It has been a while since I posted anything on here. Since my last post I have graduated, substitute taught, worked as a math interventionist, and most recently got my first full-time teaching position! I accepted a position as a high school math teacher in an Alternative High School.
The exciting thing about this position is that this year the school has taken a new approach with the alternative high school, which is now the Fusion program. What makes this unique is that our students will have full access to things at the high school that they have never had before, the library, a counselor, sports, etc. However, the more exciting thing is that a majority of our students will be able to spend half of their day at the Career Technical Center learning real hands on skills that I cannot provide myself.
Starting this new program has come with some bumps in the road. My one (and only) colleague, who has helped form the Fusion program, was hit by a drunk driver on her motorcycle and as a result she is on medical leave while she recovers. We have also had some other staff changes that resulted in a new counselor and secretary. We have also had to move from the old building into temporary rooms in the high school until our new space in the building is ready later in the school year. As all of this happened this summer I reported today for our first day of meetings before starting not having a schedule, for me or our students and not even knowing for sure what courses I’ll be teaching.
I’m not going to lie I’ve done my fair share of stressing out about things this summer (I’ve gotten it under control lately 🙂 ), but tonight I was reminded about what is really important. The students. We had our beginning of the year open house and I quite honestly was expecting to sit in my room for 2 hours mindlessly surfing the internet after being at school all day. I got back to my room a few minutes before we were set to start and there was already students and parents in there waiting to ask questions about what the year was going to look like. Seeing everyone there made me realize that even though I might not know what things are going to look like after the first couple of days of school it doesn’t matter because these kids are excited be there and excited for a fresh start and so am I!
My goal is to have an awesome year with this new job and new program and make it the best first year that I can! I hope to be able to spend a few minutes each day to reflect on the day and share my experiences on here.
It’s hard to believe but my last week of student teaching and my undergraduate education at Grand Valley is here. As I look back on the semester I haven’t blogged nearly as much as I did last semester. It is probably because by the time I left school I was so tired I do not think I could have written anything that was coherent. This semester I had the opportunity to student teach at Oakridge High School teaching a wide array of classes. I taught geometry, pre-calculus, calculus, and a personal finance course. Many times I was learning the material the night before I was supposed to teach it, but I learned so much this semester and I am grateful for the opportunity I was given.
Areas of Growth
Using Formative Assessment
Throughout my entire teacher preparation courses it was stressed how important using formative assessment during each and every lesson is. We got strategies on how to do this but I never felt that they would be beneficial for my planning because they would either take time to look through, like exit tickets, or the assessment wasn’t recorded. I looked to find ways that I could use formative assessments that were quick and could be recorded so I could look at the data again later. My first idea was to use Socrative but this led to the issue of if students would have a device everyday and what they would be doing on their phones during instruction. I then came across Plicker Cards on Twitter. With this I was able to quickly scan students answers with one smart phone, mine, and then was able to save the data so I could look at it later. This let me target specific students for more one on one help during the time students were working on homework. I also noticed that when I started using the cards students who said at the end of the day said they didn’t get it yet asked more questions than they would before. I don’t know if in fact the two are correlated but it seemed to be related.
Building a Positive Classroom Culture
The students that I had this semester had a set of expectations of how a math class should run and my expectations were very different. I had to work across weeks to get where I wanted to be. Subtle shifts in the way we did things was very important. I slowly changed the way we did lectures so that students were more involved. They slowly came around and many more students were willing to participate, which changed the way the class felt. Students were on top of each to address any disruptive behaviors before I had to. It was nice to see that my students wanted to learn and did not appreciate the disruptions. I also slowly introduced more group work into class. At the start students were unhappy with this and struggled to work together. The more we did this they saw that the group work wasn’t voluntary and began to work together effectively. In fact one of the last activities I did was a walk around activity where students worked in small groups to do review problems for an upcoming test. During this activity I think I might have answered 5 questions during the time when about 10 groups walked around and worked on 20 problems. They relied on each other to answer a majority of the questions they had! They also worked for at least a solid half an hour. This is a huge step for this group of students and it was amazing to see the growth that occurred. In fact once we got to this positive classroom environment students were understanding the material better than they did before.
Things that Work
Short Lecture Time
One of the teaching methods that my CT shared when I started the semester was that he tries to talk for no more than 20 minutes in any given class period and the time we have left in class is used for working on homework problems. I tried to stick to this during the semester and it seemed to really pay off. Students would generally have about half the class to work on the homework assignment. This allowed students who got the material to get it done and then find something productive to do. It also allowed students who were struggling with the material to get one on one help in class so that they did not have to go home to complete it and then get frustrated, struggle, and fall behind. Once my students finally understood why I was running class that way and started to get everything completed before they left class. This freed up so much time in class because I was not being asked to spend 15 minutes on homework questions at the beginning of class. This definitely helped to change the classroom culture in a positive way.
