Made Up Solutions?

Looking back at my problem solving interview many things become clear. First and foremost, my student used many different methods to solve all the problems: quick facts, using the "standard" algorithm, using a counting strategy and direct modeling. Maybe because my memory is selective and I probably didn't really pay that close attention, I truly don't remember using manipulatives or strategies other than standard algorithms. When elementary school comes in my mind, all I can think about are MAD MINUTES!! Never once do I recall being allowed manipulatives ( I can actually picture my mean 2nd grade teacher calling them toys....if she ever saw them..).  I think that's why I always get so excited by my "special" way of doing subtraction. I never got the chance to explore my thinking and to find an algorithm that makes true sense in my head, is exhilarating.

Another thing that comes to mind about my student is that once he noticed the unifix cubes in front of him, he never looked back! Even though he was more than likely exposed to the standard algorithm to set up multiplication/division problems, he didn't use them unless it was a last resort and the manipulatives were confusing him. If you look at the pictures below, you will see that M is solving a problem with the cubes. In short, the problem says there are 45 students that will be on 3 teams, how many people on each? In terms of a standard algorithm, this is a division problem; 45/3=15. However, M didn't see it that way. He counted out all 45 cubes, then grouped them in to threes and then counted how many groups of three he had. In all actuality, this is a very complex strategy. It appears that he realized that he is trying to see how many times 3 goes in to 45 because he separated the blocks into groups of 3 rather than making three large groups and dispersing the blocks equally. See below...

I think that there are a couple of different ways other students may have solved this problem. The first is by separating the cubes in to 3 different "teams". Count out and put cubes one cube in each group until they are all gone. Once they are all gone, re count (to double check) how many cubes are in each group: 15.

Another way a student could solve this problem is by first counting out all 45 cubes then subtracting 3 from the group until the all the cubes are gone. Once all the cubes are gone, count all the groups. This strategy is very similiar to M's strategy but it is turning the problem into subtraction (and eventually addition) instead of putting them in to groups of three from the beginning.

Making Moves!

Although I could chose a lesson from my math class, I want to look at my first "teachable" moment for math in my OJT (on the job training) setting.

Last week, my class began volunteering at the Capital Area Food Bank. We go (starting last week) every Tuesday to volunteer there. This is part of the OJT curriculum; going to a job site and learning vocational skills such as team work and collaboration.

The job that the Food Bank gave us last week was to build boxes so that later other volunteers could fill them with food for families to come to pick up and take home. By the end of the day, there where hundreds of boxes completely put together. Right before we left, one of the students asked me, how many boxes did we put together? Although it was very tempting to just tell him the answer, I encouraged him to discuss it with his peers. Here is how the conversation went:

R: How many boxes do you think we put together Ms.?
Me: Well, what resources do you have here to answer that question yourself? Count them individually? Ask your peers?
R: I could ask B. B do you know how many boxes we put together?
B: No...I didn't count them one by one how should I know?
Me: Well let's think about this (I scan the room) how many palates do we have full of boxes?
R: 5
Me: How many boxes are on each palate? I know we aren't going to count them one by one so what strategy can we use to figure out how many boxes there are?
B: I know that there are 3 boxes down and 3 boxes across and they are 8 boxes high. But what do I do with that?
Me: I don't know, what DO you do with that?
R: Multiply....?
Me: EXACTLY!! If you need to, get your phone out and use the calculator function to see how much it ends up being...
B: 360 boxes!

**Pictures from the Food Bank**

Looking back on this conversation, I used several Talk Moves: asking students to apply their own reasoning to someone else's reasoning, prompting students for further participation and wait time. I was constantly trying not enable them but to encourage them to use the resources they have in front of them to solve everyday math problems. They should use their calculators, talk to their peers, look up words etc.

If I could re-do this lesson, I would expand this lesson to the entire class. Everyone should know how hard they worked and everyone should get the opportunity to apply the math skills they acquire in the classroom in the real world. I also think it would have been neat to hear the students bounce ideas off of each other and solve the problem together.

Upon reflection and based on feedback from previous coordinating teachers, I feel the talk move I need to utilize more is using wait time. I always feel the urge to answer questions for the students instead of letting them try to figure it out themselves. It's not that I don't want them to think for themselves, it's just that it's habit! Especially if we are doing an assignment and I ask them a question and it takes them more than 3 seconds to respond. I will quickly interject and move on. I have got to get to a point where I am comfortable and patient enough to let the students figure things out on their own. Everything doesn't have to be so perfect and fast paced!!!!


Although unrelated to math, I just wanted to share a picture from my classroom. This past week we celebrated one of my student's birthday. Here is a picture of the class celebrating it!

