Final Coaching Session of Teacher Assisting

I have recently completed my final coaching session for my teacher assisting semester.  We first talked about my portfolio that I have been putting together all semester.  This included the feedback and evaluations of each target.  Next, we talked about the semester as a whole.  Finally, we talked about my goals as I enter student teaching.

The portfolio was discussed and why I received the points the way I did.  The professor gave his feedback and why I received them.  Where I could have when a little more in depth and avoid using the “I believe” statements.  How he graded it and his explanations of each lined up exactly how I felt.  This was really nice considering how much time and effort I put into my portfolio, to be on the same page as my professor was a benefit.

The next discussion topic was about the semester as a whole and how I felt the semester went.  Overall, I felt this semester was a success.  This was my first time actually teaching so I was a little nervous, but the more teaching I did, the more comfortable I got. I definitely feel that I have improved very much and continue to work towards becoming an effective teacher.  Reflection is something that I have noticed every teacher must be a part of.  I found myself reflecting on every lesson and finding out ways I could improve it for next time.  This was thinking about it in my head, talking to my CT, talking with my placement partner, or researching on the internet.  It may have been as simple as re-wording things that would help students understand it better.  I have worked quite a bit to improve assessing students.  My field coordinator for the College of Education was very impressed by the number of times I assessed my students during his observations.  However, I feel I did a lot of assessing until the last week of teaching where I did not do it as much.

A few areas that I want to improve on as a I get ready to student teach is keeping every student challenged throughout lessons.  I tend to cater towards most of the average students, but do not attend as much to the less advanced or more advanced students.  The advanced students seem bored and disengaged while the less advanced students seem confused and disengaged.  Doing this could be incorporating differentiated instruction into my lessons.  This could be as simple as giving two questions out with different levels of difficulty, to the amount of support each student has, to group sizes, to what they are allowed to use to solve problems.  I could learn more about this talking with other teachers, talking with professors, and researching on my own time.  I want to learn more about how to keep everyone engaged throughout the lessons and I will have more resources to look towards as I prepare and take part in student teaching.  Also, I did a lot of assessing throughout the semester.  Towards the end of my teaching, I started to not assess as much.  I need to work on keeping up with formative assessment throughout lessons since I know how much assessing students is so important.

Finally, a goal of mine in student teaching is having a good CT.  Someone who will help and support me during this process.  I had a great CT for my teacher assisting semester.  Anytime my placement partner or I needed something, she worked at making this happen.  She gave us a lot of useful information to use during our lessons and provided her advice whenever we asked.  I am hoping that I will get a CT like her, since I could learn a lot from that person and they could help me and give advice that would assist in me become a more effective teacher.  I never realized how important a good CT was until I talked to my classmates about theirs.

Leading up to student teaching, I have a summer and whole semester to prepare.  For four weeks I will be teaching in Tanzania as part of a study abroad trip and during the fall semester I will be substitute teaching.  During these times, we discussed how important it will be to keep up with how I will work towards reaching my goals during student teaching.


Assessment in Action

I had recently completed a blog post about my experiences in my attendance at Math in Action.  I said that I really wanted to put some of the things I learned about there in action in my classroom.  I learned about this website called beta.socrative at a session called Formative Assessment in a Tech-Based World session at Math in Action.  If you would like to know more about this conference, you can review my blog post entitled Math in Action.  The site, beta.socrative, requires every student to have access to the internet.  They answer questions assigned by the teacher.  The teacher then can review the students’ answers and track how well they are doing.  The teacher can use this as a formative assessment to clear up any misconceptions a student or class could have by seeing if individuals get multiple questions wrong in a row.  The site is a very useful tool teachers use to formative assess students.  I have recently tried out this software in my placement’s classroom.  It was quite interesting and I feel the students had a lot of fun experiencing with it.

We were reviewing for the end of the chapter test when my teacher assisting partner offered the idea of one day we could introduce beta.socrative to our students.  So, I created a quiz for the students as part of our review game.  The chapter spanned circles, volume of various three-dimensional figures, areas, surface areas of three dimensional figures, and classifying three dimensional figures.  I did several true and false, short answers, and multiple choice questions as part of the setup.

