# Reflections from the Field

I still stalk conversations from twitter every night to see what’s going on in the world of education – the latest trend seems to be that school is starting in the rest of the nation. I’ve been reading up on people and have been incredibly jealous of the teachers who are *returning* to their classroom rather than starting from scratch. I’m about a month in – I’m thinking I’ll use this post to decompress some of the things that have been running through my mind.

I made the conscious decision not to reteach algebra to my students, even though I knew *everyone* would need an algebra review. The result has been an emphasis on finding congruent segments as an excuse to solve linear equations, then jumping into the Pythagorean Theorem to check their knowledge of exponents, then connect it to the distance formula to see how they do with the coordinate system. I think it hits most of the major algebra areas they’ll need to start the year: solving linear equations, plotting points, using exponents, and evaluating expressions for x = something. This has essentially been the last 3 weeks of class. It’s been a very flexible unit, since I am continuously discovering and assessing where their gaps are.

The result has been mixed and frustrating and demanding, but ultimately valuable for my students (I think). Many students have gaping holes in unexpected places – a student who can solve linear equations like a champ has no idea where to plot a point on the coordinate plane. None of my students know how to add/subtract positive/negative numbers (-3 – (-4) blows their mind). I haven’t touched the distributive property yet, nor have I had them deal with fractions *too* much – I need to choose my battles. I find that the most important thing in the first few weeks is to build that mathematical confidence – to not freeze when they see a variable and throw their hands up in defeat. For the first week, this meant a lot of hand-holding and one-on-one visits to desks, which was difficult to plan for. Once enough people got comfortable, I started segueing into working with groups and peer-tutoring, which was better for both myself and the students.

It’s been hard to plan lessons since I’m unsure of where my students holes will be. It also means I’ve fallen into the trap of direct instruction far too often than I would’ve liked. As I surveyed the class, I tended to find that a good portion of the class was completely on board because of their strong algebra background, and the other portion was completely lost because of their weak algebra background. It was hard to find a good structure to get everyone involved – half the class can get the answer in their head and thinks the work is below them, the other half doesn’t know where to start and has shut down because they’re not sure what to do. I would walk around the class and every paper would be blank – sometimes because they were lost and sometimes because the work was being done in their head. The first few days of this were difficult – I need to find some better activities for next year that have more of an extension for the kids who don’t need the algebra review. Or, I need to implement a better structure for group work and peer tutoring.

I’ve also had to sacrifice some of the grand ideas I had for group work and collaboration and self-reflective thought. Scratching a week of material, expanding a single-day lesson into 3 days, or coming up with lessons/classwork on the fly hasn’t made it possible for me to plan my group work as much as I would like. Reading Sam Shah’s reflection on his first two days made me anticipate my second year – now that I have the frame of the unit and problems and activities, I can start playing with the structure and removing some of the direct-instruction aspects that I need this year just because I don’t have the time to make it dynamic/group-centered/higher-order. My aversion to assigning problems from the book (because they’re TERRIBLE, especially in a geometry class) has had me creating all my assignments from scratch so I know I’m assessing the skills *I* want to assess, not the ones the textbook thinks are important. Also, because my kids have such poor algebra skills, I need to make sure the problems I give them will actually assess the geometry concept I want to teach, not whether or not they remember how the distributive property works (not that I’m avoiding these problems – I just need to pick my battles at the beginning of the year).

Next week will mark the end of this unit and the beginning of a unit on logic and deduction and argument. I’m looking forward to the feeling of actually *teaching* something – of assuming that *nobody* knows what I’m about to talk about, rather than having to guess how many kids will remember the midpoint formula from last year and will be bored throughout my whole lesson. I’m hoping to plan ahead enough that I can have some sort of overarching project/theme/idea – this was hard to do for these last weeks when my ‘teaching’ was really just an excuse to do algebra review. I’m also still on the fence about how much it was worth it to skip the explicit algebra review and jump straight into geometry. I think next year I will at least start with practice adding/subtracting positive/negative numbers, since the consensus this year is that nobody knows what they’re doing with these, but still use congruence to review linear equations and the Pythagorean theorem and distance to review the coordinate plane.

Anyway – I think this satisfies the nag that I haven’t updated my blog in a while.

Two thoughts: 1) there are *negative* numbers? What kind of magic are you espousing? 2) Are you calling me a nag? 😉

Some god reflection here and I hope you realize how remarkable you are in that you truly assess, reflect, and build off of what works and doesn’t in your classroom. It never stops if you’re a passionate teacher. You will always be reflecting and adapting. Some of my most amazing colleagues are the ones that constantly evolve and learn like it’s their first year even though they’re starting year 20 or 30.

“how many kids will remember the midpoint formula from last year and will be bored throughout my whole lesson.”

I wanted to offer an alternative lesson you could use that would probably be knew for a majority of your students. I talk about it in my blog (listed below), but in short, I talk about a better way of finding the distance and midpoint than the typical plug and chug formula.

-Nathan