Oops...

I realized I totally neglected this blog throughout my first year of teaching! I really wish had I reflected more in here, but that just didn't happen. I'm really in the mood to start a personal blog right now, so hopefully that desire and interest will carry over into the start of the school year so that I can continue this blog about my teaching.

It's been QUITE a while...

Well, once student teaching got in to full swing, it was VERY hard to keep this updated. I've had so much lesson planning, worksheet making, and sleep to catch up on! I have been taking notes in my notebook, though, during student teaching, so this weekend or whenever I get free time I plan to get back on here and do some updates. Of course, they will say the date of the day I post, but I will make sure to include the date that the event I'm talking about happened.

I can't believe I've slacked so much on this! I love to write things down so that I can remember them, but I just have not had time to do this over mandatory things I have to turn in. At least this blog will be up-to-date soon!

The one day of school this week...

Due to snow, Montgomery County has only been open one day this week (in fact, they cancelled school for today around 5 p.m. yesterday before the snow even started!). I did get to go to school yesterday on a two-hour delay. I learned that teachers only get a one-hour delay, so that was something new to me. Anyway, here are a few observations.

Scheduling

Krista and I were talking on the ride home, and we agreed that the two-hour delay schedule is PERFECT for our school. The classes were an hour long each, and the students were actually busy the whole time. Normally, in the 90-minute classes, the last twenty or thirty minutes are just a complete waste of time as either the students finish their work fast and nothing else is planned, or the students have just checked out for the day. But, on the schedule yesterday, the teachers had enough planned and the students were on task the whole time. I wish every day was scheduled like that!

Distractions

I've noticed that particular students will just keep asking me questions to keep from doing work. I do my best to not answer their questions and encourage them to do work, but it's kind of hard when that's all they're doing. I think one way to avoid this would have been for me to take five minutes at the beginning of class to introduce myself and for them to ask me (appropriate) questions then if they wanted. My CT didn't do this, though, and I think I'm just more of a distraction in class because of it. Hopefully this trend will die down, especially when I'm teaching!

Intro to Sec. Math Class

On Thursday, the Intro. to Secondary Math class had a worksheet about subtracting whole numbers to complete. The front side involved no "borrowing," and the back side was all "borrowing" problems. I worked with one student on this worksheet who had problems doing 8-7 without counting on his fingers. I suggested that he draw 8 objects and take away 7 of them (there were no counters of any kind in her classroom...). It seemed to work with him, and he used that method when he needed to throughout the front side. When we got to the back of the worksheet, I showed him the "borrowing" method with base-ten block drawings (again, no base-ten blocks in the classroom). I had him model the first number of the subtraction problem, try to take away the number of ones in the second number, realize he couldn't, trade one ten for ten ones, and then complete the problem from there. He said that method helped him to see it better, and I told him I would actually bring some base-ten blocks in for us to work with the next day they have school (whenever that may be). I felt pretty proud of myself because I actually used something I learned in a class (Elem. and Middle Math) to help a student! I think this class will be a great outlet for those activities, as a lot of the topics they will be covering are actually the same topics we talked about in that class. Should be a fun time, and I can't wait to get started with that class!

Snow day problems

The problem with missing three days of school in a row (especially a Monday-Wednesday) is that students do not remember what happened on Friday. In the Algebra I, Part 2 classes on Friday, the students reviewed for a quiz they would have coming up on slope-intercept form and writing equations of lines. When they came back on Thursday, they started to finish their review sheet, and my CT pretty much had to reteach the entire thing. She told them they would have a quiz on the material the next day they had school, but I really doubt the students will remember anything, let alone study, for this quiz. As cool as it is to get off of school for a day, it really hurts the learning process and makes planning difficult as well.

Snow Days

One of the benefits of teaching is snow days! But, when you are a student teacher, snow days are not too great. My first day at Eastern Montgomery High School was on Friday but have not been back since due to the 10+ inches of snow we got this weekend. While one or two days off is nice, I need to get back in to the schools! Anywhere, here are some reflections on my first day.

Intro to Sec. Math/Personal Living and Finance

Mrs. Ratliff's first period is a remedial math class where they talk about business and finance, too. On Friday, we played the game Life and let other students catch up on work. I helped one group of students with the rules and how to play the game. First off, I was very surprised that no one had played the board game before. That was quite a staple in my childhood, but I guess these families didn't play a lot of board games together. Second, many of the students could not make change or figure out how much they got if they passed two paydays. I can tell that I will have a lot of work to do with this class, but I'll have a lot of fun coming up with some fun activities and tasks for them to do in class!

