Teaching Pascal's to some Rascals

I taught my lesson plan to the same group of students who I did my pre-assessment with. The students attend Cabrillo College and are in an intermediate algebra class. Before I began to implement my lesson, I discussed the KWL charts that the students turned in to me in our prior meeting. During the week, in between our meetings, the students said that they had covered a lot of the things they were curious about in their “would like to know” section. After briefly discussing their KWL charts, I began with my pre-assessment for using Pascal's Triangle to understand Binomial Theorem.

I began by giving the students ten minutes to research Pascal’s triangle and expanding polynomials. I believe that recognizing patterns is a very effective tool in factoring. All of the students brought their laptop computers and went to work. I think that it is imortant to advocate use of technology in the classroom. But, occasionally teachers need to be careful. Computer are full of distractions and I made sure to stop them at ten minutes so that they couldn’t get distracted and start searching the web and going onto social media websites. Then I had each of the students share something that they learned during their research period and we had a discussion about their findings.

    The students shared that the first row of Pascal’s Triangle was the ones, the second row is the counting numbers, and the third row is the triangle numbers. I asked the students if they knew what the triangle numbers meant. They did not. I explained that they followed the formula:

 xn=n(n+1)/2

          They are called the triangle numbers because of the image below. I think of it as the stacking numbers, as if one was to make a pyramid of cans. After the discussion, I was able to determine that the student's understood the basic principle of Pascal's Triangle, but they hadn't had enough time to research the many uses of it (including binomial expansion).

          After the pre-assessment, I decided that a great starting point would be to have students fill out their own Pascal’s Triangle and to label the columns. I gave them a sheet with the first 15 rows blank and had them fill it out. This took about ten minutes and the students did the activity with very little help. Then, I discussed all the patterns that could be found in Pascal’s triangle, such as: the diagonals, horizontal sums, squares, the Fibonacci Sequence, and exponents of eleven. 

             Then, I showed how some binomial expansions worked. This part of the lesson I used direct instruction and I lectured them for approximately 15 minutes while using the white board. I showed how Pascal’s Triangle helped to explain Binomial Theorem. The students recognized the pattern and I did a couple of examples on the board and then had students try one on their own; then holding up their answer when they got the question. 

                 As my summative assessment I had a worksheet for the students to work on and fill in with my help. I remembered from when I did my test run pre-assessment that two of the students were slightly more advanced since it was their second time taking the course. This was there second time working with binomial expansion. I gave two of the students a harder sheet and the other two students an easier practice sheet. They worked on the questions and I walked around and provided help when I was needed. 

               Overall, I was pretty happy with the adjustments that I made to my lesson plan after turning in assignment 2A. I think that I did a good job of including technology and engaging the students into the curriculum. I think that I did a good job of differentiating my assessments (I didn’t do this as well in the pre-assessment). I found that assessing becomes a little easier once you get to know the students better. I think that students need to spend a lot of time practicing math (it’s a good form of assessment too) and that teachers need to give students more time to practice in class. I really liked the discussion that I had with the student’s as a pre-assessment. I don’t think that discussions are used nearly enough in mathematics. 

              I only had about 50 minutes to work with the students. If I had more time I would have given the students a lot more time to research Pascal’s Triangle. It is one of the most interesting tools in mathematics, and I think the students would find it interesting and it would be a valuable use of time. I had a really good time doing the lesson plan and I am working on finding ways to differentiate all of the assessments that I use in and out of the classroom. 

Pre-Assessment

                I ran study hall for the baseball team this week. I have four students who are currently enrolled in an Intermediate Algebra class. It just so happened that the students are at the point in their units where they are transitioning from graphing equations, to factoring quadratic equations. The week long unit plan that I made for assignment 2A is on factoring and the different techniques that can be used to solve binomial equations. The student-athletes that I was working with mostly fall into the category of advanced support to average students.

                I decided to have the students create a KWL chart. A KWL chart include what a student Knows, Would like to know, and Learned. The chart should be filled out throughout the week and updated as students learn more about the concept. I plan on having students use the KWL chart as a “ticket to exit” and plan on returning the charts to the kids so that they can keep using them. I think that the most important pre-assessment is when you are starting a new unit. It is essential that teachers get an idea about what students already know about a new concept.

           
              I began my pre-assessment by handing out KWL charts to the four students that I had, and had them fill out the first two columns of a KWL chart. I was surprised to find out how much the students already knew about factoring. After they filled out the K section we had a discussion and I learned that for two of the students this was the second time they had taken the class; that probably explains why the students already knew quite a bit about factoring. I believe that they probably just need more time practicing it.

              
                I found that the students had more problems with filling out “What they wanted to know” about factoring. The two students who had previously taken the course had a much better idea of what they wanted to learn. To aid the other two students, I broke down the ways that factoring would be used in a week long period. This helped them to come up with some things that they were curious about. When I have students create a KWL chart again, I plan on breaking down exactly what we will be doing over the week at the start of the class. I think this will help students to fill out the first two sections of the KWL chart.

