To assess a student's level of mathematical thinking

Embed math assessment into realistic problems and real-word contexts

2 minutes

In today's world, children are being taught social skills through their peers and "screen time." Because of this I use Tribes strategies in my classroom to teach social collaborative skills as well as the Common Core Standards. I use the Tribes process in order to involve the students right away in their learning by asking an inclusion question. The purpose of this is to invite students to reflect on and share their own experiences - to make the feel included.

When I do this I have my students sitting in groups of 4 or 5 or at the end of a community circle. I ask the students to talk to each other about a question that will tie to the content of the lesson.

Today's questions are:

*Have you ever used a book order? *

*How did you find out your total cost of the order? *

*What are some strategies you might use to find the total?*

Let the students talk for only a couple of minutes while observing to make sure everyone in the group has had a chance to share. Small group share lets every student feel included and increases participation. Shy students get to share in a smaller group where they might not otherwise.

30 minutes

This Book Order Assessment is great to use because it really shows students thinking with which operation to use - "Do I add, subtract, multiply or divide?" (5.NBT.B.5 and 7) Can they transfer the correct numbers - one mistake students make is to copy the book number and not the price, and the progress of the operations - switching from repeated addition to multiplication or repeated subtraction to division. Do the students round to the nearest dollar to simplify the work? (5.NBT.A.4)

Before I pass out the Book Order Assessment, I talk to the students about showing their work. This is an assessment for me to "see their thinking" which shows MP 2, and I can't see what they are thinking if there isn't any work on the page. Showing their thinking will get a student more credit for their work, and no credit is given if they only show the answer even if it is correct.

This is not an assessment I give back to the students to correct. It is an evaluation tool for me to see how the students think they should complete the problems. I do share this with parents during conferences.

I also take this time to point out that the Book Order Form they use for reference is from 2011 and they can no longer order from it. This takes away the students' desire to shop for books they might want to order. It takes up a little bit of space to store but I have found it very worth while.

This student shows their thinking through writing math algorithms. She did not have a correct answer on #3 but was able to come up with a reasonable answer. I gave her full credit for the problem because her answer was reasonable and I can work with her now that I know this. Her work also shows that her level of thinking does not yet include multiplication as her first method to solve the problem. However, she did relate addition to multiplication in numbers 1, 6, 8 and 9. Her work shows that she isn't deeply using division, other than very basic division. On question #9 she used addition instead of division. I noticed this on a couple of other students papers so this is a question I am going to need to look into and see if it is worded correctly. I need to see if it is the language and not the math that caused her to add instead of divide.

As of a year latter I haven't made any changes because I want to go into the next year with this same test. If I notice the same mistakes I will question students as to what they though and why they made the mistake. If needed I will make adjustments.

This student is at a different level of thinking when compared to student 1. They use multiplication and specifically the strategy of "solve a simpler problem". This is shown in problem number 1 when they wrote 11 x 4 = 44 and then they added one more group of 4 to get 48. They did the same with problems 7 and 9. This student did not get full credit on problems that did not show work. They did not receive any credit for #10 because it was an incorrect answer and there wasn't any work for me to see their thinking. I do give credit for students who have the correct answer and show their thinking. My purpose for this is because the students need to be able to explain how they get the correct answers and I focus on having them show me multiple ways to get the correct answer.

Not only do I make comments for myself on the student work, I also comment in my record sheet to help give me a better picture of my students mathematically.

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