Formative Assessment, Technically

As a departmentalized fifth grade teacher, I work with about 90 students.  With that number of students, it isn't always easy to get one-on-one time with each of my students to formatively assess their grasp of mathematical concepts, as well as their ongoing use of the Standards of Mathematical Practice.  

When looking for opportunities to integrate technology into mathematics instruction, it occurred to me that there are many apps that provide a great fit for gaining essential information that I could use to inform my instruction. Many of these apps would fall into the category of "Interactive white boards."  Some of these are Educreations, ShowMe, and Explain Everything.

Although each of these has components that are unique to their individual app, they have the same basic functions.  Students can show their thinking by drawing, inserting pictures, or typing text.  An additional feature, which adds a level of metacognition, is that students are able to record their voice to explain their thinking.  Finally, students are able to share these recordings with their teacher by submitting a shared link as an assignment in Canvas, an email, or by posting an embed code on a wikipage.  

I chose to use Educreations for this feature because it is free (Explain Everything in iTunes) and it does not require users to be 13 years of age (ShowMe).  My students had previously used this app for myriad assignments in both reading and science.  This was the first time that I asked them to use the app to explain work in mathematics.  (Full disclosure:  I am in a classroom with 1:1 iPads.)

To begin, I selected an item from their Unit 5.1 Lesson 3 (Engage NY) homework.  The students received the mathematics instruction found in this lesson from my amazing colleague, Bill Joolingen.  The lesson's objective was to use exponents to name place value units, and explain patterns in the placement of the decimal point I was curious to hear students explain their thinking when solving this problem.

  

As I listened to students' recordings, I was able to hear them not only explain their mathematical thinking, but also take risks that they may not feel comfortable doing in front of the class.  It was so interesting to hear students alone with their thoughts.

I know many of us struggle with assessing the SMPs.  The use of videos such as these provide a window into a students use of the Standards of Mathematical Practice and give us, as practitioners, a starting place at which to inform our differentiated instruction for students.

Additionally, we are provided with an artifact of each students proficiency or need for support that can be saved and shared. This can be a valuable tool for communicating with parents or with other educational professionals during response to intervention collaboration.





The following videos are the recordings of two of my fifth-grade students, as well as some of my thoughts after hearing their work.

Student 1:

When listening to Student 1's recording, it is obvious that he is struggling with language acquisition, specifically with language found within the mathematics discipline.  Although his work is sound, as an English learner, he needs more exposure to mathematical terms and opportunities to speak mathematically. 

Student 2:

First of all, I think that Student 2 disconnected the microphone at about 2:25 in the video, so I was unable to hear all of her thoughts.  :(  During the portion that I did hear, it sounds as though she has a grasp of the procedure, however I would love for her to work more on her explanation.  I want to hear why the decimal point is "shifted to the left" when I am dividing by 10^2 and to the right when I am multiplying by the same number.  Just before the three minute mark, she could be explaining that, but I can't know for sure because of the loss of sound.  I included the video to reiterate the point of how crucial it is to be able to hear the student explain their mathematical thinking, as opposed to just watching them complete the problem.

I am overwhelmed by the amazing amount of information I obtained by watching these videos on many of my students.  I look forward to using the app more in the future for other formative assessment opportunities.

Thanks for reading!

Same shift, Different day

Another of the Common Core memes has found its way across the internet.    In this incarnation, a basic algorithm is show at the top and described as the "old fashion" (sic) way.

At the bottom of the page, you will find a seemingly convoluted way to reach the very same answer and it is described as the "New" way.

I steer clear of these memes as they are obviously loaded and created by people that aren't truly researching the new Common Core State Standards but instead by people that have clearly have an agenda decidedly against CCSS.

Successfully I stayed clear, until I was called out on my Facebook page by a member of my own family.  She posted the picture and asked me to explain to her and her friends the reasoning behind this type of math.

As I am sure that I will need to access this reply again, my response follows:
Let me begin by saying, that paper shown in that picture is obviously written by a parent, perhaps frustrated, maybe even with an agenda against Common Core, who is trying to make a point.

I do not know a teacher that teaches that second way as "the new way."  There are, however, teachers that would accept that answer as a correct response...I would be one of them.  Stay with me for a second before you form your opinion...

The top algorithm is the ultimate goal, but that algorithm is devoid of meaning unless students have built a good number concept.  Introducing the algorithm too early is one of the reasons that adults today struggle with math.  They didn't understand the concept, they were just taught the shortcut.  In the long run, their mathematical prowess would be damaged, although it may not become evident until higher level mathematics.

To build that good number concept, we teach kindergarteners and first graders (especially) to work from landmark numbers (5s and 10s) which it looks like this student was using.  If I saw a third grader doing that, I'd be worried.  I'd worry that his/her number concept was weak.  However, think of how much more information I would get from the second problem than the first.  If a student wrote 32-12=22...would you be able to adequately analyze the incorrect student response in order to design a lesson for remediation?  It would be hit of miss.  I prefer not to teach like that.

Now, if I saw a Kinder or first-grader completing that second problem, I would be blown away at their mathematical critical thinking.  The fact that they could deconstruct the problem in order to get to an answer would lead me to believe that this students has a firm grasp on concepts needed to move toward the algorithm.

The Common Core mathematical movement is really a move deeper instead of a movement to a "new way."  We want students that think critically about math so that they can apply that critical thinking to other facets of the practice.  

If we only teach them the shortcut and they don't understand the concept behind it, we are doing a disservice to our students and the future leaders of our nation.