The Power Behind High Expectations

While discussing the question of “What can I do to help make math accessible to all students?,” there were many answers that were good. However, the one that stuck out to me the most was having clear, high expectations for each student. Personally, this was my main support throughout high school and even college. There was always someone pushing me to do my best and even aim for a little above that. I was fortunate to have my parents and sister as part of these people, however, I know that not all students are able to have this kind of support. As a teacher and role model, it is important to show your students you care about them and their success, not only in school but in life as a whole. From a previous course, I heard about a man named Daniel Kish.

Since then, I have done further research on this man and his interesting life. I have watched a ted talk, listened to podcasts, and read many articles. Daniel Kish was a man born with ‘retinal cancer.’ Throughout his childhood, Daniel was not given special treatment by his mother, family, teachers, or peers. This was not done out of hostility, but instead on purpose. In doing this, he was forced to learn how to adapt to his surroundings with the abilities he does have. He began to use sound to “see” his surroundings; this is known as echolocation. Kish would make a clicking noise with his tongue and listen for the sound waves to bounce back to him, making him aware of the surrounding space. Had he been given special treatment such as a personal assistant or a wheelchair that wouldn’t allow him to run into anything, Daniel would not have acquired the skills he has today.

This situation can be compared to many common cases we will face as teachers such as students of another race, financial status, or popularity level. No matter the background of the students, they should all be given high expectations that they are able to rise and work towards. I know that if I had not been given such high expectations to strive for, I would have fallen short of my capability. In order to execute this in your classroom, here are some common rules to keep in your mind:

  1. Avoid labeling your students, even if it is just categorizing them in your head.
  2. Learn about their career path goal and discuss it as though they will make it happen. Avoid using “if” statements.
  3. Hold them to expectations and discuss with them what happened if they fall short and how they might fix it next time.

Along with these three things to keep in mind, I think the most important thing for a teacher to do is truly believe that ALL students are capable of learning and succeeding with your highest expectations for them.

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Increasing Student Participation

Student discussion and input can greatly impact learning in a positive way. The issue is that there are always students who are more vocal and have higher status. A few student will throw their hand up every time a question is asked to the class. Meanwhile, there are students who are constantly concerned that their question or answer is wrong. A major question we have to answer is: How do we get all our students to provide their input?

The article I read, “Increasing Student Participation” from The Teaching Center, which is part of the University of Washington in St. Louis. The article gave several ideas, but the ones I found noteworthy, along with some of my own ideas, are the following:

  • Set up ideal physical setup for discussion
  • Set expectations
  • Establish environment of caring and respect
  • Have class schedule set up for time for discussion
  • Respond positively to student ideas

Set Up Ideal Physical Set-Up

According to the article, there are many things that a teacher can do for the class to prepare them to participate in discussions. One thing is just the way the classroom is set up. The article suggests creating a U shape with the desks, which helps, since the students are facing each other and not just the teacher.

Set Expectations

Also, set expectations for how much each student should participate. If the intent is to have every student contribute, let them know that every one of them has to contribute. One option is to have participation be part of the grade, but if we do our job as educators, getting students to contribute to a discussion should not have to be something that we have to force them to do, but eventually something that they will do on their own with our support.

Establish Environment of Caring and Respect

One idea that the article did not address but I’d like to is establishing an environment of respect and caring. If we as teachers make it clear that every student’s input is valued, no matter their status in the class, then students will respect what other students are saying and not degrade them for it. As a result, students will not be afraid to speak their minds as much as they would otherwise.

Have Class Schedule Set Up for Time for Discussion

One way to promote discussion in a classroom is by allowing plenty of time for it in the proper way. If a teacher only asks for questions and students’ thoughts at the end of a lecture, they may not remember what they thought throughout the lecture. On the other hand, if a teacher stops after every fifteen minutes of a lesson and asks a question to the students and asks for their questions and comments, the students may better remember what they just learned. Also, asking a question and taking responses immediately is not always the most effective way for students to formulate ideas and give a response. Giving students 10-15 seconds to think allows everyone to come up with an idea before anyone else responds. Mixing up discussion methods can make it so every student can give a response. Moving from partner groups to small groups to large groups to a whole class discussion can make it so every student feels comfortable sharing at some level.

Respond Positively to Student Ideas

For students that lack confidence, pointing out their good ideas is very important. Even if their answer is not totally correct, pointing out what is correct or paraphrasing so it is correct can give them a confidence boost and think of their response as valuable. As stated in the last section, having students submit responses online or in some other private way and responding positively to that will give them the confidence to participate more in partner groups, where positive feedback will give them the confidence to participate in small groups, and so on.

