Category Archives: formative assessment

Making Corrections is Valuable

I love, love, love having the kids make corrections on quizlets (formative assessments) and tests (summative assessments). It requires them to actually look at my feedback and to maybe even learn from their mistakes.

For corrections on the last test in FST, I also had the kids write down one thing they’re proud of or one thing they thought they really learned. I got some great responses back, and I hope it helped remind them of what they did well rather than just focusing on mistakes, so I’m glad I had them do that.

Sample responses:

“I did really well on my factoring. I was worried about it and it went better than I thought. Happy about it.”

“I did well on the quadratic formula.”

“I liked Part 1 because I didn’t get any points off, and I did good with my negatives.”

“Last year I feel like I didn’t get a single quadratic problem correct. I feel like I understand them a lot better this year.”

“Factoring went well and I really have cemented the material in my brain.”

“I learned how to graph equations and find the x-intercepts.”

“I think I really mastered the factoring aspect of this unit.”

“I showed my work.”

“I slowed down this test!”

“Overall, I did OK.”

“I did well at taking my time and going through my work.”

“Test was easy but J. did better than me, so I’m salty. I’m over it. Otherwise, test went pretty well. What really helped was coming in and reviewing with you. Thanks, Ms. Cummins.”

Sometimes these kids drive me crazy, but sometimes they can be thoughtful and serious and make me proud.

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Filed under formative assessment, FST / Algebra 2, grading

Exit Tickets and Group Work Norms

Ever experience kids packing up 5 minutes before the bell? I definitely did during student teaching, but half-way through, with support from my cooperating teacher and help from another math teacher, I decided to implement exit tickets. It definitely made a difference. Kids worked until the end of class when I handed out their exit ticket sheets and put the prompt up on the Smartboard. It was great. The other math teacher who did exit tickets used a weekly sheet with a space for each day’s answer, so dutifully followed her lead, but I didn’t really enjoy keeping track of the sheets for a whole week and it was a pain to pass them out at the end of each class. The kids complained that it took too long to get their sheets back so they didn’t have enough time to answer the question.

So anyway, this year I plan to just have a bunch of half-sheets of paper printed out for exit tickets. I am wasting more paper this way, which is a concern of mine, but it’ll have to do for now. On the back of the half-sheet there is a participation reflection. I’m  focusing on group work and creating healthy math culture in my classroom this year, so I want to remind the kids of our group work norms every day, and I want them to do some reflection on the day, hence the three questions on the back of the exit ticket.

I really like all of the norms I’ve decided to use, but unfortunately there are twelve of them, which is probably too many. I should try to shorten the list, but I don’t know which ones to give up. They’re all important to me!

Well, here’s the file with the exit ticket on the front and the reflection on the back. Nothing fancy, but check it out, and I’m interested in hearing your thoughts. Do you use exit tickets? How do you implement them, and what do you like about them? What classroom norms do you use? How do you get your students to think about your norms?

(I don’t have any word processing software on my computer, so I just use google docs for everything, but in the process of uploading my documents to scribd, the spacing gets a little weird, but you should still get the idea.)

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Filed under culture, formative assessment, group work

A Favorite Math Lesson Resource

I want to share one of my favorite resources for rich math lessons: the Mathematics Assessment Project, which is a collaboration between the University of Nottingham and UC Berkeley. I love the structure of their Formative Assessment Lessons. According to the website, these lessons are designed “to reveal and develop students’ conceptions, and misconceptions, of significant mathematical ideas and how these connect to their other knowledge”, as well as “to assess and develop students’ capacity to apply their mathematics flexibly to non-routine unstructured problems, both from the real world and within pure mathematics”.

When I taught middle school summer school, I used a couple of these lessons with great success. I love how they include matching and sorting activities that require the students to come up with their own mathematical justifications. When I tried these out in summer school, I had small classes and had the students do it individually, but this year I am definitely going to follow their suggested structure of using small groups because I want to see more mathematical discourse among the kids. I also want to do a better job of creating the final product and displaying the work on posters. In my summer school class, once the kids finished sorting they would just toss the cards in the trash (or worse, leave them scattered on tables or the floor for me to clean up). So this year I will definitely use the small group format and require the posters, which will hopefully get more students to explain their thoughts and reach a deeper understanding.

Conveniently, I was able to find a MAP lesson for each of the first four units in my Functions, Statistics, and Trigonometry (FST) class. (Students at my school have the option of the Geom–>Advanced Algebra–>Pre-Calc route, or the Geom–>Algebra 2–>FST route. So the curriculum for this class is comparable to the second half of an Algebra 2 class, I think. First year teacher here, so I can’t comment too much on “typical” math curriculums.)

