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.

9/27/12 Readings

The text presented some better ways to introduce recognizing patters and sequences than ways I have seen in text. I like the idea of using objects that the kids can arrange rather than a table of values or pictures on a worksheet. I was also excited to see it because it has a large connection to the material I am currently teaching. Getting students to shift from very computational/memorized fact mathematics to algebra, where students compute to solve a problem is tough. I think it’s analogous to the transition when kids go from learning to read to reading to learn.

I used to work at Ypsilanti High School in Michigan, where they actually had Algebra Project and YPP afterschool. YPP was sort of co-funded through a grant that I was working under providing free afterschool tutoring. I never sat in on Algebra Project classes, but I did participate in a few of the YPP meetings, which I thought were great. The students mostly played math games with college kids, and then learning the games and played them with younger students at local schools. Anyway, I really agree with Moses that students need to be proficient in math science and technology in order to function as a productive member of society. Successive generations will have to be able to do jobs that machines cannot do. I tell them that I don’t care if they can solve 8x + 10 = -2, a machine can do that, that if they don’t want to be replaced by a machine than they really need to learn how to take messy problems (ie contextual problems) and make sense of them. Most of the time I feel like many of my students don’t really get the connection, or don’t feel like making the effort. It is tempting for me to frame these things as a civil rights issue, but I have not yet because I am cautious about how they will respond, or I am scared that they won’t care.

I read both the calculator article and the technology article about using the equations applet. I thought the equations balance was a clever way to teach the concept of equations and examine the relationships of the values. The writer was correct that we have to emphasize the math, not the technology. I use graphing calculators every day in the classroom, and when I show a new concept we usually go over how to do it by hand first, and then I show them how to do it in the calculator. Using the calculator also allows us to do more complicated problems or contextual problems that might be computationally overwhelming if we didn’t have the calculators. I really should get better about using more technology in the classroom also (besides my graphing calculators) but I occasionally get sucked into a textbook/EOC vortex that favors those kids of problems.

9/20/12 Readings

“Poverty: Teaching Mathematics and Social Justice,” by Leah McCoy presents some great ideas for math lessons. I liked the lesson about budgeting different income levels, but I also think that it is not very mathematically advance, for instance, I don’t think I could justify taking the time to do that in my algebra 2 class, but that it would work well in a middle school math class. Lessons like these can really bring home the idea that people use math every day and that it is important. A higher math skill lesson like the one mentioned later in the text about plotting school district income and the EOC scores and then fitting a line of best fit is actually something that I could do in my class.

I also think it can be enlightening for students who do not live in poverty to see a budget like the on in the article. If I were going to do something like this in my class though, I would have to set it up differently. My students already know about living in poverty, and perhaps I would correlate careers with an income, and then have a variety of incomes to budget.

I wish I had some revelation from the Middleton, “All Students Are Motivated: Why it Matters do Understand the Reasons Students Do What They Do,” article, but I honestly don’t. It followed one student through her school day, but it basically just told the story of that without much else. I suppose that I am responsible for inferring that teachers work with children, and children are much more sensitive than adults, especially to their environment, peers, and how they perceive actions of adults and other people. Children are more likely to view actions through an egocentric lens and take everything personally, and perceive things and directed at them even when they are not. (i.e. Grace thought she was being punished when the teacher put her in a different group.) Since we are teaching children we do need to be more sensitive to some of the things that help them work well and motivate them and things that make them shut down. Or maybe there was something in that article that went over my head.

In the 1999 Middleton article I agree that students need a high degree of success in order to engage in math. I think this is because our culture does not value math. I hear other people say all the time, mostly adults, “I’m just not a math person,” “I don’t get math,” “ I can’t do math.” It is accepted as ok and normal to feel that way about math. But I have never heard anyone say that they don’t get history, or they just can’t read. Math is more difficult that a lot of subjects, and there is usually a right answer, verses in a few other subjects where there is a broader spectrum of right and sort of right answers. Math requires a lot of work, so if students feel like they are not likely to succeed, they feel more comfortable failing because so many people around them have given up and turned out fine. Giving up on math is low risk, giving up on reading is very high risk.

It also seems obvious that the challenge level cannot be overwhelming or too high or too low for engagement.

