Last Day of Student Teaching!

Cant believe this semester has come to an end. Seems like I just started my student teaching and now I am saying goodbye to my great cooperating teacher and all of my students.

Makes me really look forward to having my own classroom and teaching in August!

Week Fourteen Prompt (4/18 - 4/22)

Week 14 Prompt
Question 1: What strengths, skills, and characteristics do you have that make you a good secondary mathematics teacher?

Question 2: What aspects of teaching mathematics to secondary students still pose a challenge to you?

1. I believe I have several skills that make me a good secondary mathematics teacher. I believe every effective secondary mathematics teacher needs to have a strong base of content knowledge, but also be able to effectively communicate this knowledge. I think I possess this skill because of the feedback I have received from students, teachers, and colleagues. Without the ability to communicate the strong content knowledge, students would not be able to benefit from your content knowledge.
Another skill I believe I possess which makes me an effective secondary mathematics teacher is the ability to keep students engaged throughout the lesson. I am able to use my creativeness and content knowledge to create learning activities and opportunities for my students. These opportunities keep students actively engaged in the new material. These lessons help student build an interest in the concepts being taught.

2. A challenge I possess while teaching students in a secondary classroom setting is pacing. I find it difficult to find the correct pacing to move through the material. Some students require a fast pace through new material and others in the same classroom require you to move through material at a much slower pace. The difficult task is to find a pace that will accommodate both types of students. I feel with more experience teaching this process will come a lot easier to me, but right now I continue to have to make changes to my pacing to help students.

Week Thirteen Prompt (4/11 - 4/15)

Question: What role do you think homework plays in learning mathematics? What type of homework policies and procedures will you put in place in your classroom? How will you grade homework and how will you use homework grades?

Homework is an assessment in a mathematics classroom. It assesses the students understanding of the topics and concepts being taught. The homework gives the students and the teacher feedback on what the class struggled with, what may need to be re-taught, and what things students should refocus on. I use the students feedback on their homework and their homework scores as an evaluation of my teaching. If the homework’s skill level is appropriate and students do well on it, I know I can move forward with new topics or challenge them with more applied problems. However, if the students struggled with homework that should have been relatively easy, I know I need to re-teach the material and find where the class is struggling the most.
During student teaching my cooperating teacher has a set homework policy. For homework from the textbook, I walk around the classroom checking each student’s progress on the homework and scoring them a 1 through 5 (5 being scored for a complete homework assignment, and a 0 for nothing at all). I am not a big fan of this strategy because I have noticed several students writing in random answers, or simply copying down work from other students as I walk around the classroom checking on their peers.
I like a homework policy my high school calculus teacher used when I was in her class. She assigned the homework the day before, and the next day she would have students write question problems on the white board. The rest of the class would then try to answer the problems on the board, and if they couldn’t then my teacher would walk through the process of solving each problem. If a student was able to answer the question, she would have the student explain the process or would explain the student’s process depending on what she had planned for the rest of the period. Once all questions were answered, my teacher would pull a bag out with five marbles in it. Three of the marbles were green and two were yellow. A student would pick a marble out of the bag and if they pulled a yellow marble everyone would pass the homework in and she would grade it for correctness. If a student pulled a green marble, they would put their homework in their folder and my teacher would continue with the day’s lesson.
This policy forces students to ask questions on their homework, and complete it for correctness in case they are asked to turn their homework in for points. It also helps the students explain their mathematical knowledge to others. I believe I would use this policy in my future classrooms and grade their homework assignments on correctness. Because different classes will be turning in different amounts of homework, I would make homework 10-15% of their final grade.

16 Days Left...

With the end of student teaching rapidly approaching, I began my final chapter I will be teaching in my Geometry classes. This chapter is centered on polyhedrons, or three dimensional shapes. In this chapter we will focus on surface area and volumes of different polyhedrons and how to arrive at the several different formulas. I have found that many of my students have trouble forming the three dimensional objects in their mind or drawing them on their paper. I have been gifted with the ability to be able to draw many of the objects with ease, mostly because of my mom who is an art teacher at a local elementary school in our town. I have grown up drawing and increasing my drawing ability with the help of my mom.

