I think we are heading in the right direction. We have a lot of things in place. I found myself nodding along the way thinking yes we do that. What we are missing, however, is the idea where we help students see the relationships among math and other disciplines. I don't think this is a problem that is unique to math, however. Moving forward I think we need to consider how we are teaching. To me that is the biggest area we are lacking in meeting what NCTM is calling for.
I wonder if the relationships with other disciplines will get easier as we pin down what each grade/class should teach. I think right now this idea is in contention with figuring out how to cover our standards, first, leaving no time left to talk with the other departments. I think the other disciplines (those with standards anyway) are doing the same as us; scrambling to fit everything in before worrying about creating connections. If we can figure out who teaches what with not so much overlap, it might open up some room for increasing the depth of instruction. Of course, only in a matter of time, just when we get comfortable, will we have another set of standards to adhere to, more hoops to jump through, and the cycle will start over again :)
I think we are in the right direction, but don't think we will solve the cross-curricular issue. It seems we have been battling the discussion with other disciplines for a very long time. It was far easier, as you can imagine, when I was at elementary...collaboration with the other two sixth grade teachers. I can not imagine how we can possibly collaborate with other departments when we struggle to find time to collaborate within the department. Answer? I wish I had one.
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Do we have equity and access in math? You bet...we have motivation to excel with advanced math classes an AP...we have expectations and support for most struggling math learners through math matters and r.t.i. and curriculum custom designed by our math teachers.Are we perfect? Probably not...BUT...if we continue to engage in good professional discussion we will continue to get closer!!!I agree with Luke's comments on teaching strategies...always continue to learn 'by fire' what this means!!! Wish I had the crystal ball for effective instructional techniques to help our students succeed in math in the future...
1st off, I am concerned about opinionated writing when I do not know who the author is??? Who is the author(s)? .Maybe it was in the references but I do not have that page. I have some concerns- when they say all students need a deep and broad understanding of mathematics they need for college and careers. We need to be more specific . Do we realize that only approximately 60% of the students are going to a 4 year college and of that only 50 % will graduate??? We need to be more specific with what we want student to know. I do not agree that EVERY student needs to get through algebra 2 skills or can? That is not realistic. We need to show what math skills they need to know in Careers(What does Careers really mean???) . We need the local businesses input on exactly what they need? We need to be specific and really hit on the problem solving portion of their skill on how to handle a concept when they do not understand. If a student doesn't understand why they need to know the exponential function model and use it on a regular basis of course they will not do well. WE need to narrow our scope so that all student can master and apply the basics in a problem solving way. Just ask an upper clansmen to simplify fractions - the reason they struggle is because they knew the skill and didn't use it for awhile. "If you don't use it you lose it!" We need spiraling at all levels and the motivation why they need to know is critical. I have only got through the first few pages so far and this is my opinion. - Luke
One of the notes I made was on page 4 in response to the line, " In short, the current PreK-12 system of mathematics education compromises the vision of making mathematics truly work for all students." My question is will we ever have a PreK-12 system that works for ALL? I know the reading disagrees with me but I do think there are limits for some students.
