7th Grade Math

I currently observe a 7th grade math class at C.D. Fulkes Middle School in Round Rock. It’s interesting to see how to manage a class in middle compared to 4th because I thought they would act differently but they still act the same. The students talk while the teacher is working on the board or lecturing and they’re also very excited about answering questions and seeking teacher approval.

This teacher actually teaches math in a problem solving way. He even uses the Van de Walle book! Maybe this is because he just graduated from school 3 year ago, but he says the book was the best textbook he had to use during college. When he introduces a lesson he wants the students to explore what they are doing.

One Friday he was introducing adding/subtracting integers to the kids. He gave the students a number line and different problems and told the students to solve them. All the students thought this would be easy but they realize that some of the numbers had a funny sign in front. The students were allowed to work with their desk partners to come up with their answers. The teacher walked around and observed what the students were doing. They worked for 20 minutes and then he brought the class back together to have a discussion over their answers and how they solved the problem. This teacher is very good at using revoicing. Most of the time he has students who are not paying attention repeat someone’s thinking. Many of the students know that he is going to do this so they stay focused on what all of their classmates are saying. I believe he has already established the mentality that no answers are wrong and the class is here to help each other not put down.

After the discussion, the teacher was able to evaluate where there thinking was and what they needed to work on for next week. I asked him where he was going to start and he said he is going to use manipulatives and number lines so they can understand visually how to add and subtract integers.

If you ask any of the students in his class if they enjoy math, they will say yes because we get to DO more than WATCH.

Math Talk

The two talk moves I chose to pay attention to during my CT (technically she is not my CT just the partner 4th grade math/science teacher)’s lesson are restating and wait time. I chose restating because I believe it important for children to be able to understand what their classmates are doing. This could also help their thinking when solving a math strategy. It also allows the student who strategy is being shared around the classroom to be the teacher because the whole class is discussing what the student did and it can become useful on future problems. I also picked wait time because right now at my elementary school we are working on 2 different content areas to improve the school every other month. For the months of November and December the teachers are practicing questioning and wait time/altering the question so all students can answer questions is supposed to be used more in the classroom. I wanted to see how my CT was able to incorporate this in her lessons and how the students are adjusting to giving everyone a chance to answer questions instead of “the high level students” being the only students answering questions.

I usually only see my CT having students restate a student’s answers while they are practicing problem solving as a class and group discussions over word problems. Much of the time my CT does direct teaching where the students are given a warm-up. There might be discussion over the warm-up if the student does something different than the rest of the class and still gets the correct answer. One time my CT had a student restate a student’s answer because he was falling asleep so she used it as a “wake-up tactic”. LOL! The remainder of the time I see discussions over solving problems and what the students did. She will have the students explain to the class what he/she did, have another student repeat what that student did, and then she explains it to the whole class via demonstration so everyone can understand.

My CT is very good at wait time even though the awkward silence sometimes causes the other students in the class to start talking to each other because they’re frustrated that a student has not given an answer yet. I think sometimes the struggling students get frustrated because they want the teacher to ask another student BUT she continues to rephrase the question until the student is able to give her some answer. I think other students get frustrated because they are use to always being called on and instead she tries to call on ALL students instead of the few that are always raising their hands and eager to answer questions.

While I walked around the room I tried to use both strategies with my students and I got the craziest answers. **MEMO: my students have colorful personalities and they like to say whatever is on their minds** They were practicing area (of different size rectangles and squares combined together) in word problems. One girl thought this was really easy and was flying through the worksheet while the student next to her continued to struggled. I asked them both to stop and ask him, “What are you doing to finding the area?” He explained how he was drawing squares in all of the shapes but it started to get really frustrating because he was not sure if his squares were big or small enough. I asked her to explain what he is doing and she explained it then I asked her to explain how she found area of these shapes. She talked about length and width and how they determined the inside and she combined the two different shapes to get her answer. I asked him to repeat what she said and he says, “I’m not sure Mrs. Crawford but I know she draws no squares. I then asked her to show him what she was doing because that might make it easier for him to understand seeing a visual representation. He thought he got it so we (me and the student) decided to try it together on the next problem. We were going through the steps of what to do first and he just stared at the shape like…I dunno what to do first. So I asked what do we need to find area what are those two important things called and he was like ummm the sides. I said correct great and what do we do with the sides and he just stared at me. And continued staring. And then he would look at the problem and stare back at me. I think I’m going to enjoy wait time because this is when the teacher and student have a staring contest to see who will win, the teacher always wins. He started getting frustrated and began drawing squares inside the the shape. I asked wait what happened to this new strategy we were trying. He stared at me with these pitiful eyes and says, “I had to give up you wouldn’t DO the problem you just stared at me.” I chuckled inside and then we worked the problem TOGETHER.

A Math Game

I chose the Covered Parts activity to do with my numbers game. I actually used a group of 4 students to work with. Two of my students (boy and girl) were high level learners. Currently in math, they are working on their 11 times table for their warm-up practice. The other two students are the low-level students in the class (boy and girl). The boy is repeating the fourth grade for the 2nd time because he moved to Texas from Honduras during March. The teachers believed he would be more successful staying in the same grade rather than moving on to to 5th. The other student recently immigrated to Texas from Mexico. She also is being tested for dyslexia.

