When it comes to team collaboration at my school I think our math team is at the "norming" stage of team development. We meet every Friday morning to discuss what we are doing that is working and we also talk about what isn't working for specific students. We then share our own strategies for those students or even strategies we use for our students that may work for other students. This has become a normal thing and everyone on our team is comfortable with sharing how things are going in their classes. I would not put our team at the performing stage yet because we do not really have clear goals to achieve for each of these meetings. This is partly my fault as I am supposed to be the main team leader for these meetings as I am the head of the math department but I am still trying to grasp the culture and the styles of teaching that my peers are bringing to the table and I'm not entirely sure what main goals we should set to achieve. I also am at a roadblock where all the other team members see these meetings more of a requirement for their job rather than a place where great things can come from. I believe at the start of the next semester I will have our team set goals for each of our classes and then we will report what we have done to reach these goals and what is setting us back. I think that would make these meetings more effective and it would move our team into the performing stage.
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Towards the beginning one of my major goals was to develop a classroom that allows for all students to be successful. While I believe I have done well at the social and emotional side of setting up a positive environment for my students, I still need to work on delivering information in a multitude of different ways to reach as many students as possible. Something that my students have given me constant feedback on is my lack of summarizations of units and the lack of strong review sessions for the end unit summative assessments. Before I was giving only one to two days of review along with a review packet or a practice test. This led to my upper students and upper-middle students performing just find on the summative assessments but my lower-middle and lower students started to really struggle. As we move closer to finals week, our school does a week of finals where students only go to a few of their classes a day and those class periods are extended, I decided to take the next full week for a summarization of all the units we have gone over by creating formative assessment games via kahoots, creating review packets for each unit, and creating practice tests for each unit that we will complete the week before finals. Depending on how this plays out I think it would be better for my practice and for my students if I take more time to do summative reviews of each unit before jumping straight into the assessments. While this may take time from covering more material I think it will be beneficial in solidifying the knowledge of the material the students gain from each unit. We shall see how this plays out in the following two weeks.
I've had a very interesting year as a first year teacher. I'm pretty sure if anyone were watching my class everyday they would describe me as a mad scientist. I'm also pretty sure that any other first year teacher who would see the drastic changes I've made to how I deliver information from just the start of the semester to now would think I'm utterly insane. Maybe I am but luckily my insane tactics have seen positive results. I've used data to drastically change how I deliver content to my students, particularly with my AP Calculus Class. Towards the beginning of the semester I probably had 2 B's 1 A and the rest of the grades in my class were D's. This probably went on for about half the semester before I did a complete 180 on how I went about teaching the class. Before I would have some direct instruction followed by a worksheet to have students practice mastering the material along with homework out of the book. All of my students homework grades and worksheets were great but when it came time to took the test it would look as if my students barley learned anything. This was strange because I would review my tests vs the worksheets that I was giving out and it would be the same content, I would just ask different questions or problems than the worksheets. Some questions were directly from the worksheets and I would just change the numbers and the variables that needed to be solved for and yet my students still couldn't seem to figure out what my assessments were asking them. I realized what was happening though. While my students worked on the worksheets and the homework they were mainly just doing it for a grade without retaining the information. I finally realized this when I started to really pay attention to the questions that students were asking me and how often they asked me questions on the worksheets. They would ask me a question on problem one and then ask me another question on problem 3. They also wouldn't stop asking questions until I gave them the secret step or asked them the question that led them to the answer. They were doing this because they just wanted to complete the worksheet to get the grade so that they were at least doing okay in the class. After about halfway through the semester I had a serious talk with my students as a class and basically told them what we are doing obviously is not working. So I let them vote on a new way we were going to run the class. Now I have direct instruction but instead of grading the worksheets and homework we voted to make it completely voluntary. What has replaced the homework grade is a pop quiz on each section after spending a few days of practice on it. Maybe it is not as drastic of a change as it sounds but when we first went down this road after they voted on it there was some seriously negative feedback from the students. They didn't realize what they voted for until it was in action because now they were not getting a grade for simply completing a worksheet, they had to show it on a pop quiz. Something happened though when I made this shift. My students actually spent more time working together or on their own on the homework and the worksheets without asking as many questions. They also took it on themselves to find really difficult problems out of the book to solve on their own without any grade simply just to practice the ideas. Since I've made this switch, I've seen drastic improvements in everyones grade and the students actually like the new method. At this point the grade distribution in my AP calc class looks more like a normal bell curve centered around the high C area rather than a lopsided chi distribution centered on the D area. This is why analyzing data for educators is a very complex and multidimensional problem. It is pretty easy to just look at what answers most students are missing and then to reteach those concepts but it is entirely something else to look for patterns across multiple data to try to find what the cause of the problem is. I think the hardest part for a teacher to realize is when the data is telling them that there is something wrong with how you are delivering information to students. Obviously if everyone does poorly on an assessment then your method of instruction was not received well, but understanding the "why" part is a very complex problem. It requires educators to really pay attention to what their students are doing and it requires educators to really know and understand how their students are absorbing the material.
Recently I was teaching my pre-algebra students how to build linear equations. An inquiry based method I implemented in this classroom was to have students roll balls down a ramp and time it in various trials and then build linear equations that represent the position of the ball with respect to time (of course moving particles are usually represented with polynomials but using the average velocity students can build linear equations from it). It did not go very smoothly. I grouped the students up and told them what they need to do in their groups and what data they need to collect. I then told them that using the data they collected they needed to build their linear equations. My pre-algebra students have a very difficult time with this. They went through the motions and performed their trials however they were not sure how to relate their data points to a linear equation. I tried to provide minimal guidance on this as I was trying to get them to explore the topic. This lead to no avail as my students were utterly lost on what to do. I believe this happened because they were not used to having to explore a topic in mathematics. They are used to being given a formula and working from there or reading a word problem and building an equation. They were not entirely sure how to build an equation from scratch from a set of data points. This was due to a lack of scaffolding on my part I believe. We did discuss and practice how to build equations from a table of points which is essentially what they had after gathering their data but there seemed to be something missing that the students couldn't make the jump from building a table themselves to then building their linear equations. Either way it did lead to a good discussion at the end on how to build equations from a series of data as towards the end I guided them through how to build their linear equations.
I find that it is virtually impossible to write a coherent literature review without an annotated bibliography. The purpose of an annotated bibliography is to keep track of your resources and to have a description of what each resource discusses so that you may look back on it when building your literature review. The literature review should be designed in a way that separates the various sources of informations into themes. There are other methods to structure a literature review of thematically is my personal preference. Having an annotated bibliography allows you to see the similarities between resources and will allow you to quickly be able to categorize them into similar themes. I believe building an annotated bibliography first streamlines writing the literature review. It is important to note that annotated bibliographies and literature reviews are not the same. An annotated bibliography is simply a description of each of the resources. A literature review is an analysis of all the resources to see where further studies can be conducted. This is why I believe they complement each other well but alone there will be missing information. I am personally using an annotated bibliography to organize the sources for writing my literature review.
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December 2019
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