11/29/12 Reading

The tips offered by Reinhart in “Never Say What a Kid Can Say,” seem like they would be helpful in developing problem solving in students. Another way I’ve heard his key piece of advice is, “the person doing in the talking is the person doing the learning.” I think part of the value of getting kids to explain why they have made a choice about a math problem is building vocabulary and putting language to their thought process. I find that students often lack the ability to explain even their own questions when they are confused. Students are very imprecise with language and mathematics tends to be a language and subject that requires precise language.

Finding the right questions is challenging. When students have struggled with a problem I have to keep backing up within the thought process in order to figure out where they got messed up. Also finding the right questions becomes more difficult the larger the gap is between the student skill set and the level of problem being solved. I’m really struggling with questioning when reviewing for the EOC in my Algebra 2 classes. Many times students just don’t even know what the question is asking and it’s like pulling teeth to get them to start before they give up once they have become frustrated. When I can get to the sweet spot where they are not overwhelmed by the learning they really do like participating.

I like the tip about asking more process questions than product questions, I try to strive for that in the classroom. Students will directly go to answers and I’m always asking “why” they made the decision to do something in order to get at the problem solving process. With out understanding the process math looks like a bag of magic tricks, which is probably why so many kids already think that.

A few tips that I do a poor job of in my classes is providing wait time, not repeating student answers, and I do carry a pencil with me. The hardest one for me to do will be not holding a pencil. Many kids will be able to pick up on individual explanation when they are struggling, but some of them really won’t and they will try writing down what I say word for word, like if I say “f of x” they will write that, and I will show them the notation. Some of the kids have been trained to just wait of the answer rather than talking with me about the problem. I have some students really have a difficult time following dialog. However, now I’m thinking of one student I have that can hold a perfectly mathematically valid conversation with me when I am questioning him, but when he tries to write it down on his own it becomes suddenly more complicated for him. Sometimes I think they are just confused by the notation of the mathematical language.

Also, I know that the new way of teaching is all about letting kids problem solve themselves, but doesn’t there need to be lessons and lecture also? They are not going to intuit everything themselves. I just wonder where the balance is. I sort of think of activities as a way to peak interest or introduce a concept or to be a hook, but then there has to be leading also at some point. And manipulatives are great, but aren’t we also striving for the ability to abstract? Sure I can come up with problems that can be solved by drawing and manipulatives, but eventually students have to take the mental leap and use the math like a tool, because that what it is. It’s a tool that helps me figure out things that would take me too long to figure out with manipulatives, or too complicated to figure out through some tangible way.

11/15/12 reading

I agree with much of the Black article. I loved how he used the term black box for the school. At my school last year we used to joke that school was the “magic box” and just because students where in the magic box it meant that they were learning. Teaching standards are always being raised and the pressure comes down to teachers because we are the ones with the job to teach, but there are really more factors than just the teachers.

One point that I find surprising was the opinion that assessment boosted low achievement. I always feel like many of my lower achievers lose motivation from a flow of low grades.

I do agree that teachers can learn a lot from assessment, because I really get a feel for how students are progressing from quizzes and tests. It is sad that often student work just get copied and isn’t and accurate reflection of their ability. Although I do find less copied homework when I assign activities and less text problems.

Multiple choices tests are easy for the education structure to understand. If teacher assessed students on class performance of applying knowledge, the numbers wouldn’t be so clear cut, which would make every ones job a little bit harder. I even find myself being really ridged about my grading just so that I feel like I am being fair to all the students.

The Maxwell article about assessment with portfolios was great. At the Montessori middle school that I worked at last year we graded with portfolios also. On parent teacher conference night the student sat down with the parent in the classroom and showed and explained their progress to their parents. At that school the range of items required for the portfolio weren’t as extensive, it was more about work they did really well on and work that they had struggled with. The students also had to write a reflection for each piece or work. I preferred the requirements offered by Maxwell, especially the part about mathematical attitude and the mathematical connections. I think it’s important that the students develop a positive attitude toward mathematics and problem solving and the ability to apply and see where their mathematical knowledge fits into the world.

I thought it was interesting that the article pointed out that the idea of having to do a portfolio made the teacher change the types of assignments given. I like the idea of having students do a math portfolio and collecting something that they feel they can be proud of. It’s also important for students to see their own growth and to take pride in it.

Also, I like the idea of using a math log to get feedback on student understanding of the lessons and what they struggle with, but then I also worry about how much time it would take up. I typically have a reflection question at the bottom of every class work sheet I give them in class that asks them to name one thing they understood and one thing they still have questions about. It’s helpful to get that info, and it would probably be even more helpful to get an even more detailed and human account of what they are struggling with in math class.

NCTM Suggestions

NCTM website suggestions for communicating with parents were good. My favorite was contacting parents the first week of school so that the first communication is positive. I wish I had tried to call all my parents the first week of school when I started this year. I will start the next semester that way.

Knox County already has the grade book online, which is great because parents can check it whenever and they don't have to wait for a report card. Also, my school sends report cards home every 3 weeks (instead of 4 and a half), and every report card day is actually a parent night, so parents can come to the school and talk to teachers if they want to.