Student Communication & Collaboration
As I already talked about earlier with building a positive classroom culture student communication and collaboration is something that really seemed to work for my students and I. When students are working together and talking about math they seemed to be much more involved in the learning process. When they started talking with each other their understanding grew and they became much more self directed and seemed to want to do well and understand the math. As their communication skills grew so did their understanding and achievement.
These are just a few of the big ideas I gained from this semester. I learned so much and grew as teacher in the short three months that I had here at Oakridge. I know now that I am ready to handle my own classroom so now I need to working on finding a job!
I recently had my second content observation for my student teaching. I wanted this observation to focus on how I was using my time in class. As I teach my pre-calculus class I’m feel as though I’m not getting through the material as quickly as I could so I give my students time in class to work on homework. My goal is that they should be able to finish a majority of the homework in class so that they have the support that they need. When looking at the data that was collected I spent 15 minutes on the warm-up and going over homework, 35 minutes on the material from that day’s lesson, which left 10 minutes for homework. My goal everyday to to try and give students at least 20 minutes a day to work on homework.
In the coaching session I started to think about where I could save time during a lesson so I get the amount of homework time in at the end of each hour. In thinking about it I do not like spending the amount of time we spend going over homework. Besides the time it takes I feel like I lose a lot of the class because generally only a few people need to go over that question. I would rather spend the time while we are doing homework to work one on one with students when they are stuck. Part of the problem I have seen this semester is that a majority of my students lack the confidence in their abilities to do the math. Many times the homework includes questions that requires students to use what we talked about during the lesson to apply to a new type of question. These typically are the ones that I have to go over. When students ask these questions I hear, “you never showed us how to do this type of problem so I can’t do it”. I want them to be able to reason through it but thats a skill that has not been built up until this point. They have a hard time understanding the value of a productive struggle and that problems worth solving do not always have an answer that can be found in under a minute.
I also have realized that I spend way too much writing definitions and going over them during a class period. In an ideal world I would like to have students homework be to go through the definitions for the next day. The way I envision this working the best would be in a one-to-one environment where I could do some kind of short video of audio presentation. I don’t have this luxury right now so I thought about trying to give students definitions pages so that they have them already down on paper and we can get through them much quicker.
As I think about the future I want to make sure that the limited time I have in class is being used in the most productive ways. I have a better understanding of where time goes during a lesson and want to use that to help me budget my time more effectively. I also want to build up the idea that applying what we learned to a new type of question is a good thing and the hand shouldn’t go up right away. All of this is going to take time to build up the confidence in students but I know it can done and I’m excited to see the effects during the rest of the semester and in my future classroom.
As I was trying to decide what do on Halloween in my classes it just did not seem like a good idea to try to start something new. Halloween was already falling on a Friday and with students dressed up and myself dressed as Olaf, from Frozen, I had a feeling there would be too much of a distraction to try and start new material. I also did not want to waste the day by doing nothing so I turned to the Three-Act-Math Super Stairs task. This task was at a level that was below where my students are but challenging enough for us to take the hour to work through it. You can find the link to the task here.
We started by watching the prologue video and then I asked students what questions they had about the videos. Each class was able to come up with a good set of questions.
One of my favorite non math related question was “how does he not fall on his face?” Apparently my students would not be comfortable doing the Super Stairs.
I did pose my own question about how long it will take will take him to do the super stairs. I was surprised that this question didn’t come up especially since the video of the super stairs ends part way through. I then asked my students what information they wanted to know. Once my students realized I was not going to tell them the answer we started to get some good ideas about what we needed to know.
After we defined what was the difference between steps and stairs and looking at our estimates for the number of steps taken. Students were confident in their answer that there was 462 steps were taken. I think it helped that this number was within 100 steps of any estimate that students gave.
We next turned to how long it would take to complete the super stairs. Each class took different approaches. My first class decided to time the amount of time that it took to do each set of super stairs. They then divided the time by the number of super stairs that happened in the given amount of time. The goal was to find how long it took to do each super stair during each set and then use the five times they found to find the average amount of time spent per super stair. They then multiplied their average by 462 to get the amount of time it would take to do the entire super stairs. My second class decided that they wanted to look at the time it took going up and the time it took going down. They talked about trying to time the turn around time it took on each super stair. The struggled with timing that and decided against timing that and figured the time for that would work its way in with their timing errors on the time up and time down. They found the average time it took for him to go up and the average go down one stair and multiplied those numbers by the number of steps up and the number the of steps down and added the times together.
