Upon working with a student in my math group this past week, I discovered a very interesting strategy of solving computation problems that I have not yet seen. I would say that this strategy is a mix between using manipulatives and drawing out a visual representation. Therefore i think that it is somewhere in the mix of the direct model strategy and the counting strategy.
When I first observed the student solving a problem such as 34-19, I thought that he was just drawing 14 tick marks and then crossing off 9. Although this is similar to his method, his strategy proved to be a little more complex. He would draw out three large tick marks to represent the three in the tens place in 34, and he would draw out four small tick marks to represent the the 4 in the ones place in 34. He would do the same thing for the number 19 - draw out one big tick mark to represent the one, and nine small tick marks to represent the nine in the ones place. Then he would look to see that he did not have enough tick marks in the #34 tick mark group to take away nine, and so he would X out one of the large tick marks and turn it into ten small tick marks. Then he would X out nine small tick marks, and count up the number of small tick marks he had left. He would write this number down. Next he would take away 1big tick mark from the #34 tick mark group, and then also write down the number of big tick marks he had left right in front of the number of smaller tick marks he had left. He would fill in the answer right under neath the algorithm of the problem that he had previously drawn out.
It took me quite a while to understand this student's method of solving the problem, because frequently I had a hard time distinguishing between which was a big tick mark, which was a little tick mark, and which tick marks had already been crossed out. However, this is a strategy that this student has used for a while now, and as long and I was able to have him explain it to me so that I finally understood what was happening, and also so that he was able to properly let someone else know how to do the strategy, then I am alright with letting him use it to solve problems.
If I had to think of two other strategies that this student might use, I think I would see if he could fade the tick marks into just drawing out 34 tick marks ( all the same size) and then just crossing out 19 tick marks to see how many are left. However, I do realize that this method might be a little more remedial, because when the student gets to the higher numbers - like 68, it is not realistic to have them draw out 68 tick marks.
Another method might be to use that same tick mark strategy, but only write one tick mark for every five numbers. Therefore the student would get practice counting by fives and he would also not have to use as many tick marks. However this may also become confusing to transition between counting by fives and ones if you did not provide the student with multiples of five.
big tick marks : smaller tick marks:
I I I ( 3) i i i i ( 4)
I ( 1) i i i i i i i i i (9)
after borrowing :
big tick marks: smaller tick marks:
11 ( 2) i i i i i i i i i i i i i i (14)
I (1) i i i i i i i i i (9)
=15
Tuesday, October 19, 2010
Saturday, October 9, 2010
Mathematics Identity Blog Entry 3 - Math Talk Moves
A math moment that has really stood out in my placement was when I was observing my cooperating teacher working with a student in the resource classroom one-on-one. For most of the day I am out pulling small groups from general education classrooms, and I do not usually get to sit and observe my cooperating teacher teach. However on this day, I had the pleasure of watching her play a math game with a student to help improve his computation fluency. The object of the game was to fill a board with manipulatives by rolling the dice and adding the numbers together. The student was adding the the numbers together and he was frequently one number off every time. For example, he would roll a 3 and an 5 and he would say 7. The teachers response was just repeated practice and allowing him to use a number line to visually see the numbers. My cooperating teacher also used many of the five productive talk moves to guide the students understanding. When the student would add up the numbers correctly she would revoice the problem by saying something like: "You're right 3+2 is five!" She also repeatedly let the student have plently of time to sove the problem (using move #5 : waiting using wait time) I believe that this was effective because it allowed the student not to feel rushed, therefore increasing his chances of correctly solving the problem.
Given the circumstance, I think that this lesson was close to perfect the way that it was played. However, if you had a large number of students to teach at once, I think that this lesson could also be played in a large group, and then the students would have access to their peers thought-process about the computation problems. If they were working in a large group, a teacher might be able to ask students to use the talk move # 2, for example we could ask the students to restate someone else's reasoning about how they solved a problem. This may be beneficial to certain students because maybe hearing the explanation from a peer would help foster understanding.
Given the circumstance, I think that this lesson was close to perfect the way that it was played. However, if you had a large number of students to teach at once, I think that this lesson could also be played in a large group, and then the students would have access to their peers thought-process about the computation problems. If they were working in a large group, a teacher might be able to ask students to use the talk move # 2, for example we could ask the students to restate someone else's reasoning about how they solved a problem. This may be beneficial to certain students because maybe hearing the explanation from a peer would help foster understanding.
 |
| manipulatives used for the game |
 |
| a place where the student could visually represent the computation problem if the number line was not sufficient |
Monday, September 20, 2010
Mathematics Identity Blog Entry 2 - Stepping Into Teaching
Upon being assigned to Gullett Elementary School for my internship this semester, I have become very familiar with the campus and much of the teachers and staff. It is a very happy and welcoming school with animals and artwork along every hallway. It is also a very open campus - meaning that their are "wings' of grade level classes - so that the school has a very in-door/out-door feel to it.
