One of the principals of education here at Mills is collegiality. What does that mean exactly? Well, it means that as educators we should work together not only to help educate our students, but to understand them. We should collaborate not only at colleagues, but with families and the community. The problem is there is not always time for this. It is built into many of our assignments and I greatly appreciate this because in order to collaborate out in the teaching field it takes practice and having a certain mind-frame to continue working in this way. This semester we are working on our second set of investigations in the preschool and I am very excited to be teamed up with someone who I have been working with and building a friendly relationship with for the last year and a half. He and I finally found the time to talk about our project, yes it was in a parking lot on the way to something else, but we found the time. The conversation with him was fantastic and a lot came out of it for both of our takes on the project we will be doing with our kids for the next few weeks. I left the conversation feeling extremely encouraged by the collegiality that we had both carried out and excited to move forth with the work we could do together. He and I think fairly differently and it will be good for both of us to gain the perspective of the other on our work with the children. Hours later this is the text he sent me in excitement over the new direction I had given him for his final days of the investigation:

I am very excited to be working in the older age group of the preschool. I want to be a classroom teacher, but I believe it is important to take into account young children’s development prior to school to have a full understanding of the elementary school experience. Although we were exposed to Piaget and others in regard to early childhood development last year, I want to delve deeper into understanding how and what this development looks like on the ground.

I really want to teach second or third grade, but through some of my student teaching posts last year (especially my first grade) I became very aware of various stages that children seemed to be in. I know that there are no strict age boundaries to Piaget’s stages or Erickson’s stages of psychological development and because of that I want to have a deeper understanding of the early side of these stages.

As a student teacher in my preschool I must set a goal for myself each semester. From my student teaching experiences last year, I have seen the importance of tone and way of phrasing questions and comments with children. I believe that it is important to give children a lot of autonomy and allow them to make choices for themselves, however there are times when as a teacher I need to recognize that it is better to make statements rather than phrasing things in a question form. These are typically times when I am not really giving the child a choice in the matter, it is a necessity thing that they must do. I want to work on being more conscious of how my phrasing gives children options, limited options or more of a direct command. As an elementary school teacher coming into preschool it will be important for me to hold myself back and observe rather than jump into every situation. Through practicing that restraint I hope be better filter my words and tone.

This is a poem that came out of one of the dilemmas I faced with my 4th and 5th grade class. We had been reflecting on how to set the tone for our classrooms. One of the strategies that emerged was creating written agreements between students who were at conflict with one another.

**She is my Enemy**

She is my enemy and always will be

She was exactly like this last year you see

She is bossy, mean and selfish too,

I could yell at her til I turn blue.

I’m not selfish, bossy or mean

He lies so much it makes me green

When I talk *he* laughs or walks away

It makes me do the same when he wants a say

Now kids, I understand you’re mad

Let’s talk about three things the other does that make you feel bad

When I speak she rolls her eyes,

He does too, don’t trust his lies

Well that sounds like a good one to add to the compromise

Anything else to add before we sign?

Sometimes he walks away as I’m in mid speaking line

Oh, yeah but if you do it to me that’s fine?

These are written down as things to work on

I do not need a friendship to spawn,

A promise of tolerance to one another

So our classroom can move into recover

No more rolling eyes or walking away,

Thank you for talking this out today,

Now go out and play

Is this how we should deal with children who will not get along in our class? Is there a better way to set the tone of friendship and community in the class?

Filed under: Student Teaching

My Mills classes have come to a close. I am so glad that I picked this graduate program. I cannot believe that some programs think a person can be prepared to teach on as little as six weeks of student teaching. That is not enough. I have been student teaching since day one of my year long program at Mills and I still don’t feel like that is enough. I guess it will be tested this week though…the week I have been looking forward to since I heard about it…my full takeover week. What is a takeover week you ask? Well, it means that I am the classroom teacher for my first grade class that I have been student teaching in since January.

