Is high school math impossible for ...

Discussion in 'Secondary Education' started by GTB4GT, Feb 2, 2016.

  1. GTB4GT

    GTB4GT Cohort

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    some people? I am reaching out to my more learned colleagues. Assuming an individual has not been diagnosed with any type of learning disorder or disability, is there any research that would indicate that algebraic based math is, in fact, beyond the capability of some people? again, I am looking for more research based answers although I am interested in the opinions of other math teachers as well. thanks for any replies.
     
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  3. MathGuy82

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    That's a good question! I've taught math for the past 10 years and yes I think there are a few that will not set their mind to learn it. Maybe it's not that they can't they just have no motivation and it makes us teachers think they can't. I do think there is a very small percentage "that can't". Some would get mad at me for saying that but yes. I've heard several stories of people close to my age that said they either cheated or the teacher just passed them in high school so they could get by.
     
  4. GTB4GT

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    thank you for the response. I was/am puzzled by the lack of responses as I was of the opinion that most any topic in education has been well researched.

    with that being said, many years ago (in a different field and perhaps in a galaxy far, far away:)) I was taught that performance issues ALWAYS boiled down to two things...the person in question either A) CAN'T do the things required of him/her or B) the person WON'T do the things required of him/her. In case A, additional training was provided until such time that it was determined that the scope of the job was beyond the person's capabilities. In case B, the person would be removed from the job without further ado.

    So in the field of education...how does one ascertain whether a "low performer" either CAN'T or WON'T be able to do the required work? and how should each case be handled? TIA for any replies.
     
  5. a2z

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    I do think there is math that gets past certain people's intellectual capability, but I do not believe basic algebra is past the average person's ability if they do not have a disability.

    I do think there are many people who can't do math because they have not had the proper education in math for a myriad of reasons from too rapid a pace for them, lack of attention, poor teaching, poor curriculum, etc. So, they may not have the skill set to do basic algebra in high school. That is different than can never learn to do so or beyond their potential which is what I am thinking you were asking.

    Upper level math is a whole different story. Now if you look at some data gathered about the average IQ for different types of careers, you will see that some careers are beyond that of many people's ability. A physicist, chemical engineer, or philosopher has a much higher average IQ than most. But basic algebra 1. No, I believe that barring intellectual disabilities or learning disabilities everyone at one point had the capability of learning it. The question is, has so much damage been done that they will ever try to attempt to learn it later in life without all of the baggage? I think many of the can'ts have a reason that they, at this time, can't. Not that they were never capable. Does that make sense?
     
  6. GTB4GT

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    An extremely lucid post and yes, it does makes perfect sense. It then begs the next question. If I may paraphrase your post, most enter the world with the potential to do high school algebra.But for a myraid of reasons, some do not realize this potential. How should we as professional (math) educators handle this situation? To continue to push them into higher levels of math seems absurd but I am unclear as to a possible solution outside of reducing the math requirements for graduation (similar to the requirements of my generation. It was possible to graduate with only 1-2 years of math but 4 year options were available for students with mathematical inclination).
     
  7. mathmagic

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    Teach them the next steps based on their current success, while building as strong of a growth mindset within them as possible, given the circumstances. Anything else is just going to lower their mathematical self-esteem, and lessen the chance of future success. I'd rather have someone stronger with basics with a willingness to learn and grow.
     
  8. Caesar753

    Caesar753 Multitudinous

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    I was on the fast-track in Math and took Geometry Honors in junior high school. My brain was not ready for it at that time. I was a smart kid and I had a good teacher, but I just couldn't wrap my head around the concepts. I ended up with a C in the class, which for me was really more like an F because I was a kid who got good grades. I retook the class in the summer of my junior year to try to fix that C on my transcript, and it was like a completely different experience for me. I magically understood everything. I ended up with like 110% and a solid understanding of geometric concepts. For me the difference of a few years made all the difference in the world when it came to learning and understanding the material. I suspect that many of our students would have similar experiences. Not everyone is cognitively or developmentally ready for certain material at the same time.
     
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  9. GTB4GT

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    Interesting idea and post. Do you think the education system should pursue placing students in courses based on their abilities at the time (rather than moving them on an annual schedule). Would that process be manageable? How would we ascertain where a student should fit?
     