So far I have only participated in the resource room during the math period of the day. I have observed my cooperation teacher working with a small group of three for math intervention. She uses games and interactive activities to keep the students engaged in the lesson. The lessons are designed to meet the needs of the students individual areas of struggle in math.
My cooperating teacher is one of two resource teachers at Gullett. However, the other teacher is a reading specialist, therefore my cooperating teacher leads all of the mathematics, science, and social studies intervention groups. This means that she is very well verse in mathematical strategies and activities to implement with students who have learning disabilities, or students who just struggle a little bit with the general education curriculum.
I am worried about mathematical vocabulary. For example, I am constantly afraid that I am going to slip up when it comes to using the words "re-group" instead of "borrow" when talking about subtraction. I think that there are so many different ways of teaching math, as well as so many different ways to solve individual math problems, I am constantly concerned about confusing students when it comes to understanding math. I think that in the future when I am teaching these methods of computation, I am going to need help with thinking outside of the box for other ways to solve the problem so that I can show my students all possible ways.
PICTURES TO OUTLINE MY PLACEMENT:
 | |||||
| One of the many animal cages that fill the halls | . |
 | |||||||||
| Resource Room / Learning Lab |
 |
| Many "Math Tool Kits" can be found on the shelves of the Resource Room |
 |
| another section of the math shelf |
 |
| temporary organization of student's work |
 |
| behavior / emotion check-in table |
 |
| Working at the math table |
September 2nd In-class reading response
1) Problem solving is important to teach students because then the students are able to apply those problem solving skills to other aspects of their lives. If you only teach students the skills they need to know to solve particularly problems, then they are stuck only having the ability to solve certain problems.
2) I hope that I will be able to transfer positive math emotions to my studnets, but I do know that many times teachers unwillingly pass on their sub-conscious math emotions to their students.
3) Negative views about the constructivist-oriented approach: 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". I believe that their are going to be pros and cons to any type of theory about learning math, because we all share such different emotions about the subject. However, I do think that exploring and learning that is student led and student centered has more of a chance to sticking with the student in the long run.
4) I believe it is never a good idea to push your opinion about math, or anything else, on someone else. By telling struggling students that "It's easy!", we are implying that they are not as smart as others. I know that I have been guilty of using this phrase before in order to encourage the student that they can accomplish something, but in reality I know that it actually probably inflicts negative attitudes about the task at hand.
5) Examples of tasks to assist studnets with learning disabilities excell in math include: using visual representations to tangiblly represent the math problem they are solving. This may include using base ten blocks or manipulatives. Another task would be to have the students re-explain how to solve the problem after they have come up with their answer. This will help them to better remember their method for solving the problem, and help to ensure their understanding of that problem type in their future.
2) I hope that I will be able to transfer positive math emotions to my studnets, but I do know that many times teachers unwillingly pass on their sub-conscious math emotions to their students.
3) Negative views about the constructivist-oriented approach: 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". I believe that their are going to be pros and cons to any type of theory about learning math, because we all share such different emotions about the subject. However, I do think that exploring and learning that is student led and student centered has more of a chance to sticking with the student in the long run.
4) I believe it is never a good idea to push your opinion about math, or anything else, on someone else. By telling struggling students that "It's easy!", we are implying that they are not as smart as others. I know that I have been guilty of using this phrase before in order to encourage the student that they can accomplish something, but in reality I know that it actually probably inflicts negative attitudes about the task at hand.
5) Examples of tasks to assist studnets with learning disabilities excell in math include: using visual representations to tangiblly represent the math problem they are solving. This may include using base ten blocks or manipulatives. Another task would be to have the students re-explain how to solve the problem after they have come up with their answer. This will help them to better remember their method for solving the problem, and help to ensure their understanding of that problem type in their future.
