Idea: Different look, same value
Reflection 1: I understand the idea about equivalent fractions well mainly because I understand how things are related and match up. What this means is, I can see how there parts of a whole and if you have the correct number of these parts to make a whole, than you have made a whole.
Reflection 2: Many children may not feel the same way as I do when first learning about equivalent fractions. For a child with a fairly concrete mind, once they are told that a whole is a whole number (3, 4, 5, 6 etc), than it is challenging for them to understand that there are many pieces to the while that they do not see (halfs, quarters, thirds etc).
Reflection 3: I'm glad to see that I am thinking about student's developmental stages as a student teacher. I am a psychology lover and have a large background in psychology (and eventually would like to continue in this field), therefore it is important to me to really see the cognitive, behavioral and physical stages these students are at.
Monday, January 30, 2012
There's More to Math
Idea: We do things, without knowing we do it.
Reflection 1: This comment from math class a couple of weeks ago was important to me because it not only applies to just math, but to many things we do every day. These are the things that are so second nature to us. I think that it is important for math to become something second nature because math is all around us, whether we notice it or not. We do small calculations, estimations, find patterns, and process a lot of information at once in our heads as well as multi-task in our environment. There are a lot of variables around us, as well as statistics and spaces. Learning new math concepts works the brain. It takes a while for these things to become second nature. I think that is why learning time is so precious for these understandings to ground themselves. For students to be successful they need to practice and rehearse these new things. For example, I still need to use my fingers to calculate 6x8. Many people can come up with the answer automatically. It takes practice and exposure to something many times until it truly sticks. It's like learning another language. When you are not immersed within the language it makes it a whole lot harder to become fluent.
Reflection 2: I definitely want a fluency for my students, and I want a fluency or myself. After my first practicum, I felt that I would never again have fluency, a sense of confidence in my practice. I think you can always start over when you learn. I know that we are life long learners. Once we stop learning, or chose to stop learning, I don't think it is impossible to begin a learning journey again. You may be bruised a little, but it's not impossible. For one student in my last practicum, I think the above idea didn't really apply to her new adjustment to the classroom. I think perhaps she didn't do things, without knowing that she could. She needed stimulus, someone to lead her. I don't think I did enough to help her, but I recognize now that there are many sides to a learner and encouraging them to enrich themselves in the lesson can't hurt.
Kicking the Habit - Textbook Trouble
I 
Idea: Textbooks are trouble
Reflection 1: Like many teacher resources, textbooks guide students through their learning of concepts but for some reason textbooks are missing the boat on the way students learn and providing a way for a teacher to use the resource effectively and efficiently. I say this because many unnecessary concepts are introduced at inappropriate age levels as well as man examples are insufficient. I don't necessarily think that textbooks are complete trouble, more so they are an option. One that can be a crutch to many teachers who rely on it because they are lacking skills in the area of math. During my practicum I would say that I relied on the textbook because purely a lack of expertise. The textbook was available for me to use - and of course I took advantage of the information inside.
Reflection 2: I seem to be very back and forth about the use and perhaps abuse of textbooks for teaching. When I used the textbook I would get confused while was teaching. I tried too hard to have the students follow what was in the book . I'm not really a learner who learns incredibly well from reading (I have now learned) I learn better when I see it happening, it demonstrated. I think this is just what I'll need to do with my students.The students need to do more inquiry instead of simply believing what the textbook says to be true. I think it's more important for students to find that out themselves. S0 ... I guess no textbook.
Idea: Textbooks are trouble
Reflection 1: Like many teacher resources, textbooks guide students through their learning of concepts but for some reason textbooks are missing the boat on the way students learn and providing a way for a teacher to use the resource effectively and efficiently. I say this because many unnecessary concepts are introduced at inappropriate age levels as well as man examples are insufficient. I don't necessarily think that textbooks are complete trouble, more so they are an option. One that can be a crutch to many teachers who rely on it because they are lacking skills in the area of math. During my practicum I would say that I relied on the textbook because purely a lack of expertise. The textbook was available for me to use - and of course I took advantage of the information inside.
Reflection 2: I seem to be very back and forth about the use and perhaps abuse of textbooks for teaching. When I used the textbook I would get confused while was teaching. I tried too hard to have the students follow what was in the book . I'm not really a learner who learns incredibly well from reading (I have now learned) I learn better when I see it happening, it demonstrated. I think this is just what I'll need to do with my students.The students need to do more inquiry instead of simply believing what the textbook says to be true. I think it's more important for students to find that out themselves. S0 ... I guess no textbook.
The Secret Key
Idea: The secret key to mathematics is pattern.
Reflection 1: I found this line on a math website a while ago while I was trying to look for math lessons and it seemed to have stuck in my head not because I love it, find it inspirational or truly understand it. I think it stuck with me mostly because it is so definite, clear and confident. Now that I think about it, to better understand what it mean, I first need to look it up. What is pattern?