This chapter presents a unique opportunity to incorporate my drawing ability and also technology to help students be able to visually see what these objects look like. I have been able to use a free program called Google SketchUp. Google SketchUp allows me to draw three-dimensional solids and rotate, zoom-in, zoom-out, create a cross section, label, measure, and manipulate three-dimensional objects. This helps students become engaged in the lesson and gives them an opportunity to see a model of the polyhedron. Google SketchUp offers a vast number of different tools that I have found useful to use during this chapter.

Test Scores - Reflection/Goals

Yesterday I finished grading my recent test over Chapter 10. I was pleased on how the majority of the students did on their tests. It seemed like the students either really understood the material, or struggled with the material taught during this chapter. I wanted to see why this was happening and how I could help those students who needed the extra effort.

Today I started the classes off by talking to the students to see what they thought about the test. I explained to them there seemed to be no middle ground on the grades, and I could tell who really understood the material and who struggled with it. I reminded them that I am always available before, during, and after school. As a class we talked about what they struggled with and how I could help them. I did not receive very much verbal feedback from the students, so I decided to change their Bell Work. I made a prompt for them to respond to and turn in to me once they finished.

"What can Mr. Wolfe do differently to help you understand the material for effectively?"

Here are some of the responses I received:

"I would like if you gave us more guided notes. It helps me follow along better."
"Can we review more for the test the day before?"
"Can you do more examples of the new stuff we learn?"
"I want more activities and projects on the stuff we learn. It helps me see how to use the things we learn in class."

I responded to the students individually and I took their feedback seriously. This chapter I will be trying to incorporate more of the suggestions they gave me in my lessons.

Long Needed Update

Spring break has come and gone, and I am now nearing the end of my student teaching experience. After tomorrow ends, I will have 4.5 weeks left of student teaching at Muncie Central High School. My Learning Assessment Model Project is finished and submitted to Ball State. My next focus goes to my online portfolio where I will upload different artifacts that pertain to the INTASC principles. I have also began the long process of applying for jobs at different school districts. This has been a very exciting part of college and I cannot wait to see where I end up and what I will be teaching.

The first nine weeks have also come and gone in the second semester. I got to experience the hectic times of students trying to boost their grade and turn in mass amounts of late work right before I submit their final grades. I have learned how to be stern with them and stick to the rules that Jane (cooperating teacher) and I have set forth. It can be hard to stick to these because your tendency is to help them, but you must stick to the guidelines.

This has been a very rewarding experience for me as a student and future educator. I have enjoyed my time so far and have learned a lot about my students, teaching, and me. I cannot wait to see how the last section of student teaching shapes up. This experience really makes me look forward to the future when I have my own classroom.

Week Nine Prompt (3/7 - 3/11)

• Describe one “teaching moment” from the past few weeks about which you are proud. In particular, think of a time in which you designed a task or an activity, gave an explanation, asked a question, or answered a student’s question with an example or explanation that really helped the student(s) to make sense of mathematics or to understand a mathematical idea more deeply. This “teaching moment” could have occurred when working with an individual, a small group, or the whole class. How did you know that your actions resulted in student learning?

• Describe one “teaching moment” from the past few weeks in which you felt particularly challenged. What mathematical idea/concept/procedure were you trying to help students understand? What was so difficult about helping them learn it? What obstacles were you encountering? Now that you have had time to think about the situation, what would you do differently the next time if you were in the same situation again?