My first class found the time that it should take him to complete the super stairs at 8.3 minutes and my second class found that it should take 522 seconds. At this point I was curious about how their answers compared to the estimates that the made for the time. All of the estimates in both classes were in-between 2 and 3 minutes. I asked the class if they were satisfied with the time they found even though all of the estimates were well below the time they found. I was surprised when they tossed their estimates out to go with what they found. I then showed them the final video and we talked about how our time was way off and what could have led to this error.
We talked about how their timing may not have been as accurate at it could have been. My first class wondered how by taking the average of the the super stair may have affected their answer rather than timing the time up and the time down. Someone also brought up the idea that when we found the times we may have had a problem when we were converting the units. The answer they got were pretty close to double so they wondered if maybe the times they found were for 2 steps instead of one. Unfortunately we ran out of time in both classes and were unable to fully explore that idea.
While working on this I noticed a few interesting things about my students:
- My students have a hard time asking for what information they need.
- They were mad that I was making them answer the questions instead of me answering them.
- They wanted to give up to early.
- They have a hard time collaborating with each other to work through the process.
These are all areas that I want my students to be strong in and now I must think about how do I best support them in this growth.
A few weeks ago I attend the Fire Up student teachers conference. I was able to attend three sessions that got me thinking about the kind of teacher I want to be. I attended sessions on how best to deal with difficult situations, how to embrace mistakes, and fostering a growth mindset that left me with the most to think about.
The first session about dealing with difficult educational situations really reminded me about how important relationships are. He spoke about how at some point there is going to be a situation where you say the wrong thing or you have to address an issue that is causing problems. The better the relationship that you have built with the student or parent the better the outcome the situation will have. It brought me back to the idea that I heard during my teacher assisting seminar, that students do not care what you know until they know that you care. I want to take the first month of the semester to spend the time getting to know everyone of my students and finding something about them that I can relate to. I also want to work on building a positive relationship with parents. I’m not sure what this will look like yet. I imagine it taking the form of calling to introduce myself before the school year starts and making periodic phones calls throughout the year. I also think a quick email home to parents at the end of the week would be a good idea. This is the area that I want to work the most on as I get my own classroom.
As I think about the other two sessions a common theme emerged about embracing mistakes and using those to help build upon what we are doing in class. I want my students to see that mistakes are a part of the learning process and something to be celebrated and not something to get dragged down by. I want to build up the idea of a growth mindset with my students. I want them to see that mistakes are what help them learn and that we often in fact learn more from mistakes than when we get the right answer on our first try. This is going to be a tough sell for students to embrace because students are trained to always get the right answer as soon as possible and if they do not it somehow says something negative about their intelligence. Right now I do not have all the ideas about how to set up this types of classroom. After these presentations I have a renewed interest in finding out how to do it and more resources to help me than I had before.
Overall, I think the Fire Up Conference helped me to see in what areas of my classroom norms I am happy with and where I still want to grow more. I really excited to see where my students will be able to go once I learn more about how to best support their learning.
I recently took over our section of geometry in my student teaching and had my first observation. This observation focused on the level of engagement from students over the course of the hour.
At this point I’m still working on setting classroom norms and expectations so with this observation I was hoping to get a sense of where the class was at and what I still need to address. The first aspect I feel like I need to address in participation when I pose a question to the class. I want the class to have more discussion and more involvement from my students. I’m looking into the possibility of using Socrative to possibly jump-start this. I also need to work on giving more time so that everyone has time to think of answer so that I can get responses from more students.
The other big area that I need to address is what my expectation are for when students are working on homework. Ideally I’d like to discuss the day’s topic for about 15 minutes and then try to have at least 20 minutes for students to work on any homework they have. The goal of this is so that students have the support that they need while doing the homework so they can ask any questions they still have before they try to attempt it at home. However during yesterday’s time for homework there were several students who decided the time would be better used as a social hour.
Now that I have a clearer picture of what my expectations are and what the classroom dynamic is like we have some things that are going to be addressed more explicitly. Overall I think we are off and running to a great semester!
Update: A about a day or so after I wrote this originally I saw on Twitter about using a resource called Plickers, which gives each student a unique card to select from four different answers and the teacher uses their smartphone or tablet to scan the responses. I’m thinking this might be a better tool to use then Socrative.
Recently I got the chance to observe another math teacher at my placement and see what their approach to teaching math is and think about how this style is influenced by their beliefs. I had the teacher that I observed answer the following questions about what they think it means to do math.