OK. I have finished reading the first 22 pages and some of my questions have been answered. I am warming up to the author, whoever it is? Are we all working together in effective ways- teachers,mathematical coaches (Mark), supervisors , principals, PARENTS and the COMMUNITY? I think a huge challenge is to get parents and community involved. I think when we change schedules there needs to be more professional development on how that effects teaching students and how we can still be effective. On the principals of Mathematics I think we do a very good job at Assessment & Professionalism. Curriculum Ok and getting better. I think we really need more help in Teaching, Learning and Tools and Technology. WE need more instruction on USING INSTRUCTIONAL STRATEGIES THAT SUPPORT STUDENT LEARNING! I feel we were doing good when we implementing the CPM curriculum because we were really discussing teaching strategies (weather or not you agree with the curriculum). we now use the curriculum, however the professional development on these strategies seems to have gone by the wayside - especially for our new teachers who got none of the instruction or coaching. We really need to work on teaching our student how to persevere in solving challenging problems and their reasoning behind their solutions. We need help as teachers on how to motivate our student to persevere! Lastly technology training is essential - the students are ahead of us and are technology is unreliable in the district to say the least. This needs to improve. We need to learn more on this. Time is an issue - where, what and how? How do we encourage our community that attendance in school is important? How do we clarify this to our parents and get them more involved? More Question s than answers. - Luke
I think you have valid questions and concerns. I would just echo the motivation... kids give up! Because somewhere inside they don't care enough. Time is a huge issue, we have to figure out ways to keep instruction rich, but don't have the time:/ As far as the rest, I think we do encourage parents and I think we clarify to parents(at least the ones that come;)). Again it goes back to involvement, not sure how to get more involved. Only way I know of is giving away free stuff;)
Ok so I went off a bit:)The more I read the more I got a bit disgusted, and here’s why. It kept discussing providing all students with a deep and broad understanding of mathematics. Bottom line is we don’t, way too often. Before you stop reading let me explain a bit. In my own classroom I don’t sometimes because I have to get through this, that and the other prior to the end of the year. So what do I cut out, the deeper understandings because they take the most time. Sometimes we don’t because we don’t know how, and other times we don’t because we think they don’t matter. I have sit in on conversations and heard people say connecting things to the “real world” isn’t our job, our job is to teach the math. Of all the reasons that one gets my goat the most, IT IS OUR JOB!!! If most of our students leave our classroom and have no clue how to utilize the math we taught them outside our walls we have done all of those students a disservice. With all that said, we also have to make sure we don’t tear ourselves down too much. MUCH of the blame is on the students, why? Because I have seen a lot and heard a lot about what you all are doing in your classrooms and you are providing the opportunity to them. Problem is provision of something doesn’t cause acceptance from them. However, I still think the opportunities we are providing are too little and not often enough, for reasons discussed previously.Within the vision portion I kept thinking about this phrase, “Are we, as the teachers, the ones letting society down?” The article keeps implying we need to this, we need to change that, we need to allow for… Heck with that. We are busting our butts! Hopefully in the right direction;) It spoke of engaged mathematical students… I ran a project of sorts in Algebra II the other day and the lack of engagement from them within a hands on activity got me so frustrated I don’t know if I will run it ever again. It says it wants teachers who focus on truly leaving no child behind… I WILL NOT DRAG kids ahead who don’t want to try. I WILL LEAVE KIDS BEHIND who will not grab my hand for help. Part of the article discusses having proper support and resources from the central office/admin… well I don’t think I have to discuss how we all feel there. Lastly in the parents section it discusses that they are stakeholders and fully acknowledge the importance of …. Lets stop there and recall parent teacher conferences, when we call home and get the family dog… Bottom line, this won’t change with us. Most of us are striving to be better, striving to create the classroom discussed, but it won’t work without the students accepting their role. Students are the biggest part of the equation and they weren’t discussed.The rest of my thoughts come from the Principles portion. My thought is there are 2: Learning and Teaching. Teaching comes from us teachers, we have to do a better job of allowing change in our habits and in our instruction. A change in what we teach, and sometimes a change in why we are teaching something. But more importantly for this to work the learner needs to be actively pursuing their role, learning. I agree some changes can help create more quizzical learners, but they have to put in their time and many aren’t. Sorry for the rant but bottom line for me is this: I don’t feel support from everywhere I should, there are things we teach we don’t need to, and we do need to give students more opportunities to discover mathematics and use it in relevant ways.- Dustin
"family dog" ...classic Radloff.
I think we should be as blunt as this study thinks it is being. Okay it talks about barriers and what it take to make mathematics work for all. Way to much not in my control. I'm tired of being told of the "team effort" needed when we know we cannot count on parents, admin, and community. At least not for just this pure math agenda. I do think a big part of the 7 principles listed we do fairly well. But when they throw out words like adequate time, tracking practices, struggling students, it shows how academic these type of agendas are. These people love to give that ultimate "best case senecio" when a little practicality would be nice.The world is not ending based on our current math curriculum. Urgent is being a little dramatic. Give some credit for how far we have come, and some common sense approaches to keep improving!