  10. Caesar753

    Caesar753 Multitudinous

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    I have long believed that students should be grouped by ability rather than by age. I don't know the logistics of how that would work or if it would even be doable, but it seems to me that it would be a much more reasonable setup than what we have now.

    In one grade you can have some of the teeniest, tiniest, most immature (not necessarily behaviorally immature, but as far as their interests and skills) kids you've ever seen sitting in class next to these huge, hulking, facial-hair-covered, deep-voiced kids. It's very odd. If they can develop at such different paces physically, it doesn't seem unreasonable to me that they might similarly develop at difference paces cognitively, emotionally, and academically.
     
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  11. GTB4GT

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    Thank you. I share the same opinion as you about grouping by ability vs. age. Do you (or others) have any thoughts as to why we don't do this? Other than the "we have always done it this way" mindset?
     
  12. Puppet Debris

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    Well, personally I don't think students should be forced to take algebra. My dad was a farmer, just like most all the neighbors. Within a 3 mile radius, not a single one of the 20 or 30 dairy farms were left by 1990. I became a teacher. I went back home and explained some basic algebra to my dad. He said he understood it, but added, I have never needed to use anything like that.
    Sure the world is a lot different now days. But I still think it would be ashamed to take students meant for hands-on vocational courses and force them to take algebra. Such students would probably be under control of others forever after.
     
  13. GTB4GT

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    I disagree a bit. I think all students should be exposed to algebra 1. It is a "gateway drug" (if you will) to higher math.
    Then, if the person has no competency in this area, then guide them in a more suitable direction. With that being said, my school district (and I suppose many of the others nearby) really does not have the capability to offer effective vocational courses. What to do then?

    I do agree with the idea of making a person incapable of doing algebra take more (and higher level) math courses as being patently absurd.
     
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  14. Ms.Holyoke

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    I understand what you are saying, but I disagree.

    I think the issue that we have is that much of math curriculum in schools today is practice in repeating procedures that have been demonstrated to students. I agree that the skills that arise from this are primarily computational, and would not serve many students who are not going into math/engineering/science very well at all.

    However, in mathematics classrooms, I think that students should have the opportunity to solve problems, justify their solutions, think logically, communicate their ideas, and listen to others. These skills will allow students to "do" math--to think for themselves, think through a problem, and decide what is important and how to proceed. These skills are important for students who do not pursue math in the future as well. In addition, in high school, students are very young and they may not know exactly what they want to do in the future. They may choose not to take Algebra, and when they get to college, they will realized that they can no longer major in engineering, math, or computer science because they do not have the pre-reqs. Catching up would be incredibly difficult.

    In addition, barring any intellectual disabilities, I do believe that all students can learn algebra. However, algebra is tricky, and not all students will learn from a traditional teaching style. They may need context, technology, manipulatives, or more. But yes, I think all students can and should learn algebra.
     
  15. Ms.Holyoke

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  16. Ms.Holyoke

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    I'm not sure if I completely understand this. I agree that students develop differently, but we already have tracking in high schools. In tracking, you see that white and Asian students are often placed in the higher tracks, but black and Latino students are often placed in the lower tracks. I think that grouping by ability would just lead to more racial segregation, even if it is unintended.
     
  17. GTB4GT

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    I disagree.What does math ability have to do with race??!!! The suggestion was to group by ability...not by any other factor.
     
  18. Ms.Holyoke

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  19. GTB4GT

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    Thank you for the link. It was pretty well balanced (especially for a NY Times article;)). FWIW, my experience in the classroom more aligns with the observations of Professor Haller (cited in the article) rather than the critics.
     
  20. Caesar753

    Caesar753 Multitudinous

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    The issue of students of color being underrepresented in higher-track courses is a much bigger, systemic issue. I don't think, however, that it means that we should continue grouping students by age level when that clearly isn't working.
     
  21. Ms.Holyoke

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    Can you explain why you think it isn't working and what the benefits of grouping by ability would be?