Are You Teaching the Test or is the Test Teaching You?

1.
-When I first walked into my high school I was completely overwhelmed. The school was so much larger than the high school I went to. Before I met my CT for the math class I spoke with the department head of special education. She informed me that their high school was used as the model for all other SED programs in the district. I thought to myself "Wow, I feel very lucky to be here. I am going to be seeing a lot of wonderful teachers." As I walked into my math classroom I was a little bit surprised. The walls were bare, the students seemed to be segregated into different parts of the room. Something was even more interesting was how staffed they were. Not including myself, there were four adults in the room for a classroom of less then 20 students. How rare!! There were two teachers and two TA's. I thought the classroom was for just one math class, but I quickly found out that it was one classroom for THREE different classes; Math Models, Algebra and Geometry.

-As for the hallways, one word; CROWDED!!!! Students everywhere, some walking, others rushing and a few in the corner just staring at the ceiling. Another interesting thing is that the SED classes are all next to each other and in the same hall way. Logistically, I think this is great. The students don't have to walk all over campus to each class. However, it's like they put all the students with special needs in the corner. It's a catch 22 really but I'm leaning towards not segregating the SED students into one hallway.

-The really neat thing about the high school I teach at is it seems to have all different mixtures of culture, race and economic status. I'm not sure of the exact percentages but from what I can tell, everybody is a minority because there is no majority race.

2.
-A lot is going on in the classroom I teach math in. There are 3 different subjects being taught. The students that are in Geometry class leave with one of the teachers to go work in another classroom. While the other students stay in the main classroom. The Math Models students sit in a circular table and work while the Algebra students sit at desks in a row and are taught by the main teacher in the classroom. I would like to say that the teaching in the classroom is top notch and the kids seem to be learning at a rapid pace. Sadly, I'm not so sure this is the case. The teacher often raises his voice at the students, points out their mistakes in front of the entire class and tells them the only reason it's important for them to learn this material is so he doesn't get in trouble for them failing the TAKS again.

-I often find myself sitting in a desk next to students trying to go over problems they have missed. However, this will not be the case after this week. I will be spending my time working with small groups of two on computation and word problems.

3.
-I really don't know very much about my teacher's beliefs in terms of mathematics learning. The only thing I do know is that he is very supportive of students utilizing the resources they have in order to solve problems they don't know. For example, the students are always welcome to use the calculator or any notes they have taken in class, even on the tests. I know this because I have seen and heard the teacher mention it in the classroom and encourage the students to use these resources.

-I definitely agree with allowing the students to utilize the resources they have. Because the know the basics operations of math (addition/subtraction/multiplication/division) I say let them use any resources they can. When in life will you not be able to ask for help? Grab a calculator? Use the internet? Granted there are times in your life where you may not be able to afford a calculator or the internet but you can go use the library's internet for free. I feel that there will always be some sort of resource available so why pretend in the classroom that there won't?

-I'm not sure that my identity is forming or growing currently but one thing I am in tune with as of now is how negative attention can effect students. To see the hurt and embarrassment in the student's eyes and body language was painful. I hope I will not say such things to make my students feel that way.

4.
-I am so worried that my blunt personality will get in the way of my teaching. I can be confrontational, overly honest and rude. Although these aren't my finest personality traits, they are at my core. I lack patience at times and I hope that through my student teaching and mentoring by my teachers, I will become slow to anger and quick to listen!

-I also worry that I won't be good enough!! Maybe I won't know the right strategies or the right things to say. I might not know how to communicate or be culturally sensitive enough.

-Although I know I will not be perfect and will stumble in many ways, I hope that I continue to grow and develop my skills by always seeking professional development and staying on top of the latest research based practices.

OR ??

Will I be:

Response to Readings

1. It differs in that it taking a problem-solving approach to solving math dives right in to showing kids how this math really applies to our life. I feel that this method doesn't make the student feel like they are actually doing math. For example, in my setting now, my resource class is doing an airplane project. They are working in groups to create an airplane maker company. They have to figure out the costs for different services they will offer and then later they have "clients" who want to buy a plane with different services. They have to use the costs they assigned and calculate the final price. In short, they are using variables and expressions in a real life way.

2. I'm afraid that my ideas on math will make me "skip right over" math in the classroom. For example, when I taught a 2nd grade GED class last fall, that was the only subject that I only taught 2 lessons in over the course of 4 months! Every other subject I had between 3 and 5!

3. It sounds like to me that this group of people may be "teaching to the test" instead of actually teaching their students. You have to think about what your goals are for the end of the year, where do you want your students to be at? Obviously you want them to do well on the TAKS/STAR but are you only going to focus on those criterions?