The article “Increasing Student Participation” gave some intriguing ideas for how to get more students involved in discussions. I think that this is a very important subject to bring up, because all through my education, there were always people who would contribute every day and people that wouldn’t contribute at all. Sharing ideas can be a great learning experience for everyone. Hopefully we can use these ideas to have all our students contribute in meaningful ways.

http://teachingcenter.wustl.edu/resources/teaching-methods/participation/increasing-student-participation/

Equity in Education: The Relationship Between Race, Class, and Gender in Mathematics for Diverse Learners

Equity in Education

Reading about a particular case study for class caught my interest. It was the case study in which a particular school was placing the majority of non-white students in below grade level courses, while just over one-tenth of white students were placed in these same classes. I was curious to learn what could possibly make such a disparity occur. I found the article “Equity in Education: The Relationship Between Race, Class, and Gender in Mathematics for Diverse Learners,” which was written Debra Rohn from the University of North Carolina at Charlotte for The Urban Education Collaborative. The article addresses how race, class, and gender affect learning outcomes and gives some theories on how to fix it.

The first topic discussed is “race and mathematics.” There is huge differences in average test scores between African Americans and Whites and Hispanic Americans and Whites, to put it plainly. This could be the result of direct discrimination, such as placing students of other cultures in classes below grade level just because the teachers do not expect them to do well based on their race. The article seems to suggest, though, that the more likely scenario is the expectations put on minorities by society as a whole. They are likely not expected to do well, and they realize this. The article suggests that many of them probably give up on their math abilities, since mathematics is widely viewed as a “White subject” in America. The article makes the claim that even when African Americans succeed in mathematics, some would describe themselves as “acting White.” Now, at first, this may seem to be more about equality than equity, but the solution that I gathered from the article is to give extra psychological help, of sorts, to children that are minorities. In an equitable classroom environment, students would be taught that a student’s race does not take them out of the running for a career in mathematics. One major issue is that the students are believing that they cannot pursue success in mathematics simply because of their race, and in an equitable classroom, they would be taught to think otherwise.

The second topic of discussion is “class and mathematics.” This has less to do with the idea that someone is behind someone else and more to do with the idea that students from lower socioeconomic status are set behind. When a child is raised by a single mother who may not have even graduated from high school, that mother is probably going to work long hours, which leads to her not being able to be with her children as much as parents from higher socioeconomic status. This leads to less development for the children of the lower socioeconomic status family, since they had less chance to communicate and do learning activities such as reading. This does put them behind from the beginning. A solution to this is for teachers to quickly realize this, and, rather than put them on a lower track for the whole education career, give them added supports and multiple modalities to work with.

The third topic was “gender and mathematics,” which focused on how many people think that men are naturally better at mathematics. There have been studies that show that this is not the case. As with race, the differences in test scores most likely comes from them thinking that they are less able to do mathematics, so they give up on being as successful as they could be. Also similarly to race, the solution is to eliminate these ideas in our classrooms, so that everyone gets a clean slate and can pursue whatever career choice they would like.

My view of this is that the solutions to all of these are to either reinforce positive thinking so that everyone believes that they can learn mathematics or help those that are behind so they can catch up to everyone else. Of course, one shouldn’t assume that a person that is African American or a woman isn’t at a disadvantage, because they could be someone who has a difficult past. Even if a classroom was all white males, we as teachers should know what past they come from, so we can potentially help them come out of it with hope of a better future. I can use this information to help my students overcome racism and sexism to pursue their dreams. I can use this information to help students who come from difficult beginnings get to a place where they can learn more information easily. The point is, teachers should learn as much about their students as possible, and cater to that. That is the point of equity. That is how it can be used with race, class, and gender.

Promoting Equity in Mathematics

From the little bit that we talked about equity in class, I realized that I did not know exactly what this word meant or how it applied in schools. I thought that equity was creating same lessons and teachings and giving all students the same opportunity; however, after reading Carly’s blog, I understood that it is way more than that, so I set out to find an article to better inform me about what equity was and how to promote it in our classrooms. The article I found was

