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.