Blog Entry 4- Invented Math Strategies

            My student at Houston Elementary used several strategies when attempting to solve math problems. She set up the problems originally using the traditional algorithm that she had seen so many times in the classroom. This is to say that when presented with a subtraction word problem orally, the student would first write on the paper: 7-5=. She recognized that this is the standard form of what I would see on homework or a test. She did not seem to have her math facts memorized, but that did not stop her from using student-invented strategies alongside those taught to her in class to creatively solve multiple problems.

            One problem is as follows: John had 13 pennies. He lost 4 pennies. How many pennies does he have now? My student would identify that lost meant that the pennies were removed and that must be subtraction. She wrote 13-4= on her paper. Then she grabbed some of the cube manipulatives and counted out the total number of pennies he started with which were 13. She then removed 4 of the cubes to represent the pennies being lost. Then she counted up the remaining cubes and determined the answer to be nine. She then wrote 9 on her paper to complete the equation.

            The student was familiar with the standard form of how we expect children to set up a subtraction problem. For the actual process of finding an answer she used direct modeling with the cubes and counted to find the answer needed. This was just one of several strategies she could have used to solve the problem.

She could have used mental computation. Visual representation is not necessary for all students to solve the problem. She could have counted down in her head to solve the problem. I notice that many students use this strategy with varying results. This is a fast way to solve a problem and is useful because manipulatives may not always be present. The major drawback is the process is invisible to the teacher. If a mistake is made there is nothing that can be referenced to see where an error occurred.

            Another strategy that she could have used is subtracting by counting up. She could have started with 4 and counted up to 13 noting how many units were between the two numbers. This is helpful in identifying the relationship between addition and subtraction.  This strategy does have limitations when dealing with bigger problems such as 99-23. The thing to take away from this is that there is no one way to solve a problem and it is important to encourage students to use traditional and student-invented strategies to gain a better understanding of mathematics. Counting Up Subtration Model

Mathematics Identity Blog Entry 3- Math Talk Moves

1)   Chapin’s Five Productive Talk Moves

a)    revoicing

b)   asking students to restate someone else’s reasoning

c)    asking students to apply their own reasoning to someone else’s reasoning

d)   prompting students for further participation

e)    using wait time

2)   I did not begin teaching this week and am finishing up my baseline assessment so I can create a lesson plan for next week. I did observe my teacher lead class lesson and I helped when appropriate. The lesson was over finding the greatest common factor and I saw many of the talk moves in action, particularly in the guided practice. The teacher did a good job of revoicing and prompting for further participation. She gained information that would not have been otherwise due to prompting and then explained it in her own words back to the class so others could understand the method that their classmates were using. The students were responsive to the lesson.

3)   I think that the teacher did a great job of using talk moves as she deemed appropriate for the class and the lesson.  I would have considered expanding upon what the students said by having the students relay and compare the methods used by their classmates. I think that this shows how well a student understands a method while solidifying the idea in the students mind by having them analyze and relate to it.  I think that this may have also confused some of the students and may have been hard for others. If they got stuck, I would have to guide them with questioning and probes into a positive train of thought. I think that they lesson have been even better if these other techniques were included. Implementation is easier said than done however.

Blog Entry 2

1.

Initial Impression of the school: This middle school brings me back to my days in a middle school. The sizes of the kids I always find interesting in the middle schools. Some are tiny and others tower over me. The lockers and hallways are systematic and familiar.

What is on the classroom walls: My class has posters that remind students of classroom rules and consequences. They also have a multiplication table that the students refer to regularly.

What are the hallways like: There are four halls (A-D) and students are allowed to only walk on the right side of the hallways to help with traffic flow. It is clean and there are ample trashcans, water fountains, and bathrooms.

What is the culture like: The teacher’s are the leaders of the school and most students respect and enjoy following their lead. There are many different ethnicities at the school, but there is no feeling of segregation or hostility they all seem like they are on the same team which is nice.

2.

What is the classroom like during math: The class is largely based on worksheets, which is sad. There is a lot of time spent on warm-ups and homework. There is one teacher and 4-8 kids per class.

Teachers: There is one teacher in the room at a time. She teaches from a research based workbook program.

Topics covered: Place value, computation, prime numbers, GCF, LCM…

Students Engagement: Engagement varies between students, some are eager to learn and others have no faith in their own ability to do the work or otherwise seem not to care. I would say 50/50.

What am I doing?: I am assisting the teacher in any way possible as of now. I have been administering baseline testing and will begin teaching a small group next week.

3.

Teacher's belief about teaching mathematic?: The teacher seems very knowledgeable and has plenty of insight as to why her students struggle the way that they do. Some ideas are more negative than positive however. She believes that all students can learn if they put forth the effort. Education is a two-way street, she says I will do my best but they must meet me half way.

4. 

What am I wondering about my own mathematical teaching identity?: It is easy for me to say that I do not want to be like my CT, but it is easy to be judgmental when I am not in her shoes. I want to build on the good things that she does and be better in other areas. I value student rapport very highly; if I want a student to work for me then I need them to feel comfortable with and want to please me. It is also easier to get a student to open up to you that way and you can gain valuable insight to where a learning barrier is taking place.