    My first concern would be the following: What criteria will teachers use to group students? It seems like "ability" will be viewed one-dimensionally with this system. Yes, students of color are often unfairly tracked into lower-level courses which can cause them to fall behind their peers. Therefore, it seems to me that students of color will similarly be tracked into low-ability tracks. In addition, this could lead to some students graduating later than others of the same age. This could cause issues with drop-outs and more issues.
     
  22. Caesar753

    Caesar753 Multitudinous

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    When we group by age rather than ability, we are forcing students with wildly different skills to participate in a lesson that is likely built for students in the middle. The teacher scrambles to differentiate, and sometimes he or she needs to teach three or four or ten different versions of the same lesson in order to reach all the students in the room.

    When we group by ability, we can deliver instruction that is more tailored to our students' skills. We do this with sports all the time--the freshmen football team, the JV team, the varsity team. If you're new to the game like the freshmen are, you focus on conditioning, rules of the game, basic skills. If you're seasoned and skilled like the varsity players, you focus on the nuances of game play, improving your existing skills, and even more conditioning. Coaches coach those three levels differently, certainly with a bit of overlap, because the kids are at different levels and need to develop different skills. Why shouldn't this be true in Math?

    We do some ability grouping in Math already. If you're advanced, you might take AP Stats. If you're struggling, you might take Principles of Math. The problem that I see is that when we focus more on the age/grade level of the student than on their skill at math, we promote students ineffectively and, ultimately, to their detriment. If you can't pass Algebra 1, you shouldn't be in Algebra 2. We can get into all the politics of why students can't or don't pass Algebra 1, but the fact remains that they need to be able to demonstrate proficiency in Algebra 1 concepts before they move on to Algebra 2. If we promote them because they kind of got it and/or because they're going to be in the 10th grade and/or because they're a member of a minority group, then we are most definitely setting them up to be less than successful--because how can they be successful in the next level course if they haven't been successful in the previous level?

    Foreign language instruction is moving towards a proficiency-promotion model. Once you can demonstrate proficiency at the novice high level, you move onto the intermediate low level. Ultimately, the plan is to move away from course titles like Spanish 1, Spanish 2, Spanish 3 towards Spanish Novice, Spanish Intermediate, Spanish Advanced. There is a very specific set of criteria for each level, so it is very apparent where a student is currently at and where he or she should move. "I can present basic information on familiar topics using language I have practiced using phrases and simple sentences." "I can recognize a few memorized words and phrases when I hear them spoken." I would like to see a similar movement in Math.
     
  23. GTB4GT

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  24. Ms.Holyoke

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    I don't have much teaching experience yet, so I definitely value what you have to say since you are much more experienced~ I'm still struggling to understand how ability grouping would benefit our students.

    I completely agree that a student who has not mastered Algebra 1 would not be successful in Algebra 2. But in my experience, when a student fails a class, they either repeat the class or they take a lower level class. Is this what you mean by ability grouping?

    In addition, you stated that we should not promote students because they are a minority. I never stated that we should place our black and latino students in higher level classes because of their skin color. I stated that research suggests that they are unfairly tracked into lower level courses even if they are able to succeed in higher level courses.

    My other question is, what abilities will teachers group based on? Is it a test? And how early does it start? Is a student who is placed in the lower-ability group at age 9 likely to stay in that group until graduation?

    In addition, will students in lower ability groups require more time to graduate? If so, how will this affect the drop-out rate, especially for low-income students?
     
  25. a2z

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    I read the article you posted. They sort of said this. They said that they found black and latino students tended to be placed in lower tracks which suggests that it might be a reason to stop white flight. However, they also said they couldn't prove the cause and effect. They just noticed a trend that could suggest it was purposeful.

    I also found the part about schools with more black teachers tended to have few black student in special education. There may be that correlation, but there was not proof at to why. It was suggested that having more black students in special education was a conscious decision to remove them from the regular population. That could be true or it could be that back teachers didn't like the program so they didn't suggest evaluation. One thing it did not say was at schools with black teachers and few black students in special education that the students were, in fact, performing at higher levels academically. Since we know entry into special education over the decades (and even now) is fraught with inequity and differences in implementation and recommendation.

    So, from what I have read over the years in these studies is that they point out what they see, but really can't prove what the underlying reason for the difference.
     
