Many Schools, One Focus

Throughout this winter quarter we have been in many different schools for our methods classes. Being able to see a glimpse of how other schools function and operate has allowed me to compare and contrast those schools to my placement. I enjoyed spending time in different schools because it allowed me to see that although schools may differ in their population, curriculum and policies, all schools that we have been in focus on putting students and their learning first. I think this should be a given for elementary schools, but it was nice to see that all schools are doing their best to serve their students in the most effective way possible.

One school we were places in was very different from my main placement, even though they were probably within 10 miles of each other. My school has a diverse population with a high Hispanic influence.  I just learned that 75% of the students in the dual-language program in my school are waivered into this school because they live outside of the school's limits. Having the draw of a dual-language program has added to the diversity of my school. I was able to see a classroom at a school with very different demographics. The classroom had less racial and cultural diversity than my classroom, which reflected the community this school was placed in. In this school I was able to see a classroom that was part of a "gifted" program. I find it interesting that this school with a more homogenous student population has a gifted program while my school, with a more diverse population, doesn't offer this sort of program. I did find that this "gifted" classroom was more homogenous when it comes to race and culture, but it had a more diverse range of student's needs. In my classroom, we only have one student with special needs, and there were at least five students in this other classroom with special needs.

Another school that we were able to work in this quarter allowed me to see what a new and remodeled school looked like. My current placement is in a school that hasn't been remodeled in a while and it is build in a very strange way. We are also facing overcrowding issues which is complicating things. The school already has three portables with six classes inside them and the school is finding it difficult to get another portable. One of the classrooms is in a room with zero windows too. Even with space issues and an older building, I find that the staff loves their school and that they are doing all that they can to trouble shoot these unique issues. This other school we were able to visit had new classrooms that shared a common grade level area. They also had new computer labs, display cases in the hallways and multiple stories. I liked being able to see the different school layouts because it allowed me to see how different schools utilize their spaces differently.

The final school we were in this quarter was very unique. It was as school that looked completely different than my placement school. This school was built in pods and had very wide hallways. I believe this school serves a population of students with many different needs. They have a pool, bikes in the hallways and big therapy rooms that I was able to see. This school was very confusing to me at first because I felt that I could have gotten easily lost in the different pods and floors. I loved to see how student's with special needs were able to navigate their school and classroom and how they were an actively engaged member of their classroom.

All of the schools we were in this quarter were unique, but again all of them had such an important focus on what was best for their student population. I enjoyed being able to see all of these schools and compare them to the one I am placed at now. No matter what the school looks like or what kind of student population it serves, it will always face certain problems. I think with a dedicated and caring staff that focuses on student success can overcome any challenges that they may face.

Math Field Trips

Since we are having our kiddos from one of the elementary schools come to our university for a field trip, we are going to do a "math walk around" and "mathematize our school". I think this is such a great idea for a field trip because usually we don't take field trips that have anything to do with math. Why can't we incorporate math into every field trip? We can take what we are learning in math and make a sort of math scavenger hunt for the kids to do during lunch or during a short break or just as we are walking about.


I would love to be able to incorporate math into field trips because I think it should be emphasized that math actually rarely happens in the classroom in real life, but mostly happens out and about, in the "real world". I'm excited to see what our professor comes up with for our math field trip, and hopefully I'll be able to recreate it for a future class of mine.


I would also like to know if anyone has experienced a field trip that had a strong math component to it and where this field trip was to and what was done on it.

Math Inquiry Lesson

I had my second observed lesson by my field instructor this past week and I decided to do a group inquiry math lesson. The students had to create a table by measuring an ice cream cone and paper scoops and then to take that information and turn it into an algebraic equation. I was surprised to see that all of the 5 groups were able to come up with an equation with very little or no help from me. I liked using questioning to guide their thinking and make them think more critically about what they were doing.

I really enjoyed this lesson because it looked so different than our other math lessons, which are all typically direct instruction. I think the students could really benefit from more inquiry lessons because it allows them to take their knowledge and apply it in a new way. I think my cooperating teacher would like to do that too, it's just always a battle of time and trying to stay on track with the curriculum.

Hopefully I'll be able to work in a few more inquiry style lessons this year because it made teaching math more comfortable for me. It really takes some of the pressure off of the teacher because I'm able to spend some time with small groups instead of trying to instruct the whole class. I don't have to think of a way to say something so the whole class gets it, rather I can focus on the needs of one group and where they are in their thinking. Students were also able to learn from and help each other which I really liked.