Mathematics Identity Blog Entry 1 - Math LIfe Story
PEAK EXPERIENCE
My peak math experience happened in 11th grade in Algebra 2. I was on the "regular math track" in high school, meaning Calculus was one of the only advanced placement classes i was not planning on taking. Needless to say, I did not have a very positive self image about my math skills since most of my friends were enrolled in Calculus AB and BC. However, in my regular math class junior year I finally became proud of my math performance because of the inspiration that my Algebra 2 teacher gave me. She encouraged me and the rest of the class that we did not need a math label on us to determine our math ability. This has helped motivate me to push my self in all areas of my academic career, but especailly in math. As a future teacher I know that this experience will stay with me, and help impact the math lives of my future students.
NADIR EXPERIENCE
The lowest point in my math life came shortly after my highest point. My freshman year of college I was enrolled in a regular college math class to earn my basic math credit. To sum it up, it was HORRIBLE. The professor was an esteemed engineering professor, and did not seem to be able to connect with students students at a beginning math level. I experienced a lot of anxiety throughout the semester, and I hope that I will never pass on such frustration and low self esteem to my future math students.
TURNING POINT
In terms of my math life, I believe my turning point occured when I took M315K and L. I absolutely loved the fact that the classes were geared towards future teachers, and the professors actually took the time to expalin the "why" behind the number problems. This experience helped to connect my life as a math studnet to my future life as a math teacher. I am reminded that those two lives must co-exist if I plan on best serving my students.
OTHER IMPORTANT SCENES
1. I can un-doubtedly say that my Dad prefers math more than my Mom, who prefers reading and writing. I have very distinct memories of sitting at the kitchen table and attempting to understand the scribble scrabble of my notes and my Dad's handwriting as he helped me solve loads and loads of middle school math problems. (tears were usually involved) 2. Another important scene that comes to mind is when i taught my first math lesson. Almost exactly a year ago I was in my general education placement and I discovered that the subject of math was my most preferred lesson to teach !!
GREATEST CHALLENGE
I believe that my greatest challenge in math is my belief that I am not good at math. I know that this perception of myself can only hinder rather than help me, but it is a hard habbit to break.
SPECIAL EDUCATION TEACHER
I am very passionate about the field of special education because I cannot wait to truely make a difference in people's lives. I believe that I can especially impact the lives of future students in terms of their math beliefs, because I am living proof that every math story does not have to end negitively.
My peak math experience happened in 11th grade in Algebra 2. I was on the "regular math track" in high school, meaning Calculus was one of the only advanced placement classes i was not planning on taking. Needless to say, I did not have a very positive self image about my math skills since most of my friends were enrolled in Calculus AB and BC. However, in my regular math class junior year I finally became proud of my math performance because of the inspiration that my Algebra 2 teacher gave me. She encouraged me and the rest of the class that we did not need a math label on us to determine our math ability. This has helped motivate me to push my self in all areas of my academic career, but especailly in math. As a future teacher I know that this experience will stay with me, and help impact the math lives of my future students.
NADIR EXPERIENCE
The lowest point in my math life came shortly after my highest point. My freshman year of college I was enrolled in a regular college math class to earn my basic math credit. To sum it up, it was HORRIBLE. The professor was an esteemed engineering professor, and did not seem to be able to connect with students students at a beginning math level. I experienced a lot of anxiety throughout the semester, and I hope that I will never pass on such frustration and low self esteem to my future math students.
TURNING POINT
In terms of my math life, I believe my turning point occured when I took M315K and L. I absolutely loved the fact that the classes were geared towards future teachers, and the professors actually took the time to expalin the "why" behind the number problems. This experience helped to connect my life as a math studnet to my future life as a math teacher. I am reminded that those two lives must co-exist if I plan on best serving my students.
OTHER IMPORTANT SCENES
1. I can un-doubtedly say that my Dad prefers math more than my Mom, who prefers reading and writing. I have very distinct memories of sitting at the kitchen table and attempting to understand the scribble scrabble of my notes and my Dad's handwriting as he helped me solve loads and loads of middle school math problems. (tears were usually involved) 2. Another important scene that comes to mind is when i taught my first math lesson. Almost exactly a year ago I was in my general education placement and I discovered that the subject of math was my most preferred lesson to teach !!
GREATEST CHALLENGE
I believe that my greatest challenge in math is my belief that I am not good at math. I know that this perception of myself can only hinder rather than help me, but it is a hard habbit to break.
SPECIAL EDUCATION TEACHER
I am very passionate about the field of special education because I cannot wait to truely make a difference in people's lives. I believe that I can especially impact the lives of future students in terms of their math beliefs, because I am living proof that every math story does not have to end negitively.
Subscribe to:
Posts (Atom)