Math Strategies: Blog 4

When I first started this semester, I was able to observe the students in my placement work on several basic skills (such addition, subtraction, and multiplication).  During this time, the students worked on addition problems, and I noticed them using a method I feel I was not familiar with.  They would expand the numbers in the equation, add their place values separately, and then together to find the answer.  For example, 71+54=?  The students would separate the tens (70, 50), then the ones (1,4), and then add them (70+50), (1+4).  Then they would take those totals and add them together (120+5=125). 

            Another way a student can solve this problem is by adding 1 to 54, and changing 71 to 70.  So then the problem would become 70+55= 125.  Going off the expansion example, another strategy would be to subtract 1 from 70, 4 from 54 and add 70+50, 1+4.  Then add both sums together.   A different way would be to subtract 4 from 54, and add those 4 to 71 (causing 71 to become 75, and 54 to become 50).  Then 75 and 50 could be added together to find the answer.  Finally I know that 30+30=60, so if i took 60 from 71, I would have 11 left.  Then I could add those 11 to 54, causing 54 to become 65.  Now, I can easily add 60+65 because I know in the tens value 60+60=120 (because I know 6+6= 12 so I just add on a zero), and in the ones 5+0=5. So when I combine 120+5, I get 125.     

            When working on a different problem, (21*2) I noticed that one of the students changed the problem so that the smaller number was on top and the bigger number on bottom.  I noticed the student would do this for all their double digit by single digit multiplication.  One strategy that could have been used would have been to add, 21+21, instead of multiplying.  Another strategy would be to expand 21 (20, 1) and multiply each digit by 2 (20*2, 1*2) and then add the sums.  To make the numbers smaller, I could also split 21 (10, 11) and then multiply 10 by 2, 11 by 2 and then add those sums together to get the same answer.    Those are a few ways I can think of how to solve a problem like above using invented strategies.  

(pictures to be posted soon)

Blog 3: Talk moves

1.     This week has been a little out of the ordinary in my placement.  Illnesses and meetings have caused these two days to go by fast.  Even though the teacher may not be here, the students are and so is “MATH”.  However, I think there are two types of math.  The first type of math is the type your teacher teaches.  It’s the kind that either goes by the curriculum or to your needs, sometimes goes off a book, and is taught by the teacher him or herself.  The second type of math is what I sometimes call “substitute math”.  This math (as you probably have already guessed) is usually formulated with packets of review, math problems that have been seen before, TAKS (or STAR) questions from past tests, and is discussed when the teacher is out of the room.  This week, I saw both types of math in my setting.  The first day here, there was a substitute because my cooperating teacher was ill.  So, students worked on their problem of the day (which is sometimes done even when the teacher is present, but it is mainly “Daily 4” that they work on when they arrive), and a couple of TAKS related problems.  Now, even though these questions are formulated to resemble TAKS questions, I still think students can be taught how to solve these problems (such as a mini-lesson).  That however did not happen.  Students were given the problem of the day and worked on it alone (which is what normally happens), however when a student finished the substitute would then check the students work and go over it with that student alone until another student finished in which she turned her attention to the new student.  Once the students were finished they moved on to their TAKS problems and the same procedure took place.  However, she did project some “talk moves” when working with the students.  She would restate the students’ problem solving strategy, and ask the student if she explained it correctly.  I think I would have allowed students to share strategies with each other, and even ask if they could explain how they thought someone else solved the problem.   I also would have worked together on each of the problem.  I think having the students see different ways to solve a problem (even a TAKS problem) could benefit the student and can lead to higher thinking. 

2.     When the teacher was back in the room, students started working on “Daily 4” and different strategies to solving problems (such as algorithm, number facts, and expanding the numbers).  Before showing each strategy the teacher would ask the students how they would solve the problem.  Then she would explain back to the student and ask if that’s how they solved the problem.  Finally she’d ask if another student understood and if they could add on their own way or what they thought.  Some of the strategies the students would use were strategies the teacher explained, which would excite the student.  I think the teacher did a good job with the “talk moves”.  I don’t think I would have changed this lesson.  I really liked how she allowed the students time to solve it their own way, and then asked the other student to explain.  Finally she showed several strategies they could use, and she stressed they could use whichever strategy they prefer.  I think this is important because sometimes students feel like they are restricted to one strategy when in fact they are not.  It still allows a sense of exploration, but provides help if needed.

