Specific to mathematics education, discuss any policies or practices in the classroom that you have seen or believe might lead to inequities or inequalities for particular students or groups of students. Regarding equity and equality, is one more desirable than the other?
I have noticed as I am planning lessons, it is increasingly difficult to cater to all students in the classroom, regardless of their level. I feel that I am often short-changing the students who have a solid grasp on the material in the attempts to get the students who are struggling to understand caught up with them. In this case, the goal is not to have equality because while that would be helping the struggling students, it would be a disservice to the students who already understand the material. Rather this is a problem of inequity which I feel that I need to put more time into alleviating. I think that equity is more important than equality, but that it is also more difficult to achieve, and that oftentimes teachers, in the interest of time, settle for trying to achieve equality.
ReplyDeleteIn the Westchester school where I am student teaching, there are two tracks in the 7th grade and three tracks in the 8th grade classes. It's obvious that this practice leads to inequity to the students in the low track. When the upper track students studying how to solve linear inequality problems, the low track students were learning how to solve one-step linear equations. More than two thrid of the low track class are bilingual and/or minority students. Some of the low track students are very smart, but those students either have a hard time to follow the classroom rules or have a very short attention span. It seems that the school district try to pursue equality rather than equity.
ReplyDeleteI have seen the same problem as Jennifer-- usually, the students who have no trouble understanding new material end up bored in class because they have finished their homework before most students have completed the Do Now. I try to help the "fast" students by explaining whatever they don't understand -- since they usually do the homework before the material it covers is explained to them -- but then for the rest of the period I'm not sure what to do with them. Sometimes they'll volunteer to help students who have missed class, but they're also likely to become disruptive.
ReplyDeleteOn the other hand, one of the classes I student teach has a large number of students with IEPs, and my cooperating teacher uses the same lesson plan for this class that he does for his others. The students (for the most part) seem to keep up as well as the other classes do, with no more extra help from me than I give the other classes. The availability of their resource teacher surely also helps make up for the challenge of keeping pace with a regular class, but I like this as an example of equity of opportunity-- they can see the same material (but are given extra help as needed).
As for equity vs. equality, I like to say that the latter isn't well-defined on the set of human beings. More accurately, I think it's a useless concept for human affairs because there are too many variables involved in simply describing a person and his/her circumstances for it to ever be applied. Equity, on the other hand-- at least as I'm taking it-- refers to the "equality of opportunity" ideal which I think our founding fathers had in mind. Allow-- even encourage-- people to be different; just don't restrict them for it.
That said, Wendy's example makes me think that "equity" doesn't deserve quite as much credit as I'm giving it. If it refers to the "separate but equal" sort of tracking that places smart students in slow classes because of other factors, I'm against it. Unfortunately, I'm pretty sure that means I have to cheat-- so, depending on which definitions you use, I may be for both, or neither.
The middle school (grades 6-8) where I'm teaching at has two tracks for each math class. I'm assisting with the higher level 6th grade classes and student teaching the lower level 7th grade classes. This is an obvious equality issue, because the group of high level sixth graders will have an opportunity to take algebra, and pass the regents exam much sooner than their seventh grade counterparts. Like Wendy said, a lot of the seventh graders are smart enough to be in a higher level class, but 'behavior issues' hold them back.
ReplyDeleteRegarding equity, I feel that each student, regardless of the track they're in, should be given the opportunity and resources to push themselves to, and above, their learning limit. Having said that, it is difficult spend more time helping the students that need it while simultaneously challenging the faster students. Now that there are two teachers in the class, a lot more individual attention can be given to each student. We try and develop a set of 'challenge' problems for the faster students to work on once they're finished with the daily lesson. These questions try to deepen the mathematical understanding of the current topic, or lead them into the next subject area.
We don't often talk about hetero-normativity and math education, but I've run into some fairly blatantly exclusive moments this semester in my teacher's AP statistics course. One such problem went something like this... suppose there is a girl in a room with a bunch of people. What is the probability that she will meet a guy who is taller than her (given the normal distribution of heights of guys and girls in the room). What is the probability she will meet someone x inches taller than her, etc...
ReplyDeleteWhile this might seem like an innocent problem, I wonder if our math teacher would ever ask a question about a girl meeting a girl shorter than her, or about two guys of the same height meeting at chance. I think problems like these, while fun to calculate, rarely ask the same questions of same-gender relationships.