  26. Ms.Holyoke

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    I am currently taking a class called Critical Race Theory in Education so I'm sure I can report back with more extensive research and evidence for what I am saying. I did read an article about a teacher who said that she believed that a few of her black students could succeed in the higher level math class, but the principal did not follow through with her.

    I personally do not believe that the number of black and Latino students placed in lower tracks is something we should accept as educators. I think there is something wrong with the system if this continues to occur.
     
  27. Caesar753

    Caesar753 Multitudinous

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    In my experience, students are promoted no matter what, even if they fail or lack the skills necessary to be successful in the next level. Either grades are inflated (intentionally, usually the result of threats from admin, or unintentionally, through improper grading practices) or students are simply pushed along to the next level. Take a look at failing schools' test scores: what you'll see to be a general truth is that students are "passing" their Math classes at rates of 60%, 70%, 80% or higher, but they are failing the standardized tests at rates of 2%, 5%, 15% (with those percentages being the pass rates). Even accounting for issues with inequities involving standardized test questions and whatnot, the disparity there is absolutely undeniable and clearly points to problems of some variety.

    I can't speak to the hows and whys students were tracked before they get to me. What I focus on is what I can do for them and how I can move them forward from where they are now. That's every teacher's burden.

    As I referenced earlier with changes to foreign language instruction, I think that ability groupings should be based on demonstrated proficiency levels. Can the student identify a matrix? Can the student add two matrices? Can the student multiply exponents? Once the student demonstrates mastery in a given area, he or she should move on to the next thing. He could fly through certain standards, spend a little more time on others, and ultimately get where he needs to go. Pick three or four of the major topics in Algebra 2, find out who knows those topics well, and put all those kids together in one class. I see no reason that a student should be "stuck" in a low track unless he consistently fails to demonstrate mastery, in which case the low track is where he should be, regardless of his race or ethnicity or SES or any other factor.

    Again, I don't have all the kinks worked out. I even stated before that I don't know how the logistics would work with ability groupings. I would think that a student shouldn't be hindered as far as graduation because he still needs to meet the same requirements as every other student. Instead of pretending or guessing or assuming or hoping that he knows Algebra 2, however, we will have definitive proof that he knows Algebra 2, because he demonstrated proficiency before he moved onto the next level.
     
    Last edited: Feb 10, 2016
  28. Ms.Holyoke

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    I understand what you are saying, but I think we're going to have to agree to disagree. What you are saying sounds ideal: the idea that we would group students without any relation to race or SES. I do not believe this occurs in schools today, and ability grouping irrespective of age would make these inequities even larger. In addition, once students are placed on a track, it is often very difficult to leave a track. The idea that students would be able to leave a track sounds great, but I don't think it happens much in practice.
     
  29. a2z

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    It depends on what the track looks like and how the classroom is run. I agree that it gets to a point where the gap is so large that jumping tracks is near impossible. I see that in my district and it is irrelevant of race. So, the question becomes, how is the structure of the track created and how does each track push those who can move forward and keep plugging with those that continue to struggle. I don't think in many classrooms across the country we handle this well. Most kids that make a leap do so because of some outside intervention in addition to what they are doing in class or some major breakthrough in emotional thinking or reasoning skills.

    I think it is important in all classrooms to design work and assessments that will show those who are going beyond in addition to the norm. Making an assessment like this can be difficult with the grading system we have. I've seen tests like this in HS classes and in college where there may be one or two scores above 90% with the cluster down at 60%, but it wasn't because the 60% was a poor assessment of skills but that the assessment had a baseline at 60% giving room to see the few that were stellar. These tests were usually curved and those who scored high tended to be better able to apply the concepts to novel materials. But we are stuck in this mindset that a 60% is failing regardless of how the test was developed.
     
  30. Caesar753

    Caesar753 Multitudinous

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    The question as it was posed to me in this thread involved the word "should", which is certainly both hypothetical and ideal. In a hypothetical and ideal world, I think that ability groupings would be better than age-level groupings. You're inserting the current status quo into a hypothetical and ideal situation. Before any such ability grouping model were put into play, the issues you raise would obviously need to be thoroughly researched and ameliorated.

    Since ability groupings aren't your cup of tea, are you prepared to say firmly that you believe that age-level groupings are what's best for students? If so, why? Is it based only on racial issues? Should a student's racial identity be the key factor when designing and delivering instruction? If not, what should be the key factor?
     
