The test scores were disappointing. As long as equations were in slope-intercept form, my students did pretty well. But, if they had to rearrange the equation in order to solve it, they would rather guess an answer than try to get y by itself. We had spent days on both standard form and point-slope form. We had created foldables for each. And, they had seen lots and lots of practice problems. They were even allowed to use their interactive notebooks on the test.

But, somewhere along the way, I had failed my students. Looking back, I realize that my students had never really had to learn what form of an equation they were dealing with. I would tell them that we were working with standard form that day or point-slope that day. That would tell them what page in their notebook to reference. On the test, however, all of the forms were jumbled up. I had not given my students practice determining what form an equation was in.

I especially realized this when helping students with test corrections. I learned how to do test corrections from my cooperating teacher at the middle school level during my student teaching. He set up test corrections in such a way that students had to think through the problems they missed. They had to actually discuss math. Then, they have to express either their mistake or what they have learned in writing. And, the results were priceless. The group set-up for test corrections actually hasn't worked as well for me in my classroom since I have such small classes. Usually, I love, love, love my small class sizes. But, this is one activity where it is better to have twenty-five or thirty students in a room.

During test corrections, students would constantly be raising their hand and asking me to help them with a problem. I heard "I don't know why I got this one wrong because I just guessed" way too many times. First of all, the logic of that statement does not make sense to me. You got it wrong because you guessed. Anyway, my first question would almost always be "What form is this equation in?" I heard way too many "I don't know" responses. Eventually, I would be able to coax an answer from them, but it was a frustrating process for both of us.

When I look at a linear equation, I immediately try to classify it. My students don't have this intuition. The fact that we need to do this is something I should have taught them. Next year, I will know this from experience and will do better!

While reviewing for the semester test, I decided to take some of the time and review the types of linear equations. While browsing an antique store last weekend, I saw some flyswatters that had been decorated with fake flowers. The sight of these flyswatters brought back fond memories of the flyswatter game that I used to play in middle school.

The flyswatters I used for the Flyswatter Game. |

The premise of the flyswatter game is simple. On a dry erase board or sheet of large paper, write out all of the vocab words for a lesson, chapter, unit, etc. Form two teams. One person from each team takes the flyswatter and stands on a line in front of the words. (It's your decision whether students will start by facing the reader or the words.) Read a definition. (You could also project it on the screen.) The first student to swat the answer with their flyswatter gets to stay in the game. They will go to the end of their team's line. The other student will be out. (If both flyswatters land on the same answer, the one on the bottom wins.) The game continues until only one team remains.

I wanted my students to have more practice determining what form a linear equation was in. I also wanted to re-emphasize how to recognize the equations of horizontal and vertical lines. My categories were: Standard Form, Point-Slope Form, Slope-Intercept Form, Horizontal Line, Vertical Line, and None of These. I prepared a Smart Notebook file of 30 or so linear equations. After each team sent up a member, I would project a new equation on the Smart Board. Students would have to determine what form it was in and swat the correct answer.

Where the Swatting Occurred. My dry erase board does not photograph well, apparently. |

I'll be honest. The game didn't work out as well as I had hoped. The problem wasn't with the game, though. The problem was that I still had implicitly instructed my students how to determine what form a linear equation was in. This led to many students just swatting random answers. I still have so much to learn as a teacher!

We spent several class days building understanding of slope and rate of change. Overall students did exceptionally well with that concept. Then we introduced linear equations and it was like they had never learned what slope was at all. They struggled through the whole unit - and the test grades were miserable. We start systems of equations in January. I'm reading as many ideas online as I can to prepare for that unit. Students obviously aren't ready for the next step and yet I am required to go on! Foldables, notes, examples, and more ... looking for ways to build conceptual understanding of linear equations! Thanks for sharing your experience.

ReplyDeleteI really enjoy reading your posts.

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Elizabeth

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Ugh! The dreaded linear function unit. If my students could possibly hate anything more than this, it would have to be the 2 weeks worth of word problems (the book calls them "classic puzzles"...my kids call it the world problem weeks of doom) that I make them do after the systems of equations unit! Anyway, I'm right in the middle of my 5th year teaching this same unit (to 7th and 8th graders). It's just too abstract, and they can see pretty early on that no one in the real world is going to run up to them on the street and ask them to classify the form of a linear equation...darn! They know my secret! I try to explain "form" to them as a stamp with blanks that need to be filled in. When I win the lottery, I'll have VistaPrint actually make me these stamps! We spend a lot of time talking about when each is important (oh look, wouldn't it be nice if I gave you a point and the slope and asked you to write the point-slope form? It would be sooo mean if I wanted standard form. Good thing I'm such a nice teacher!) Also, around year 2 of your same problem, I stopped teaching the forms in isolation. We usually spend 2 days (45 minute periods) on slope-intercept followed by a quiz, 1 day on point-slope, 1 day on slope-intercept and point-slope, another quiz on both, 1 day on standard, another quiz, and 2 days messing with all 3. Good luck! I look forward to hearing more - I'd like to start a modified interactive notebook with the kids this semester.

ReplyDeleteI am very happy to see your post.I am also a math teacher and i get more ideas in your blog.Really it's more helpful for me.The Equation

ReplyDeleteThe dollar store sometimes has these huge fly swatters for sale, could be

ReplyDeletereally fun:)

I love your fly swatter idea! It's such a small change that turns it into something fun! I'm not suprised you love your cartesian plane either- it's great!

ReplyDeleteThanks! My students loved it, too. I pulled it out again this week to use with function machines. Instead of graphing our functions on the Smart Board and small dry erase boards, we graphed them on my giant coordinate plane using giant foam stars. Way more fun! And, it helps my kinesthetic and tactile learners so much.

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