Gay, lesbian, and bisexual youth as well as children with queer parents are our students whether you realize it or not. This problem I mentioned above is not an singular example... same-gender relationships are systematically left out and excluded from our examples, our data sets, our stories, and the histories that students see in schools and in math curricula. Why I don't think it is necessary to go overboard with inclusive examples, I do think that we have opportunities to both raise awareness and inclusiveness in classrooms. Maybe looking at statistics and data around bullying could provide a more just alternative than another hetero-normative relationship problem? Consider how you might challenge gender and sexual norms in your classroom, giving a safer space to those who identify outside of the norm in your math class.
Our students simply are not identical. Yet, while their backgrounds (especially prior knowledge) should help inform our differentiated instruction, no student should ever be negatively effected by the low expectations of their teachers. I do not believe that we should treat each of our students identically, we need to be aware of their learning styles, personalities, strengths and weaknesses. That said, we should have high expectations for all of our students, and we should not be satisfied by offering a lesser education to certain students.
ReplyDeleteI've been thinking a lot about racial stereotypes lately, and how the expectations some teachers set for their students based on these stereotypes can negatively influence the academic experience of these students. Yet, to deny race, culture, home life, and prior experience completely in our teaching is not only insensitive, I believe it is inappropriate. So, if equality means treating each of our students as if they do not bring a unique set of prior experiences to the classroom, then I am not for it. If equity means giving each student access to the same high level of education in a way that is unique to the individual, then yes, equity is what I try to foster in my classroom.
I agree completely with Beatrice's first paragraph above that students' unique personalities and learning styles should be embraced, but that we must have consistently high expectations for all students' abilities to learn even while we tailor the method of our instruction to accommodate student differences. In this way, like most of the post-ers above, I believe that equity is more important to foster in the classroom than equality.
ReplyDeleteThat said, equity is more difficult of an ideal than equality. When we think about how, whether we like it or not, the reality is that standardized, "equal," measures of students' performance and achievement will be crucial for allowing these students success (SATs, etc.). Standardized tests, built on the principle of equality, not equity, are naturally biased and give an advantage to some groups over others. I suppose that equity with regard to standardized testing is in giving all students equal opportunity to demonstrate their mathematical knowledge and ability on these standardized tests. But does this sound terribly like a "teaching to the test" methodology?
One group in my classroom/school that I am concerned about is the group of bilingual students who travel together with a bilingual teacher to all subjects EXCEPT MATH. This practice does not make sense to me, and I am often frustrated because I feel that their quizzes and assessments are largely assessing their language skills, rather than their math knowledge. For example, the other day one of the Chinese-speaking students was struggling with translating word sentences into expressions, for example "two less than five times a number." He called me over to remind him what "less" meant. I was interested that he clearly looked at the words word-by-word and that was the only word that he didn't "understand." But he still got the problem wrong because the phrasing is actually quite tricky. Same goes for geometry problems with all the terminology. I find that the bilingual students, when they learn a new word in math, translate it into Chinese, so instead of storing just the word and its definition, they have to translate the word into Chinese, and then think of the definition. This extra step, I think, certainly puts them at a disadvantage.
I also agree with Beatrice that no student should be negatively affected by prior knowledge of academic ability. I also believe this is true for student behavior. It's funny I am watching Full House right now, and in the episode (the one where Stephanie gets back at Gia by posting her grades up for everyone to see) Gia mentions that for once she wishes she could have a teacher who has not heard of her before. In my placement I see students constantly being judged by information teachers have received from other people. One of my students came into class a few weeks back and was really upset. I went over to talk to him while the class was working on the Do Now, and he asked if he could sit in the back for today. He seemed really upset and I asked what was wrong. He told me that he was jumped before school today, and I could see how shaken up he was. I felt so bad for him, after all he is just a kid, and no one deserves to be jumped. After class I spoke with my teacher regarding what happened, and she didn't seem to have much compassion. She told me she has heard from people that he has lied about his mother in the past, so maybe he was lying now. She said that if another student, such as NAME, was jumped it would break her heart, but with this student she just didn't know. I said that I believed him, and that for as long as I had worked with him he has not given me a reason not to believe him. It is not fair to treat students differently before meeting them. Teacher-student relationships and compassion for students should not be affected by experiences former teachers have had.