  31. GTB4GT

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    I will say this. You admit you don't have "much teaching practice yet" and are taking a class called "Critical Race Theory" (which implies you are a student) and yet you are disagreeing with what actual teachers in actual classrooms with actual students are seeing with their own two eyes. Look we respect your opinions and your desire to engage in debate, but there are millions of theories and many of them contradict each other (read the Times article you linked closely). Sometimes wisdom comes from experience and not textbooks.
    From what I have seen, students are more comfortable with grouping. I see more effort and engagement when they feel comfortable with their peers. They have enough self awareness as teens to know their abilities relative to their peers. Ask any high school student why they didn't ask a question in class about something they didn't understand. The universal response? "I didn't want the other kids to think I was stupid." Their image to their peers is more important to them than understanding material. In y experience, kids progress more when ability grouped. The material has to be perceived to be within their reach before any effort occurs.You can show me theories until you are blue in the face but I am simply reporting what I have seen.

    To borrow from Caesar's analogy, an athlete on the freshman team does not want to compete with the varsity kids if he/she is not ready for it. AND they know that. It's true for academics as well. The kids are more self aware than you might imagine. And it's not about race either.
     
  32. Ms.Holyoke

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    That's a good question. I suppose it depends on what the ideal world would look like.

    In this ideal world...
    Would all students have equal access to tutoring/extra support/test prep outside of school?
    Would all students enter kindergarten with access to pre-school or kindergarten readiness programs?
    Would the lower ability class not be considered the "dumb" class?
    Would students in the lower ability class see themselves as intelligent?
    Would students be easily able to move into and out of different tracks? (So placing into a low track in 7th grade wouldn't limit their future opportunities)
    Would there be absolutely no racial/ethnic/gender bias for placing students in tracks?
    Would there be a holistic way to view ability to place students in tracks? Will students have multiple ways and opportunities to show ability/competence?

    If the answers to these questions were yes, then I think I might consider ability based grouping over age-level grouping in schools. I completely see the point you are making. I feel like differentiating instruction is very challenging and can't always be done effectively due to time/other constraints. When you asked if a student's racial identity should be a key factor in deciding how to run schools, I would say that our schools currently do not provide equal opportunity to all students and that changes that we make to our school system should take these into consideration.
     
    Last edited: Feb 10, 2016
  33. Ms.Holyoke

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    Thank you for sharing your experience.

    I said that I do not have much teaching experience because it is true. I have observed in classrooms and taught in summer programs, but you're right that I won't know what it is like until I have my own classroom. I shared this because I acknowledge that you and others have much more experience than me and valuable insight to share. However, I have studied to become a teacher for 4 years now and I am student teaching next year. I am very passionate about teaching and education, so I thought that this could be a place where I could learn, share my ideas and experience, and engage in productive discussions. The ideas that I discussed in this thread mainly came from a college professor with years of experience teaching high school English. But if my ideas are not valued because of my lack of experience, then that's fine as well.
     
  34. renard

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    I don't think anyone is implying that your ideas are not valued, but they are so idealistic and adversarial to an alternative viewpoint that it's clear you are still a student (with respect). Both age grouping and ability grouping is problematic, for a variety of reasons (as no method is perfect). There are many positive aspects to ability grouping, which exists in my school system. I'm not saying it is better or worse, but I have seen a grade 9-12 low ability group function well. It was a math class, with at-risk gang members, a cognitively-delayed 16 yo, a low-academic with no behaviors 9th grader, etc. It wasn't perfect, but at least they weren't wasting their time with their age peers. They actually got to participate , rather than stare out the window and wonder what the hell a quadratic was.
     
