As a kid in the late 80’s, I spent most Saturday mornings watching Pee-Wee’s Playhouse and yelling each time someone said the secret word. If the secret word this week would have been “assessment,” we would all be hoarse from each time I had to “scream real loud!” This week was filled with lots of talk of assessment and formative assessment, its uses, and how we all felt we were doing with it. By the end of the week, all of this talk played a big part in the direction of my teaching.
After having a three-day weekend celebrating Martin Luther King’s birthday, my students and I returned Tuesday, preparing for an interim assessment on Wednesday. My learning targets for the assessment were:
1.) I can graph a linear equation.
2.) I can find the slope of a line if I’m given two points.
3.) I can write a linear equation if I’m given two points.
My students were seated in their cooperative learning groups and class began by them discussing the different ways to graph a linear equation. Some students preferred to use a table because they were more comfortable with that from previous years and one student said, “All I do is type the numbers in my calculator.” However, most preferred using the slope and y-intercept because it was the fastest. When it came to finding slope, the discussions became more like debates. Students knew that slope was a ratio but were disagreeing on which number went on “top and bottom” and whether or not the answer was positive or negative. (I have been trying to push vocabulary this year and the use of “numerator” and “denominator,” but it hasn’t fully caught on yet). After a little clarification, students did well finding slope a few more times. When it came to writing equations, we again had disagreements as to what the slope was, which then affected the y-intercept. Again, after a little discussion, it seemed that students knew how to write a linear equation.
Wednesday brought us our interim assessment, including my first attempt at a performance task. First, students were asked to graph lines and I saw the same mistakes that everyone probably sees from students in their classes. By far, the most common mistake was students switching the slope and the y-intercept. When finding slope, there were two common mistakes: (a) writing the ratio as x/y and (b) simplifying incorrectly. When I say simplifying incorrectly, I’m saying students were simplifying 10/5 to equal 5, or things similar to that. The frustrating thing about this is that, although students knew that slope was a ratio of the change in y compared to the change in x, their slope was incorrect due to a completely different skill. Adding to my frustration were the questions that asked students to write a linear equation. Again, some students made simplifying mistakes with the slope which then made their y-intercept incorrect. When grading these questions, I tried to award points based on each part, unique to each student’s answer. For example, if students had the wrong slope, but their y-intercept would have worked for the point they chose, they would get at least one point because they knew how to find a y-intercept.
Then came my performance task:
The Black Hills Whitewater Rafting Tour Company charges a guide’s fee plus a certain amount per person. When ten people go rafting, it costs $425. When fifteen people go rafting, the cost is $600.
What is the equation that fits this situation?
What is the fee per person?
What is the guide’s fee?
What would the total cost be if I could get a group of 25 people together?
If I had to take a guess, about a quarter of my students got all of the questions correct. Of the remaining students, some could get the fee per person or the total cost for 25 people. However, most students missed all of the questions. This was not what I was hoping for. I know the point of a performance task is to measure how well students can apply the knowledge they are obtaining in class and this showed that students could not apply much that they had learned in class. It just seemed as if students were not used to something like this and were unsure where to even start. I’ll come back to this assessment soon.
Wednesday’s early release brought us to the library in order to discuss the topic of “Formative Assessment.” My assistant principal and I had been discussing the idea on and off for two days, so when it came to discussing the different aspects in groups, I had given it a lot of thought. In my group, we kept returning to the idea of using the data from your assessment in order to change your teaching or the direction of your lessons. As we discussed these things in my group, I kept thinking about my data from earlier in the day showing me that students had not shown mastery of the learning targets. On my drive home, I had plenty of time to think about how I was going to change my teaching the next day.
However, due to yet another cold day, my district was out Thursday. I emailed students telling them that Friday we were going to do an assessment retake after going over all of the questions from the original. I also started changing my thinking my grading on my ride home. My assistant principal and I had discussed earlier in the week what the meaning of a grade was and that we should actually be measuring mastery of a standard over time. So, I decided I would try something different when grading student quizzes Friday.
We began class Friday with me discussing common mistakes on the assessment and heard a lot of disgusted moans as students learned how close they were to correct answers. The best example of this was when we looked at the performance assessment and I showed students that I would have thought of it as two ordered pairs, (10, 425) and (15, 600). All I had to do was write those two down and students soon realized is was nothing more than finding the slope and the y-intercept. I then informed students of my change in grading philosophy for the retake. I was not going to average the two scores like I had done in the past. I would take the higher of the two grades of the two assessments. This time, my performance task was:
A gym charges a membership fee plus a certain amount per class you take. When you take 5 classes, the total charge is $290.When you take 7 classes, the total charge is $300.
What is the equation that fits this situation?
What is the fee per class?
What is the membership fee?
What would the total cost be if I attended 20 classes?
After grading the retake, here is some of the data I recorded:
1.) About two-thirds of the students improved their scores, some by as much as 50%.
2.) Some students need a whole lot more than a discussion of mistakes in order for them to improve. Almost all of these students are in my Enrichment and Intervention class receiving tier 2 interventions. So, I guess I have the correct students placed in that class.
3.) Even though I gave students who earned an A on the original assessment the choice of not retaking it, many still did, trying to improve their score even a little.
4.) Once students were shown that the performance assessment was nothing more than two ordered pairs and they were to find the slope and y-intercept, they really did well knowing which value was the fee per class and which value was the membership fee.
5.) It seemed that, giving the students the opportunity to receive the higher of the two grades they earned instead of the average of the two, most students tried harder than usual.
Overall, this week was filled with lots and lots of talk of assessment/formative assessment. I feel that my formative assessment Tuesday told me that students were prepared for my interim assessment Wednesday. This turned out to be false and I used my data to change the direction of my teaching for the week. I gave students another opportunity to show mastery of their learning targets and many improved. This coming week will see a very likely shortened week, due to the cold weather again. I am also in the process of rereading Embedded Formative Assessment by Dylan William. I’m hoping to write a post later this week of some interesting things I find in the book.
If you read this far, thank you so much. Feel free to comment on what you agree/disagree with or what you use or are going to use for formative assessment in your classroom. Stay warm!