Reasoning, Waiting, Repeating...

Ever since being introduced to the talk moves of revoicing, repeating, reasoning, wait time and adding on I have seen there usefulness in the classroom. I've enjoyed practicing using these moves in my placement during our math lessons because it slows the pace of the lesson down and allows more students to participate. I think there is always a struggle between slowing the pace of the lesson down, which will probably help with comprehension, and staying on pace with your lessons. I have to think that understanding something more in depth has to help student later on in their math education.


I've had trouble with revoicing when I'm unsure of what the student said, or how to explain their thinking. In those cases I ask the student to repeat themselves or ask another student to repeat what that student said and hopefully that will help clarify it for me. I find that students speak the same language (and sometimes the teacher doesn't) and they can communicate ideas more clearly than I could. I still feel awkward asking multiple students to repeat a good point that I want to highlight because I think 6th graders aren't used to this and they might feel silly repeating something.


I also feel a little awkward increasing my wait time, but I know it's so beneficial for those students who need time to gather their thoughts. I think students need a little while to get used to wait time, but if you implement it from day one in the classroom then it will become expected. This is something I want to continue working on.


I can see these talk moves being a form of classroom management as well, because all students should realize that they have to listen to their classmates thinking and they have to have mathematical ideas that they are willing to share in a safe environment (even if they're not correct). I think children are just like adults in that they learn a lot more from interactions and discussions rather than being talked at for a long time.


I'm excited to continue using these talk moves and improving on them. I hope my students will benefit from them in the future!

Many, Varied & Unique

I have been lucky to get to observe at least 8 other classrooms at my school from all different grades. I think it's interesting to see how different teachers are, even within the same grade or school. I've been able to see classrooms that do all instruction in English and other classrooms that do half the day in English and half in Spanish. I think one of the most obvious differences in classrooms is how the teacher gets their students' attention. My teacher uses different strategies. Sometimes she says give me 5 and sometimes she'll sit quietly at the front of the classroom until the class quiets down. I've seen a bell used in other classrooms, sometimes teachers use a clapped pattern, others have a chant, among many other strategies. I like the idea of a bell because I don't like shouting over students to get their attention, but I'm open to trying many different strategies until I land on one that works for me and my students.


I think a lot of classrooms have different techniques for transitions. Surprisingly, the younger grades I have observed seem to have quicker more organized transitions. I think some classrooms spend more time in the beginning of the year dedicated to working on transitions. I think by 6th grade we expect students to know how to transition quickly since they've been in school for a while, but I still think 6th graders need a lot of work on quick transitions. I think it also helps them work on organization which they will really need to master by the time junior high or middle school rolls around.


Another difference that I've observed in my classroom and others is how teachers check homework. In my classroom, my teacher selects two students who go around the classroom during independent reading and check off students' planners for their parent signatures. In another classroom I observed, the teacher had the students line up at her desk first thing in the morning and had them bring their stack or homework for her to personally check. If the homework wasn't up to her standards she would write "D.I.N.O.D.I.T." on the top of their work which stood for "do it nice or do it twice". This made me feel really uncomfortable because it felt very business-like and not caring or understanding. I think different teachers find different methods that work for them, but this is not something I will try. I think it is very important for me as a teacher to see their homework, but I want my students to know that I care about them as people more than I care about their homework.


This reminds me of how important it is to be critical of myself as a teacher and reflect upon my practices. I think teachers tend to get into certain habits that work for them, but I hope to always be open to changing my methods and practices to benefit my students.

CGI Trajectory and other Mathematical Things

After I was able to have a math interview with my third grader at Woodmoor I was able to get a better sense of the CGI trajectory and how to figure out where students fall on it. I was able to tell that my third grader fell in multiple categories, depending on the problem. For one of the math problems I gave her, which involved division, she was able to solve the problem using derived facts. Then for a different division problem she used direct modeling to come up with her answer. I found it very interesting that she fell into two different categories for the same skill (division). I think this is possible, but I found it odd that she was in two very different categories for the same math operation. I was wondering if it was typical for students to fall into two different categories that involve using the same operation, or if they usually fall into the same category when they are using division, for example?