Promoting Equity in Mathematics: One Teacher’s Journey

Alan Tennison
        The first thing in this article that stood out to me was the definition of educational equity as “the concept that all students, regardless of their personal characteristics, backgrounds, or physical challenges, must have opportunities to learn mathematics. Equity does not mean that every student should receive identical instruction” (page 28).  It was nice to see a definition laid out for me so that I could actually learn what equity is.
        One huge problem that schools have today is that they place students into classrooms based on how the teachers perceive their abilities. This is hard because there is no right or wrong way to do it and students get placed into the wrong groups because they are not test takers or they are very quiet or other outside factors that do not deal with their intelligence level. Then these students are in these “low-track classrooms” where the curriculum is easier, the teachers are less experienced and the other students in the classroom are less-engaged. This creates a great divide among students in the low-track and the high-track and the low-track students have little to no hope of ever catching up with the high-track students.
        The overwhelming issue that this article talked about was that once students are tracked into lower achieving classes, the expectations go way down and the material seems useless to the students. Personally, it makes sense. If I was a student that the school deemed “low-achieving” and I was put into a math class where I had to re-learn the material that I did not master well enough the prior years, it would be a lot easier to give up and not try as hard.
        The author then discusses how he tried to change this by ending tracking in his school and making it so that all students had the same expectations. The result of this was that the students attitudes changed and they cared more about mathematics. He began to use problem-based learning that incorporated many different math concepts and students could now make connections as to when they would ever use the topics in real life. The percent of students enrolled in a math course their fourth year increased from 10% to 60% and the average math ACT increased from 16.9 to 19.9. As we are all math people, we know that numbers do not lie.
        In my opinion, I think it is important to create classrooms with students all along the spectrum in terms of “perceived mathematics ability” as every student has something to learn form one another. Pairing a student who completely gets a topic with a student that is lost helps them both. The confident student explains the topic to the other and this helps him/her understand their thinking and helps him/her remember how to do the problem. The student that does not understand gets the information explained from someone who has also just learned the material, so they are able to better explain the material student to student.

Making a Math Classroom Equitable

This week in class the concept of mathematical classroom equity was introduced, which is a concept that immediately elicited my attention. I have often contemplated the idea of equity, but in the concept of equity vs. equality. It was a topic introduced to me a while ago when I found this image:

Image result for equity vs equality

At the time I was considering the argument of equity vs. equality in a political sense, because in our current political climate many groups campaign for equality when they really wan equity. I had not thought about it in an educational sense.

So, when the topic came up in class that we would be looking at Case Studies and deciding whether they were equitable or not, I was immediately interested. My main item of discussion and knowledge for equity in the classroom comes from our assigned reading of chapter two Equitable Mathematics Teaching from Strength in Numbers Collaborative Learning in Secondary Mathematics by Ilana Seidel Horn. URL: https://drive.google.com/file/d/0B1zVoWMFl08-TGN2NWxQMXVPVGc/view

I found the chapter intriguing to read and took out many good points and concepts from it.  The first thing is how the book defines equity in math as “equitable mathematics teaching involves using models of instruction that optimally support meaningful mathematical learning for all students.” Meaning that teachers should be using a variety of methods and techniques in order to reach students of various learning styles.

The second thing I found most helpful was the three practices they listed for collaborative learning environments that influenced equitable math teaching.

  1. What counts as math involves how mathematics is presented to students and the messages about what success means.
  2. Pedagogical practices focus on the work of teaching.
  3. Relational practices address the relationships that students build with others in the school and classroom.

Finally, the four principles for equitable math teaching where:

  1. Learning is not the same as achievement.
  2. Achievement gaps often reflect gaps in opportunities to learn.
  3. All students can be pushed to learn mathematics more deeply.
  4. Students need to see themselves in mathematics.

There are many things here that I would love to implement into my own classroom. Like, using group based work in order to help build the classroom as a community of learners so that way they feel part of a collaborative effort. They could take on a role in their team that meets their strong suit. Also, having across classes activities. That is to say, the algebra students work on the calculations to some 3-dimensional shapes the geometry students are making. That way they feel more connected as a school.

Having students see themselves as mathematicians is also so important. I am a firm believer that everyone can do math, because it is a universal language that can be taught in many different ways. If one way is not working for a student, then it should be I as a teacher to make my classroom equitable so that that student can find a way that helps them learn math. Every student deserves a fair opportunity to learn such that they can be at the same level as all of their peers. Constantly berating students with quizzes, homework, and tests when they are doing poorly does not mean they are going to learn math. Students learn math in many different ways, but they can all learn math.

After learning more about equability in education I like to see equity more like this:

Image result for equity vs equality

After learning all this information about how I can make my classroom equitable, I wanted to be able to see it in action. What are the different ways equity can be incorporated? So, I went to the National Council of Teachers of Mathematics and found this video that showed me a lesson of how a teacher used equity in her math classroom. URL: http://www.nctm.org/Conferences-and-Professional-Development/Principles-to-Actions-Toolkit/Equitable-Pedagogy/

In the video the students are learning about finding the area of a square, and they all have to go to the board to present how they found their area. They are all in partners by the looks of it, and the partner groups have varying degrees of difficulty in their square. What I mean by this is some students have a regular square that has a flat side on the bottom, but other students have their square skewed so a corner is touching the bottom. Like this:

The students who may struggle more would be given the square on the left so they could count the grids from top to bottom and left to right then multiply to find the area. While the students who understand it more get the square on the left where they have to combine the areas of a square and triangle to find the total area. This way both groups of students are given materials at their level of understanding.

