was there long enough to read about #MTBoSblog18 and thought it seemed like a very doable challenge. I happen to have a few little files to share, so here goes January!

A while ago I wrote about this strategy for teaching students to solve exponential equations (without logs). It has been a pretty effective lead in for exponential equations and also evaluating logs, as students get to practice using all different kinds of exponents and combining them with different bases.

This year, our school has been going paperless making great efforts to reduce our paper usage, so I had my teacher's aide help me convert this activity to a reusable form for my dry erase sleeves.

For level 1, students choose the correct exponent to complete the equation. Fraction and negative exponents are used.

For level 2, students choose a base and an exponent to complete each equation.

For level 3, students must use the same base to complete two different equations.

 
When they're done, I go straight into solving exponential equations with the use of like bases. It's a super easy transition. Logarithms are next, and this activity really sets the stage for answering the question "What exponent goes with base ____ to equal ____?". 

Here are the files:

Level One
Level Two
Level Three

Happy 2018!

Inside Out Quadratic Formula

I noticed that my students, while using the quadratic formula, typically had trouble in one of two places. They either find the wrong value for b^2 - 4ac, or they have trouble simplifying the radical.

I decided to try having my first-timers evaluate the formula from the inside-out. Maybe if we put our focus on the most-likely-to-mess-up parts of the formula minus the noise of the whole thing, then we would be more successful and consistently correct.

Here's what I mean:

The solution looks like this: First, we find b^2 - 4ac.

Next, we simplify the radical. My students are awesome at this when it is an isolated operation, but often struggle when its part of a larger problem.

Then we put it all together.

At this point you may be done, or maybe you need to reduce.

Time will tell how much of a difference this approach makes (if any), but I have noticed a few other benefits:

We don't have a learning target for the discriminant in our curriculum, but if we did this would be an easy lead in. That number we found first? It has a name, and it can tell you what kind of solution you are going to have before you do anything else.

Also, I kind of like how the solution seems more efficient . . . it feels less noisy and crowded compared to writing out all the parts again and again as you simplify the answer.

How to Drive to Sonic

Recently I noticed my students having a few misconceptions about the different strategies for solving quadratic equations:

A student assumed that a non-factorable quadratic had no solution.

Several were surprised when quadratic formula and completing the square yielded the same solution.

I came up with this little analogy to help clear things up, and it ended up working pretty well.

I started out by talking about how students might drive to Sonic, a favorite fast food place that is 10 miles away from our tiny town. Students named several paths and we talked about their pros and cons. The interstate is fast, but it does not provide a direct path to Sonic. Most students would choose to take Old 40 highway, but it is well known for road construction and can be blocked for days/weeks/months at a time. Someone even pointed out that there is a dirt path through a corn field that many of us have used to bypass the road construction. Perfect.

Solving a quadratic equation is very much the same.

On the left you have your quadratic equation. You want to get over to the solution, on the right. Factoring, complete the square, and quadratic formula give you three potential paths to get there.

Sometimes, when you take the factoring route, you find that your equation can't be factored. When this happens, its like a road closed sign on the path to your solution. The solution is still there, but you'll have to take a different route to get to it.

Other times, when you're completing the square, you run into a bunch of fractions. We aren't afraid of fractions here, but they can turn an otherwise straight path to the solution into a long and winding road. If we're looking for the most efficient way to get there, we want to avoid this situation.

Then there's the quadratic formula. It may not always be the most efficient, but it always works. It is particularly useful for avoiding the road block and the winding road. 

To follow up this discussion, I asked students to be in charge of road signs for these three paths. Your job is to put up some signs instructing people on which road to take. What do the signs say? Here is what one group created:

 My favorite quadratic formula sign said "when you don't want to think about which road to take". They're not wrong.

For a follow up activity, this card sort would be perfect.

Visionary

I always think its silly when people start a blog post by talking about how long its been since they've blogged, but . . . It's been over a year and that's probably worth mentioning. If any dear readers are still here, thanks for not giving up on me.

I'm starting the third week of a brand new school year. There have been some growing pains, but I will talk about those another day. I want to talk about one of our back-to-school inservice meetings. Our principals shared about the book Soup by Jon Gordon. At one point, they would describe a characteristic of a good teacher, and ask our groups of four to name one of our colleagues who most represents that quality.

One characteristic that was mentioned was "visionary". We were asked to name a colleague who is always evolving and learning new things, striving to get better. I was touched that many of my colleagues named me. This is the kind of teacher that I want to be and that I try to be, but I haven't felt particularly visionary in the past year(s). Even this year is off to a rough and chaotic start.

In all fairness, I've had a lot of life happen outside of the classroom. Our now two-year-old son has had multiple surgeries to repair his cleft lip and palate. Then last spring our family grew by one more through what can only be described as a surprise adoption. The rare and special nature of how our family has grown is not lost on us, and we are thankful.

Being parents of three (particularly the two littles) is exhausting. Some days are all about survival. I'm going to cut myself some slack for my absence from blogging, but still . . .

I've been thinking about how this is the place where my vision began . . . The blogosphere is where I began to be more adventurous as a teacher . . . trying new things . . . writing about them . . . learning from others. I thought if I came back here it might trigger what I've been missing.

So here I am . . . inspired by my colleagues' perspective of me, inspired by a gentle nudge from @druinok a few months ago, and inspired by watching TMC17 from afar. I could spend a few more hours re-reading and editing this post, but instead I'll #pushsend.