This week I was teaching an introduction to area of a kite, rhombus, and a trapezoid. I found an activity that would guide the students to find the formulas for figuring the area of each of these shapes by having them cut out one of these shapes and rearrange it into a rectangle or parallelogram. If they did it correctly the base and height of the newly formed rectangle would help them arrive at the formulas because the diagonals, height, and bases were labeled before they cut apart their original shapes. I showed them how to do the first one and let them work together to figure out the other two.
It was great to see how the students worked together to find the formula. I heard several students saying they could understand where the formulas came from. This is why I wanted them to do his activity. They were able to see why the formulas were what they are and how they are formed. It was great to see students excited to “find” the formula. They were able to understand why the formula was what it is, and this gave them an idea of how other formulas might have been formed. One of my students actually used this procedure to show me how he would find the formula to find the area of a regular polygon, and he was correct!
One teaching moment that I was challenged by was when we were learning about the are of a regular polygon. I was trying to help them with the formula, which involved being able to tell the difference between a radius and a apothem (and know what an apothem is). This was a huge struggle because they were not paying attention and putting any effort towards the lesson. I tried to find an engaging activity to do with the students but I was unable to come up with one. This might have been the reason why some of them struggled with it as well. Unlike the lesson with the rhombuses, kites, and trapezoids, they were taking notes and completing examples with me.
Even though I gave them time to ask questions, nobody asked any. I had to change my daily plan and add a day where we worked on this section again. Another reason they might have struggled is because they needed to use trigonometry as well. Even though a majority of my bell work consisted of trigonometry, some students still struggle with this. If I would have done this lesson differently, I would have created an engaging activity, much like the one I used with the trapezoids, rhombuses, and kites. This would help the students see where the formula comes from. I would have also given them more examples to work with, and possibly given a sheet of examples for group work. This would have been something that would benefit their learning.

Week Eight Goals (2/21 - 3/4)

Week Eight Goals:

1. I need to be more strict when it comes to classroom management.
I have one class that is a little too social during work time and during my instruction. I have cut back on the time that I give them to work on their assignment, and I have also implemented Bell Problems. I need to become more strict when dealing with the source of the problem because it is effecting the other students in the class who are trying to work.

2. I want to find time to go to extra curricular activities that my students are in.
I have had several students tell me they are involved in track and field, the school play, and other sports and clubs. I want to go to several of these events to connect with students. This will help me know their interests and what they do on their free time. I think the students will appreciate me taking time out of my schedule to see them perform or compete.

Week Eight Prompt (2/21 - 3/4)

Week Eight Prompt:


Think about what you are learning from examining and grading students’ written work. (This written work can be homework assignments, quizzes, tests, or anything else in writing that students produce, such as a short response to a question you pose at the end of class.) Specifically,

• Identify and discuss (briefly) three things you are learning about students’ mathematical understanding from examining and grading their written work.

• Identify and discuss (briefly) three things you are learning about students’ beliefs and/or attitudes about mathematics and/or learning from examining and grading their written work.

• How has your planning and teaching been impacting by what you have learned from examining and grading students’ written work?


After grading my students’ homework, I have noticed several things about their understanding of mathematics. I am able to see what level of understanding they are at. I am able to see this by looking at their mistakes they are making on their work. I still have several students who are constantly making simple multiplication, division, and sign errors when multiplying positive and negatives. This has helped me to target these students who need the extra help an attention. I am also able to see the students’ thought process as they work through problems. I can see where they are making mistakes, where my instruction might need to focus more on, and how effect my instruction is. I use the graded material as feedback for my instruction. I find it very helpful to see how I can improve my instruction based on how the students are doing, and what I need to focus on during the next lesson.
I have found a lot about students attitudes towards mathematics by grading their homework and quizzes. Students tend to take the easy way out and don’t put forth as much effort as they can. I have noticed students do not complete their homework because they would have to do it at home and they do not want to. They will stop at problems that require them to apply their understanding in a different way (word problems, problems that require student to apply previous knowledge from different chapters to solve, etc.) The majority of the students want the easiest way out, and their work reflects that.
Like previously stated before, I try to use graded work and tests to evaluate how I am doing as a teacher. I will try to find common mistakes that students made and go back over my lessons to see if I covered them fully. This is something that I think will help me become a more effective teacher. Another way the graded work will impacts my planning is that it changes the types of bell work I do. I want to help them build the skills that they struggled with, so by looking at concepts they struggled with I can create bell work that focuses on these skills. This will help the students strengthen these skills that they may be weak on, and will help them recall the information to build upon.