I am writing this after my very first day of the week. People keep asking how it went and, well, it went well as far as takeovers go. Being a student teacher is hard and inauthentic. It is really difficult to step into someone else’s classroom and try to take charge when students have gotten used to things being taught a particular way. But overall, it went well. This is the math lesson that we went through Math Lesson for Monday .

We got through many of the routines that they are used to and I even got to teach a new lesson that is all mine. I want my students to begin to act, but it is hard when it is something new and kids are shy. We have been slowly introducing pieces of acting over the course of the last week and a half through morning meeting and modeling. Today I talked to my students about norms for acting and more specifically for reader’s theater. I discussed with my class how the most important rule is that we all take care of each other’s feelings because acting is a brave thing and it takes a lot for people to stand in front of other to act. We came up with a chart of norms for us to follow before my very brave reading group who has been reading the play the Three Little Pigs for a week and a half performed. The actors explained to the class that reader’s theater is all about acting with our voices. Then we read our play together. The audience was captivated. Although there were some management issues at the end of the long day, the majority of the class was extremely respectful of my actors and my actors did a wonderful job. After we finished and took a bow and then reflected on the experience as a class. Students talked about how it felt to be actors and how it felt to be audience memebers. At the end the whole class gave me a thumbs up for wanting to try reader’s theater as a class.

My students have been working on developing their strength at counting and thinking in terms of 10s. The students’ ability as a whole on adding one more or one less to another is extremely strong. They have more recently begun adding 10 more and 10 less to a number. This is important for my students to know because a strong understanding of our base tens system in necessary to move on in our math system. After having a strong understanding of adding or subtracting one, adding or subtracting ten is the next logical step for my students to take.

In addition to this task we have also been working on fact families in fact family houses so students can get faster at recognizing things like missing addends and figuring out subtraction sentences that work for the complete addition sentences in front of them and vice versa. We are hoping that through fact families our students will begin to see how addition can help with subtraction and vice versa to make them faster at figuring their math facts.

Sharron has recently discovered her voice in mathematics and enjoys verbally sharing about the math that she does. She has become vocal about how she does her math in class and during our reflections for the class she is often eager to share. I have been observing Sharron during math time to witness this. A few weeks ago the students had to take a benchmark assessment for the district. This was still fairly soon after we had started the idea of our fact families. In reviewing Sharron’s benchmark she has correct almost every question referring to missing addends, however she has erased some of these “correct” answers and bubbled in a different one. Unfortunately my students are not yet used to showing their work on tests like this. I cannot tell why Sharron erased these answers and put other ones. Because of this I decided to interview Sharron and find out more about her thinking.

Sharron and I went into the hall with some of her familiar math materials. We had her 10s and 1s blocks, 100s chart, 10s and 1s chart and a whiteboard/marker. We started off with a familiar activity the students have been doing with my CT, I wrote a number on the whiteboard and asked her to show me the number with her blocks. The first number was 63. I asked her to show me 10 more and tell me what it is. She added a 10s block to those already existing, counted and told me there were now 73. When I asked her how she knew she explained that you have to add one more, I asked for clarification and she said that you have to add one more 10s. We tried again with another number, 27. She showed me the correct combination of blocks and when I asked why she pointed to the 2 in 27 and said that she had to have 2 tens blocks. I asked her to find 10 less. She took one 10s block away, counted and told me there were 16. When I asked her to check she counted in her head again and told me there were 18. I asked her to count out loud for me and she was able to give me the number 17. For the next number I asked Sharron to take out her 100s chart. I asked her to find the number 81. She pointed to it, but when I asked her to find 10 more she immediately when back to her blocks, made 81 and then made 91. Although she was unable to do this task on the 100s chart, she immediately gave me the number 91 without counting her blocks.