At the beginning of the review day, my partner and I gave out cards to each of the students to put them in groups.  We did not have access to computers for every student.  We ended up having eight groups in total, so we only needed eight computers.  During our review game, we sent out one question at a time to all of the students.  We could track which group got the assigned question right and wrong.  If the students got an answer wrong, they did not get any points.  If they got it correct, we randomly pulled out a point total for all the groups and assigned them that total.  We displayed the scoreboard on the whiteboard.  After we assigned scores, in order to check if only one student was answering a question for the group, we randomly pulled a card.  The student with the corresponding pulled card would have to explain to the class their group’s thinking through the process.  We feel it is important for every student to be accountable and know why a certain answer is correct.  We fielded any questions and concerns to clear up any misconceptions students might have had.  We then sent out the next question to the students and repeated the process.  At the end of class, we totaled up the points and the ones with the most ended up winning the game.

The review game went very well with the students considering it was something entirely new to them.  It incorporated beta.socrative which I have really wanted to try out since learning about it at Math in Action.  The students had a lot of fun and it was something different they could do for reviewing for a test.  They also really enjoyed the competitive style game.  If I am every in a school in the  future where every student has access to computers, I would definitely incorporate beta.socrative more into my lessons.

Second Observation Coaching Session

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My teacher assistant partner and I were observed while we co-taught a lesson. The day before we covered a lesson about converting decimals and fractions into percents. On this day of our observation we decided to do an activity to go along with that lesson. What we did was we got quarters, dimes, nickels, and pennies and modeled percents using the various change. We had each of the students in groups of two or three and they modeled on their own each of the listed quarters, dimes, and nickels. They then set up a proportion where they had how many change and value of change as the numerators respectively and how many make a dollar and one dollar as the denominators respectively.

They then had to come up with a decimal, then convert it to a percent. We then had them choose any amount of pennies the groups wanted. Finally we had them pick various dimes, nickels, and pennies to come up with a value that could end up going over one dollar. We then discussed their findings, and that concluded the lesson.

My focus was on engagement for the observation. For the most part it went very well. I thought and the observer felt for the most part, every student was on task and engaged in the activity for the majority of the hour. I was a little skeptical about the activity since we did the lesson before and the students really grasped it. I was not sure if the students would become bored of it and tune out. The opposite happened and it seemed every student within their groups really enjoyed doing the activity and were engaged in learning about converting change into percents.

I know this to be true because the notes that were recorded by our observer seemed very accurate to the way I thought the lesson went. At the start, everyone seemed engaged in the activity and as the students finished up at different times, they then got a little off task then. I also know most were on task because I would go over to random groups and call on a random member a question about how they answered a question. Every student was able to answer my questions effectively. Other group members did not step in and answer, instead the person I chose on answered it. It shows that every person was responsible for his or hers’ answers. While we walked around the room, there were no conversations that were off topic. Every student was able to finish the worksheet provided for them, with a very good grasp of the activity because during our de-briefing, we called on random students and they were able to answer the questions effectively. I went around when the groups were finishing up and asked some of them what they thought of the activity. It was a significant “I loved this activity!” “This was really fun!” It was nice to see how an educational activity could be so fun for students. When asked why they liked it, they said it was a nice visual to the lesson from yesterday and that pretty much every student likes working with change. Also, there was an overwhelming response to the choices options. The “You Pick” section where students chose how much of each change it seemed they took a liking to. It gave them choice which most students love.

Towards the end of the activity, students were finishing at different times, and it was hard to keep every student engaged when they did this. One example that we discussed was the fact of using a worksheet that would be almost impossible to finish in class. Throw in more challenging questions at the end to keep everyone engaged, and keep a benchmark of where we want every student to get to so we can then de-brief.  When we see everyone has reached the benchmark we can pull the class back in and say that is good enough so then discuss their findings up to the benchmark.  If the students want to talk about the challenging problems, go over it with them individually, or with the whole class depending on if the class wants to and you know you won’t confuse anyone about the lesson. This keeps every student engaged throughout the entirety of the activity and shows differention. It allows more advanced students to tackle more advanced topics. Also, it allows more advanced students not to finish early and waste valuable class time.

The whole observation and coaching experience has been very helpful. It has given me time to really reflect on the activity and lesson. There was the idea that keeping a worksheet long enough so pretty much every student would not finish was something I have never really considered. It was also really nice to see how I thought the lesson went and how the observer felt the lesson went seemed to mirror each other. It is difficult when the observer said this happened and you think “oh I do not remember doing this”. When you and the observer on the same page, it seems teaching is becoming more and more natural.