I don’t know that I agree with the gender stereo typing about girls in math anymore. I think I had stronger feelings about it when I was in college (the first time), but in high school it seems less relevant. Maybe my view is skewed because I am the teacher and not the student in my class, I can’t really tell, but right now I don’t perceive there to be a difference.

I do agree that the “Current practice leads students to develop attitudes that value speed of computation, following the example of the teacher, and correctness of answers over learning and understanding.” I do want students to be able to do problems quickly, because that usually means that they know the material well and don’t have to struggle through deciding what to do. I do want my students to arrive at the correct answer. Whether or not a student finds the answer by following my example or not doesn’t bother me. I see kids taking short cuts or writing things differently, or finding a different path through a problem and I try to embrace that. However, I really only see a handful of students getting creative with math and problem solving. Maybe that is the result of years of drill, or lack of something else. Most of my students will give up on a problem unless I give them a recipe to follow and show them a few examples. I am working towards trying to get them to try to work through problems that they may not have been told how to do, but may be variations of problems similar to ones they know how to solve. (Maybe that is my differentiation).

Another point that I found interesting is that “Japanese students are expected to be more self-motivated than American students. In Japan over control of tasks by the teacher is minimal, effort is valued over ability, and determination of interest and success are primarily left up to the student….teachers in the United States are expected to make instruction interesting and appealing, and students are less likely to be blamed for inattention if the topic is personally unappealing.” That makes me wonder what kind of standards the teachers are held to. When I am planning my lessons I always have this Knox County pacing guide and I am thinking to myself about how I can possible only spend the amount of time allotted to each subject. I think it’s wonderful to have high standards, but I would like more freedom, more time to be creative, and less presser about how my students will be evaluated on the EOC and how I will be evaluated on the EOC. Really we are forcing students learn things that they don’t really care about, which is why we are having this motivation problem. Frankly, I think much of the standards we have for school, especially high school are really not necessary. Do students really need to take 4 years of college bound math? Probably not unless they want to go into the sciences or are still unsure about a career track. Maybe we could incorporate math classes in more practical ways.

The excerpts from “Fires in the Bathroom” included a lot of questions and statements that would provide important material for teachers to reflect on. The questions in the beginning probe the teacher to ask themselves if they have made their expectations clear. I felt like the student quotes were an accurate reflection attitudes and things that I hear students say.

Teaching by the book, especially in math is really boring, for the students and for me. One tip that I heard about someone using was that in work problems that they would change the names in the story to their students’ names. I tried rewriting some of the story problems in the text and changed the names and put things in context of our school and students seemed more open to working out the problems just from that small change, even though it was something really simple.

9_13 Readings

The “Group-Worthy Tasks,” article by Lotan reiterated much of what is already known about group work. It must be complex, it must have multiple skill level entry points, and each individual should feel accountable for their contributions to the group. These are all ingredients of successful group work. I felt like such conclusions aren’t really leaps of genius, but that much of that can be figured out from experience. One point that stood out the most to me was the importance of group work that had multiple ways for students to show intelligence.

In the piece “Rethinking Mathematics,” Guttstein and Peterson emphasize putting math problems in context of fighting injustice in the world. They make a case that students need to learn math so that they can gain critical thinking skills and understand things like pollution concentration or understanding if racial profiling is happening. This is a sort of “hook,” for student interest in the math problems. The authors recommend that teachers use social justice to peak student interest rather than following a more teacher centered approach with typically neutral mathematics problems. I think this can be done to a degree in the classroom, but it has to be tailored to the student’s interest. I also think it can’t be shoved in their face all the time because it’s a bit of a drag, and teachers should also try to include more “fun” problems also. One negative for the teacher is that they would have to do more research in order to create accurate problems, and one benefit is that students are prompted to think critically about the problems of other people in the world and the problems and injustice that they face themselves.

 “Blades of Grass: How Many Are on a Football Field” was a very charming lesson that seems to exemplify student centered learning. I loved how the teacher let the students make decisions and felt confident that they would discover their own mistakes and arrive at a good estimate. I do wonder about how long this lesson took. It seems like it would have taken a very long time, but it also sounds like it was the kind of concrete project that allowed all student levels to participate and it would be something that they would remember. One important part of making the lesson successful that the writer mentioned was that the question and process had to be open-ended, and that the teacher did not tell the students how to do the problem. The teacher was a guide through a student led journey of fully understanding a problem.