As a teacher, I am constantly analyzing what types of tasks I am asking my students to do. I often search for quick, short warm-up problems that I can get my students working on when then enter the classroom. I then ask students to anticipate what the learning objective for the day will be based on their experience with the warmup. These warmups are my way of setting students up for learning in my classroom so I have to be very careful with the tasks I choose. Then real life happens, and I forget to create/prep a warmup for a class, so I do a quick search on the web to find a filler resource. This happened to me the other day, and with a few factors (end of break, rough night for sleep, late start to the school day– it was canceled first, then switched to 2 hours late, if that doesn’t cause confusion-, running behind schedule because daycare drop-off didn’t go smoothly, etc) I end up with this.
I have a group of 6th graders this year, and they are struggling with graphing. Let’s face it, I have many 8th graders and even High School students who struggle with using the coordinate plane properly. So although the Math Standard I decided to address is outside of my target grade level, I figure it is a good way to ease back into the school year for this group so we can start looking at some algebraic relationships. Looking at the CCSSM, this is the standard that correlates with this worksheet (although the sight I got it from labeled it a 7th grade pre-algebra assignment).
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
So away we go. Students meet me at my door, I hand this to them as they enter and away the hour starts. One thing that should have alerted me to incoming troubles is the fact that I did not get any questions on this sheet, students started working on it and had it completed fairly quickly. Depending on how students handle the warmups, I will either have them anticipate the learning objective before or after we discuss “answers”. I do this so that dialogue or questions that may come up as we share answers do not influence initial thinking. This was a day where, since they handled this so expertly, I asked them the following question before “correcting” the warmup.
“Based on the warmup you did today, what do you think the learning objective for Math is today?”
Typical learning objective definition for me is listing all of the student’s responses (except for duplicate ideas) on the whiteboard, having a quick discussion with students on things we can revise/edit, and producing a refined result. This result has 95% of the time been exactly the learning objective I have in mind- and typically worded so succinctly for students that I find this invaluable to my classroom. That last 5% of the time we come up with a statement that is close but needs some minor work. On those, I will go through and “correct” the warmup with the class and we will return to the learning objective to see if we need to refine it again. After the group discussion on the answers for the work, students will create a statement that is correct (I will also do this the other 95% of the time, but no revisions are made because they were right the first time!).
Results for the learning objective:
I wonder where they got that idea? Well, let’s look back to the handout I distributed…
It’s mentioned three times on the worksheet- it’s what I want for an answer right? Talk about stifling learning. The sad thing is that I have done countless worksheets similar to this one when I was a student and also have given these same types of worksheets to my students in early teaching years. Doesn’t this demonstrate proficiency? I would say no, especially when 80% of the ones I have handed in get part one totally wrong, but part two right. Students do not take the time to check answers, and they especially don’t take time to compare between different problem types. My typical student will give me answers in the form of (Y,X) for part one- but they get part two right because there is no letter at (7,-6). It’s not understanding, it’s answer getting.
So, after that short debacle I took the remaining sheets I had for the next class and cut out what I didn’t need. This is what I gave students the next hour:
They took the sheet from me and walked into the room, looked at it and did something I appreciated: They asked me about the graph instead of doing nothing or connecting the dots (I have had students do that). I walked up to the board and wrote a simple direction.
“Tell me the location of 6 points (letters)”
I purposefully left out any formal vocabulary (graph, coordinates, ordered pairs, coordinate plane, XY axis, plot, etc) because I wanted to know what students were thinking when looking at the graph. It was very clear which students understood coordinate pairs. There was no way students could obtain a correct answer because they couldn’t find a point at an alternate location. The surprising thing is, every student got 100% on this warmup. The other surprising thing is, when they did a picture graph during class where they were given coordinates to plot, ~50% graphed it incorrectly. Tomorrow will be time for personal conferences about that issue to see if we can clear up and cement concepts.
Oh, and what did my learning objective look like with the “revised” warmup?
I’m pretty good with that for now- it gives me a great base to build more upon.
Be careful what you give out or assign, make sure that students are supplying the intended learning objective- not you in the form of a worksheet.