Observing Others

I had the opportunity to observe a 6th grade classroom. In the teacher’s classroom, at the front of the room there was the “I can” statements posted for all the students to see. The tables were arranged as followed:


 She used multiple manipulatives in her explanations including a poster showing mean, median, mode, and range which was the lesson of the previous day.  She uses a coaching technique.  That is, if students get the “okay” from the teacher or a confirmation from at least three other students, they then move around the room and help out any of their fellow classmates who seem to struggle.  The teacher often poses questions to the tables and allows students then to collaborate and work together.  They then are called on and critiqued by the teacher.  Throughout the process of questioning the table, the teacher walks around and listens to different tables’ discussions.  She emphasizes putting the math language into the students own words.  At the end of the lesson she asks “thumbs  up and down about how comfortable you are with today and yesterday’s lessons” since the lessons are very close together.  She has an interactive math notebook that she has all her students fill out.  It serves as a reference.  On the right side of the note book is what they learn from the teacher, formulas, and notes from the lesson. The left side of the notebook is used for student thoughts. Anything that students use to help them remember can be written in this section. It kind of mirrors the Cornell style note taking strategy.

When asked, the teacher I observed said ideally, mathematics is like conducting an experiment. There is a process that students follow to figure out a problem. She also stated that ideally, a mathematics learner is like an explorer. A learner needs to solve problems and sometimes figure these problems out on their own. Students need to explore a solution to a problem. Since the solution is already there, they are not inventing a new way to solve it, instead just figuring out what exactly that solution is. Finally she said ideally, a mathematics teacher is like a coach. She has incorporated an approach in which students act as “coaches” to other students who struggle. She even stated this during the lesson before she was asked this specific question. A mathematics teacher needs to guide students who struggle, but not be too much help where you just walking them through step-by-step.

I feel that the coaching session in which students help out others who are struggling could be an effective strategy when used appropriately. Sometimes a teacher cannot be helping out multiple students around the room at one time. It is nice for students who understand the topic help out addressing misconceptions others may have. Another strategy that was used that I have already incorporated in my lessons is writing the “I can” statements for the day where every student can see it, and acknowledge it. Students need to know what they are going to be learning for the day.  It addresses the learning goals for the day.   At the end of the lesson, students can determine if they have understood what they were supposed to.   I really enjoy how she set up her room. Collaboration and problem solving in groups. There are tables with at least three students per table. It is nice to bounce ideas off one another and work out difficult problems with multiple points of view. I have incorporated a lot of collaborative learning in my lessons, so it was nice to see this used so much in another teacher’s lessons. The interactive math notebook I could see being effective. Many schools are transitioning to the Cornell style notes. If any school wants to transition to these types of notes, this could already be used. It is nice to when students record their thinking during a mathematical process. I can see this being very effective since it gives students something to look back on and make sense of the information that was presented to them.

One thing that I did not enjoy while observing was the fact of a lecture based classroom. Pretty much everything done in class is presented by the teacher, students write down notes, then do their homework out of the book. There was some questions posed to tables and they worked out problems together. However, most of the class period was the teacher talking, and students became restless. I observed many students zone-out and become disengaged. A good lecture is better than a poor collaborative learning activity, however it is tough to keep middle school students in their seats and engaged throughout a long lecture.

I have learned about some nice aspects and strategies that I could use in my teaching practice during my observation. The two big strategies I really enjoyed learning about and seeing them put into action was the use of students as coaches and the interactive notebook. There are strategies that you can pick and choose what you want to incorporate based on your own teaching style. Collaboration with other teachers is an great way to improve and become more effective teachers.

First Observation Coaching Session

Today I was observed on a lesson on finding the surface area formula for cylinders and rectangular prisms.  The class is mostly based on lecture, so this lesson I wanted them to discover the formula on their own.  I had already done this with a previous class and it worked great.  I was warned by my coordinating teacher that this is one of the toughest lessons for students to grasp.

I began the lesson linking back to previous lessons.  I had students find the circumference and area of a carnival ride which was a circle.  I had students go up to the board and explain their work.  I then posed a question to them.  I took out a piece of paper and wrapped it like a cylinder.  I stated that the circumference of the folded paper is 11 inches.  If I were to unroll it, would the length also be 11 inches?  I had them think, pair, share and after some discussion we decided that yes the length of the paper would still be 11 inches.  We then talked about what exactly surface area is.  I then handed out a net of a cylinder and explained that using everything we just did, determine how to find the surface area of a cylinder.  After some discussion with the groups, some groups got an answer, but two of the groups ended up getting the right formula.  We then discussed as a class the surface area of a cylinder.


