Blog 4

Blog 4 invented strategies

I have not been able to really think of beside some mental computation going on in my student teaching. I have seen one student work out a subtraction problem where they broke up the problem by a fact that they knew. The problem was 700-549. What the student did was subtract 700-550 to get 150 and then add one more to 150 to get 151. The only way I knew what the student worked out the problem like this was because I asked if they could explain what they did. I have seen this strategy before but I wouldn’t of known the student used this strategy if I didn’t ask. I was glad the student worked the problem out that way and encouraged the student to continue to use the strategy and to show what they thought that way I could see it when I looked at their work.

Based on the Student’s explanation the student solved the problem 700-549 like this:

700-549

Step 1) 700-550=150

Step 2) The student knows that 550 is 1 more than 549 so the student knows they need to add one more to 151.

Two other ways to solve the problem:

700-549=

Different Method

Step 1) 700-500= 200

Step 2) 200-49= 151

Math Talks Moves

1.1 Revoicing
I have a really good example of revoicing a student's response this past week. I wish I would of taken a picture of the students work and how I wrote down his explanation. The students were working on a scavenger hunt where they moved around the classroom and work on various fractoin problems.  One student was working on 4/8+2/4 and he work out the problem and got the correct answer. He had completed the problem quickly so I wanted to keep him busy so I asked about how he solved the problem. The student explained to me the he multiplied 2/4 by 2 to find the answer. On the students paper he wrote 2x2/4x2. I went to the white board and said so you are telling me 2/4x2 is equal to 4/8. The student agreed and then I wrote is 2/2 equal to 2. The student took sometime to reply and the he said no 2/2 is one whole. We then started to talk about how he worked out the problem correctly but his explaination was different. I wrote out on the board and ask if 2/2 and 8/8 and 1 are any different. The student said that 8/8 is bigger and then we talked about part of a whole. The student then realized that he was simply multiplying the problem by 1. I didn't really think much about our conversation that day but looking back at it I see how the conversation the student and I had was much more than simply saying yes the student wrote the problem down right. Restating the student work can really bring out more from students and how they deal with math.

1.2 Asking students to restate someone else's reasoning
 I think this can be an effective strategy to reinforce others students strategy and alllow the student to examine his explanation when someone else states it. It makes me think about how something might make sense when they say it but everyone else does not get it. I think this strategy may be ineffective if other students are not grasping what the student is saying or if anyone understands. I think it might guide discussion but I'm not to sure if I would want to leave students feeling like they are right when they might be misintepreting a concept. I think using other strategy works well for asking students to restate someone's reasoning but on it's own I don't think it can really stand on it's own.

1.3  Asking Students to apply their own reasoing to someone else's reasoning
I think this is what should be combined with asking students to restate someone else's reasoning. I think this type of questioning is good for allowing students to look at how they understand a concept. I like how it is the why that is important and not if the student disagrees or agrees.

1.4 Prompting students for further participation
Participation is very important for effective discussion. I think I as a math teacher need to create an environment where student can be open to discussion. It takes a lot for someone to put their thoughts out in the open. There is a certain vunerability when anyone talks about what they know. Especially when they are not confident in a certain subject or topic. I would want discussion to be as equal as possible because I have seen that it is often the ones that don't need help are the ones who talk the most.

1.5 Using wait time
I think I'm improving in this area but there are times when I can't help but jump in. Ten seconds does feel like a long time but it is needed. I think that I sometimes I want to go over something the moment a student might make a mistake. I am able to wait when I'm thinking about letting the student process the information but I do admit I often don't give a student enought time when they make a misstep. I definitely is a skill that I would like to work on.

2. Thinking about the revoicing from this past week, I think the discussion was really effective. I think it was a really good teaching moment for me as well as the student. I think I will be more aware of how to lead a discussion and how it could take off into deeper understanding of a topic. I don't have any photographs from this discussion. I took a photograph of a student's paper but nothing is clear on the photo.

3. I think about the conversation the student and I had and I feel like I could work on allowing the discussion to be more flexible and for me to be aware of it. I went into the discussion thinking about how 2/2=1 and how is it different from the number 2. I think the conversation went really well but I think I might of only of let it go off in one direction. I think I could of explored how 2/4 times 2 is different from 2/4 times 2/2. I think these type of discussions really help a students' understanding because they are analyzing not only a problem but their understanding of math.

Mathematics Identity Blog Entry 2 - Stepping into Teaching

1.

Walking into the classroom, and the right side of the room.