I do agree that the opinion of the NCTM in this article is far too rigid, taking only one perspective into account and it is not the one of the teacher. We have made great progress, IN SPITE of all of the obstacles that have been put before us, and we will continue to do so.
Love your last statement John. The world is not ending....give some credit for how far we have come and some common sense approaches to keep improving!
There was a lot to read here. I guess I will start at the beginning and work my way through my comments as I read. First, statistically speaking, they did not give a whole lot of contextual knowledge of their studies to thoroughly support their statements. When they say that four million five-year-olds enter school and less than three million of them graduate from high school, does this include homeschool students that "graduate" from high school. According to the Institute of Educational Studies, "In 2007, the number of homeschooled students was about 1.5 million." Assuming that some of these students may have started as five-year-olds in the public school system and then withdrew, this fact could more than account for the disparity between graduates and entrants. Do I believe it does in actuality? No. However, it could partially explain it. Thus, this statistic could be misleading. Never the less, I do believe that there is a portion of the population of non-graduates that have to potential do graduate and are not living up to that potential due to some of the issues of their educational experiences at school. Next, the author(s) move on to use specific examples of percent of students that can perform certain skills. Again, I must suggest that as recipients of this information, we should be upset with the lack of background information. They do not tell us the questions that were posed to the students that assessed whether or not students could perform the skill. The low percentages could be a result of poor assessment techniques (biases of context, poor wording, the lack of use of a calculator for exponential functions, etc) and not student understanding. Also, they pick out some very specific examples of skills. I would be tempted to believe that they chose isolated instances (outliers) that best support their implications and not the norm of what students demonstrated in understanding to gain the appearance of strength in their insights. Next, going back to their original number of 4,000,000 five-year-olds that enter school, the fact that "less than 10% of 12th graders can apply an exponential function to model population growth" means that less than 400,000 individuals can perform this task. I wonder how this compares to the number of population projectionist occupations there are in the United States. Is this an acceptable number? Also, this statistic could possibly be explained by the fact that most students have taken the required amount of math credits by their senior year and are no longer enrolled in a math course. As Luke mentioned earlier, "If you don't use it, you lose it," which could explain why this number is as low as it is. This number could possibly be higher if they assessed juniors, instead. Now, does this explanation also bring up an issue concerning the retention of mathematical concepts of our students? Absolutely! However, the point is: we shouldn't be so quick to take their numbers as measurements of the norm, instead of as statistical outliers that could mislead the audience of the document. Finally, I found it ironic that they would use such tactics and then identify the issue of the expectation of citizens to "make wise decisions and judge the wisdom of those made by civic leaders in today's data-driven society."
It would appear that, on the first page, what NCTM is calling for is more statistical literacy. Yet, the mathematics society is still finding it difficult to require statistics as a required course for all students. DC Everest and most other districts attempt to integrate statistics into other curriculum, but, oftentimes, this results in short, disjointed units that have little depth or application and result in poor understanding of even the most basic of statistical concepts. If statistics is to be a focus of mathematical instruction to come, as I believe it should, we will need to increase the amount of and quality of the instruction of these topics. This may require training for teachers who have not used or taught statistics in a while, as well as a restructuring of the secondary mathematics curricula.I also had some issues with a few of the last few statements of the "Urgency" section of this document. First, the author(s) choose to paraphrase from Darling-Hammond by saying "The economy simply can no longer absorb unskilled workers at middle-class wages, and this reality threatens our societal infrastructure over the long term unless we give all students the skills they need to compete in a knowledge-based world." Without delving into a political rant on the idea of money distribution to consumers rather than investors that the first part of that statement hovers over, I would like to, at the very least, point out the issue with the second part of the statement. The idea that we can "give" all students skills suggest that they are merely computers that can be programmed and reprogrammed and completely ignores the reality that students play the most pivotal and active roles in their own education. Although in some ways teachers can "fail our students and our society," as the author(s) point out, shouldn't the students and parents be held accountable for their failures, as well? I will say that, without having read the rest of this document, I'm sure that NCTM will follow-up with suggestions as to how to encourage and increase student and parent involvement, as those are two of the biggest determinants of student success; despite being something that is, more or less, out of our control.With regards to the NCTM’s Vision, I believe the DC Everest is meeting some of the objective, but not all. First, I believe that our district objective of increasing literacy is forward-thinking. It is becoming more essential that students make sense of problems in a variety of contexts and are able to communicate conclusions and reasonings in a way that exudes confidence and understanding while instilling those same feelings in the audience. Even with (and especially for) our large Hmong population, it is important for teachers to hold all students to a high level of literacy. We do a nice job here of supporting students, but holding them to the same standards, instead of compromising expectations. It is just another facet of the principle of having students make sense of and persevere through problems.