4. NO! You have to let go of the control and allow the student to do it themselves. It's like the saying, "If you give a man a fish he will be hungry tomorrow. But if you teach him how to fish, he can get his own food." I may have misquoted but in the end it tells us to teach them how to do it not do it for them.

5. "Students sometimes got different answers for the same problem. Instead of erasing an answer and changing it to the answer of a more capable student, the students justified their own answers. Through their conversations they made sense of the problems and found their own or others' errors." pg 271. Isn't that what we want our students to do anyway; figure out what makes an answer right or wrong?

My Math Life Story

1. In order to find my peak experience in math, I had to travel all the way back to 5th grade. It was here that I beat every person in my class at Mad Minutes. Although I recently found out that Mad Minutes are probably not the best practice for encouraging camaraderie or a positive learning environment, I thrived in this competitive scene. I lived for the times that I turned my paper over first after completing 100 problems in a minute (40 more than the usual 60). I'd like to say that I enjoyed these experiences because it was a time in which my math skills were being harnessed however this is not the case. I relish the taste of victory! Always have and probably always will. Thinking back to those days I get a since of accomplishment and I hope that I can provide these same feelings for my future students. However, because of how competitive games and activities such as Mad Minutes become, I feel that this is probably not the best practice and I don't see myself using this strategy in my classroom. Even though this was one of my favorite experiences of my all my school years, I would rather come up with games/strategies that encourage team work and a positive work environment instead of a desire to one up thy neighbor!
2. The worst experience I've ever had with a math class is my experience with college algebra. My senior year of high school, I took an online dual credit class at a community college. All of my life I have made A's in math so I thought this class would be no different. Even better, I would receive college credit! How little did I know!! Turns out, the class actually required work and time! Two things I did not intend on putting into that class. Nonetheless, I powered through and ended up trying really hard to maintain an A in the class. My effort was in vein. The following roadblocks kept me from obtaining my goal: 

• The program for homework assignments wouldn't load on my computer. 
• Two out of my three tests were LOST in the mail and my teacher didn't believe me. 
• During my final, I was required to take it at a testing center. At the time, I was really sick with the flu and coughing like crazy! While I was taking my test in a very small but very full room I began to cough a lot and was obviously self conscious about it. So, I decided to grab my test and walk out of the room to ask the test administrator if I could go get a drink of water to try and calm my throat. The test administrator promptly informed me that now that I have exited the testing center, I may not go back in. Consequently, I was not able to finish the rest of my test! 

       To sum up, that's 2 lost tests and a half way completed final!! To say I didn't get a good grade is a   severe understatement. For the first time in my life I failed a class. It was awful. 

     3. The turning point on my view for math happened when my teacher had the faith in me to place me in gifted and talented math. I had no idea that my teacher felt that I was capable of being in that kind of rigorous curriculum. I literally showed up to school on the first day, picked up my schedule for 6th grade and saw that I had been placed and referred for gifted and talented. 

     4.  One really important scene in my math life is the way I learned subtraction. I was lucky enough to have a teacher that loved teaching different strategies to accommodate different types of learners. One of those strategies is called the Indian Method for subtraction. At the time I had no idea that this was not the "normal" method for subtraction. It wasn't until my M316K class that I realized people don't subtract the same way I do!! Furthermore, people learn all types of ways and use all different strategies to subtract numbers. Another scene in my math life that stands out is a project that I did in an AP Calculus class. My teacher thought it would be great if we spent two weeks working on how to draw pictures with our graphing calculators. In the end, the only thing I can remember from a year long class is making a block letter J and a stick figure appear on a graph. Sad isn't it?

       5.  My greatest challenge was definitely my experience with my online college algebra class. I was humiliated after doing so poorly in a class due not to an inability to complete the work but instead to several roadblocks and a lack of common sense. Failing that course made me rethink college all together. If I couldn't even pass a community college course, what made me think I would do ok at UT? It took a good friend of mine to finally get through to me and make me realize that the only person to blame for these mishaps was me. I didn't fail because I have a disability or because I didn't comprehend the material; I failed because I didn't think things through and made poor choices. In order to do well at UT I need to put time, effort and a will to learn into my classes.

        6.    I want to be a special education teacher in order to change the experiences that so many parents of children in special education. So often I hear how terrible the life skills classes are or how students color all day long in a secluded classroom. I want to create a classroom environment that uses life skills and academics to improve my student's lives. I hope to teach mathematics in a more indirect and community based way. For example, this past Spring I was in a placement that took their students to the Austin Area Food Bank on Thursdays. Here the students had to weigh boxes of food, know how to add and subtract weight to meet requirements etc. I want to use and teach practical math skills.