Strategies for Solving Linear Equations

Getting ALL of your students proficient at solving linear equations is the Holy Grail of any Algebra teacher. Just about every PLC team I've been on has attempted to re-tackle it as an (in-achievable?) SMART goal.

SMART goal setting season is upon us once again in these parts, and the early formative data from our Applied Math (after Geometry, before Algebra 2) students suggests that we MUST place an emphasis on solving equations with variables on both sides of the equation.

We're going to share the following strategies with our students:
Algebraic:

• have students draw line through equal sign
• distribute first to eliminate “( )”
• combine like terms on left, combine like terms on right
• eliminate the smaller coefficient term
• backwards order of operations
• write answer as “variable = number”

Verbal:

• write out algebraic steps/thinking in words

With Multiple Fractions:

• multiply every part by least common multiple of the denominator

Common enough, I know. What I'm really sharing with you is the posters I made to put up in our classroom. If you're going to do something you're feeling a little deja vu over, the least you can do is apply some of your creative juices to change your attitude. :) I made these images at PicMonkey using a combination of textures and text, and just used the Microsoft Picture Viewer on our PCs at school to print them on a full 8.5x11 sheet.

Is Learning Invisible in My Classroom or Does It Just Not Exist? A Rationale for Data Team Analysis

"We don't know one percent of one millionth about anything" - Thomas Edison

Teachers are paid to see what no one else can, you know? All of the learning and growth our students (hopefully) gain for the time they're in our classrooms - you can't SEE it. Not even on tests or projects. Like many of the forces and ideas John Lloyd mentions in this TED_Ed animation, learning and knowledge are also invisible. We only see the effects of the two.

Painting an image around the data you garner in your classroom is can help you see those effects. In the same way you feel a gust more than a breeze, more assessments give you more data (and more effect to see).  Sitting down with student examples in your PLC or data teams and making inferences about learning, mistakes, and building blocks and then making hypotheses are the educational equivalent of laboratory trials.

I don't intend to be hyperbolic, but when we make purely inferential decisions based on the population of students in our own classes for our instructional design, we place ourselves somewhere on the scientific spectrum usually reserved for bloodletting or other medieval medicines - you're doing things because they seem to make sense. Yes, a veteran teachers can draw upon their years of experience to increase sample size to an extent, but they aren't doing their colleagues any favors, and there are two possible final outcomes: (1) they retire and no one around and most of their knowledge and expertise leaves with them, (2) they burn out and cannot change when they day (inevitably) comes.

My encouragement to anyone who feels like their team or department doesn't willingly want to engage in common assessments, data analysis, or other research/scientific methods is to start with something simple. We have a data team meeting template from Lead and Learn in our district that is OVERWHELMING if you've not scaffolded your team with supports and celebrations up to it.

Here are some of the ideas and principles that have worked on our team.

If I were having this conversation with people in my building right now, some one would be thinking (or saying) right about now,

"I don't need a data team or a PLC to know what my kids know and don't know."

Perhaps that's true.  My carrot for that teacher (since we all ultimately want to know what's in it for us) is to suggest that even if your class is learning at or above grade level and you have all of the tools and techniques, when you share that expertise with others, you'll end up improving the quality of the students who come to you. Who doesn't want a leg up?

My summary question:
When you look deeper into your students, do you see more or nothing?

Kickstart Your New Semester Resolutions With Unstuck

I found Unstuck as a genius recommendation in the iOS App Store in November and it helped me though a lot of frustration I was having over my students' (lack of and organization of) notes in their notebooks and folders.

Unstuck's purpose is very straightforward; to get you past your obstacles, unstuck, and back to productivity. Initial workflow is intuitive, but the further I got through the process, I felt a little lost in menus. It must take a lot of work to get unstuck, 'cause I felt like I was answering questions longer than I expected to. :)

Another strength of the app are the tangents you can follow like historical/contemporary figures who have been similarly stuck, tips for getting started, and several thought-organizing tools for you to work through if you are still not appropriately inspired. Here are my results:

I guess questions are good; this page told me a lot about myself.

To wrap up the story, going through my stuck moment did help me to clear the clutter. The lesson I took from my report was that I needed to be more clear in my intentions for note-taking, and less vague on what things I want me students to be focusing on. I went to an adapted Cornell Notes style (here's a great C-Notes in math class how-to from Blogger Druin) that I'd used with some success in the past, and several students responded very positively. At the very least, when looking at their notebook while offering help, I (and the student) could quickly flip back through their pages and sort through pages that were homework and those that were in-class notes because I had a clearer idea of what that page should look like in the notebook.

Everyone's a winner.

APPLICATION FOR YOUR CLASSROOM:

• New lesson ideas
• Problem solving for leadership teams, committees, PLC or data teams
• Goal setting for students
• Team/ community building
• Intervention strategy brainstorming

More resources:

Unstuck Community on Tumblr

Review: Getting Unstuck Now Has An App
Review: InsideFMM.com iPad Productivity App of the Year