Week Seven Prompt (2/28 - 3/4)

Week 7
Think about the questions students ask you about the mathematical concepts and procedures that they are studying in the classes that you teach. Also, think about how you respond to these questions.

Give some examples of questions that students ask you about mathematical concepts and procedures. How do you respond to their questions? What do you learn from their questions? What have you learned from responding to their questions?


I try to welcome student questions as many times as possible during my lessons. I don’t want to have students fall behind because they are confused and didn’t have the opportunity to ask. When I am teaching I do not feel students take advantage of the time I give them to ask questions. There are a few students I can count on to ask questions that others may have. When they ask these questions, it is typically for me to clear up something I said or for me to explain a procedure I carried out, or for me to check their work (this seems to be the most popular question) “Did I do this correct? Is this answer right?”. There are a few students in all the classes that have asked a question about linking concepts together. More questions are asked individually rather than as a class. The comfort level of one on one interaction probably plays into this.
When students ask me to check their work, I try to have them explain to me what they did to get that answer instead of me just simply seeing if they have the right answer. I want them to be able to explain how they arrived at the answer and the process they took to get it. This gives me an opportunity to assess their understanding, and answer their questions as well.
With more advanced questions, I try to help them answer their own question rather than just simply give them what they are looking for. I want them to learn from their questions instead of me telling them the correct answer. This will help them learn and work at a deeper level. I lead them to the correct answers.
Responding to their questions has taught me what students struggle with during lessons. I can focus on things that I know they will struggle with while I teach them. I have also learned after I answer their question, to ask if they understand what I just said. I have had several times where I will answer their question and then move on to someone else, and I notice they still have a confused look on their face. By asking if they understand gives them a chance to ask a follow up question or for clarification.
Once I answer a question, especially on a homework problem, I like to observe them work through their problem they are working on to see if they are understanding what I helped them with. This gives me an opportunity to check their understanding and level of ability on the new material.

Teacher Thoughts

As a teacher I am finding more value for the little things in life such as:

-Paper Clips
-Post-It Notes (Sticky Notes)
-Working Dry Erase Markers/Overhead Markers
-An abnormally strong Immune system
-Hand Sanitizer
-Kleenex
-Patience
-Extra pencils and paper for those students who somehow forgot theirs
-The "ah ha" moment from a student who was struggling with a concept but now understands it
-A "thank you" from that student
-Presidents Day, Snow/Ice Days, Two-Hour Delays, etc

Its the little things in a teacher's life....

Week Six Goals (2/14 - 2/18)

Week Six Goals:

1. I want to get more of my students involved with my lessons.
There are students in each of my classes that will sit there during my lessons and not participate, even when I try to get them involved. I need to find a way to have them involved in their learning process. With the chapter that I am teaching now, I think there are several engaging activities that I can use to help the students become involved in the lesson. The activities will allow students to actually see and experience the math concepts being taught.

2. I need to have the students work until the end of the class.
Recently one of my classes has gotten the idea that they can stop working 5 minutes before the end of the class and socialize with each other. This has led to several discipline issues that I am having to face. This week I want to become a little more strict with students during the end of the class. This has only become a problem in one of my Geometry classes. I think if I am able to keep them busy until the bell rings, the problems that arose should not be an issue anymore.

Week Six Prompt (2/14 - 2/18)

Week 6 Prompt

Think about the discourse occurring in the classes that you are teaching. (One way to think about discourse is the dialogue that occurs in the classroom.) In particular, think about the questions that you are asking students and about their responses.