The teachers that I observed said that doing mathematics is like working a puzzle, a mathematics learner is like an explorer, and a mathematics teacher is like a coach. The day that I observed the class was doing a review day for an upcoming quiz. The review was set up so that each student had a whiteboard and did problems that the teacher gave. They were working in pairs that provided support for students to work together if they got stuck or a way for them to check to make sure that they got the right answers. As they finished their work students would raise their whiteboards for the teacher to check them and give them either a “yes you got it” or a “nope you didn’t get it yet”. There was one question in particular that a lot of students were getting wrong and the teacher started sharing whiteboards from groups that had the correct answer and having other students going to other groups to help them solve the problems and understand what they should be doing and what they were doing wrong.
After watching the review activity and looking over the answers to the above questions the way that the class session was run made so much more sense. I can see the idea of working a puzzle come through when the teacher was explaining how to find surface area and volume of prisms. He talked about identifying what the question was asking and then to identify what information was needed to solve for what it was asking. I think this speaks to solving a puzzle because those two things are key in solving any puzzle. When I saw him giving whiteboards to struggling students to help them solve the problem I was unsure about how it was going to play out and if it would just lead to students copying their peers work so they could get the right answer. (After watching I didn’t get any indication that this was happening.) I think this strategy fits well with the way that this teacher views learners as explorers. From my observations giving the students the whiteboard was a way for them to explore what they did wrong and what misconceptions they have by seeing what others did and then to discover what they should be doing. Lastly when observing the overall teaching style for this class session the coach persona seemed to fit well with how this teacher was teaching. The approach seemed to be to give students everything they need to solve the problem but ultimately it is up to the student to solve the problem. When these needs varied by students and he adjusted to what the particular student needed to be successful.
After the observation it became much clearer how our beliefs about teaching impact the way we teach. If I were to have observed this lesson without asking the questions that I did I think I would have had a much different view on what I had seen. However, by seeing what beliefs this teacher had about teaching math gave me a clearer lens into why he teaches the way he does and even gave me a few ideas that I may not have thought about before because our views on teaching are different.
Back in February I was able to attend Math In Action (see post here) and in one of the sessions I attended I learned about the use of Task Cards in math class. The basic idea is that you make cards with different math problems of varying difficulty. Each student then gets a card to become an expert on. The great thing about this is you can give students cards based on their ability with the content and what they will feel most comfortable explaining to others without anyone knowing the differences. Here’s a copy of the task cards that I used as a review of the measurement unit we had just completed.
For each card students do their work on this grid and then their partner for that cards checks it and initials the smaller box if it is correct or helps them to figure out what they did wrong. And then they move on solving the rest of the cards that their peers have. Now on to what we did.
We switched up the way that I had learned about it at MIA a decided to do a “speed dating” session in order to provide some more structure for our students as this was the first time we had tried anything like this. We lined the desks up in two rows with the desks facing each other. I gave each student a card and told them that this was going to be their card that they needed to know how to explain to a classmate if the classmate got the question wrong. We explained that we would give them a time limit, we started with 2 minutes, 1 for solving the problem and 1 for talking about the solutions. We had to extend this time a little bit as we kept going. After that two minutes one of the rows of students were to move to the next seat over and we would start over again.
If you really want to get into the speed dating theme like my CT did you can add the candles on the desk, turn off the lights, and Google some elevator music in the background. Fair warning on this 7th graders will laugh every time you say speed dating or say you should only be talking to your “date”. They did feel awkward when two boys were across from each other but all that fades away rather quickly and our students worked remarkably well.
That being said I learned a lot from doing this the first time. First I didn’t plan well for the time it would take to set up the room and explain what they were supposed to be doing and have them actually get it. We spent close to 20 minutes going over how this would work before students were confident enough to start on their own. It was all worth it in the end when they got to work but its something that really needs to be taken into consideration.
Another idea we talked about doing was making two sets of the same 15 cards so that the class could be divided in half and everyone is still doing the same questions. This would have been beneficial in our case because we didn’t have enough time for each student to get through all the cards. I think this could save a lot of time because students are answering 15 questions instead of 30.
Overall I was really pleased with how this activity worked. Once students got the hang of what they were doing they were on task for at least a solid 25 minutes and even seemed a little disappointed when we had to stop before they had gotten to all the cards. I even had students ask the next day if we were going to be able to finish them. The next time I do this I’m going to definitely have to plan for the startup time better and I think I will go with the two sets of the same 15 cards to make sure students are getting the most out of the cards.
Recently we covered the Pythagorean Theorem in class and I was looking for a proof to use to discover the theorem when my CT gave me one of the area based ones that she has used in the past. I decided to use that one and do a whole class discussion about using this for the proof. We started with this jumbled mess of pieces and then formed them into two squares with each having four of the red triangles.
