E. Evidence and Commentary of Classroom Practices

E.1 Academic Language

I created this list to print and display in my classroom. Each box represents a standard size printed page:

There are lots of terms that we use in math class that we don’t hear anywhere else, such as x-intercept. There are other terms that we use in math class that have a different meaning than if you were to hear them outside of math class, such as domain. Students that have never learned the mathematical context of these vocabulary words will need instruction to help them understand the meanings and start to incorporate them in their own communication. In order to aid in the instruction of academic language, I print the new vocabulary and display it in the classroom. This helps student learning of academic language because they can see the new word in addition to hearing the word. With practice students will be able to use the new vocabulary themselves, in verbal and written form. 

In the future I might include less vocabulary terms. Students are supposed to know x-intercept and y-intercept already. I think academic language learning will improve if there are less words to focus on. I would like to have only 1-3 terms per section.  

E.2 Differentiated Learning

Example assignment - Problems to choose from:

Example Student Submission:

One method of differentiation is allowing students to demonstrate their knowledge in a method of their choice. Another method is allowing students an element of choice in the assignment. I created an effective differentiated assignment that includes both of these features. Students were provided four problems and they could choose which problem they wanted to solve. They had to show and explain how to solve the problem, in the way they thought was best. The following photo is an example student submission. They were allowed creativity and encouraged to make their submission easy to read and understand. They were offered extra credit if their explanation could sufficiently teach a peer how to solve the problem. The differentiated aspects of the assignment had a positive impact on student learning because students were able to choose their method of expression and the problem they solved. The above student submission was an excellent example of a student demonstrating her thorough understanding of the problem and how to solve it. 

If I were to do this particular assignment again, I would keep the four options. Allowing students to choose which problem to solve gave them a sense of power and ownership over their submission. If I were to do this problem again, I would choose a problem that could not simply be entered into Photomath and solved. I had several submissions that looked exactly the same, used “x” for multiplication, and used factoring methods we did not learn in class. If students must use their brain to solve the problem rather than use an online solver, that will improve student learning for students that would normally just copy down an answer from online. 

E.3 Educational Technology

Desmos is a very cool technology that did not exist when I was in high school. As a teacher, I use Desmos.com/calculator regularly in my classroom. Here is an example of a screen I showed to my students:

My students were learning how to graph sine and cosine. Desmos has a nifty ability to dynamically change variable values. On the first line I wrote, A sin x. Students needed to learn that the amplitude, A, determines how far away a peak will be from the midline of the sinusoidal wave. On the second line I put a slider for variable A. Desmos puts a “play” button next to the variable. When I click the play button, the value of A will cycle from -10 to 10 and the graph will display the appropriate wave. This example is one way that I can effectively use technology to increase student understanding. Using the colorful and easy-use Desmos website, students can visually see the effects of changing variable values. Further, my students can Desmos themselves and experiment as they wish, which continues to enhance student learning. 

To modify the above artifact, I will modify the representation of the x-axis. Typically in a sine or cosine wave, you use radian values on the x-axis. Normally radian values are shown in terms of “pi”. Above, there are no pi values shown on the x-axis. So I would modify Desmos settings to make the x-axis increments be pi/2. The following image shows the settings open on the right, with the new step “pi/2” entered under the x-axis settings. Now the x-axis has radian labels. The graphed wave is the same. 

E.4 Professional Communication

I regularly send emails to families so they can stay current on how their student is performing in math class. Here is an example email:

Sending these regular emails has been a superbly effective way to maintain communication with student families. Many parents have responded to my progress report emails. This response, in many cases, initiated several back-and-forth conversations with parents that lead to improved learning outcomes. 

I have been pleased with the positive effect these emails have had on student learning. There have been parents that have been surprised to see that their student has not been doing the required assignments, so the parents have intervened to be sure that their student does their work. I’ve seen students make remediation efforts because their parents have approached them about their math grade. I’ve also had parents email me with clarifying questions regarding class policies. 

To improve these emails, I have shortened them as much as possible. Nobody wants to read an unnecessarily long email! I keep them as friendly as possible. I’ve decided to send them soon after a unit test, so that students have the maximum amount of time to remediate test scores before the end of the grading period. The best improvement has been thanks to my district’s tool, Skyward. At my last school, I informed parents that grades were updated on google classroom, and that required parents to log in using their student’s credentials to find their grade. With Skyward, I can now email with an attached grade sheet for each individual student! Now parents only need to click on the attachment to see what their students’ current grade is.