On Friday I started a new chapter. This new chapter is over Transformations, which is almost completely different from our previous chapter on Trigonometry. The first lesson I taught was over Translations and how to carry them out on a coordinate plane. A question I asked during each of the three classes I taught this lesson was “How can you apply a translation in a real life situation?”
This question allowed me to see if my students understand what a translation is. A student used an example of a teacher moving where two students sit in the room. The teacher wants to keep them together so he must move them the same number of desks. This response really surprised me because I did not think about using the desks as a coordinate plane. I thought this was a great way to apply a translation to a real life situation, so I used it as an example in my last class as well.
A majority of my questions are to assess my students’ understanding of the concepts and topics I just taught. I use the questions to see if I am moving to fast through new material, need to go back and clear up misconceptions, or have students apply the new knowledge in a different and more challenging way.
I have realized how hard it is to get students to give you feedback, so whenever I do get a student to share their opinion or ask a question I try to thank them. I am hoping that this will give other students more confidence when asking or answering a question. Student responses are typically not very in depth and are mostly asking for clarification. When they answer my questions, they can sometimes surprise me at how fast they grasped the new knowledge or the level of understanding they are at.

Week Five Goals (2/7 - 2/11)

Week Five Goals:

1. I need to become more strict with students and when they turn in homework and other assignments.
I have been very lenient with students turning in their assignments late. I want to give them credit for their effort, but I feel like I have been cutting them too many breaks when it comes to late assignments. I have now completely taken over the three Geometry classes and I make all the decisions with the students. My cooperating teacher is usually more strict when it comes to late work, and I feel she is very fair when it comes to this topic. I want to start to place stricter limits on due dates. This will help me control the classroom more effectively.

2. I want to find a way to help motivate those students who are doing poorly on the tests because they do not care, and not because they do not understand the material.
There are several students who are in my Geometry classes who seem to be strong mathematics students but are doing poorly on the quizzes and tests. I have talked to them multiple times about what they need help on, but they say they are understanding it. I need to find a way to reach them and help them understand the material. If I can find a way to motivate them to learn I feel they will do a lot better in the class and grasp the concepts being taught.

Week Five Prompt (2/7 - 2/11)

Week 5 Prompt:
Describe and discuss one mathematical error you have seen students make or one mathematical misconception that they hold that surprised you. How did you help students correct this error or misconception?

Describe and discuss one important mathematical connection that you have seen students make. What factors contributed to students’ success in making this connection?




One error I have seen a number of times in the Algebra class deals with students trying to add and subtract positive and negative numbers. They struggle when they are faced with adding or subtracting a positive and a negative number, adding two negative numbers, and subtracting two negative numbers. They could not understand how or why the answer would be positive or negative. I talked to several of the students individually during their work time and used the concept of money and debt to help them with this. If they were adding a negative number and a positive number (like -10 + 4) I would say, “having negative $10, is like being in debt or owing to me $10 dollars. Then if you pay me $4 your debt is going to be smaller and it would be -$6.” Putting this in terms of money seemed to really help these students grasp the concept.
Another way I tried to help them drawing a number line so they could visually see why the answer would be positive or negative. This really helped for one of the students I work with. She was able to get a better understanding with the concept of adding and subtracting positive and negative numbers.

There was one student in the same class that really surprised me on her connection with the two-step equations they were solving and the relations between dividing a number across the equation. My cooperating teacher and myself have been teaching them a certain way to solve these equations. If you were given an equation 12 = 2x + 4, and asked to solve for x, we taught them to subtract 4 from both sides and then divide by 2. While working with these a student asked me if you could divide by 2 first like she did on her paper. Before looking at her work I began to explain that if you do that you need to divide the 4 on the left side too. She showed me her paper and said she did. I apologized and told her that was correct.
This surprised me because we did not teach this concept. She saw the answer would be affected if she did not divide the 4 as well. That was really interesting to me because she was able to form that by herself. She was able to recognize this because she worked out the problem without dividing the 4 and realized that the answer she arrived at was too big and did not make sense. It was great to see a student look at her answer and see if it made sense for the problem she was working with.