Left side of class

back left corner of the classroom

Initial Impression of the school: I think this middle school is an excellent school. The entire staff was more than willing to work with me. Administration was very supportive of their teachers and was very involved with school functions. 

What is on the classroom walls: This math class had many posters that would help the students. Some were problem solving strategies, Order of Operations, and math facts.

What are the hallways like: The hallways are well monitored and pretty organized. There is always a teacher who is in charge of watching the halls before and after school as well as in between periods. In the mornings students line up along the wall and wait for the day to start. 

What is the culture like: So far my time spent  with my special education teacher has been really fast paced. It seems like it could be overwhelming but my coordinating teacher is always on top of her responsibilities. The school seems to be a well oiled machine. Everyone seems set into a routine and it seems to be a very positive learning environment.

2.

What is the classroom like during math: The classroom is set for students to work with their peers they are sitting around. There are four students per table. Most of the time the students are working on worksheets for an assignment. Sometimes the students are moving from table to table because the teacher is having the students move from table to table so the student can use different manipulatives or tools to solve the problems. 

Teachers: When I am there, there are 3 adults in the classroom. One general education teacher, one special education teacher, and myself. We are all usually walking around the classroom and helping the students. 

Topics covered: Exponents, order of operations, and negatives have been covered so far. The topics covered in the classroom are based on what the math department has decided to cover.

Students Engagement: The students are typically engaged the entire period. There are three adults in the classroom so student behavior is easy to monitor. 

What am I doing?: I am usually helping a certain group of students or walking around the class and helping students that my need additional help. I have at times asked students what they did in a math problem and if there is another way to solve the problem. Most of the time, I am having students write out their solution because they may only have an answer written down so I want to see what they did to get their answer.

3.

Teacher's belief about teaching mathematic?: The general education teacher is returning from a 10 year lay off. She was a small group instructor before for some school program I can not recall at this time. She is starting to get the hang of teaching a whole class. She has been open to suggestions and ask question about how she is presenting content. I think she is very flexible about teaching math which I think is necessary because there are many paths math may take an individual. 

I like how the teacher has the tables set up as stations with different materials to help the students solve problems. I think it helps the students get some movement throughout the period and allows them a chance to look at a problem differently. Making the students move from station to station may take a student away from their specific learning style but it does change how a person may look at a problem. I think it may make the student analyze not just the problem but their resources around them and add another dimension of critical thinking. 

4. 

What am I wondering about my own mathematical teaching identity?: I'm wondering how well I'm going to be able to present my knowledge to the students about the content. I know I can solve any problem the students will have to do but can I help the students understanding the content. I am hoping I'll be able to create a positive learning environment and that I can help my students find their own methods to solving a math problem. I think routines and building relationships with students is important in a math class. They help maximize learning and create a atmosphere where everyone is has the same goal in learning mathematics.

Response to Reading 9/2 Jackie Beltran

1. The problem solving approach teaches students to figure out a way to find an answer a problem as opposed to regurgitating a equation when they see a certain type of problem when you only teach certain math skills. A down fall with teaching math skills is that you are limiting yourself only that certain type of problem.

2. I think I will try to push the concepts students form about math. I would want the students to think about what we are doing and try to find out why the concept works rather than just give them the concept. For example, I would want the students to figure out squares are rectangles by working with the definition of what a rectangle is rather than just say a square meets the definition of a rectangle.

3. When only teaching basic facts and ideas you are really limiting the student to only those facts and concepts. You are not allowing the student to explore and gain a better understanding of what math is about. Another concern is that math in real life is not simple basic facts and concepts so not teaching the student how to explore math would not allow the student tools to solve real life problems.

4. I would say it is easy because it might be difficult for the student. Instead of helping, I would rather see what the student is thinking. I would ask something like, "how are you going about this problem" and "does that method make sense." I would try to work with what the student is thinking and not try to go about how I would solve the problem because everyone thinks differently.

5.  It allowed the student to work and be flexible in how they went about solving a problem. It was individualized to each student since they were all able to approach it in their own way. The students were able to bring their prior knowledge and use it to connect with the task.

Mathematics Identity Blog Entry 1 - Math Life Story

1. Peak Experience
I think one of the high points is my math life has to go back to the beginning of when I concerned myself someone who could excel in math. It was in 4th grade in Mrs. Miles class when I learned how rewarding math could be.

