Wednesday, March 31, 2010

The Process

I currently use an augmented version of our school's assessment system. All of our teachers are using standards/skill based grading allowing for re-assessment, but because of the technology I have available in my classroom (ie. class set of laptops), I can do some things that my colleagues can't.

Skills List
The system all starts with the skills list. This isn't news to you because if you're reading this blog, you're most likely reading dy/dan as well. Our district made the move towards standards based instruction a few years ago with some of our campuses throwing out the textbook pacing and teaching a standard at a time. We have decided to go one further and break up the thicker standards into smaller more manageable skills. Each student gets a skill list where they keep track of their progress. They also have a "playlist" where they set goals for the week.

Online Examples/Study Guides
I spent the better part of the last two years populating our school website with examples. They have been organized by text section, state standard and soon, I will have them done by skill. Many of these were recorded during class and are the result of student generated questions. I hope to upgrade these examples so they are a little cleaner. The study guides are simply .html exports of the ExamView tests I have created. In hindsight, I think I'll go back and make all the study guides short answer as opposed to multiple choice. I have found that too many student won't show work otherwise.

Ideally, I would like the skills to be just that, skills. I want my students to access these study guides and examples on their time which would free up class time for projects and problem solving. Based on conversations I've had with my 7th graders, they are realizing the power of being able to access these resources at their convenience which gives me confidence that a classroom inversion is more likely next year. It's tough to have them unlearn certain behaviors, but because my classes are really a two year program, I see much growth the second year.

Pre-test, Common Formative Assessment, Test #1...
Call it what you want, it's basically the first test I give my students which sets the bar for them in the grade book. This semester, these tests have been administered solely through the ExamView Test Manager. Students access the tests through the EV Player and go to work. Once a student finishes the test, they get immediate feedback on each question. They know what they answered correctly and what they missed before they leave class. Skill lists are updated on the spot. Students have been taking screenshots of their feedback sheets and save them to their folder on the server. These screenshots double as proof of their completion of the assessment as well as a set of practice problems they can do as they prepare for re-assessment.

I set up all of the tests so that students can access them only once. This prevents them from simply memorizing the answers from a test and then doing it again. That's why dynamic questions are a must. I have a set of post tests ready to go--it takes just a click of the button to calculate new values for the test. On most tests, I will make some of the questions short answer so students have to do some explaining. There is not an equation editor available for students while they take the test so I have to be careful which question types I use for free response.

In order for a student to take a re-assessment they have to do a couple of things.

  • Demonstrate they recognize the mistakes they've made and show me they know how to fix them.
  • Sign up. (h/t to Kate for the form idea)
I've tried to make all of my expectations as transparent as possible. There really are no surprises when it comes to test time. Here's the floor of what I expect you to know, now show me. It's been interesting talking to parents about this because they like the system but can't believe it's this simple.

Work in Progress
I just learned that I can also attach a link to a video or audio file in the test player. This will allow me to use these media as prompts for future test questions. I'm not exactly sure how I'll use it but I can see myself doing a screencast of myself doing a problem incorrectly and having students pick out the mistake. I can also see showing a clip of a projectile and asking students to find it's highest point.

My plan for next year is to develop a set of projects for students to do that incorporate a group of skills. Students will only be able to work on the project once they have demonstrated proficiency in that given skill set. My farming project may act as a true semester project this way. But instead of waiting until the end of the semester to give it, I will give it to them at the beginning of the year and say they have until the end of the semester to finish it.

Anyone up for developing some projects?

Tuesday, March 30, 2010

Bottom's Up!

A few of you have asked for more explanation on using Diamond Problems and/or Bottom's Up for factoring quadratics. I figured showing you would be easier than writing about it. So here you go:

If you have any other questions, let me know and I'll be glad to see what I can do to help out.

Sometimes You Just Have To...

"Hey, Mr. Cox, can I take the post test for skill 34?"

"Sure, it's in the post test folder."

"What's the password?"


"Are you sure, it doesn't work."