Algebra I, Part 2

Mrs. Ratliff has two Algebra I Part 2 classes. A few of the students are the same from last semester, but some of the students in Part 1 had failed. There are also students in both classes that took Algebra I Part I in last year, so they are having problems recalling the information they learned. A lot of the students are really disrespectful, so I'll have to establish myself as an authority figure so that they will respect me. The way they were treating Mrs. Ratliff on Friday is not how they should be behaving, and I will not put up with it!

Planning

Planning is fourth block, which makes the end of the day come really slow. We talked about what I would be teaching, and my first unit is on polynomials and factoring. I'm pretty excited about it, because I loved that stuff when I learned it and it'll be a challenge for me. I can use some manipulatives that I've learned about, and hopefully I'll get a good variety of types of lessons to practice. I guess the hardest part will just be where to start!

Overall, it was an interesting but fun first day. I have my work cut out for me, but I am ready for the challenge and excited to do so!

Assessment Standards and Practice

Well, it's been quite a while since I updated this! I've started my final semester as a student (so crazy!) and actually begin going to my student teaching assignment tomorrow. But, in class today, we talked about assessment and I learned some interesting things

Standards

We discussed the NCTM Standards that were outlined in the 1995 document addressing assessment. There are 6 standards, and I found the openness one very interesting. The standards say that the assessment process should be open in all aspects: students should know what they are being assessed about, teachers should know what students expect, students should know how they're doing in the class and receive feedback about what they have done. It's interesting that this is a standard because too often teachers give tests without any indication of what they're actually assessing. As a teacher, I will do my best to uphold this openness standards. It's very important for students to know what they're being assessed on and know how they're doing in the mathematics classroom.

Assessment Task

We looked at a task that was given to a 6th grade math class to assess their knowledge about fractions. After looking at the solutions and the reasoning behind their answers, it's clear that these students needed more instruction about fractions. Tasks like this, as opposed to traditional tests, can really show teachers what their students know. It required answers and explanations. It also required creating an example like the task they began with. The teacher also interviewed some of the students that worked in groups and listened to their reasoning and explanation for their solution. Teachers can learn so much about students' understanding by using tasks like this on a regular basis. This information also helps with lesson planning in addition to grading. I've never thought of assessments as a task, but after exploring this task, I think they are a great way to assess students and gather a lot of important information.

Well, I head back to Eastern Montgomery High School tomorrow to start observing and planning for my student teaching! I'm very excited, a little nervous, and ready to start teaching!

NCTM Conference in Nashville

From Nov. 18-20, I went to Nashville for the NCTM regional conference with Krista, Brynn, and Val. Not only did we have a great time together, I learned a lot about teaching mathematics from the sessions and vendors!

The opening session talked about mathematics and music. The speaker integrated the two in order to teach students about mathematical terms, as well as using music theory and instruments for concept instruction. He wrote songs about concepts to help his students remember, as well as used guitars and sound waves to show students about sine and cosine functions and other mathematical terms. I had so much fun at this presentation and fully intend to use music and songs in my classroom!

I also learned so much about the SMART Board and TI-Nspire calculator. One teacher from Ohio records his lessons and posts them online. That way, students that are absent will get to experience the lesson as well. Also, he posted tutorials in order to avoid re-teaching certain topics. I thought it was so cool that the SMART Board records lessons and voice, and I think this is a great way to include struggling students. Also, the Nspire can do some great things, but I need to learn more about it before I use it in the class.

Another session I went to talked about math and art. The teacher used paintings to help students learn about different math concepts. She also had students recreate the paintings in their exploration the topics, and she posted them in the classroom. What was really cool about this was she used free paint color strips and recycled papers for her students to make the artwork. This just goes to show that teachers can use really creative ways to teach without spending much (if any) money at all. So neat!

I got some really great books and games, too, to use in my classroom. I'm pretty excited about everything I got out of this conference. I really hope that I can continue going to conferences like this. Even if my school won't pay for me to go, I would like to go and pay for it myself! Professional development is so important, and I really wish that teachers would use the opportunities and take them seriously! So many teachers there weren't open to the ideas they were hearing about, and I think that is such a shame. I think that just goes to show how different generations of teachers are. A quick, funny story to illustrate this: We were about to get dinner before the first session of the conference and we had to cross a street. The red hand came up saying for pedestrians to stop, but Brynn and Krista kept walking. Val and I stopped, and a group of teachers were in front of us. They yelled "That's why we are teachers, we follow the rules!" Valerie and I laughed, and when we told Krista and Brynn about it, Krista yelled, "REFORM!" Just a great example of our generation of teachers vs. the older generation of teachers.

High School, Cool Activities, and More!

Well, it's been quite a while since I last posted! Since then, I have moved on to observing Algebra I and Algebra I Part I at Eastern Montgomery High School. There are very different issues to deal with in high school, but I really do love it so far! There is only one week left, but I'll be there for student teaching. So, I'm excited for more!