We also are doing a better job of using formative assessments to identify gaps in essential knowledge in the students and using it to differentiate instruction. Although there is still not enough time to meet with each student one-on-one, we are doing our best to come up with creative solutions to supplement student learning and alleviate student misconceptions. We are still having difficulty coming up with a system that holds students accountable for remediating, while still maintaining the stance that student grades be devoid of student behaviors.A discussion that is currently happening in the Math Department is how to delegate the standards so that each class doesn’t have to cover as much material and go into much more depth rather than breadth. In this document, the author(s) comments “In far too many classrooms, schools and districts, the PreK-12 mathematics curriculum devolves in repetitive, fragmented attention to isolated skills, devoid of their conceptual underpinnings, as teachers are expected to rigidly adhere to the dictates of textbooks, pacing guides, and low-level assessment. In the race to check off a list of disjoint objective, students never develop the bigger picture of the mathematics they are learning.” We are starting to get away from this, and with an attentive eye and some creativity, I am confident that moving forward we will continue to make progress.We are making great strides in the use of authentic demonstrations of understanding through tasks and real-life applications. With these opportunities, students are asked to independently persist through problems through the use of manipulatives, computers, and mathematical tools. These tasks are developed with the idea that students can solve problems in a variety of ways and come up with different viable answers, as long as they are defended with mathematical reasoning. It requires them to make a plan, perform research using available resources, and build and communicate arguments that justify conclusions using a logical progression of math ideas. As our world becomes more technologically-advanced, it is imperative that we create students who are problem-solvers, not calculators.
Many of the procedures that students were traditionally taught are becoming obsolete, as computers easily work through these problems in a fraction of the time, with far more accuracy. Students that come out of programs in other nations around the world have been shown to have much higher computational procedure proficiencies than our students. What we must focus on to continue to have success in the global market is to have individuals join the work force who are innovators. For this reason, I believe that by integrating more of these mathematical tasks we are providing students with the deeper understanding of how to manipulate the numbers and operations they learn in class to make better-informed decisions and become more successful and valuable members of society. Although it would be nice to provide students with the answers to every problem they will ever come across, this is an impossible task. So, it becomes obvious that the best action we can take is to provide students with the skills and then, as a culmination, prepare them on the process of using a network of background knowledge, given information, and hard work to come up with meaningful conclusions and how to use them. This might require us to reach across curricular lines and collaborate with other departments in the creation of the most meaningful and necessary activities for students. We are making progress on such ambitious goals, but still have a ways to go. The unfortunate reality of the current student culture is that there is growing demand for students who will persevere through the complex problems of an ever-developing world and less students willing to do so. The author(s) ask us to “Imagine a world where all students become mathematical problem solvers, working on problems that may take hours, days, and even weeks to solve.” Jokingly, my response to this was are these all AP classes?, as these are the only classes that students will seem willing to struggle through and dedicate ample amount of time to. I do feel that we, as teachers can make a change on this culture by asking students to struggle through complex problems much earlier in their math careers, however, again, this seems like, perhaps, the variable in this equations with the highest rate would be the students, themselves, or the parents. The other obstacle that teachers face is the uneven eminence of top-down policies that require a large portion of allocated “prep” times to perform tasks that actually might harm instruction rather than help it. Currently, teachers are spending more time scrambling to jump through narrow-scoped hoops, when they should be participating in discussion and development. Focusses are moving from quality instruction and assessment to higher grades, standardized test scores, and AP class credits. Although I believe that it is necessary to hold teachers accountable for their instruction, a system should be in place that supports and encourages discussion and collaboration, and not competition and insecurities. These "Principles to Actions," do a thorough job of advocating for themselves as promoting math instruction best practices and call out the teachers that "cling to unproductive beliefs and perpetuate ineffective practice that undermine attempts to change." What they neglect is the fact that, in the current atmosphere that surrounds education, teachers have had increased concern with two things: money and security. Although I'm sure very few teachers got into the profession to strike financial gold, it is difficult to put their jobs and finances in question and ask them to take risks with their instruction. Although I have not been in the profession a long time, I can understand that teachers who have been at it for a long time and found success, as it has been understood by them, to be unwilling to change their instruction, especially if their well-being depends on it.