  35. Caesar753

    Caesar753 Multitudinous

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    I value your opinions. They seem to be well-considered, and I appreciate that. I think that your lack of experience is showing, though. That's not a bad thing; it's just a thing. I wonder if you will hold the same views in 5 years or 20. Have you ever heard the saying "A little learning is a dangerous thing"? I think it applies here. :)

    Just about any teacher who has taught in an inner-city/at-risk setting with a diverse student population will tell you that there is an obvious and fairly universal correlation between student achievement, socioeconomic status, and behavior. If we really want to make changes when it comes to tracking students and ensuring that all students, including students of color, are fairly represented in advanced courses, we need to start at the beginning of students' educational careers, and maybe even before then. We need to address poverty, access to educational materials in the home, access to educational activities outside the home with family members (visiting the library, shopping, going to the zoo), access to healthcare, access to proper nutrition, and good parenting. Students whose parents lack parenting skills, who live in poverty, who don't get to see the world, who don't have and read books in their homes, and who don't eat enough healthy foods are entering school at a disadvantage. If you're worried that students can't ever "jump the tracks", let's stop looking at the jump from 7th grade Math to 9th grade Math and instead focus on the jump from Kindergarten to graduation. If a kid is behind the 8-ball in Kindergarten and doesn't develop the skills he needs to be successful later, he's likely going to flail through all the rest of his education. That's partly why we administer Kindergarten Readiness tests to incoming Kindergarten students (at least of a certain age)--we know that they need to possess certain skills and abilities in order to be successful at this level. Why we abandon that idea in later grades, I'll never know.
     
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  36. GTB4GT

    GTB4GT Cohort

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    Caesar, I have been reading on this site for +/- 5 years. I want to say that your posts in this thread are the most well-thought out and articulate that I believe that I have ever read on this site. thank you for your contribution and participation.The one above gets straight to the heart of the matter...it's not about the boy or girl and the school or the color of the skin, it's about what happens (or doesn't happen) at home in most instances. The fact that many of our kids are lacking in this most basic need is truly heart breaking if one has any sense of compassion for these young people (which i believe is a trait we all share).
     
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  37. Ms.Holyoke

    Ms.Holyoke Connoisseur

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    I do agree with this. I was assuming that whatever program we implement would start at the early grades. If a student got to 9th grade and could not perform basic algebra, then I do think it would be best for her to be placed a in class that catered to her needs. But looking at the big picture, it seems like a system like this is failing our students. I would like to see what I believe in 5 years though. :)
     
    Last edited: Feb 10, 2016
  38. Ms.Holyoke

    Ms.Holyoke Connoisseur

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    Firstly, I don't think Caesar ever stated that it was not about the color of their skin or race. You'll probably tell me that I have no experience or don't know what I'm talking about if I state otherwise, but I will say that the inequities in our schools today are very much about race and racism. I have noticed a lack of awareness about racism on this forum (which is upsetting considering that this is a forum of teachers) so I don't expect to change anyone's mind.
     
  39. Caesar753

    Caesar753 Multitudinous

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    Feb 10, 2016

    Students are currently in 9th grade without being able to perform basic algebra, or read a moderately complex paragraph, or write a sentence, or think critically about any number of topics. It happens daily at every at-risk/inner-city school. We are already there. The system that we're using, based on age-level groupings and social promotion, isn't working.

    Every kid brings something to school that can serve as an advantage. The problem for them is that they aren't being set up and taught to use those to their advantage. This is partly because there are 20 or 30 or 50 other students in the class, each of whom has diverse needs and gifts and areas for improvement, some of whom have behavior issues and/or more severe academic needs, and the teacher is scrambling to reach everyone. If the teacher could work with a group of similarly-abled students, then there would be more time and space to address these special talents and gifts. Students in enrichment programs or gifted and talented programs get access to that additional, focused time and space. Students in special ed get it, too. My belief is that all students should get that.
     
    Last edited: Feb 10, 2016
  40. Caesar753

    Caesar753 Multitudinous

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    Race is certainly an issue. So is gender, socioeconomic status, language, culture, and any number of other self-identifiers. It's fine if we want to pick one and work to make it better, but we can't discount the others.

    I am of the opinion that socioeconomic status is probably a clearer indicator of academic success or failure than race. I am not sure if the research would back me up on that, but it's a trend that I've personally witnessed.
     
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  41. GTB4GT

    GTB4GT Cohort

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    Feb 10, 2016

    Caesar, I am of the opinion that parenting skills/parental involvement is the most critical leading indicator of academic success (although correlation between the 2 may be quite high as to be practically one and the same) although, like you, I am not sure what the research would say.
     

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