Then, we moved on to rectangular prisms.  I handed out the net of a rectangular prism and said determine the surface area of this now using how you solved the surface area of a cylinder.  After some time of visiting groups, we came together as a class.  Two students were able to get an answer.  Upon discussing, it was difficult for the rest of the students to see the surface area of this prism.  They kept wanting to say four sides are congruent instead of only two.  I drew pictures on the board, used their net, and drew on another prism.  I then had one girl explain it in her own words and the class went “ohhhh, now I see”.  I was waiting on that moment for a while.  I still feel that only about half the class really seen where the formula came from.  We were then out of time and the lesson was over.

Talking with my observer later, I feel the first part of the lesson, finding the surface area of the cylinder went pretty well.  The students seem to understand where the terms came from, and when I did some sort of formative assessment with it, most seemed to get it.  I feel I could have done a little more assessment such as talking to pairs about the formula, or addressing it to more students.  The surface area for a rectangular prism did not go as well.  There seemed to be a lot of confusion, and some misconceptions that I had not previously planned to address.  There were a lot of confusing looks on students faces and I attempted to explain it with multiple manipulatives, and it still fell short.  It was not until I had a student explain it in her own words (student language) was when more students seemed to grasp the concept of surface area of rectangular prisms.

I feel most of the students got hung up on the net part of the rectangular prism.  They were more focused on seeing the two rectangles on the end, then finding the area of the long rectangle down the middle like shown below.

net 3

They were also finding it hard to see how the sides mirrored each other when it was folded up into a prism.  In other words, the length on the bottom face was the same as the length on the top face.  They were finding this difficult to grasp.

I think I need to come more prepared with possible misconceptions students may have.  I had already taught this lesson before, and they got it very well.  However, every class is different.  One issue that does not come up in one class, may in fact come up in a different class.  One suggestion that was brought up during the meeting was the fact of using concrete examples then move to the abstract.  I really like this approach.  Students can come up with values by measuring first, then seeing the surface area formula.  I think it would have worked great with the rectangular prism since many students could not see the sides mirroring each other were congruent, so this would have solidified their understanding.  There would be a set procedure the students would be following which may have made it easier for students to understand.  Also, a suggestion was made to use a bigger manipulative compared to my hand held prism.  Then as we reasoned about the prism, we could color each face a the same color as the face that is congruent to it.  Students can have a visual then of which face is congruent to each one.  The formula may have come easier to some of the students then who were just not getting it.

Debriefing afterwards and writing up this blog post has some great benefits as I continue to grow as a teacher.  The smaller things that I would have forgotten about we touched base on and how to correct it.   One example was one student asked “why aren’t all the sides the same?”  and I answer “because they are all rectangles”.  I feel this could have been handled much differently.  Also, I would have never considered just the way I was holding the smaller prism in my explanation could cause confusion for students since I was moving it around and not keeping it in one place.  Students could lose track of where the faces lined up were.  Reflecting on the process has also given me ideas on how I would have attacked the lesson differently and what changes I could have made.  Some ideas were mentioned by both of us that would have strengthened the lesson all together.  I have mentioned earlier about the larger, colorful manipulative and using concrete numbers first.  In the end, if the students are struggling badly, maybe throwing in a short lecture would benefit and tie up any loose ends.  It is always great to reflect on any lesson.  This is where the most learning about yourself as a teacher can take place.

After the lesson and communicating with my observer I feel the first part of the lesson with cylinders went pretty well and the second part with a few tweaks could be an effective lesson.

Overhead Projectors vs. Chalkboards


Chapter five of the Teaching Gap by James Stigler and James Hiebert brought up a key point to Japanese lessons vs. German and American lessons. Something that could be overlooked to contribute to why Japanese scores are near the top in the world in math, while American scores are more middle of the pack was discussed in this chapter. The idea to teach lessons using overhead projectors or chalkboards was talked about as a major difference between the two countries education

American math lessons rely heavily on overhead projectors or Smartboards. These lessons seem to be pre-arranged by the teacher on how the students will learn the new material. It has a step-by-step process where the teacher may cover up some material on the overhead so students do not jump too far ahead. Using overhead projectors seems to not produce a coherent and connected lesson since something learned will be erased and replaced with something else. The ideas continue to be erased throughout the lesson and do not flow together for discussion. There is really not any room for discovery by the students since their attention needs to be focused on the teacher, otherwise they may miss some key information since they do not explore in the material. It is laid out by the teacher on how they feel the students should learn the new material.