Gotta be FLEXIBLE

Tuesday, February 8th

Today was supposed to be the day I taught an introduction to trigonometry to my three geometry classes. However, when I was going over the homework with the classes from the previous two lessons, which were over The Pythagorean Theorem and Special Right Triangles, I noticed a majority of the class was still struggling on the material. I wanted to keep moving on to the new concepts, but without a solid grasp of the older concepts I felt that moving on would end disastrously. After making a decision I decided to go over several of the problems on the worksheet and then give the rest of the shortened class time to the students to work on their homework that was suppose to be due today.

I am now learning that a teacher needs to be flexible with their daily and weekly plans, have confidence in their decisions, and have plenty of erasers to change the lesson plan book.

Snow Day??

For the first time in my life, I think I am hoping we do NOT have a snow day. In the four weeks of student teaching I have began to realize how much planning goes into teaching. Teachers have to think about what topics to cover, how long to spend on each topic, assessments, making copies of worksheets, and assess student learning just to name a few.

It is interesting to see and experience the other side of teaching. I have got to learn to be a little more flexible. Maybe I need some practice on being flexible. Changing my mind.... bring on the snow/ice!

Week Three Goals (1/24 - 1/28)

Week Three Goals:

1. When teaching during class, I want to keep the students involved in the lesson.
On Friday when I was teaching, I noticed several students seemed lost when we were going through examples. If I were to have students walk me through what I should do to solve an example, this will help students stay focused and involved in the lesson. I can find students who seem to be struggling with the concepts being taught and have them explain their questions to the class, answer their peers questions, or even come to the front of the class and work out an example with help from the class. This will help me assess the students, and help keep the students involved in the learning process.

2. During teaching, I want to carefully pace myself so students do not fall behind.
During the lesson on Friday, I felt like I was moving too fast through the new material. I was going at a pace that was comfortable for me, but as new material it could have been a little overwhelming. Next time I want to move through the material at a slower pace and continuously check with the class if I need to slow down or if I can move onto the next concept.

Week Three Prompt (1/24 - 1/28)

Week Three Prompt:
Think about the lessons that you are teaching or observing this week. Usually the primary way teachers describe lessons is by their content topic, which is easily tied to a content standard (or maybe two content standards if the lesson merges algebra and geometry, for instance.) But there are (hopefully) process standards that are also being addressed, even though they might not be explicit in a lesson’s description. Obviously not all process standards need to be incorporated in all lessons, but over time students should experience aspects of these process standards in the mathematics classroom.

Describe/discuss ways that the five NCTM process standards are being addressed (or not addressed, if that is the case) in the lessons you teach or observe.

On Friday I took over all three Geometry classes at the beginning of the new chapter. The lesson I taught on Monday focused on The Pythagorean Theorem, how to find missing sides of a right triangle, and classifying triangles using the properties of The Pythagorean Theorem.
Problem Solving:
The problem solving process standard is being used when the students and myself work through word problems involving the Pythagorean Theorem together and individually. These students have to apply what they know about the Pythagorean Theorem to a real life situation to arrive at the correct answer. Students are challenged with several different types of problems so they can use their problem solving skills to solve the problem.
Communication:
There is plenty of communication during these lessons. While I teach these lessons I try to get the students involved with the learning process. After teaching the necessary concepts, I have students verbalize the steps they took on different examples I give them. This helps them communicate mathematics between themselves, the rest of the class, and me. It helps them gain a better understanding on the new concepts.
Connections:
This particular lesson has a lot of connections to the previous chapter. The previous chapter dealt with similar triangles and proportions between sides. The next couple sections have students learn about special right triangles (45°-45°-90° and 30°-60°-90°) and the ratios between their sides. This also leads into right triangle trigonometry where students will use their knowledge of proportions between sides to help find angles and missing side lengths. There are a lot of connections between the topics the students have already learned, and what they will be learning in the near future.
Reasoning and Proof:
The way the book teaches the Pythagorean Theorem seems to leave out why it works. There are no proofs offered on the Pythagorean Theorem and students are not required to know why it works, but only required to know how to use it and apply it in different situations. I would love to have the students explore the many different proofs, but because of time restraints placed on the class I have to pick and choose what they are spending their time on.
Representations:
In this chapter, students have the ability to see multiple representations of how to use the Pythagorean Theorem. They have been able to use real life situations and multiple representations of different problems. I can still try to present them with different representations throughout my lessons. This will deepen their understanding of the concepts being taught.