Side note on what she taught:
Mrs. Miles had just taught us a trick to multiplying two digit numbers that are the same and both end in 5 (EX: 25x25).  What she taught us the the last two digits will always be 25 (5 times 5 equals 25). For the 10s digit place you would add a 1 to one of the ten's place and then multiple the number together. The 25x25 problem would work like this:

25x25 -> 5x5=25 ->25 would be your tens and ones place in answer. 30x20=600. 600+25 equals 625.

Anyways, Mrs. Miles had a competition to see who could do these multiplication problems the fastest. It was set up that the winner stays and the loser goes. I was one of the first students chosen to to go to the dry erase board to  participate in the race. I ended up being undefeated. No one ever beat me at the race. Mrs. Miles even called a teacher to show her how fast I was at it. I still remember the trick and even though next week we moved on I still felt proud knowing I was the best in my class.

2. Nadir Experience
My worst math experience had to be taking my first calculus test. I was a freshmen and my study habits were not as good as they are now. I thought I was prepared but when I opened the test there was nothing I really knew how to do. I failed the test. I think I only knew 3 problems and guess the rest of them. (I got a 55 on the test so I was lucky with my guesses). When I turned in my test I felt so disappointed in myself because I have never failed a test in my life up to that point. I didn't know how to really handle it.

I ended up barely passing the second test and then I started to look for resources to help improve my grade. I went to class, office hours, tutoring sessions, and went over my homework at least two times to make sure I understood the material. I ended up passing the class with flying colors but I had to really become involved in my learning.

3. Turning Point
I think I always felt this way but I never had a term for it. This summer I took my Foundation math classes and my professor used the term "lazy mathematician."A "lazy mathematician" is a way to look for the easiest way to solve a math problem. Finding a pattern, knowing tricks, or short cuts to solving a problem is what makes a "lazy mathematician." Of course, it is essential  to understand the concepts of math because a lazy mathematician has to understand the concept if they want to find the easiest way. My foundation math classes this past summer helped me define how I like to do math. I think to see what the problem is asking and the best way to solve it.

4. Other Important Events
8th Grade Math
When I was in 8th grade my math teacher was not to fond of me. I was the one to blame. I will admit, I was an immature student. I did however do all that was requested and did it to perfection. I always had a 100 or above in math for a grade.
What really upset my teacher was when she would hand us worksheets that we would complete, I would finish them before she was done teaching us how to work the problems. I would always turn in my paper as soon as she finished her lecture. I would have the entire period for free time because I would finish my work. After awhile my teacher decide she needed some way to keep me busy. To take away my free time my teacher would have me teach the class or go around the class and check other students work. I didn't mind though because it kept did keep me busy.

SIMMS - Systemic Initiative for Montana Mathematics and Science
My 9th and 10th grade year, my high school block took SIMMS for math. It was the most challenging years of math I have ever had. Through SIMMS I really learned how to be a problem solver when it comes to math. The SIMMS website is: http://www.montana.edu/wwwsimms/ if you would like more information on it. My teacher had us work on unit that would have us lead to math concepts. Instead of giving us the math concept our teacher had us figure it out ourselves and then teach us the concept. The unit were very challenging and really helped me with critical thinking skills. I really enjoyed the math classes and liked how I had to figure out what the concept was instead of it being given to me.

5. Greatest Challenge
As far as being a student my SIMMS class were the biggest challenge because it really made me push myself and made me think critically.
As a preservice teacher (and I'm sure this will arise again when I'm a teacher), I find that the right way to reach a student can be difficult. My first student internship in a 2nd grade general education classroom, I found myself trying to help a few students try to catch up on some of their math skills. I was only with the students twice a week and I'm not sure their teacher was doing her best to help these students. When helping these students I found myself becoming stressed that I couldn't help these students fast enough. It was like each week these student struggled more every time I saw them. I think a lot had to do with my teacher and it made me sad knowing that their teacher would do nothing to really help them. I feel like there are some good teachers out there and some bad teachers out there. I hope I'll be one of the good teachers out there that can notice when students need help and have the ability to help them in math (and any other subject for that matter).

6. Special Education Teacher
I have wanted to become a special education teacher ever since my mom started to work with students who were medically fragile. I was really inspired by my mother's students and really wanted to work with students with special needs. I really felt like my mom's student change how I look at things and makes me humble for anything that I'm able to do.
For teaching math, I feel like math is just another form of critical thinking and problem solving skills. You can memorize concepts, shortcuts, and be flawless when it comes to arithmetic but if you don't know how to go about a problem then you can not implement anything you know. Having experience with different problems really helps but being able to problem solve and think critically is the most important part. Doing math is a way of thinking more than it is computing numbers in my opinion.