Response to Readings- Week 1

1. How does taking a problem-solving approach to teaching math differ from first teaching children the skills they need to solve problems and then showing children how to use those skills to solve problems?

Problem solving is essential to life, and it just as important in solving math problems. You can be great at math skills, but not know who to mark out extraneous information and determine what a word problem is asking.

2. How do you think your experiences, feelings, and beliefs about math will impact the kind of teacher of math that you will be or the kind of teacher of math that you want to be?

I do like math for the most have always been good at it. It will push me to learn how to teach different strategies to those whom math does not come as easily. It will also lead me to push those who do well so that they do not coast.

3. Not everyone believes in the constructivist-oriented approach to teaching mathematics. Some of their reasons include the following: There is not enough time to let kids discover everything. Basic facts and ideas are better taught through quality explanations. Students should not have to "reinvent the wheel." How would you respond to these arguments?

These theories have some truth in them, however, learning needs to be active and exploration is an ideal way to go about this. I am a fan of the Montessori method and this has proven successful for many children.

4. We sometimes want to jump in and help strugglng students by saying things like, "It's easy! Let me help you!" Is this good idea? What is a better way of helping a student who is having difficulty solving a problem?

It is better to give them direction with meaningful prompts and strategies. You cannot demean the student for struggling, not should you do the problem for them. What defines a "good idea"? Giving students strategies that they can use in and out of the classroom is the best way to help a student.(ex. catch a man to fish v. teach a man to fish).

5. Reflecting on how tasks were defined in the Van de Walle chapters, how did the tasks presented in the Behrand article to Learning-Disabled students help in their mathematical development? Please give specific examples.

The tasks helped to expand the methods and thought process in regards to a certain concept or skill. It shows a practical application important area.

Mathematics Identity Blog Entry 1- EHD's Math Life Story

1. Peak Experience

I suppose that to talk about the what is perhaps the greatest joy brought to me by math, we would have to go back to when I was in the second grade. My parents instilled the importance of education in me from a very early age. My job was to make good grades, so I could get into a good college, and in turn get a good job. I went to St. John's Episcopal School and we used to take timed math tests on these things called, "Holy Cards." They actually were shaped like a birthday card and had rows of holes all the way through them; they had simple computation math problems on top and what you did was put a piece of paper between the card and answer all the questions, front and back, before the two minutes timer went off. I cannot remember whether I did both the addition and subtraction cards or the multiplication and division cards, but I did get a hundred on both of them one day. Quite a feat as a little tike. I was ecstatic, I begged the teacher to let me call my dad and tell him I had achieved perfection. The teacher didn't let me, the wench, but I will forever remember the overwhelming joy I felt that day.

2. Nadir Experience

I would have to say my worst experience with math would be when I failed my first math class, which was in college. Technically it was a D, but I had to retake it to continue the progression. I took it again and got a B, at the time it was devastating for me. At that time as a student I did not reach out and go to office hours, not that I really do now, but in those types of large impersonal classes you need to get your face in their and you need to get help if you are struggling. I have always been to prideful in my mathematical abilities, and it took a while but fall I did, and hard. I was going through other things in my life at the time, and the one of the few constants in my life was no more. I got over it but it was not good for my view of math.

3. Turning Point

I think that my turning point was a slow and wide turn that really started my freshman year in high school. I coasted through every math class I had ever taken and got a 790 on my PSAT math, ( I think I got a 760 or 780 on the real thing). I was in and AP Calculus class with some of my friends and I didn't like the teacher and I did my coasting/sleeping through lecture and half-assing homework. I ended up getting a 2 on the AP test at the end of the year (3 is passing). It was never really the same after that. I went into college as an Applied Mathematics major, but my heart wasn't in it. I realized I did not want to do something as trivial as crunching numbers in a cubicle for fifty years. I would of probably shot myself. That turn led to several more turns, which led me to where I am today.

4. Other Important Scenes.

I was really proud of my SAT scores, but at the same time gave myself [a hard time] for not achieving perfection, for missing that one smart question. I wish I could call it stupid, but that would just be ignorant. I also had multiple years with math class averages at or over a 100. (Elementary, Middle, and High).

5. Greatest Challenge

I would have to say either the college calculus course I mentioned above. I wish it was something I succeeded at but realistically, it doesn't get more basic than this. It was just me and the material, I didn't bother going to a majority of the lectures and definitely didn't go to any office hours or TA sessions. I missed so much class time that when I showed up for one of the tests, I asked who the guy up front administering the test was. Her reply, "That is the professor, our old one passed away." My response, "What happened did he get in a car accident or something?" Her response with a look of disgust, "No, he died of cancer." That gives you a timeframe for how long I had been away from class. It was my superior intellect versus the test, just like it had been nearly my whole career and the test beat my ass. Serves me right.

6. Special Education Teacher

I want to be a special education teacher, because I have experienced secondhand (my brother, Blake) how terrible some of them are out there. Those kids deserve better. In my opinion it takes nothing but the very best teachers to meaningfully teach kids in special ed. I am not the best, but I can tell you what. If I have learned anything from math (my greatest challenge) it is that to be the best you have to work hard, you have to put in the time, and you have to ask questions. I seek knowledge now more than ever before, because it is something meaningful and something I am passionate about.