Noelani+and+Jason

4/11 I was happy to see this article again. I read it in my multicultural education class a year ago. One thing I remembered that struck again was the comment on the bandaids. Being able to buy bandaids that are "flesh toned" and have them match. It is such a trivial little thing but so indicative of the society in which we live and things we can take for granted.

The other thing I thought about as I reread this article was the things I do in my classroom that are unconsciously biased. I noticed after last weeks conversation and reading this article that there are several things that could irritate or be offensive to my students. Here are the two that seemed the most striking and irritating to me personally and philosophically. -I occasionally hesitate to call on ELL students during class or accept less rigorous answers form them. -I have had several students complain about the fact that after almost a full year I am still unable to correctly pronounce their names. (That is something I have hardly ever had a problem with my own name.)

4/3/2012 As I red this article I was struck by how the teachers related to the students cultures. I kept comparing my situation to that of the school reviewed. In my school the majority of students are white but i have a minority student population that is not insignificant. I have 2 russian students, 1 italian, 3 students from the Congo, quite a few latino students that claim heritage from all over central and south america, 3 african american students 5 pacific islanders, and a few others that hail from other cultures and countries. As I was reading this article I kept thinking that they were demonstrating not a culturally relevant method of teaching but a bicultural relevant method of teaching. Specifically what methods will empower students but also culturally empower latinos.

I realize that they did generalize the culturally relevant part especially in the discussion of Ms. Herrera's class. They mentioned that she infrequently mentioned Mexican culture in her lessons but used a more general approach of making everyone into a larger community family. They go on to talk about solidarity and how this is a way to get access to the culturally relevant side of teaching. They specifically had a section here where they discussed parenting workshops and how that is a deficit way of thinking. It reminded me of the Algebra project. When trying to get parents engaged in education our interactions should not be as a preacher telling them what to do do but rather as a colearner trying to figure out what is best for the students.

3/27 The part of this project that intrigued me the most was how it mentioned that the students where becoming more reliant on materials. As I have been working with students I have noticed that students frequently ask for worksheets or homework when we are doing more lecture based lessons. This may be an indication that the students are ready for a more hands off approach or just that they lack the skills to stay focused during a lecture which was also mentioned in the article.

When I was thinking about this article I was reminded of the Suzuki music teaching method. This method again has the philosophy that the only way for children to fully engage with learning is to have a community including family members involved in the same learning activites. In the Suzuki case they were learning how to play musical instruments but in practice it sounds very similar to the community and family involvement discussed in the algebra project.

3/20

I found this article, Putting Students on the Path to Learning, very interesting but it immediately raised the questions, what is an expert and how do you determine when students are in the expert category and should be transitioned to minimal guidance? It seems in my mind that in order to effectively use the theory under discussion in this article the teacher would have to be a master of formative assessment and have a thorough understanding of the level of students abilities.

3/6

The task of developing a classroom where problems are used to drive the formation of content in the minds of students still seems like a difficult concept for me. The development of norms for classroom discussion seem critical as students have typically not developed the habits to successfully engage in this type of open ended inquiry environment. At least this is what I hear anecdotally and have myself experienced when trying to engage in problem solving sessions with my students.

I appreciated the comments that when we are panning these problems it is important to have everyone in the classroom support all work done. In addition to this the importance of the role of the teacher in highlighting student to discoveries that lead to the goal is critical. The issue that I have as a new teacher is that when I use problems in my classroom I miss developing a wide range of topics that are related to the problem either because I am too focused on the content that I want the students to learn or because I have not developed an effective classroom environment for the necessary discussion.

2/28 I appreciated the comments on how problem posing can increase the moral and ethical discussions involved in mathematical situations, e.g. three people splitting the driving responsibilities on a road trip. One reason people can't relate to mathematics is because in some mathematics classes the majority of problems are decontectualized drills. If I read the article right the research has at least anecdotaly shown that given a chance to create problems given addressing situations that are more personalized can expand student thought processes in unexpected ways.

I found the comment on van den Bik's study that showed students are less likely to make mistakes on problems they created themselves interesting. Is that because they were making easy problems as we discussed or because in vreating the problem they were really expanding their understanding?

2/18 While reading the article by Strong,Thomas, Perini, and Silver the discussion of a test caught my eye. This how they explained one could create a more fair and balanced test. "...a four-part grid would address each dimension of mathematical learning and all four mathematical learning styles by asking students to compute with fractions, explain how fractions work, apply fractions to a real-life situation, and solve a nonroutine problem using fractions." This reminded me of the six boxes that Ralph described having his students make when learning about new types of equations. If I remember correctly the boxes were the equation, a table, a graph, a real life problem, and I can't remember the other two. Another example of this was from Leonard with his "A" question that we went over in class. He said he had students take a test that sounded like it checked for understanding and mastery but then gave the "A"question to those who finished which checked for real life application.

The last part of the statement on tests was that students should be able to solve a nonroutine problem. I was confused as to what was meant but I think this is clearly explained in the next article on "light bulb questions." By nonroutine they mean a question that is given in a way that the student needs to create the structure for solving the problem or choose the problem solving strategy. As quoted by the author, "...problem solving (Polya 1957) involves students making their own decisions and formulating their own plan to solve the problem."

This seems like it would be an interesting test. 2/7 Working inside the black box,

One of the ideas for implementation that stood out to me was that students who create their own questions in order to review material tend to outperform those that don't. This ties in with a comment that you made about how as students one of the most difficult things to learn is to take a definition and create questions and examples to help develop an understanding and familiarity with that definition.

This whole concept is related to the section devoted to the idea that good pedagogical skill in questioning comes from creativity and a deep understanding of the fundamentals of a subject. This seems kind of circular in that we want our students to be able to create and ask themselves content and strategy related questions after a unit which will help them gain the understanding that is needed to ask real thought provoking questions to review for summative tests.