Finally, in the video you can see a great example of peer collaboration. When two students with the harder square are at the board presenting, one student asks them how they got the area of their triangle. This forces the two students presenting to explain their rational, allowing the teacher to check their thinking, and the student who asked the question gets to learn something new.

One adjustment I would make to an equitable classroom would be to find a better way to mix students at the upper end and lower end of the class to see how further growth and understanding could be resulted from that. Right now, to me, it seems like equity is giving the “smarter” kids material for deeper understanding and other students material to try to reach the “smarter” kids. Equity has been an interest of mine for a while now, and I am excited to learn more about how to implement it into my future classroom.

Tracking In The Mathematics Classroom

The article that I read was “Promoting Equity in Mathematics: One Teacher’s Journey” by Alan D. Tennison, published by NCTM (link: http://www.nctm.org/Publications/mathematics-teacher/2007/Vol101/Issue1/Promoting-Equity-in-Mathematics_-One-Teacher_s-Journey/). After searching for articles involving equity in the mathematics classroom, I stumbled upon this article when I began to look through the NCTM website. Throughout the article, Tennison describes his personal experience with equity in the mathematics classroom as a teacher. The specific topic of discussion in this article is tracking, or grouping students based on their abilities in different mathematics classrooms. He discusses that although tracking may be helpful to students who are high-achieving, it has proven to be detrimental to poor and minority students in the past. At the end of the article, Tennison describes his own experience with creating a heterogeneous classroom where there is a standards-based curriculum and students with differing mathematical abilities are put in the same classroom. The curriculum was split up into units where there would be a central problem relating to other areas of study that the students would investigate throughout the unit. Within Tennison’s school, he found that students who participated in this track were more likely to enroll in four-year mathematics courses in high school, and had a higher average ACT score by 3 points. The article overall begged the question about the value of tracking in high school, causing me to reflect on what I consider its value to be in the classroom, as I had always considered tracking a positive part of schools because it challenges the students that need more challenge, and gives the students who may need more support in their classes the support they need to be successful. However, there are more questionable aspects of tracking than meet the general onlookers eye.

Tracking is a controversial topic in education as often times the students who are in the “lower” track are often overlooked, and as Tennison writes in his article, they are trained to memorize formulas rather than problem solve. The problem there lies within the instruction itself, which is at the core of equity in schools. Teachers ask that students in “lower” tracks memorize formulas because do not believe that the students are capable of learning the material to the same standard that students in the “higher” track are. Tracking inherently predisposes teachers to have prejudices about students in the different tracks. While in general tracking may seem like it has benefits, the way in which it is too often carried out negates these benefits.

The information that Tennison provided can be used in the future when designing my own curriculum, especially if I am given the opportunity to teach students who consistently struggle in mathematics. A portion of the problem that he mentioned in the article is that students in tracks that are not advanced focus on drilling different formulas for memorization, not problem solving. Problem solving, critical thinking, and other skills that can be developed in the mathematics classroom are focused on in the higher-level tracks. Therefore, if working in a school where tracking is part of the curriculum, the students in “low” tracks may especially benefit from a curriculum that focuses on problem solving, and critical thinking. Thus, the modification I would then make is to implement the standards-based curriculum heavily into tracks where students more noticeably struggle in mathematics to promote equity in mathematics. Tracking in itself does not allow for full equity in the classroom because it separates students based on ability, but there are ways that teachers can work toward creating the most equity they can if working in a school where tracking is present. Tennison’s proposal for creating a heterogeneous classroom prompted me to:

  1. Ponder the value of tracking in the classroom
  2. What teachers can do to help students who have been placed in a lower track if a school does implement tracking
  3. What the underlying benefits are of having a heterogeneous classroom

Therefore, I found a chapter of a book that discusses tracking in schools, and its implications. This chapter addresses the concerns listed above about tracking, and discusses its strengths and weaknesses. The link to the chapter: https://www.google.com/urlsa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0ahUKEwjbJbT49DYAhVL2oMKHb3SBqcQFghJMAQ&url=https%3A%2F%2Fwww.nctm.org%2FHandlers%2FAttachmentHandler.ashx%3FattachmentID%3DxjfHMap4gFw%253D&usg=AOvVaw03miqiCNC8UgoGsqh6nfsj.