Stepping into Teaching: Ashley Trevino

1.)  Passion and excellence were the initial impressions I received from the current school I am located.   The school is very structured and organized.  Students, parents and staff are involved with different projects that take place during the school year; and parents are not afraid to help out with these events.  Teachers and staff have warm positive feelings towards children, both in their class and outside their class.  These staff members however are not the only ones who encourage their students and peers. The principal here at this elementary takes time to greet the students of the schools and encourages his staff members to strive for excellence. 

a.     Hanging on the walls and in the halls are calendars with upcoming events, PTO meeting times and date, and school district information.  Students’ works are displayed all along the walls in the hallway and on the windows.  

b.     The school does try to be diverse and make the students culturally aware of other cultures present (both in and out of the school).  There are some culture holidays are celebrated by the school (such as a dinner or play) and other culture holidays or information is discussed in class. 

2.)  A normal math time would look like this: students come in and sit at the table to work on “Daily 4” or problem of the day.  “Daily 4” usually consists of one digit multiplication, four digit addition, three digit subtraction, and the last section is usually a question/problem over a topic discussed in the classed.  While students work, the teacher usually watches over and assists them in a questions or problems they may have by scaffolding or reminding them different strategies they have learned.  Sometimes “multiplication stories” are read and gone over with the students after “Daily 4” is finished.

a.     At this moment, the topics being discussed in class are: placement value, decimals, number order, multiplication, four-digit addition, and three-digit subtractions (borrowing). 

b.     Solving problems, on an individual white board for each student, and verbally explaining to the teacher how they solved the problem or why they did a certain technique keeps the students engaged.  When students try something new, the teacher encourages for them to explain their thoughts and uses a “yes, and” statement instead of “yes, but” or “no”. 

c.      During this time, I am usually around the students watching them work and helping them if they have trouble.  I also encourage students to explain and teach me how they solved the problems.  

3.)  My teacher will try to keep her students on the same levels as their peers or the curriculum level, however she will accommodate or modify the lesson if students are not understanding, or if re-teach needs to happen.   I agree and like her methods of teaching because if the students can work at the same levels as their peers or the curriculum, then we should push them towards that with accommodations and modifications as needed. 

4.)  I am worried about how to correct my students without shutting their exploration down. At times their methods or strategies may not work, and I don’t want to discourage them from trying again.  Explaining terms and assuming students know or understand what I am talking about worries me, especially if they do not have a clue as to what I am saying.  Sometimes explaining is difficult because even though the term, topic, or strategy may be a simple concept, I tend to use too many words to try and help someone understand. However, sometimes confusion instead of understanding is the outcome.   At this moment I feel like I am trying to find my own math identity and wonder if I ever will.  Then again, maybe I just haven’t realized that I do have a math identity and just need to time, like my students, to explore it. 

Response to Readings 9/2 (ashley trevino)

1. It gives children a chance to experiment and learn in their own way to solve the problem, instead of just telling and showing them its done a certain way.
2. I think my experiences with math will help me, hopefully, teach math in a very positive way.  I have had a few great math teachers and I've had my share of teachers that were not so positive.  So, I hope to remember both the good and bad and use it to remind me of what I want to be and what I do not want to be.
3. I have mixed feelings about this argument.  I do think its great to allow kids time to experiment and discover things, but I also know there are children (such as my self) that like to know the stops and basic facts before doing anything.
4. I think asking the children if they would like help is a better option then just jumping in.  Sometimes kids need time to try things and figure out if that is what they need/want to do.  I feel saying "It's easy" only makes the student feel as if they cannot do it, or wont be able to do it since they are having trouble now.
5. It helped them relate to the problems and experiment in their own ways by using manipulative or every day objects that they could relate to.

Entry 1: Math Life Story

Peak Experience

            Through out school, math has been the scariest subject for me.  So, it came as no surprise when I entered Calculus that I doubted myself a great deal.  As the semester began, I began to think to myself, “I am never going to get this.  I have no idea what is going on.” Later that week, I decide to go get help after school to find out exactly what I was doing wrong, and why I wasn’t able to solve the problem(s).  I’m not sure what it is about asking for help that makes me nervous, but I was timid at first to enter the instructor’s room.  Forcing myself to overcome this fear, I walked in and finally asked for help.  My instructor was glad to help, and we sat and tried to figure out what I was doing wrong, or not understanding.  After several minutes of trying to work out a problem, the instructor realized what was holding me back.  The model and explanation he had given in class was beyond my understanding.  After breaking down each step (so I could clearly see what was happening) and trying different strategies to find the answer, I began to understand the problem more and more.  Now though that was an accomplishment for me that was not the “peak” of my story.  The best part was the very next day in class we were given a Pop Quiz over the information we had just learned.  “How is that the best part?” you may ask.  Well, come to find out majority of the class did not do so well on the quiz, whereas I scored an excellent score.  That moment was one of my best moments in math because for that moment I began to realize “I could do math”, and that is very rewarding feeling me.