At first I was going to pair the high level learners and the low level learners up with each other but I wanted the high level learners to also serve as teachers so I paired a person from each group up with each other. I picked a lesson that will allow the students to use something they are familiar with (addition and subtraction) and also able them to use manipulatives if needed. While using the covered parts activity I said a story problem so it would be realistic to the children while they were trying to figure out the answers. I used the number 20 because it involved multi-digit addition and subtraction. The kids were able to catch on fairly quickly. It was really easy for the high-level learners to catch out and figure out the answers in their heads without using the manipulatives; however, the low-level learners struggled and had to use the manipulatives and their fingers to figure out how many were covered up.

Student A was my low-level boy from Honduras. He said I need to learn how to count without my fingers because I only have 10 fingers and many times I get confused. I asked him if he could think of way to counting the manipulatives that would make it easier. He chose to count by 2s and realized that if he used each finger to represent 2 he would be able to solve the problem. The story problem he really struggled with was understanding that he started with 20. I said Student A has some cookies. You eat 7 cookies and you have 13 cookies left, how many cookies did you have before? He said kept saying 6. He did struggled with the join/separate start problems because he was unsure of the beginning number.

Students B were my high level students. It was interesting to see how they came up with their answers. The boy breaks numbers in half to do his counting. I asked him: “There are 20 cookies. You have more cookies than Girl B. Girl B has 6 cookies. How many cookies do you have”. He explain to me that that he’s going to break all the numbers in 1/2 so he would be working off of 10. He changed the problem to: there are 10 cookies, girl B has 3, how many do I have and figure out that he has 7, then times everything by 2 to get 14. I asked him what he would do if he could not half the numbers and he said he did not know He would probably have to figure it out in his head another but he hasn’t ran into that problem yet. Girl B counts by 4s and 5s. She also uses a lot of derived math to get her answers. Her derived math involves addition. I gave my high level learners the more difficult type problems and they were able to understand what they were finding and solve them with no problems.

I thought the idea of breaking everything into halves was very interesting. This would make it easier for even numbered problems but you would have to find another way to break odd-numbered problems and not all of them are divisible by anything beyond 1. Girl B who broke things into 4s was different. I’ve heard of people countings by 1s, 2s, 5s, 10s; but definitely not 4s. It’s interesting to see what kids see as an easy way to count up numbers beyond what teachers tell students are the easiest ways to count. I also think it’s interesting that a 4th grader noticed how hard counting on his fingers actually will be in the future. I help in middle school math classes on Friday and one of the 8th graders was using his finger in a percentage problem. I’m not sure how he was able to solve the problem but I can see it getting really difficult when you’re having to do math with big numbers. I wish teachers would encourage other methods: i.e. (manipulatives, drawing pictures, etc), so fingers could become a last option to children.

A Math Observation

My school placement is Del Valle Elementary and I am in a fourth grade reading/writing/social studies class. I’ll never forget the first time I drove up to the school. I fell in love with it! It felt like the place for me to be. I believed I really like how close the middle and high school is to my school and it felt like its own little community. The school has lots of positive messages and the school motto, which is: S.O.A.R. (Scholarship, Ownership, Achievement, Respect). The school also has boards for language arts and math so students from all different grade levels can display their achievements in those subjects. The noise level is like any other school. In the morning it will be loud, during the day it’s quiet until students are going to the cafeteria (the students have been rowdy these past 3 weeks because they haven’t been to recess in a while), then when school is about to get out the volume level increases especially on Fridays. I know the students understand how to be quiet until they get in their classrooms so that they do not disturb other students’ learning.

The fourth grade teacher team gets along very well and they spend a lot of time together outside of the school. I see the teachers being very friendly to each other and it feels like a community. Many of the students at my school are related so it’s funny to walk down the hall and they say, “Oh that’s my brother, sister, cousin, etc.” A lot of the classroom doors stay closed so I haven’t got a chance to see what the other students are doing inside. If it’s anything like my class, the teachers are trying to build students who are willing to learn independently because they enjoy it not just because someone is forcing them.

Math is interesting because the students do lots of worksheets (something I do not like). In my future classroom, I’m going to try and find a way not to use worksheets at all if possible. The teacher usually sits at the overhead and explains the lesson while the kids listen and then they receive a worksheet and get to sometimes practice with a partner but most of the time it is independent work. It does seem to be routine and I feel like the students might get bored with it. I remember one parent at Back to School night complained because she thought the math teacher could do more than what was going on. Hopefully this does not continue for the rest of the year because this could make kids uninterested in math and then they end up not liking it.

