Week 12 Reflection

The twitter session really challenged me this week to get actual evidence. I had to spend more time to have some more formal evidence to guide my instruction versus what I just know where my students are at by questioning. I am not finished with my unit because of starting late so this week the students will work on their performance task. I am nervous with how students will do for the performance task considering we don't do assessments like this very often in my class. With this said, I know what I have for them is valuable to their learning and is a real application to what they have learned.

In Gerald's blog, I was reminded how another way to differentiate learning is letting students pick what type of problems to do in homework assignments. In my next assignment I will have them pick what method they prefer more and have them do this method but must do the other method once. Then the students will have to explain why.

From reading Jim's and Jule's blog posts, I am starting to hear more and more about Prodigy. I think I will look into how this can support this class specifically in the future. I have been told that Prodigy provides many game-like elements to the classroom and students are learning without the feeling of inadequacy. This is definitely a program my Pre-Algebra students need.

This week has been a struggle in putting together my blog post because of non-classroom related happenings at the school. My principal forgot to observe me in February so we quickly had to get my second observation done this week. This was a bit stressful. Now I am looking forward to getting all of my evidence together and showing growth of students through the differentiated instruction done in the classroom.

Week 12

Essential question: What evidence am I collecting for my final project – and for what purpose?

            This week I have gained evidence from a Google Form that I had students take. The first time was looking at whether students understood the aspects of y=mx+b. The second time was looking at whether students understood the aspects of solving systems of equations through graphing.

With the first Google Form, I had students take it at the beginning of class and then I put the results up and we decided as a class what concept we needed to cover. They decided as a class to cover identifying slope from a graph and finding the y-intercept. I asked my aide to work with the majority of the group and then I took Kelsey and two other students who struggled with what a y-intercept is and what slope is. I knew we needed to cover these because of the check-in from Friday that I had students fill out on their own (see previous week’s blog). We focused on defining the two concepts on the most basic level. For example, we defined the x- and y-axis and a line. Then we looked at where the line hits the y-axis and defined this as an intercept. I kept drawing lines over and over and they had to identify the intercepts. After working with the individual group of students and the other students practiced with the aide using a worksheet, I had them take the Google Form assessment again. There was growth.

            Another form of evidence I have is homework and class practice work. If students were struggling with a specific part of one assignment, I would teach to the misconception and provide practice for students again and then have a similar problem on the next assignment alongside of new material. The best part about mathematics is that the skills are built on top of each other so having evidence of a learned concept is easy to find.

            We next covered the concept of systems of equations. As a before assessment, I had students identify where lines intersected. Students were successful in this identification therefore we moved on to graphing the systems. This was only a struggle for students who had been gone the day before with an in-depth process of graphing. Jerry was not struggling with the material we were covering so I had him and two similar students work together on an application to real-world situations of systems of equations. With a given scenario and equations, the students had to graph the income of two different salespersons. In the group, the students were able to figure out how sales each salesperson would need to have the same income. The evidence of this learning is from the paper graphs he and the others made.

Week 11 Reflection

Essential question: What are my challenges and successes in implementing my unit? 

            I began my UbD lesson plan on Thursday in my class. I arrived back from Europe on Monday and I needed to gage where my students were at with the material I had asked the substitute teacher to cover. In keeping true to one of my five elements of differentiated instruction I picked out, I needed to be flexible and start the UbD a few days later than planned. The students needed some reteaching and practice in graphing a linear equation using a table and identifying a function. Also, the students hadn’t gotten the chance in learning what slope was and the many ways to look at it such as real-life situations, on lines, and between two points.

Therefore, on Thursday and Friday we began looking and practicing how equations of a line are graphed in y=mx+b form. Students really enjoyed when I got on Desmos on Thursday to talk about slopes of a line by looking at steepness and direction (positive/negative). In fact, Jerry in particular was asking some great higher order questions to the class while using this program such as what would the slope need to be to create a vertical line? I used Kahoot to assess where students were at with slope. I discovered by the end that students needed more practice in rewriting equations in y=mx+b form so that they can identify the slope. We practiced doing this on personal white boards before moving on.

With keeping Jerry in mind and the few other students who really engaged with the graphing software, I pulled up Geogebra and set up an equation of a line that the slope can be changed and the y-intercept can be changed. A few of the students were able to connect that when an equation was in the y=mx+b form then the m is the slope and the b is the y-intercept. Not all students were able to grasp so I had students graph using a table and always starting with the x-value equal to zero they noticed that the y-value was always the b because x times 0 equals 0. We summarized the concepts we discovered by writing them out in notebooks and practiced graphing some equations in y=mx+b form. Kelsey was able to grasp the concept after writing out the process of graphing equations in y=mx+b. Grouping consisted then in individual or partners to graph some equations on their own. I had students fill out a check list on how they are feeling on the concepts. Jerry’s and Kelsey’s follow.

Jerry

	I understand fully.	I need more practice.	I still need to learn it.
Slope	X
y-Intercept	X
Graph y=mx+b	X

Kelsey

	I understand fully.	I need more practice.	I still need to learn it.
Slope	X
y-Intercept	X
Graph y=mx+b	X

            There are three students who checked that they need more practice and interesting enough, y-intercept was the main concept that needed to be covered. As I reflect, I realize that I quickly brushed over what a y-intercept is. On Monday, I will go over y-intercepts and its definition. Then I will assess students on it in a google form/quiz and also confirm students are able to identify the slope of a line. Then students will have a peer assessment by graphing a given equation, trading with a partner, talking about their process, giving corrections if needed, and graphing another equation after doing this.

Week 10 Reflection

            Man, was it difficult to pick five elements of differentiated instruction but when thinking about what I hold to be most important, it was quick in picking the elements. It was a reality check though when I compared it to my planned UbD lesson because many of what I held to be important was not listed in my unit. I found that it is difficult to explain via writing to show the planned differentiated instruction because I don’t know exactly what will need to be differentiated until I get to that situation with my students. Also as a third year teacher, I don’t think I have much tricks up my sleeve as other teachers. I am planning to document the ways I differentiate when I teach my unit but I think this will be a difficult task for me because I am not used to it.

            This week I commented on various classmates’ blogs but first I would like to acknowledge the comments they made on my own blog post. Heather gave me quite a few rhetorical questions about being flexible in differentiating for our students and how the “traditional” schooling system does not make this completely possible. In my district, the “math department” makes a point to acknowledge what is most important for our rural Alaskan students. I will keep fighting for this and making this the norm as next year we will have quite a few new people in our district. Gerald asked for some help on how to get students past a misconception and I gave him an idea. Chelsea, Jim, and Rachelle all seem to agree that flexibility is very important for differentiating instruction. I will need to keep my focus on flexibility when teaching my UbD lesson.

            On Chelsea’s blog, I added a bit of more depth on what background knowledge teachers need to have by adding in teachers need to know how students will react to content and not just know the content. Gerald’s blog helped me give some very practical and tangible ways of different tools for students to use. He got me thinking about my students’ performance assessment and in what ways they can show their knowledge. Jim’s blog reminded me on how we need to document assessments whether they are informal or formal and I reminded him of this. I plan to show this documentation to students so they have an idea of where they are at with their own learning. Kendra’s example of her UbD lesson gave me some ideas of what the organization of it could look like. I struggled a lot on the organization but now I have an idea of what to go towards.