There were 5 definitions on www.dictionary.com. I've listed the 3rd, 4th and 5th because I feel they are most appropriate for math.
3. a natural or chance marking, configuration, or design: patterns of frost on the window.
5.a combination of qualities, acts, tendencies, etc., forming a consistent or characteristic arrangement: the behavior patterns of teenagers.
I like these definitions. Math is a design. It's a group of 'things' together in some kind of arrangement but in a distinctive, specific style. Math has a meaning. Numbers are woven through, stitched, and placed next to each other to create something new. It's consistent and reliable. Sure sounds a little romantic doesn't it? A little artsy fartsy? I thought so too. But, I like thinking about math this way. It's approachable for me this way. I'm a drama student and spend most of my first year at university making jokes at the Faculty of Engineering's expense.
I am feeling closer to this "secret key" notion. In math there is a series. We add, then add, then add again to multiply. We take away, take away and take away over and over again, to divide.
I like these definitions. Math is a design. It's a group of 'things' together in some kind of arrangement but in a distinctive, specific style. Math has a meaning. Numbers are woven through, stitched, and placed next to each other to create something new. It's consistent and reliable. Sure sounds a little romantic doesn't it? A little artsy fartsy? I thought so too. But, I like thinking about math this way. It's approachable for me this way. I'm a drama student and spend most of my first year at university making jokes at the Faculty of Engineering's expense.
I am feeling closer to this "secret key" notion. In math there is a series. We add, then add, then add again to multiply. We take away, take away and take away over and over again, to divide.
Reflection 2: I have a memory for moments when I have been moved towards an idea, thought or word of wisdom. Mathematics is not my strength, I've noted this multiple times already in other posts and having this connection to a pattern and a variety of accessible definitions, helps me to understand mathematics as an art. It's some kind of production you could say.
Sunday, January 29, 2012
Think About Why!
Idea: Real mathematicians ask why
Reflection 1: It's important to me and as I facilitate student learning to create an environment for students to question the concepts I am presenting as well as question the way that they think about this new information. When it comes to math, however, I don't think that students are really given the proper opportunity or the permission to ask higher level thinking while learning math. I found in my last placement that the questions students were asking were procedural, to repeat instructions or just for reassurance that what they were doing was correct. There is nothing really wrong with those questions, but perhaps it is the territory that comes along with "math". Unlike in the literacy block, teachers do not ask many "why is that?" questions to students to explore, or dig a little deeper as to why math things are the way they are. For example to help students predict, invent or problem solve, teacher may ask, "what would happen if...?" or give the students a chance to "convince me...!". Rarely do we also allow students to express true feelings, attitudes and beliefs about mathematics. In literacy we do. In science we predict, why not in math? Why not express our attitudes towards math so that we are more comfortable and confident with the subject?
Reflection 2: I want to be this kind of teacher, able to provide students with prompting questions about math and open them up to deeper thinking rather than doing simple work sheets. I made this mistake in y first placement. I think I know better now.
I Met Math On eHarmony. It Didn't Work Out
Idea: If you are going to teach math, you have to enjoy it!
Reflection 1: If you are being forced to teach math, you better pretend to enjoy it!
Reflection 2: It's difficult as a teacher candidate to teach a subject that you yourself are not completely comfortable with. This comment if fair too commen - yes I understand that I'm preaching to the choir - but for someone who knows what to do, but just isn't sure HOW to so it, it can really make an experience difficult. I will be the first one to admit that my abilities to teach math are not acceptable - but I'm trying. How am I trying? I'm pretending. During high school and some parts of my undergraduate degree, I learned to "fake it till I make it". Sometimes if you fake it enough, you actually start to believe it. But, how do you know when enough is enough and I should "stop digging myself a grave" or 'quit while I'm ahead". I just don't want to "go down in flames" again...
"Sorry Miss. I Can't Do It. I'm Waiting for a Calculator"
Idea: Not only slowing down the Math Stations, some students in my last practicum (Grade 7) depended highly on their calculators and it was surprising by how much they saw the legitimacy in this even if the problem was age appropriate and fairly straight forward (adding and subtracting three digit numbers)
Reflection 1: From what I remember, when I was in school we used calculators. We definitely used them in Grade 8 when finding the area of a circle, and I wouldn't doubt that while the calculator was on our desks we would type in simple problems that we could have done in our heads. It was convenient. But, it's also a tool that was invented and allows us to do these "simple and silly" problems. You can't really blame the technology.
Reflection 2: But, my kids were WAITING to use a calculator - for their friend to finish and pass it over. While waiting, students would get social and not even try to attempt the problem without my prompting. Is this a norm the education system has created? Like putting up your hand, or lining up at the door before you enter the room? Unless your teacher says not to, use a calculator! It's easier.
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