I like e-mailing parents, but we aren't supposed to email, we are supposed to send everything through schoolfusion, which is a pain because then the parents need to register and sometimes they don't. Also, I was emailing with one parent and Outlook started blocking her email address so that I could no longer reply. I suppose Knox County on wants us to use our email for internal stuff.

I don't like the idea of post cards. Mail is expensive, and I personally hate junk mail, I feel like newsletters and such might fall into the same category.

11/1/12 Reading

The family math night that LaChance describes sounds like a lot of fun, especially for younger students. I can envision it working really well, especially in an elementary school setting. I would love to participate in a family math night, or even host one, unfortunately I really don’t feel like it’s an appropriate fit for the school I am in now, and perhaps would be better pulled off with more years experience, and a decent chance at some kind of turn out for participating parents and students. I would really like to see some of the activities they used in action.

A couple of the ideas from the NCTM website were good. I wish I had tried to call all my parents the first week of school when I started this year. I will start the next semester that way. Knox County already has a lot of parent contact in place, like all the grades on-line and the schoolfusion pages. I really need to do a better job of trying to keep the webpage up to date, but most days I really can’t because it is all I can do just to stay on top of grading and planning.

10/25/12 Readings

I read the “How Many Blades of Grass” article earlier and was very impressed with where such open ended questions can lead if teachers have enough time and let the students discover their own methods of solving the problem.

The Saraco article had some great ideas for a project. I’ve thought about doing something similar, but have not due to my own lack of knowledge. I also am pressed for time, but this might actually fit in great for after the EOC test. With better planning I would be able to integrate it into my school year the way it was presented. I really liked the fact that if focused on minorities and women. Like in the article, I don’t think I could name 5 important mathematicians that aren’t white males.

I also like Keleher’s project of solving contextual problems. I would worry that many students wouldn’t know where to begin the problems and I would need to make sure that there were some check in on the progress before the due date. Also, getting the problems, working through them to make sure they are appropriate and building a library of the problems sounds time consuming. Perhaps that would be a summer teacher project.

10/18/12

 I’ve never used algebra tiles, and when I came to the school that I’m working at now I was actually given some to use. However, when I asked how they were used I was only given an old book of transparencies. I looked at it briefly and then it went into a stack in my cupboard where I keep all the stuff that will most likely never get around to using. Now having read the Leitze article I see how they may have helped when I taught my students factoring. Other than that they would probably be most useful in Algebra 1. Reading the article also made me wish that I had algebra tiles when I was working at a Montessori middle school last year. It would have fit with the curriculum well.

Reading Rubenstein reminded me of what a technical language mathematics is. I usually tell students that learning math is like learning a foreign language, only harder because there are calculations involved. Students have to acquire this language in order to participate and become part of the discourse community in the classroom. I just finished teaching a chapter about polynomials and one piece of working with polynomials includes naming them by their degree and number of terms. I focused on this the first day and continued to use the specific language (i.e. cubic trinomial) and asked the students to use it also. It was difficult at first, but I see some improvements. By explicitly making connections to the roots of the words I hoped to help the students remember. However sometimes I think that the specific language can also turn off students, especially when they are behind because they have less comprehension of what is going on in the classroom when the technical language is used without explanation.

I liked the fact that the Coburn article had some alternative approaches to working with polynomials. I never remember factoring quadratics the way the author proposes, and I like that the fraction methods makes the zeros more apparent, but my students freak out any time they see a fraction in a problem. Fractions combined with factoring would cause me students to use other F words. On the other hand, I liked the “push principle” used to find the sign of an interval. The last method presented to solve quadratics seemed a bit complicated. I suppose it’s convenient for finding the zeros, maybe, but I’m just not sold on it. I had to read through it three times before I could figure out what he was doing and why.

10/4/ Reading Response

Smith has some great points about how to shape class discussions so that they unfold nicely for learning.

It is important to anticipate student responses. This is something that I am still weak in, just because I have not been teaching very long.

Monitoring the student work as they are working helps keep students working and helps when deciding who to call on during group discussions. I try to point out different methods of doing the same problem. I also don’t want to embarrass people when they do not have the right answer, so I will be especially careful about calling on the students who sort of hide in class, and I will make sure I call on them when I know they have the correct answer or correct method so that I can boost their confidence.

I have not thought much about the sequencing of student responses. The furthest I have considered is calling on lower performing students more in the beginning so that they can participate. I think the Smith article points out that teachers need to pay even more attention and plan ahead of time how they want to student discussion and learning to unfold.

In the selected reading from the text one sentence hit home, “the geometry curriculum in the United States has been somewhat of an eclectic mix of activities and lists of “bold print words” –too much emphasis has been placed on learning terminology.” I think memorizing words does have a lot of emphasis. I don’t want to say that it’s not important, it is, but the language is just a tool to talk about the math, it shouldn’t be the focus. The van Hiele levels could be useful when teaching, but I don’t really think that a teacher needs to know what number level a student is at, it all seemed pretty common sense to me, and just extra educational categories that the educational people like to construct.