From a different point of view, Japanese math lessons rely heavily on chalkboards for discussion. It seems to take the approach of students actively learning together and discussing their conjectures with groups, and the whole class. The chalkboard is then filled with student work and conjectures instead of the teacher laying out the new material for the students. They continue to build on these conjectures throughout the lesson, and are left on the board for the entire class. Students conjecture on their own and the teacher serves as a guide for students to achieve the day’s outcome. It is based on more student led, discovery learning.

I could see Japanese teachers using Smartboards as a form of manipulative to solidify understanding. Smartboards seem to push teachers down the road of teacher-centered instruction over student-centered instruction. Smartboards are kind of like using an overhead projector with the teacher leading students down the path of achieving the objective for the day, while erasing work that has been completed and moving on to the next topic in the lesson. I can see Japanese teachers that might use Smartboards to be a key component to use when students cannot really visualize on their own, so it is used to make sense of the problem. An example of this is three dimensional shapes. Sometimes it can be tough for students to visualize these shapes, especially when they have to rotate them around the axes to determine the volume in calculus class. There is a reason why Japanese teachers have stuck with the old-fashion chalkboard and it works. The teacher can see how they have developed their conjectures and how they have changed over the class period. Smartboards really do not achieve this, but could serve to be beneficial when it is used as a manipulative.

I have never really considered how the way teachers use the chalkboard vs. the overhead projector can have a major effect on student learning. Work is not erased, so students can see how their thought process took place to achieve the learning goal throughout the whole lesson.

Math In Action

ImageYesterday on February 22nd, Grand Valley State University hosted Math In Action.  This is a conference for teachers and students to attend discussions on issues and possible solutions to these issues in mathematics education.  I had the fortunate opportunity to work as a volunteer for this, and attend different sessions.  It was an amazing experience in which I can take these ideas to my future classroom.

The first session I worked as a volunteer for a discussion on Formative Assessment in a Tech-Based World.  She introduced three sites that are free and teachers could use to quickly gauge student understanding.  These three sites include,, and  They require every student to have some sort of access to the internet and they answer questions about the lesson.  The teacher then can track student responses and determine if any students need extra help.  Students can show their work to a problem, and the teacher can review it.  If it is a common misconception, the teacher has the ability to post it to the projector to start a discussion with the students.

The second session I attended was Adventures with Mathematics Grades 6-8. This included five stations that included some sort of game or activity for middle school students.  The games included determining how much money you save driving the speed limit vs. speeding, a guess who game with linear cards, a rotation/reflection/translation board game, four corners involving adding integers, and a game involving graphing linear equations.  These games requires much more thinking about the concepts rather than following a procedure.

Next, I went to the Math-Team-Matics session.  The speakers talked about a mathematics completion that they set up at Grand Valley State University.  The competition includes middle school students all the way up to 10th graders.  Each team consists of six members that contribute to the competition.  For the competition, they do a collaboration piece, individual test, a relay, and a quiz bowl.  The session included the attendees explore each of the four parts of the competition.  I really liked the relay part.  It requires each student to answer a question using the information that the students before solved.  It was interesting watching teachers and college students having so much fun competing against each other solving mathematics problems.

Finally, the last session I attended included a talk on High Fidelity Teaching.  It centered around getting students more engaged in the material.  She talked about the Common Core, a factor that leads to disengagement, and growth mindset.  The factor was stereotype threat.  How stereotypes have affected students in mathematics.  The one stereotype example that was discussed at length was girls are not good at math.  It affects girls since they then feel they do not have to be good at math, and gives them a reason for saying I do not have to be good at math.  The last issue we tackled was growth mindset vs. fixed mindset.  We should want our students to experience growth mindset to get the best work out of them.  Growth mindset was discovered by Psychologist Carol Dweck, and in summary it includes not giving up on challenging problems, logical reasoning, and the desire to learn.

I had an amazing experience at Math In Action this year.  This was my first time attending the conference, and I would like to attend it again.  Any mathematics teachers in the Grand Rapids area that would love to learn more about mathematics education should definitely attend the conference.  Information about this years conference can be found at