Nadir Experience

            Unfortunately I have experienced “low points” that have dealt towards math.  However, the “lowest point” in my life that dealt with math would have to be my sophomore year of high school.  For half a semester I dreaded going to my math class.  The saddest part is that I did not dread going because it was math, but because of the instructor.  To begin with, math was already a difficult subject for me but it was worse when the instructor made me dislike math even more.  For half a semester I was literally trying to teach math to myself.  Anytime my classmates or myself would ask for an example or explanation the instructor would either tell us to read it from the book, or work the problem out on the board without explaining.  Now, I am the type of person that needs to have things broken down, explained (sometimes twice) and shown different ways (if possible) how to solve a problem, and this instructor was NOT helping me at all.  I finally had enough of it, and had to have my parents complain about him for fear of failing.  Thankfully, my parents were not the only parents who complained.  I began going to past math instructors for help, but I had a great deal of catching up to do.  It was rough, but I was able to get through the year and pass the class.  I will never forget how I felt going to that math class.  Though this may be wrong to say (and I am sure this instructor may have been an extremely gifted instructor at another time in life), I learned what I did not want to do to my students.  Most teachers can get a feel for their students if whether or not they enjoy math or are afraid of it, and I’ve learned to try and catch those negative feelings (even my own) and try to turn them around into positive ones.  Not allowing my students to see my own fear of math, and helping them any way I can is what I want and hope to be able to do in the classroom. 

Turning Point

            I hit a “turning point” my freshman year in college.  I was taking a math class (I do not remember which one) and thought it’d be like high school, easy.  Boy was I wrong! I realized during that first part of the semester that there was much more to math than I realized.  It was at that point that I regretted not engaging myself more in math.  I should have taken more advantages with receiving help and learning more about math than what I needed to know.  It was at this point too that I had to overcome my fear for asking for help (which I still have at times). 

Other Important Scenes

            Studying for math was always difficult for me.  I remember trying to remember the steps of a problem, and working them out over and over again before a big test.  I also remember getting confused as to when I was suppose to use a certain formula and when it was not needed.  So one night before a final I decided to stay up and work out some last minute problems that were really bothering me.  I must have spent about three hours working on maybe six problems; but I was determined to remember every step there was.  That next day when I went to take my final I was extremely happy to see those six problems I had studied over and over again listed as the first six of what was a twelve-question test.  At that very moment, even though I still had the rest of the final to finish, I felt as if I could accomplish anything mathematical listed on that exam. 

            When I was younger, back in elementary school, my class would play “Around the world”.  We would practice multiplication with a partner, and then before lunch we would play the game and see who could “travel” the farthest in the classroom.  The first few times we played I never got far.  I remember sometimes feeling embarrassed or sad because I would have to sit down.  When my teacher told us we were going to play “Around the World” that week, I decided that I was going to practice at home with my mom so I could “travel” far.  When the day finally came to play, I felt like I was ready.  The game started and what do you know, I sat down early.  However, I did not let that get my hopes down and I patiently waited for another round.  When the game started again, I was so proud of myself for not sitting down early.  Yes, I did sit down but I had made it the farthest I’d ever gotten. 

  

Greatest Challenge

            My greatest challenge in math has been trying to over come my fear of math.  I guess I really haven’t dealt with this challenge besides telling myself that I can get through it.  I get frustrated easily when I cannot do something right, and in return that just pushes my confidence level lower and lower.  Past instructors have tried to boost my confidence by encouraging me, and showing different strategies to help me.  This challenge is a great impact because anytime I hear “math” or see “math” I automatically get tense and put myself down (even though I know I shouldn’t).

Special Education Teacher

            Throughout my life I have always worked with children.  From catechism teaching to music and tutoring, I have always enjoyed working with younger children and seeing them light up and get excited when they have finally accomplished their goal.  However, when I entered college my choice or career was marine biology, NOT teaching.  After a few courses in that major and a couple of summers at home working with children, I realized that marine biology may not have been the major for me.  Finally, after talking with my parents I realized that some of my happiest moments when working with children was when I was working with my peers (who were physically challenged) and watching/helping my mom in the special education room at school.  Helping students overcome any obstacle they have in front of them is very rewarding for both them and me. 

            When teaching mathematics to my students, I want to show them that I am confident not only confident in them learning it, but I also have confident in myself teaching it.  Math should not be a subject in school students fear (as I did), but rather a positive subject that they can feel confident in learning, doing, and succeeding.