After we got them in the squares I told students we were going to label each side with a letter, a for the shortest side, b for the middle side, and c for the longest side. I then asked students to tell me the area of each of the squares that we created. From this we obtained the following,
Students immediately saw that the area of the squares were equal. After this we talked about if there was anything special about the red triangles in each of our squares. Rather quickly one student explained how the triangles were congruent because all three sides were the same so we have eight congruent triangles so their areas are equal . After we had these two facts nailed down I started removing triangles.
I removed one triangle from each and asked if the areas of the shapes there were still equal and I got a resounding yes from my students. I then took away another triangle from each.
I asked again if these shapes still had the same area and got another yes from the students. After this step our discussion got rather interesting. I removed a third triangle from each to obtain this shape,
I asked again if these two shapes had the same area but now this time a vast majority of the class yelled NO! This struck me, as this wasn’t something that I would have thought would have been a common answer for the class, although I will admit my CT said this happens most years that she has done this activity(There were a few students who said yes but a majority of the class was not buying it). I asked for a few students to share why these shapes did not have the same area anymore and got very similar answers from all those that shared and it went a little like this. Students talked about how the pink square in the shape on the right was messing with the area because it was somehow different than it was before. The most I could get out of them on what they meant by this was that since it was not connected to a triangle anymore by a side it had to messing with the area. Just to make sure that we were all on the same page about the shape with two triangles I added the triangle back and asked if these had the same area and again they said yes. So I took away the triangle again and asked again if the shapes still had the same area and again I got a no. I asked the class if I had changed anything about the size of any of the shapes. “No”. Then we talked about what we knew about the triangles in each shape. One student said they were congruent and another added that congruence means that they are exactly the same. I thought finally we’re getting somewhere with this. I told students to think about what we knew about the previous shapes and what we just discussed about the triangles. As I waited hands started going up and various students shared that they shapes had to be the same area because the area was same before the third triangle was removed and since we removed congruent triangles the new shape also had to have the same area. I was really happy with the fact that they were able to figure this out! So we removed the last triangle and decided that their areas were also the same and after that triangle we were left with three squares.
Since we knew the area of each of the squares and that the area of the yellow square was the same as the green and pink squares combined we rearranged the squares and wrote an equation.
I asked students if they had ever seen this formula before and many stated that it was the Pythagorean Theorem! After we saw where the formula came from we spent some time using it.
I had my second and final observation by my content area professor recently. We followed the same setup as before by identifying what we are looking to work on and then complete a coaching session about the experience. As I am nearing the end of my teaching during this semester I feel confident about the planning and instruction part of teaching for where I’m at in my growth. As I thought more about my instruction I began to wonder about what students I call on and how often I call on them during a lesson. With this I decided to have my professor record which students I called on and when during the lesson in hopes of seeing areas where I can approve.
After the lesson I felt pretty good about how it went getting more people involved, especially considering the topic that we covered was rather confusing. After looking at the chart that my professor filled out I noticed some interesting aspects about it. First off the same group of students that usually answers question had answered the most questions. There were some students who answered a question or two when they are normally quiet. One of the biggest successes for the day when our newest student, who still seems reluctant to participate in class, answered a question voluntarily. The most surprising item I saw was that one group of students only answered one question between the four of them and the more I thought about this it seemed clearer to me that this has happened on more that one occasion. The only answer that I have for this is that this group is in my peripheral vision and they are consistency one of the best behaved groups in the class so I don’t feel the need to keep an eye on them, which I have found lets them off the hook for answering questions during class. This is not my intention with the group but was an interesting observation opening my eyes to where my attention is during a lesson. Another goal of mine that came to light was that for me it’s not so much having the variety of people answering questions that is important to me but rather having the type of classroom environment that allows students to feel comfortable answering questions, without having to worry about people thinking they’re dumb, without having to worry about whether they have the answer completely correct. I think if I can set up my classroom like this I will not have any problems in getting the variety of students answering questions because a majority of them will be raising their hands to answer.
So where do I go from here? First and foremost I need to be aware or where I am at in the classroom and what groups I can see. I want to be able to get input from the group that right now I just don’t see and I think I can do that with much more ease if I am changing my position in the class frequently during a lesson. My next step is going to be looking more into what strategies can help in creating the type of classroom environment that I want. I feel like this is something that we always stress is important during the teacher preparation process but it’s something that I don’t recall ever talking about really what steps should be taking to ensure this. My goal is to learn more about this over the summer when I’m not so crazy busy and try some of what I find in my student teaching so I have an idea of what I should be doing when I get my own classroom.