1/31

The article inside the black box was a good follow up article to the back wards design discussion we had last class and fits in nice with my own personal goals for improving my own teaching. This year I have been struggling with classroom management and the communication and feedback I have been getting from my administration and advisors is that at the root of my problems is inefficient assessment and engagement in my lessons.

The "engagement" of my students was temporarily increased when under advisement I started asking for more choral responses to memorization level questions and under instruction from a teaching coach and the administration I have been following the direct instruction model i.e. I do, we do, you do or instruction, guided practice, individual practice. This type of engagement and questioning does have an appropriate place in classrooms but it is grating on my own nerves and hasn't helped me meet any real objectives of assessing or developing what was described in the article i.e. "... what is needed is a classroom culture of questioning and deep thinking in which pupils will learn from shared discussions with teachers and from one another."

"...This study suggests that assessment, as it occurs in schools, is far from a merely technical problem. Rather, it is deeply social and personal." again we get to the idea that as teachers we are being judged by a variety of complex and sometimes opposing ideas. The message I am getting from my school district is that classroom engagement is the most important part of my lessons, this is something I believe to a point, the message I am getting from the research papers and the backwards design text is that this is often so over emphasized that it consumes planning and distracts from an actual pursuit of educating for student learning.

1/17

I think a good example of instrumental understanding comes from the state core requirements from geometry about the equation of a circle in geometry

Graph a circle given the equation in the form (x-h)^2+(y-k)^2=r^2, and write the equation when given the graph.

There is no expectation of understanding in this statement at all which I believe is a reason for the preponderance of teachers teaching this as a skill to be mastered with understanding coming later if ever.

So when I have thought about how I have come to a relational understanding of mathematics it closely follows his map making analogy. I memorize or master a rule overlearn it and then in the future as I study other material I form the necessary connections or develop the drive to investigate the reason why something works. Very rarely do I feel impelled to ask right at the beginning why something is done a certain way. Even though I do enjoy this type of questioning and discovery.

9/12/2011

In the article by Eric Reece there where three statements that struck me. The first was a paraphrasing of Gatto saying that "The education system is intentionally designed to shape them into a passive mass who will, in bovine fashion, join the labor force and become unthinking mass producers and mass consumers."

"There is, to take one pervasive example, not a single item for sale at my local mall that asks the consumer to do something, make something, or master a skill"

"Students express an overwhelming feeling that only their attendance and test scores are important to teachers and administrators."

These lead to a question of how many students feel like they are learning something useful if all they are doing is taking a series of multiple choice exams.

These critiques are very applicable to how we are trained to teach and what is emphasised in teacher accountability. Speaking with a social studies teacher the other day I was told that as a new teacher the most important things I should focus on are staying on top of grading and making sure attendance is accurate because these are what will pass on in permanent records. As a supervisor of minors being accurate in attendance is important from a legal stand point. Staying on top of grades is also important in communicating rates of progression of my students and their parents. But if these are all that is being emphasized to teachers then that message will invariably be passed on to students. As I was told this though, it was implied that everything else is secondary. Actual student learning was deemed secondary to making sure kids were in their seats during class.

9/26/2011


 * How does the role of algebra as you see it compare to Usiskin's ideas?
 * I've always thought of algebra as the basic tool for manipulating mathematical ideas. Given a problem or situation we use algebra to twist the concepts in our heads to analyze the relationships and structure of the problem. This view seems to align with Usiskin's idea that //"Algebra remains a vehicle for solving certain problems but it is more than that as well. It provides the means by which to describe and analyze relationships. And it is the key to the characterization and understanding of mathematical structures."//
 * This idea is reinforced when we talk about algebra as a problem solving toolbox and formulas, equations, and expressions as the tools
 * What do you think your students think the role of algebra is?
 * Unfortunately given the dominance of multiple choice testing and skill mastery questions I believe students view algebra as a set of complex and tedious methods to manipulate numbers and formulas with very few practical applications for the lay person.
 * How do you reconcile the differences?
 * In order to reconcile these differences we need to introduce more actual problem solving and critical thinking exercises into mathematics lessons and homework. By presenting students with questions that require connections to be made and explored students will be given a better opportunity to experience algebra as a way of discovering relationships.
 * Questions that I ask.
 * As we go through the lesson I frequently try to encourage my students to participate in the lesson by asking them to perform the arithmetic steps of example problems. This would fall under the category of memorization
 * I ask students to explain or share ideas. In precalculus today I asked the students to describe what a function is this was a memorization task.
 * The home work I have been giving is typically procedures without questions.
 * When students are explaining problem solutions at to me I frequently ask them to justify their procedures or thinking. This type of questioning though also falls mostly under memorization, e.g. that statement is true because it is the definition of, or procedures without connections, e.g. x = 3 or -2 because that is what I get when I use the quadratic formula.

10/3


 * Discuss implications to your students' view of mathematics and the work in mathematics classroom that those questions have.
 * As I wrote last week the students see algebra as a set of rules that they have to memorize and repeat back when given a certain type of problem. This also leads to the idea that math classes are a hoop they have to jump through unless they are going into science and engineering.
 * Reflect on the course thus far: readings, discussion, work done in your lesson study groups. Offer constructive criticism for improvement.
 * The course has been interesting. Particularly I have enjoyed the discussions of problem based or inquiry based lessons. The only time i have tried to give my students an inquiry based assignment it fell flat and I don't think that more than one or two were able to make the connections. It was a lesson on translating and scaling functions and student where given a series of related functions to graph and asked to explain the relationships between them i.e. what was changing and what was the same.