Students

The students at EMHS are very different from the students at the high school I went to. From what I can tell, most of the students are lower SES. They talk a lot about partying, and one of the couples at the school even live together! I am definitely not used to the social environment at EMHS, but I've been learning a lot about how to deal with it.

One of the girls in the class is pregnant, and my CT told me that the student didn't know she was pregnant until she was 20 weeks pregnant! And, the other students in the school are so excited for her baby. This is another huge difference from where I grew up, as being pregnant in high school was not seen as an exciting thing.

Classes

My CT grades most (if not all) of their classwork for correctness. This seems to be necessary, as certain students will just sit there and not do anything (though I'm not sure how much of a motivator a grade is for them).

There is a SMART board in the room, and my CT has this tablet that goes along with it. She can walk around the room, write on the tablet, and the markings appear on the SMART board. It's really cool! She says she needs to do this because she feels like her classes behave better when she is walking around throughout the time she gives notes.

Cool Activities

In my Elementary and Middle Mathematics class, we did this really cool activity with Fraction Circles. Basically, we took a red plate and a white plate (Hefty brand) that had 36 indentions on the sides, found the center of the two plates, cut a slit, and put the plates together. These Fraction Circles are SO USEFUL! They can be used for probability, fractions, angles, and even trig! You can put the unit circle on them, use them for adding angles, display all sorts of fractions (any denominator that's a factor of 36), etc. I think this is an EXCELLENT manipulative for many, many grades. I plan to use it in the future!

Teaching Techniques

All my classes in undergrad and grad programs stress the use of reform mathematics to teach students. While I agree that many of the activities are beneficial for students, I think a teaching style that incorporates traditional and reform activities will truly benefit students. I think reform activities are good to use as introductions, and then teachers can use a lecture or provide a formula once students investigate and develop these methods for themselves. This stye of teaching helps to meet needs of all students, and I plan on using it in my student teaching and beyond!

Also, during my field experience, I've been thinking of activities to do based on the lesson my CT is teaching. This is really good practice for me for lesson planning in trying to incorporate reform and traditional mathematics. I hope to use these activities I come up with next semester during student teaching!

Field Experience, Week 1

So, my field experience at Shawsville Middle School started last week, and after 2.5 days there I have already learned so much!

The teacher I'm working with, Mrs. Mann, has a remedial math class 1st period to work with students who didn't pass their SOLs the year before. This class is very interesting because she has the same students in class later on in the day. She has them practice what they went over in the class the previous day, do their homework if they haven't already, and play computer games when they are finished. A lot of times, when the students are allowed to select the computer games they play, the three boys pick non-math games while the one girl picks a math game. I found this interesting because research articles I've read in class talk about how boys are more interested in math than girls. So, I thought that the boys would more likely pick a math-related game. I guess sometimes a cool video game wins out over math! Or, since they haven't done well on the Math SOL previously, maybe their interest in math has greatly decreased.

Something interesting to note about all the classes is their heavy reliance on calculators. When there was a substitute one day, he wouldn't let them use calculators on a worksheet and the students complained a lot. Mrs. Mann usually lets them use calculators, but I'm glad the substitute made them do the math on paper or in their head. It was really good practice for them, especially when some students have to do "6/2" in their calculator.

The Math 7 class was working on changing verbal expressions into algebraic ones last week. They struggled with this at first because they weren't sure "what the answer" was. They wanted the answer to be one number instead of something like "t-3." They also had problems knowing that a variable took the place of a number and didn't know how to put the expression in to words because of it. They asked questions like "How do I divide v by 2?" or "But what is x?" They also had problems knowing what operation to use and what order to put the number or variable. They thought that it didn't matter what order x-5 goes in. So, I had to review the commutative property and which operations it applies to.

A lot of their problems in class seem to stem from previous issues in math class. For example, their issues with whether subtraction is commutative or not comes from their lack of understanding of negative numbers. I asked a few students if 5-2 and 2-5 were the same thing, and they all responded that they are because both equal 3. Then, I drew a number line and carried out the subtractions, showing that 2-5 was -3. If these students understood negative numbers and that 3 and -3 are two different numbers, I think they would understand that the order in subtraction does matter.

Overall, the first week and a half at SMS has been very eye-opening. I can't wait to learn more and more about teaching throughout the next two months!

Equity

Today in my "Diversity and Equity in Math Education" class, we talked about the difference between equality and equity. One of the students in my class mentioned at quote she heard at a presentation as a metaphor for equality and equity:

"Equality is everyone getting a pair of shoes. Equity is everyone getting a pair of shoes that fits them."