Week Two Goals (1/17 - 1/21)

Week One Goals:

1. I want to make sure I talk to the entire classroom, and not favor one side over the other.
On Friday, I was going over the homework with the entire class. During this time I was answering questions students had about several of the problems. A majority of the questions came from students sitting on the right side of the room, so when I began to answer their question and go over the solution, I found myself directing my response to that side of the classroom. I need to make sure I talk to the entire class because there is a good chance someone else had the same question. I must make sure to reach those students who do not like asking questions in the class, but benefit from others asking.

2. I want to go to more extracurricular activities.
I went to a Central vs Southside basketball game on Friday and I a number of my students in attendance. By showing them I am interested in what they do outside of my mathematics classroom, I can begin to make connections with students. This will help me motivate students and gain their respect as a teacher. Going to extracurricular activities (not just sporting events) will also help me see some of my students interests, which will also help me make connections. This will also give me another chance to practice recalling their names.

Week Two Prompt (1/17 - 1/21)

Week 2:
Think about the mathematical content being taught this week in the classes you are observing and/or teaching. Choose the content topic from ONE of these classes and make a list of all the prior knowledge and skills that students need in order to understand both the conceptual and procedural aspects of this content topic. How does the classroom teacher (or how do you) assess the prior knowledge that students bring with them to this new topic? How critical is this prior knowledge/skills to understanding the new content topic? Describe the quality and/or quantity of the necessary prior knowledge that these students seem to have for this topic.

Currently we are working with our geometry classes with the topic of the similar triangles formed when creating an altitude from a right angle to the hypotenuse in a large right triangle. The two smaller right triangles that are formed are similar to the original right triangle. Some of the prior knowledge students need to have to understand this topic is as follows:
-Properties of triangles
-Hypotenuse
-Legs
-Sum of interior angles
-Altitude and what it forms
-Proportions
-Similarity
-Proof why each triangle is similar to one another
-How to multiply radicals
-Square roots

Looking at the prior knowledge the students need, I feel a lot of these topics were covered in the previous lessons. Because this happens, the teacher can assess the students in previous lessons by looking at their homework, quizzes, or asking the students questions. I go over homework every day with the geometry classes. During this time I am able to tell which students understand the concepts, and which students will need more help. I do this by looking at which questions on the homework they did not understand. This will show me what level they are at in their understanding. If my cooperating teacher or myself does not feel the class is ready to move on, based on their homework or questions, we can design learning activities for the students to strengthen these skills. It would make no sense to move onto more complex concepts when the foundation concepts are weak in the students.
For this particular topic, without knowing the prior knowledge the new concepts would be almost impossible to understand. The prior knowledge sets up the new concepts and allows the students to build upon their older concepts. Without the prior knowledge, students would have nothing to build upon. I still find myself explaining to students where the hypotenuse is and how to set up the proportions between the sides of the similar triangles. Other students pick up on the new material quickly because they thoroughly understand what was being taught in previous lessons. A majority of the students fall in between the two extremes. They need reminders every so often on how to start or which sides are being compared in the ratio. I find this rather typical of a high school mathematics class.