Currently the students are doing review over what they learned in 3rd grade and learning the basics so they can build on these basic concepts. They are practicing place value, comparing numbers, adding and subtracting 2-3 digit numbers, and also practicing their times tables. The students really just need to use their prior knowledge and remember what was taught last year and also listen while the teacher reteaches the concepts again. The students are working on procedural practice because they are only practicing the methods needed to do place value, comparison, addition, subtraction, and multiplication. I think many of the students seem engaged because they already know how to do a lot of these things. I know a few of the above level students are getting bored and are ready to learn something new. One little boy fell asleep one day BUT he falls asleep in reading also so I’m not sure if he’s just tired during the morning or if he’s really not interested in what it being learn. LOL! I don’t really see the children reflecting on what they are doing usually once they are finished they are always looking for something else to do or they’re talking to their friends. Maybe the students that are getting extra practice papers they are reflecting and searching for an easier way to solve the problems.

A few questions I’ve heard over the past days:

• When are we ever going to compare numbers?
• Why can’t I have a calculator?
• Can we get prizes for memorizing all our times tables?
• Why isn’t there a pattern in the 7s times table?

I think they enjoy what they are learning but like most students (including myself); they want to know WHY! Why are they learning these things and when are they ever going to use it. One little boy argued with the teacher one day about how he didn’t need to learn his times tables because he will make sure to always have a calculator in his pocket. It was interesting to me to see that ALL the students follow the same standard formula when they are solving the problems. I remember during our lecture over number sense how we discussed that all students solve problems differently and embrace it. I didn’t see that happening in this math class. I’m not sure if it’s because they are not yet doing problem solving or if they were taught only one standard way, this is the right way so don’t do anything else. I kept looking for someone to work a subtraction or addition problem differently and everyone did it the same. I wonder if it’s like this in all math classes.

I decided to see if the above level students actually understood subtraction and addition since they were finished quicker than the rest of the class. I asked one little boy why do you take away in subtraction. He looked at me crazy and said, “Ms. Crawford, you went to school all teachers teach you to do it this way.” I understood that and asked him if he knew why and he could not ever give me a definite answer. I asked another little girl, who is also in G/T, and she gave me the same answer. Both of these students were not able to explain exactly why and what they were doing when “taking-away” during subtraction. Maybe this is something that needs to revisited so the students can actually understanding that you’re borrowing and adding a base of 10 to the place value. This was interesting to me because I don’t know how you can continue on to more difficult mathematical concepts when you don’t know the basics. OR are teachers just making sure you know how to solve the problem and get the correct answer instead of actually understanding what you’re doing. Hmmm…

My Math Story

I have always been a lover of my math. I think maybe it’s because math seems to be the only subject that I’m good at. I was never a strong writer, history gets old after a while, and the only fun part about science is dissecting animals. However, math is super exciting!!

When I was a little girl, my teachers always found a way to make math exciting. I remember in first grade as we were practicing adding and subtracting my teacher also included a mini store in the class so we could use “money” to add and subtract. In 3rd grade my favorite teacher, Mrs. Johnson, made multiplication fun because we built ice cream sundaes based on the multiplication tests we took. I don’t think I’ve ever studied so hard for a test! And yes I did do great on all my tests so I got a full ice-cream sundae. In elementary school, I think the best part about math is that my teachers made it real for me. I got to see why I was learning: addition, subtraction, multiplication, percents, geometry, etc and how I would use it later in life.

My sixth grade math teacher was the most evil teacher I’ve ever had. I started not liking math because of her. I always dreaded going to her classroom. I was always in trouble for talking and she gave me a detention for sitting on my foot. Sitting on my foot!! Seriously??? It was not until 8th grade that I began loving math again. I didn’t like geometry it was just too complicated for me beyond what a type of shape might be. Algebra was very easy for me. I liked problem solving. I was always making up algebra problems in my head. I was definitely a math nerd! There was a special math club in my middle school. I joined because I enjoyed problem solving so much and I thought what fun to be in a club where you get to problem solve for competitions! Middle school helped me to figure out what type of math I liked.

Why do we have to take geometry? I don’t understand why it’s needed beyond what different shapes are and proofs are HORRIBLE! I wish in high school you could take only the math classes that you liked. 9th grade geometry was the worst and I really struggled! I asked my mom’s boyfriend who was an engineer to constantly help me and to this day I still do not understand any aspect of geometry. Algebra II, Pre-Calculus, and Calculus were a breeze and I always had the best math teachers! I knew that I wanted to be a teacher when I grew up and my Algebra II teacher told me to focus on teaching math because it’s a subject I’m really good at. She even gave me a nifty fraction pen to encourage my studies in mathematics.

Currently I’m an elementary education major and I plan on taking the certification test for mathematics. I really like math and I believe people who are passionate about certain subjects should also teach those subjects. In college, the only math class I struggled with was discrete mathematics. Discrete math includes proofs and other weird stuff. Somehow I managed to make an A in that class and not have a clue what was going on the whole semester! Ha! My favorite college math class was mathematics as a problem solving; just because I love problem solving! I think math is really important and you use it daily (even when you don’t think about it) so everyone needs to learn it. I believe if you have the basic skills of adding, subtracting, multiplying, and dividing then the other math concepts are not that hard to grasp.