I think this is an excellent way to look at equity in all aspects of life. In education, equality means everyone getting the same information. Equity means each student getting the information in a way that is meaningful for them. This is extremely important for all students, but I don't think that teachers do a very good job of it because they don't know how to implement equity strategies.

The class I'm taking right now is EXTREMELY helpful in allowing me to think about differences I may experience between my students and myself, and it gets me thinking about what I can do to use those differences to help students learn. Another graduate student in the Math Education program said that when she was beginning to teach, she assumed that all of her students would be like her. Then, when she got in the field, she was incredibly surprised when her students were so diverse. I think that all pre-service teachers should take a class like my Diversity and Equity class in order to prepare them for what they will encounter in the classroom.

Not only do teachers need to consider the issues of equity they will face, they need to be prepared to deal with them. Again, during their education, teachers should take a class like the one I'm in to help them prepare. In addition, schools should have professional development workshops for teachers to participate in to discuss equity issues they experience in their classrooms and learn from the experiences of others. Also, if teachers are required to present a workshop or do some research on a certain minority group and present the challenges they face when learning to their colleagues, they will learn from each other as well as learning from research they perform.

Equity issues occur in every classroom across the country. Teachers need to learn about these issues and how to alleviate them in their classrooms. This education should continue even when they are teaching in schools. With a continued education about equity issues, I believe teachers will be able to better handle them in their own classes.

Student Interviews and Children's Literature

Student Interviews

In one of my classes today, we watched an interview of a student and a teacher. The teacher had the student complete the following problem:

Blocks measure 1 1/2 inches on each side. A cube 1 foot wide, 1 foot long, and 1 foot high is made of these cubes. How many little blocks are in the large cube of blocks?

The important concepts in this problem are apparent: volume, scaling, conversions. As the student worked through the problem, the teacher asked questions about what she was thinking and how to go on from there.

I think student interviews are a great assessment method! While watching this interview, it was very clear what the student understood about the problem, as well as what she understood about numbers and operations too. Also, it was very clear what she did not understand. For example, the student was having a problem knowing how many blocks would fit along one side of the cube. The teacher tried to break it down in to "how many blocks fits in to three inches?," and the student understood that. But, she could not see that 1 foot was 12 inches, so she would use the same method as in the three-inch question to see how many blocks fit on one side. Also, the student clearly did not understand what the volume formula actually meant. She knew that she needed to use the formula, but she didn't know when to actually use it.

When interviewing a student, teachers need to be very careful about what they say. In the interview we watched, toward the end the interviewer told the student that there are 12 inches in a foot and pretty much led her to the answer. To truly use a student interview as a valid assessment method, teachers must only ask questions about what they are thinking or to explain their steps. Leading a student to the answer, while it helps them not struggle on this problem, does not show the teacher what the student knows. This can be really hard to do. I've noticed that while I tutor, I tend to lead them to the answer sometimes. I'll need to monitor this in myself this year in tutoring and working in the schools before having a class of my own.

I see myself using student interviews throughout the year. I think the best way to conduct these interviews is to set up stations around the room for students to work on problems and develop concepts. During that time, I can call up students to work a problem for me to see what they know. This takes them away from the rest of the students in a less-noticeable way. Plus, the rest of the students are engaging in worthwhile tasks!

Children's Literature

On another topic, another class I'm in requires us to develop an activity to go along with a children's book. I found a series about a character named Sir Cumfrence which deals with geometry concepts in the context of a knight and Medieval times. I was really excited when I discovered this series, and I plan on purchasing the books!

Children's literature is a great way to motivate students at the beginning of a lesson. Everyone loves children's books (even college students!), and there are many books out there that can be tied to math concepts for all ages. I can't wait to use this method in my classroom and will continue searching for books that relate to concepts that I will teach in high school.

Introduction

So, while reading in a textbook for a class, they mentioned how blogs can be used to get students to think about mathematics and express their views and opinions. I decided that I could really benefit from keeping a blog about my education in the field of Education, as well as what I do while I teach. It can be a resource to others (if anyone ever finds this...), and I can also use this in the future to keep track of what works, what doesn't, and what I've learned along the way.

I'm currently getting my Masters degree in Education from Virginia Tech. I graduated in May 2009 with a Bachelor's degree in Mathematics. I plan on teaching high school math when I finish my Masters in May. Right now, I'm enjoying classes and my last year before I venture out in to the "real world."

I hope this blog will help me to reflect on things I've read, things I've discussed in class, and other things I experience during my education. I plan to continue this on in to my teaching, and if all goes well, I may keep a blog for my students to keep up with! We will see how often I update this, but I can see this being a valuable tool for me on a daily basis, as well as on down the road.