Unit 1 – Our curriculum calls this first unit “Symbolic Manipulation” which is a decent description for it. It’s basically a review of Algebra topics they’ve previously encountered, such as the distributive property, combining like terms, and factoring. The MAP lesson I plan to use is Interpreting Algebraic Expressions. I like how this lesson helps students distinguish between expressions like (5n)^2 and 5n^2, and it also uses area diagrams that will come up again when I’m teaching factoring. I plan to try this lesson right away the first week of school, and it might be a fairly simple for this class content-wise, but that’s okay because it will also serve the purpose of introducing the students to this type of group work and what it’s like to share their thinking, which will probably be a very new experience for them.

Unit 2 – This one is all-things quadratics. The MAP lesson I want to use is Forming Quadratics. This is a great matching activity, and I like how it incorporates all of the different forms for quadratic functions and helps the students identify key features of the graphs.

Unit 3 – Polynomials. Not my favorite unit (I find long division, rational root theorem, etc to be somewhat tedious), but I can’t let that show. I think I will definitely emphasize SMP #6 – Make sense of problems and persevere in solving them during this unit. The MAP lesson here is Representing Polynomials, which is another great matching activity which connects what students already know about finding zeros to 3rd-degree polynomials and their graphs. The extension activity is also intriguing.

Unit 4 – Functions and Function Transformations. There are two awesome MAP lessons that could be incorporated here. The first one, Interpreting Distance-Time Graphs, was the one I used with my summer school class last summer (8th graders who would be taking Algebra 2 in the fall… so a very different group than the one I’m talking about now). Perhaps this one would be too simple for my FST kids, so the second option, Functions and Everyday Situations, might be a better fit. I like the open-endedness of Distance-Time, but I like how Everyday Situations has students translating between the algebra and the graph.

These lessons will be great formative assessments, and  I’m glad I can incorporate one into each unit. Hopefully you got a chance to check out the MAP website and lessons if you aren’t already using this great resource. If you’ve used these in your classroom before, what do you like about them? What about them is difficult to implement? Thanks in advance!

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Filed under formative assessment, FST / Algebra 2, group work

Formative Assessment Brain Dump

Today I enjoyed another get together with my FST (kind of like the 2nd half of an Algebra 2 class) co-worker. We had a good discussion on formative assessment and how to grade it, and many thoughts and ideas are still running through my mind, but here’s a brain dump of where I am so far.

School policy requires each class to grade 25% on “Effort” and 75% on “Knowledge and Skills”. Pretty much as a whole, the math department uses homework and quizlets (your typical formative assessment short quiz) to make up that 25% Effort grade.

Last year my co-worker graded homework for completion and quizlets for correctness, but he was having trouble reconciling the fact that something graded for correctness was going into the “Effort” grade. So he proposed that the kids take the quizlets like normal, he grades them like normal, but if the kids make corrections then they get 100%.

At first, I didn’t really like the idea, but now as I’m typing this I’m kind of warming up to it. Well, let me back up. First, I’ve done lots of reading on Standards-Based Grading and am intrigued by it, so I personally don’t really like the 25% Effort thing in general, but I have to accept it and move on. Likewise, I don’t really want to bother grading homework. I want great math to happen during class so that there’s no need to dole out the typical “page 155 #1-27 odd” homework assignments. If I feel like the kids need more practice (or if some individual students ask for it), then I can give some homework problems, but otherwise I’m not really interested in seeing a bunch of kids copy off each other every day just to get their completion grade.

But anyway, my co-worker and I want to basically have the same set up because our kids get shuffled at semester, so I’ll play along with grading homework for completion. No big deal.

Now, regarding the quizlets, like I said, at first I didn’t like the idea of kids blowing off their quizlets and then copying the correct answers for 100%. So I told my co-worker that although their effort grade will be higher from that easy 100%, I worry that their actual effort will go down because they won’t really care about being prepared for the quizlet if they know they can just correct it and get 100%. Basically, I want them to take the quizlets seriously, and I worry that they won’t if they know they can just correct it.

But, as I’m typing this, I am opening up to the idea. If I can create the expectation that they come prepared for the quizlet, and I continually emphasize it’s importance as an indicator of what they know and don’t know, then it’s very possible that they will take the quizlet seriously despite the “easy” grading of it. In fact, maybe the “easy” grading of it will take some pressure off of them and really encourage them to make corrections and learn from their mistakes. And that’s the most important thing about formative assessment, right? If they can identify their errors and learn from their mistakes then they’re doing exactly what I want, so why not give them 100%?

Grading is weird.

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Filed under formative assessment, FST / Algebra 2, grading