Word of the Week – “Assessment”

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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!


This Week in Class-January 13-17

After a two week Winter break and a cold-shortened first week back, this past week offered the first full, five-day week since December 16-20. The week started with us graphing using a table and finished with writing the equation of a line in slope-intercept form, given two points. In prior years of teaching, this would have taken weeks to get through. So, what is different this year?

First, we began the week by graphing a line using a table, something students should already know how to do. I put a problem up and allowed the students to work in their cooperative learning groups to see who remembered what to do. Some students knew what to do right away and, with a little refresher, most students caught on after showing how to find one or two points. My goal with this question was for students to not only remember how to do this, but to give myself the opportunity to sell the fact that you can graph a line much more efficiently using the slope and y-intercept. I used the same equation to show students the relationship between the slope, y-intercept, and graph. With the next question, students were asked to identify the slope and y-intercept and graph without writing the two down, if they were able. In just minutes, students were graphing lines within seconds using the slope and y-intercept. The only problem a few students were having was switching the slope and y-intercept, otherwise, things were going great.

Tuesday brought us a second day of graphing using slope and y-intercept along with students being introduced in the equations of horizontal and vertical lines. By Wednesday, students began writing the equation of a line, given a graph. Students did great with this, again with a few students in each class confusing which value was slope and y-intercept in the equation y=mx+b.

During the second half of Wednesday’s class, students began finding the slope of the line between two points. They started off graphing the points, then I forced them to find another way to find slope when we can’t fit the points on our graph. Once students were shown how to find slope, they preferred not graphing. I did not teach students the slope formula. Instead, we talked about rate of change/slope as the relationship of how the y-values are changing compared to how the x-values are changing. This seemed to work better and students didn’t get confused about what the first and second point are and what the subscripts mean in the formula. Yet again, the students did great.

The only lesson I didn’t really like this week was Thursday’s in which students were asked to compare slopes using graphs, tables and equations. Some classes did great with this, and some were completely lost. I think that next year I need to be more specific with my learning targets and more explicit with students as to what my expectations are for the lesson. However, there was one class that did great and really progressed through this lesson and topic. At the end of the lesson, I had students try to write the equation of a line, given two points, to see what information they could apply from this unit so far and what they retained from Unit 4. Some students came up with the equation, but some could only find the slope. I felt comfortable with where students were at the end of the day.

Friday brought one of those lessons that you want the principal to walk in during. If everyday were like my class was this past Friday, my classroom would be a pretty intense place. Our warm up had us finding slope and then progressing to using slope to find the y-intercept. Instead of having students input a point and the slope into the slope-intercept formula, I had students think about what the intercept would have to be to get the y-value in their point. For example, if students get a slope of 2 and their point is (2, 3), I have them multiply their slope times the x-value, 2, and see what they would have to do to get 3. In this case, students would have to subtract 1 from (2*2) which means their equation would be y=2x-1. Throughout this lesson, students were given the option of making a table and graphing in order to find the slope and y-intercept. Although many didn’t do it, I still liked the fact that students were given options and still found the answer, even if it were in a less efficient way.

Throughout this week, there were two things that came to my attention. The first is that, the more I use learning targets and write them on my board, the more comfortable with them I become. A colleague and I were discussing how much they helped us shape our lesson and formative assessment at the end of each class. By being forced to determine how I would assess whether or not a student knows a skill, I get a better idea of how I am going to get students to that point. If you are not familiar with learning targets, this website has some great information about them.

The second thing that is becoming apparent to me as this year goes on is the fact that most students will meet whatever expectations you set for them. I spent the first years of teaching feeling as if I was lowering my expectations to try to get all students to meet expectations. This year, the expectations are much higher and almost all are meeting them. If they aren’t, I am getting them into my Enrichment class to help them meet those expectations.

This coming week will be me giving an interim assessment with a performance task. I’ll report back next week with how that goes and what students thought of it. We’ll also continue to learn material that would have normally been taught in a freshman algebra class. I love the fact that Common Core has forced me to teach these things a year later, and forced me to rethink my teaching. So far, this has been the best year of teaching for me in my short, eight-year career. Have a great week!

This Week In Class – January 8-10

At Free Technology for Teachers, Richard Byrne recently shared a post about blogging more frequently. Over the Summer and at the beginning of the school year, I was blogging at least once a week and felt that I got a lot out of reflecting on what I had done that week, good and bad. When I read Richard’s post, I thought, “I really need to get back to blogging,” then waited a week to do it. I wasn’t really sure what to write about, but figured I could just share what I did this week in class and how it went.

On Monday, my district had an inservice that centered around writing culminating tasks for our Common Core units. This is still something that I often struggle with and did get some ideas of what to do differently when writing assessments. I learned that I often use too much scaffolding and take away the students’ ability to creatively solve mathematical questions. My presenter also shared a great website, the Mathematics Assessment Project, which has tasks, rubrics, and sample graded student work for “expert, apprentice, and novice” level tasks. I am starting a new unit Monday and my goal is to incorporate at least two tasks into the unit.

Due to the frigid temperatures and wind chills Tuesday, my district cancelled all classes, which meant the first day for students back to school was Wednesday. It was great to see the kids again and they seemed pretty happy to be back. We finished up our unit over functions using some examples from Visual Patterns again in order to talk about the ideas of function, linear versus nonlinear, rate of change, writing a function, graphing a function, and evaluating a function. The students did really well with this and it seems like students understood the connection between all of the ideas much better than the fragmented way I taught those concepts before.

Wednesday is also an early release every week in my building and this week we spent some time looking at the learning targets we write each day on our board. This is going to be a transition for many in my building because we are used to writing objectives that say “After completing this lesson, students will be able to:” using technical language when describing the objectives. With the new learning targets, we are now being asked to write “I can” statements for students using student-friendly language. After writing targets for one lesson and discussing targets with other students, I felt that we were getting a better idea of the essential skills students needed and how we were going to assess them. On Thursday, we looked at some distance/rate/time problems and how they related to the patterns we looked at on Wednesday, preparing us for a very important Friday.

Friday brought our Unit 4 summative assessment. After Wednesday and Thursday, I felt pretty confident on how students were going to do on this assessment and the students did not disappoint. I was very impressed with how much students wrote when they had to explain the difference between functions and non functions and also when they had to explain the difference between a linear and nonlinear function. It was nice to see so many students use the phrase “rate of change” instead of “goes up by,” although I did still some some of the latter. Overall, I felt like this was the best Common Core unit I have taught all year and the assessment showed that the students understood many of the concepts. The true test will be when my students take the ISAT as 20-25% of the test will be questions over functions, aligned to the Common Core.

Next week, we will begin our unit on linear relationships beginning with graphing and slope. According to the ISBE Scope and Sequence, this unit should take 9 weeks. I’m not sure how it is going to take that long, but I’ll definitely have plenty of time for reteaching and differentiation. I have started using Countdown for Teachers to help me plan my lessons. If you are having problems unpacking standards, this website does a great job of breaking each standard down to its “conceptual, procedural, and application” objective. Have a great week!