"Yes, I'm sure. Try again."

Oh, c'mon don't act like you haven't done something like that before.

Wednesday, March 24, 2010

Identify Your Opponent

My students have had a really tough time with factoring this year. It's definitely been a different group than in years past, but I haven't been able to put a finger on the problem. If I give them a context (ie. perfect square trinomial, difference of two squares, etc.), then they do fine, but when we got into simplifying polynomial fractions, the wheels fell off.

It became pretty clear that my students were not very good at identifying what they were up against. Are we factoring monomials, binomials or trinomials? Do I use distributive property, diamond problems or "bottom's up?"

You have to know what you're dealing with before you can pick a strategy to defeat it.

So I put on my cool shoes, gave a few hugs and went with the ELA approach:

I'm already noticing that identifying the opponent and choosing the strategy has helped with simplifying poly fractions. Let's hope it sticks.

Friday, March 19, 2010

What About Cheating?

The topic of cheating has come up a couple of times in the last week. Once with a colleague in my school and once in an online conversation. Most schools/districts have some sort of honor policy which makes the procedure pretty simple: zero on the assignment, contact home and record in the file--or some variation of this.

Buy where does learning fit into the policy? If you use standards based grading, do you allow the student to take a re-assessment at a later date? Or better yet, If you use standards based grading, why would a kid cheat in the first place? Do re-assessments encourage poor study skills as kids know they have a safety net in the form of a "do over?"

We all know what a zero does to a final grade. And that grade never reflects what a student actually knows. Should the consequences of cheating show up in the final marks at all?

And yet again, no answers, but lots of questions.

Tuesday, March 9, 2010


Joe works too fast.

Joe doesn't show his work.

Joe ends with the beginning in mind.

Today Joe took a test on being able to identify the graphs of quadratic and cubic equations. He bombed it.

Joe came back to my desk while the rest of his class was finishing their tests and had some good questions. He said he didn't know how to set up an input-output table so I showed him. I plugged in one x and found y. I plugged in a second x and asked Joe what the y-value would be. Joe did the rest himself.

Joe and I graphed his results. I asked Joe to graph a simple parabola with coeffieient of 1 on the same set of axes.

Joe said, "Hey Mr. Cox, if the number in front is bigger than 1, then it grows faster."

"And what if the number is a fraction?"

"Then it grows slower?"

"Are you asking me or telling me?"

"It grows slower."

"What if the number is negative?"

We turned the paper upside down.

Joe gets it.

His grade is different than he thinks it is.

Update (can I update a post I haven't published yet?)

Joe just informed me that a cubic with a positive coeffiecient will end up in the 1st quadrant and one with a negative coeffient will end up in the 4th. Yeah, better get on that grade change.

Thursday, March 4, 2010

Farming Project

My students are in the middle of the farming project I created last year. I'm semi-pleased with this because it encompasses many of the standards/skills we cover in the first semester and gives students a way to see how many of them apply. This year, I gave it out as an individual project as opposed to being a group project. Each student had to sign up for the number of acres to farm. This way, everyone's work would be different. Similar, but different. It's simple for me to check their work by pluggin in their acre number to the GeoGebra applet:

Task #1: Search Google Earth for the perfect piece of land (Any shape other than a rectangle). Once you have found it, take a snapshot of the land in SmartNotebook. Determine the dimensions of the property that would give you your desired acreage. Remember, you must be between 100 and 10,000 acres (round to the nearest 100 acres). Determine the equations that would model the property lines. You may use GeoGebra to help you with this, but you should also demonstrate how you would find those equations algebraically. Equations must be in Standard and Slope-Intercept Form. (Standard 6.0 and 7.0)

Task #2: The bank is willing to loan you $2000 per acre to farm your land. However, cotton costs $1000 per acre and pistachios cost $3000 per acre to farm. Determine how much money you have available for this project. Note: You must first determine how many acres you have to farm. How big is an acre? Look it up!
What inequality can be used to model this situation? (Standard 2.0, 7.0)