Week One Goals (1/10 - 1/14)

Week One Goals:

1. I want to slow myself when I am speaking.
I feel when I am in front of the classroom teaching or giving directions, I am talking faster than normal. This might be because I am not as comfortable in front of all the new students. But I want to focus on slowing my speech so the students will be able to understand what I am saying more clearly.

2. I want to see the student names when I am talking to them.
I have gotten to know a majority of my students' names in all four classes, although I feel I do not use them when I am talking to the students. By using their names I hope to convey a message of comfort. This will help me later on in the semester when I am teaching full time. I want to carry this goal both in the classroom and out in the halls or at extra curricular events.

Week One Prompt (1/10 - 1/14)

Week 1 Prompt:
Describe the environment and/or atmosphere in the classroom where you are student teaching, as you observe and experience it this first week. Consider both tangible aspects of the classroom (such as what is present in and the use of the physical space, the materials/resources available for teaching mathematics) and intangible aspects (such as attitudes and behaviors of students toward mathematics and toward learning in general). You might note whether the environment/ atmosphere seems common across all classes or if it differs and why. Are there any aspects of the classroom environment/atmosphere that you would like to change when you teach?

The room that I teach in for student teaching seems like a typical high school classroom. There is a dry erase board in the front and the back of the room. And there is also a hanging projection screen that is used with the old overhead projector. I heard rumors that there will be a projector you can hook up to the computer installed in our rooms. This classroom also has a bookcase full of math books, which gives Jane Miller and myself multiple resources we can use while teaching. There are a lot of student projects that are hanging up in the classroom as well as math posters.
There are five classes that I will be teaching this semester: Probability and Stats (I will not be teaching a whole lot in this class), three geometry classes, and an algebra class. After the first week of student teaching I have noticed a lot about the students in each of the classes. My three geometry classes and the probability and stats class are almost polar opposites of each other.
In the algebra class there are 17 kids on the class roster. This last Friday we have seven kids in class because of suspensions, ISS, and the decision not to show up for class. Tardiness to class has been and will be a huge problem for these students as well. When they are suppose to be working on worksheets or taking notes, a majority of the class either has their heads down or they are doodling on their paper. On Tuesday we will be trying to do an activity with them to try and spark an interest instead of having them take notes. Every student in this class has taken and failed or got kicked out of another algebra class previously.
There are students in the class that understand the material and try to complete their homework and know the material well enough to try and teach others. This happened on Friday and it really surprised me that it occurred. I let them go about it and sat back and listened. It made me happy to see that they understand the material. There are times where I can see that they understand it, but they have no motivation to do any work or try. I have tried several times but I am still unsure how to handle this.
This class tends to be a management problem when Jane is teaching. Sometimes I am kind of shocked at how strict she has to be during this class. I feel this is a catch-22 situation. To try and control them you need to be strict, which leads to students getting angry and not wanting to work. Having angry students will lead to having to be strict when they act out (I’ve observed multiple times that they tend to do that when they are angry). If you are not strict with them, I would feel like they would take advantage of that. This might be something I could try while teaching, but I am kind of nervous to do this.
The other four classes are completely opposite. There have been no behavioral problems yet and they seem to have the motivation to try during class. For the most part homework gets done and minimal students will sleep through notes. I find it very interesting to compare these classes with the algebra class. I know that most of the kids in the algebra class do come from rough backgrounds, and I wonder how they compare to the kids in these four classes.
There are several things that I want to try to change when I fully take over. The use of technology in the classroom is minimal. I think this might be because of the limitations of the available technology. Incorporating technology could be beneficial to students in all of my classes. Another thing that I would like to try and change is the format of the lessons. Jane and the rest of the math department have a set way of giving notes and then after notes the students work on their assignment. This gives the chance for the teacher to assess the students’ understanding after the notes. I like how she has it set up, but I think I might want to try another way of teaching them. I am still unsure what I could do, but I think I will be looking into it during the next couple weeks.