                I had made a rubric for the assessment that is posted below. The rubric was made to be evaluated at the end of the day. Obviously students won’t be able to fill out what they have learned until I have taught them the full lesson plan. The only adjustment that I would make to the rubric would be change it from “each category” to “the first two categories" (if evaluating the pre-assessment only). Besides that, all the students were able to list at least two things for each of the first two columns (I did have to help two of the students with the second column).

                  Overall, I found this to be a very effective exercise for the students. I really like KWL charts as a pre-assessment activity. This was a test-run and I do need to make some adjustments. I think that it will be valuable to introduce  the students to what we will be doing for the week before handing out the KWL charts. I also should have given or shown the students the rubric before the activity. When I do the lesson with a learning activity students should be able to list what they learned, so the rubric won't have to be adjusted after a full lesson plan. I really enjoyed this assignment and am looking forward to teaching a full lesson for assignment 3A.

Personality Test

                After taking the personality test I scored ISTP. The “I” stands for introversion, but I was very close to being extroverted. I agree with the test's results; the introverted part of me likes thinking about ideas and explanations and the extroverted side takes action to ensure tasks get done. The “S” means that I prefer facts over possibility. I think that this is a big reason why I love math and decided to become a math teacher. There is an explanation for everything in math. The “T” means that I am much more driven by facts than by values. This follows the same logic as the letter “S.” My last personality letter was almost a tie, but I ended up with a “J.” This means that I prefer structure to spontaneity. I have always been involved in many different activities at once and I don't think I could be as active without the structure I have in my life. 

                I think that many of these traits can really supplement my student’s learning experience. Although I am slightly on the introverted side of the personality spectrum; I do take action when things need to get done. I still think that I am good at talking with people and building relationships, I just prefer to evaluate and think things over by myself first. I am always surprised to see how many teachers score on the introverted side of personality tests. I think this may be because a lot of teachers are constantly self-evaluating and thinking about how to improve instruction. Most teachers that are on the introverted side are still very good at maintaining positive relationships with their students. 

                 I believe that my need for facts and to think analytically are tailored to teaching mathematics. A lot of math requires students to use certain formulas and there is only one way to come up with a conclusion to a problem. There is still some creativity in math (proofs), but it mostly requires logical thinking. I understand that a lot of the greatest minds of all time, were creative people who were able to think about problems that in a way that no one had previously. Even though I like facts, I understand how important it is to foster creativity in the classroom. Lastly, I think that classrooms need to have structure. Students can't have free reign over the classroom and need to learn organization and time management in middle school and high school.

                I am hesitant to take personality tests like this too seriously. If I took this class five years ago, I would score much more towards introverted. I used to require structure, but I am starting to like a little more spontaneity in my life. As I grow older, I have tried to become a much more well-rounded person. I have worked on becoming more extroverted, creative, and spontaneous. It is something that I work on every day. For the most part I look at these results as an improvement from what I was, and look for places I can continue to improve. I think that I will always be fact driven, but I understand there are times that being instinctive can be very valuable. 

About Me

Hey everyone,

            My name is Dylan Gavin and this is my seventh class at National University. I am in the process of getting my Single Subject Teaching Credential and am in the Master’s track as well. I graduated college from the University of Oregon in 2012. I played baseball there and was confident that professional baseball would be my next step after graduation. Because I was so passionate about baseball, I didn't put a lot of thought into what I wanted to do after college (besides baseball). I ended up getting a degree in economics with a minor in business administration.

When the dream of playing professionally ended, I decided to get away from the game of baseball and entered the business world. I felt confident that I could do any profession if the money was right. However, after three long months of cold calling I found out that this simply wasn't true. I decided to return to running the summer camps that I loved and took some time to think about what I really wanted to do. After the summer, I took a part time job and decided to work as an assistant baseball coach at Cabrillo College.

Coaching baseball at Cabrillo College was one of the best decisions I've ever made. It taught me how to enjoy the game of baseball again and reminded me of how much I enjoyed working with adolescents. Coaching baseball led me to wanting to become a teacher. I think that the two professions are extremely similar and can see why many people end up doing both. I started the baseball team’s study hall and ran it twice a week throughout the year. I also started  the Santa Cruz Baseball Academy which ran twice a week as well.

From the variety of ages that I have worked with at baseball camps, I decided that I want to teach high school students. I am in the process of becoming a math teacher. I think that math can be directly applicable to student’s lives and I can’t wait to start teaching students. I am picking up a lot of really effective teaching strategies and am excited to start using them in the classroom. I have already started incorporating many of the strategies I have learned from this program on the baseball field. 

This fall I am about to start substitute teaching. I am very excited to begin, and look forward to an adventure packed fall. The Cabrillo baseball team started this week and we are looking strong to win back-to-back conference championships. I should be able to start student teaching this spring and can’t wait for it all to get under way.  

            Well that was all about me for now. I look forward to learning about everyone else!

Best wishes,

Dylan Gavin