Task #3: Because of the high demand on fertilizer and water, you have a limit as to how much of each you can obtain. Your fertilizer supplier can provide you with 340 units of fertilizer per acre and the water district will allot you 1.7 acre-feet of water per acre. Cotton requires 300 units of fertilizer per acre and 2 acre-feet of water per acre. Because the pistachios are well established, they will require more fertilizer but less water. Pistachios take 400 units of fertilizer per acre and 1 acre-foot of water per acre. Write two inequalities for this situation. Let the first inequality represent the amount of nitrogen needed compared to the amount available. Let the second inequality compare the amount of water needed with the amount available. (Standard 7.0)

Task #4: Because of the fact that you will be “changing” an existing piece of land, you will be required to adhere to a new state law that states that pistachios cannot take up more than 60% and cotton cannot take up more than 80% of your land. Write a set of inequalities that model this. Now you are ready to graph your set of linear inequalities. But, before you do, there is one last inequality that you must consider. Is ther a limit to how large x + y can be?GeoGebra doesn't handle inequalities very well so you must turn them into equations in order to graph. Insert your equations into GeoGebra and use what you know about inequalities to determine the shaded region. Use the polygon tool to create the polygon that is determined by the shaded region. (Standard 6.0)

Task #5: How much money can you make? The current selling prices for your crops are as follows:
Cotton: $1500 per acre
Pistachios: $4000 per acre

Write an equation that involves x and y that could be used to determine potential profit.

Task #6: The vertices of your polygon from Task #4 can be used to determine your maximum profit. Use GeoGebra to determine the vertices of your polygon. Once you have found the coordinates of each vertex, substitute the values of x and y into your profit equation to determine potential profits. Which point gives you the most profit? Which lines are used to determine this point? Show how you could have found that point of intersection algebraically. (Standard 4.0 and 9.0)

Task #7: In order to maintain your crop, you must spray an herbicide to control the weeds. Glyphosate is a common herbicide used in agriculture. However, glyphosate can be purchased in different concentrations. A farmer can purchase a solution that is 54% glyphosate but your average homeowner can only purchase solution that is 12% glyphosate. You happen to have thousands of gallons of both available but, new legislation dictates that you can only use a solution of 36% glyphosate. Your job is to determine how many gallons of 54% glyphosate must be mixed with 12% glyphosate in order to obtain a mixture that is 36% glyphosate. The number of gallons of 36% glyphosate is dependent upon the number of acres you will be farming. Keep in mind that you will only be spraying the land that is being farmed and you will use .38 gallons/acre. (Standard 15.0)

Task #8: It is time to start pruning the trees and you hire three new workers. James can prune a tree in 5 minutes, Jose can prune the tree in 3 minutes and Mark can prune a tree in 2 minutes. If you have 136 trees per acre, how long will it take them to prune all the trees? Does this seem reasonable? Why? How many 3 man crews (working at the same rate) would you need to hire in order to get the work done in four 54-hour work weeks? (Standard 15.0)

Task #9: Create a final proposal justifying how many acres of each crop you will farm. Your proposal should include but is not limited to the following:

  • Picture from Google Earth (you imported to GeoGebra) of the land you are purchasing with the lines and equations that determine the borders.

  • Budget, Fertilizer, Water, State Law restrictions inequalities.

  • Profit equation.

  • Picture of your polygon from GeoGebra. Include labels for the points and the equations you use.

  • Written recommendation explaining your plan of action. Be sure to give brief explanations behind your conclusions. Your explanations do not have to be long, but they do need to justify your conclusions.

  • Your final proposal must be digital and able to be embedded into a webpage. You may use Voicethread, Slideshare, Screencast, Prezi or any other tool agreed upon between you and Mr. Cox.

I don't want this project to be so contrived. I spent a lot of time talking with a friend who happens to be a farmer, so I know that much of the information is reasonable if not accurate. I wonder if this could work if I simply told students to pick choose an amount of acreage, pick two crops and then research the given restrictions. Suggestions?

If you are interested, the project is here.