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!