After these first few questions we moved onto fact houses. The first fact house that I drew included number 5, 3, 2. I wrote three of the four problems in, omitting an addition problem. Sharron was able to quickly identify the numbers of the fact family, indicating that 5 was the greatest because it was at the end of the addition problem. She was then able to create the missing addition fact. For the second family I omitted both addition facts. Sharron was able to identify the three numbers as 7, 5, 2, but suggested that 2 was the greatest number because it was at the end of the subtraction problem she saw. I did one more fact family that was missing all but one addition problem. Sharron was able to recognize all the numbers in the family (4, 5, 9) and knew 9 was the greatest. She was able to come up with all three missing facts. Because of the discrepancy in her finding the greatest number I asked Sharron to take out her 100s chart and put her finger on 14. Then I asked her to put a different finger on 12. I asked her which was the greatest number, she said that twelve was greater than 14. I asked her to tell me why and she said that 12 is littler and 14 is longer so 12 is greater than 14. We finished up our interview with a few questions about what Sharron likes about math and what she thinks about mistakes.

I believe that for her conceptions of 10s and 1s blocks Sharron is well on her way to a good understanding. She enjoys using her manipulatives and this is something that she talked about liking a lot in math. She is not confident in using her 100s chart to find 10 less or 10 more and this would be an important other strategy for her to get a grasp of. For a next step we could work further with the 100s chart and how the columns can help us with the concepts of 10s. Another piece that I would like to make sure Sharron starts doing is drawing out her blocks. I am very happy that she enjoys using the manipulatives for math; however I want her to also be able to see how she can draw these out when they are unavailable.

For Sharron’s ideas of her fact families I am having some fears about how she is thinking about them. I am afraid that she has found some particular patterns that make this particular task easy to accomplish, but are not helping her overall understanding. This shone through when I gave Sharron one subtraction problem and what she had seemed to know got thrown askew. Because of the “mistakes” that were made I am seeing that Sharron does not have a deeper understanding for how knowing one math fact (such as 7-4=3) can help her quickly know additional facts about those numbers. She is recognizing patterns which is a key aspect of how the fact families were introduced to the class, however now she needs to be moved beyond this to see how knowing just one of these facts can translate to knowing much more math around the three numbers the family is made up of. I was excited about her reactions to math. Sharron is very eager to do and share her thoughts in math. I was also very pleased that as a learner she is understanding that mistakes are ok to make, but I would also like her to understand why mistakes are good and how we can learn from them.

Filed under: Student Teaching

In our math course at Mills, Edcuation 303, we are learning all about Math Talks and how to make math exciting and accessible to our students. Math Talks are to help students realize what they already know about numbers, make connections and hear what others have to say about numbers.

Richard Skemp wrote an article that we read addressing the important distinctions between instrumental and relational math knowledge. After reading and reflecting on our own educations many of us realized that we had learned math instrumentally, meaning that we had memorized formulas or steps to plug in when we saw the right wording for it, but did not know how it really tied together or why we did it.

Have you ever asked a child to tell you (or write down) everything they know about a certain number? You should, it is fascinating. It gives you so much insight into what they are thinking. The 100th day of school is a big deal to kids and schools nowadays, I don’t remember celebrating it as a child, but to prepare for that I introduced my students to Math Talks on Monday. We started as a group on the rug and talked about the number 10. I gave them some types of examples like sentences and equations, but did not want to influence their answers too much. The students were asked to think in quietly and after a few moments to share with a partner in a whisper voice. This gave students who did not have an idea a chance to hear others and be able to raise a hand. After it seemed like everyone had whispered to another person I asked the students to come back together and for a quiet hand with some ideas about the number10. We created a poster together and then the students were shown a graphic organizer to put together their thoughts on the number 10. The following day their morning job was to do this same graphic organizer on the number 100. We did not have a chance to debrief the morning job because it also happened to be Valentine’s Day, but what these students had to say about this big number was truly intruding. Here are some examples of the student work:

I have been working on creating my own lessons, rubrics and reflecting on them. Here is one of my first attempts European Diseases Lesson, Rubric and Reflection. I created a social studies lesson for my 4th and 5th graders on European Diseases that were brought to the Americas during exploration.