I think it's difficult to place students on the CGI trajectory at first because a lot of their thinking is usually going on in their heads. My third grader answered the final problem on the math interview almost instantly after reading the question, but I still don't think she used recall.  I can see that if I didn't discuss her thinking with her after she answered the question that I might have thought that she would have simply used recall to get her answer. But, after discussing her thinking with her I could tell that she was using derived facts to arrive at her answer. This is why I think placing students on the trajectory is a challenge unless you are able to listen to their thinking and take time to analyze what their thinking says about their mathematical progress.

Feedback Welcomed!

Throughout this whole process I have seen my thinking and teaching evolve almost daily. A lot of this change has come out of self-realization, class readings, discussions, conversations with my cooperating teacher and other's observations of my teaching. I think my field instructor has given me the most objective and straight forward feedback so far. I liked her feedback because she was able to tell me specific things I did well and specific things that I should work on.


One of the things that she suggested that I have already put into practice is using quick assessment strategies to gauge my student's understanding. For example, she said that I could use the thumbs up, down or sideways on the student's chest to quickly get a feel for what the class is or is not understanding. I liked getting this suggestion because it's not something that I've seen my cooperating teacher do, but I see how simple it is to use and how quickly I get information from the whole class. Another suggestion she had for me was to use positive discipline in order to get all of the student's attention, or get them on track. She said that she noticed that I would say things like, "table 5, I need you to look up here when you're done" or "Johnny and Susie, I want you to be listening to what April is saying". I can see that I would waste a lot of time if I constantly had to tell people what I want them to be doing. A better way would be for me to say things like, "I love the way that table 3 is looking up at me with all of their materials ready" or "thank you Jill for looking at the person who is speaking, that tells me that you are listening to them". I think that we've have spent a lot of time discussing the importance of the language we use. Even though I'm essentially looking for the same result, I'm saying it in a way that is preserving everyone's confidence and reinforcing positive behavior instead or pointing out the wrong behavior.


Of course, I loved hearing the things I am doing well, because as a student teacher I didn't expect that many of those things would come naturally. My field instructor noticed that I used proximity while I was instructing in order to keep one student in particular on track. While I was doing my poetry lesson I noticed that one boy was doodling and writing his name in bubble letters on the back of his poem. So while I was talking I walked over to his group's table and put my hand on the desk. I was really surprised to see that it instantly got him to flip over his paper and pay attention (or at least pretend!). I was also told that I did a good job of soliciting multiple student's opinions and ideas by calling on them when they raised their hands, using random popsicle sticks with the student's names on them and by telling certain students that I wanted to hear from them soon, so they could get ready.


I think right now it's very important for me to be open to everyone's suggestions because it's hard for me to tell what I'm doing well and what I need to work on. I have noticed that teachers love to give me advice, which I love to hear because I have a lot to learn from them. I've learned that my field instructor shouldn't be viewed as someone scary who could drop me from the program, but someone who has great advice and suggestions for improvement. I think that my first official observation really opened me up to hearing more constructive feedback.

Subitizing in Math

Last week we were able to work with some 3rd grade students doing math. Before that class I had never even heard of the word subitize, but I left with a new understanding of how children make sense of their worlds. After learning what the word meant, it seemed like a natural reaction for children to organize their worlds quickly by grouping things into categories. I know that our brains organize what we see quickly to help us better take in our surroundings with little effort. These third graders seemed to all be in different places in their understanding of grouping in mathematics. We were using Quick Images with these students and asking them how many dots they saw, then we asked them to tell us how they quickly counted the dots. One of the Quick Images was four groups of five dots. Some students tried to quickly count each dot and come up with a total number of dots that way. That student didn't yet understand how to use subitizing to quickly count the dots on the piece of paper. Another student saw two pairs of two dots in each of the four groups and one dot in the middle. This student felt comfortable subitizing the groups into doubles. The last student saw each group of five dots as one group and counted up by fives. This last student might have been familiar with using dice because the five dots were arranged like the five on a die. I think this example goes to show that subitizing is something that happens for each student at a different point in their mathematical progression. Some of these students are beginning to grasp the idea of multiplication while others haven't yet. I think that is part of the reason why some children are beginning to see things in groups while others are still seeing the dots as individual dots. My new knowledge of subitizing will hopefully increase as I continue to work with students of al ages. This will improve my math instruction and understanding of children's thinking.

Student 1: Counting the dots individually.

Student 2: Counting by two's in each group and one in the middle.

Student 3: Grouping by five's, like the five on a die.