ReplyDeleteAt the School of One students who are capable of being independent learners get the most out of the curriculum. Also, students with higher computer literacy, students with more access to technology, are more efficient in their learning. Inequity is created by the way educators teach, because every student learns differently and teachers cannot equally cater to every learning style(including combinations of the predominant 3). Also, the entire math curriculum is on a computer, in English, putting students who are ESL at a disadvantage. When you have a uniform curriculum and school system the students who are farthest from the norm are usually at a disadvantage and those who assimilate most closely are better off. Differences create inequality.
ReplyDeleteAt LaGuardia, students with disabilities or other special situations are allowed to request extra time on tests and quizzes. I think this is fair because they might not be able to read and comprehend the tests as quickly, or they may have extreme anxiety in testing situations. However, I think this made lead to unintended inequality for students who are not allotted extra time. There are many students who may not have learning disabilities and still be struggling with math; they can benefit from some extra time and less stress in testing situations. If teachers are really interested in testing what the kids know and not what they can complete in under 45 minutes, they should be very sensitive to the needs of ALL their students. Interestingly, some teachers at LaGuardia do allow all students to take every time if they need to (during lunch period or after school on the same day) while others are adamant about the allotted 45 minutes. This situation can be advantageous as well as problematic, but I think to be totally equal, you need to eliminate differences in testing conditions. If some kids get extra time, then ALL kids deserve extra time. They may not want to or need to utilize this extra time, but it should be their decision and not the teacher's.
ReplyDeleteLike Tomi and Karina, I'm also student teaching at the School of One. I agree with Tomi that students with greater computer literacy are at an advantage because 90% of the math lessons are conducted via the Internet. Although the current set-up at SO1 is far from being perfectly equitable, the educational philosophy behind the school's creation is based on the idea that students come into the school with unique math histories. Students are initially assessed to identify the skills they have mastered and the ones which give them the most difficulty. The idea is that daily math lessons will be designed (by an computer algorithm) to cater to the individual student's needs. Although the technology is bug-ridden and the amount of individual student/teacher interaction is limited, I believe that this type innovative differentiated instruction represents a major stepping stone in the path towards educational equity.
ReplyDeleteThese issues are pressing in all different contents. While it may be difficult for some to find/see it in mathematics, I agree that they are just as prevalent. When a student reads a text book attempting to finish their homework by doing the critical thinking problem at the end of the page, if they find that they are running into application problems that include cell phones, allowances, or something that they are not familiar with, it is going to be very difficult for them to find application or relevance. I think that application problems in mathematics are very important for students. It motivates them to "buy into" the content and at the same time see purpose and meaning in what they are doing and feel that much more accomplished when they have mastered a new concept. I feel like there has sometimes been a misconception about equality and fairness and I really summed up my own definition when I heard a teacher once say, "Fairness is not giving everyone the same, fairness is giving everyone what they need to succeed." I constantly see this present when there is the discussion of "why does he get a calculator?" and I think that it is very important for teachers to answer these questions strategically and have the right expectations of respect in the classroom.
ReplyDeleteI think that not allowing enough wait time after asking questions is one practice that may lead to inequities for struggling students. If the teacher is calling on the first student who raises his or her hand, that teacher is catering to the needs of the students who already know the mathematics content at hand. This is a selfish practice on the part of the teacher who is trying to move the class along and not teaching for understanding. Regarding equity and equality, I would have to agree with what others have said, namely that equality is not a realistic option in the classroom. Every student has a unique set of characteristics and personality traits that affect his or her role in the classroom and it is totally unrealistic to try to treat every person the same. Diversity should be recognized and valued, so I believe that equity is a more appropriate goal for a teacher.
ReplyDeleteI have seen teachers who rate the mathematical ability of their students based only on their standard test scores from the year before. So before that student enters the classroom, his/her level of success has already been determined by the teacher's expectation of the student. When the student struggling in an area, instead of trying different ways to teach, the teacher assume that it is "expected" for that student to struggle because of his/her low standardize test scores. Similar to what Wendy said about the low track students, this leads to inequity for the students. The scary fact is that I have had some teachers who were like this during my years in a NYC public high school and I continue to see more of them as I enter the career in education.
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