I have read and agree with many of the statements being made. I guess I get a kick out of the vision statements. I would like to imagine a world where most all children were interested in completing a task...Any task as it prepares them and drives deeper understanding...imagine a world where all families support and encourage learning and it's benefits... I agree with earlier statements that it will take some changing on our part, but community/parent involvement is also going to be a key ingredient. Times and cultures have changed. Family dynamics and societal expectations seemed to have changed. I caught a recent interview our local tv station about a month ago describing our improving economic outlook in central Wisconsin manufacturing. A statement made really struck home. The leader of this council stated that about 70% (if my memory is correct) of new employees w/in the past five years do not have all the necessary skills needed to do the job effectively, emphasizing "soft skills" of the jobs. ( I feel I have personally seen a decline in recent years in this department too.) Through my years of teaching I feel that some of the changes we have made to education do effect this aspect as well. We handle homework, tests, grading and a plethora of other topics much differently. Family expectations of these topic have seemed to change as well. I understand findings in articles, etc. Just makes me wonder and worry at the same time. At the end of the day, we know not all students move on to higher education, but in today's market place, certain levels of education are a necessity. How do we get everyone ready for that? How do we show families that don't necessary see value in a classroom that this is a necessity for their child as they will soon enter the job market after high school. We need productive citizens that are willing to work and take on variety of labor tasks/careers. In closing, under the productive practices and policies portions the text refers to impactful practices...does testing kids MANY times throughout the year fall under this? Just things I am struggling with...
Your question about do we have the right direction is an interesting one. I would like to know who "we" is. I believe you (Mark) have been steering us in the direction of task oriented teaching/learning. However, as mentioned by others, many of the other directives given to us by our individual buildings take precedence. These directives seem to focus on skills and RTI. These directives seem to take up so much of our time, it leaves little if any time to create tasks. Then there is the issue Dustin addressed about also having very little time in class to go deep enough and still accomplish all of the standards for the school year.I think it is going to take a lot of time to re-think my own approaches to the standards and curriculum. I am sure I can incorporate deeper levels of thinking into each of my classes. The only problem is the time to create these lessons. Then there is the training of the students to be able to persevere. I thought it was interesting how the author mentioned repeatedly the teacher's job is to stretch the students mind and allow the students to productively struggle. Productively struggling is a huge challenge.
Welcome back! Do we have the right direction? Heck yes, However on page 22 line 9 it says"Teachers must employ instructional strategies that support this vision of teaching and learning." However I agree with Steve that it seems we have more collaborative time then ever before, however we have more hoops to jump through and we really don't get the time to discuss instructional strategies that we use. We hardly ever get instruction from administration on the instructional strategies they want us to use. I feel it is all about assessment and how students do on their test, especially now when the comment in our department was made that in three years our evaluation will be partly based on how our students do on the ACT test. I want to make it quite clear : WE DO NOT CONTROL WHICH STUDENTS WE GET IN OUR DISTRICT! Please show us what you want! How do we motivate students to Persevere? How do we " actively engage students with their peers"Are there good tasks out there that we should be using? Where are they? What are they? Do we need to create them? I feel I do not have the skill or time to create great motivating task that excite student to come up with great products? Please teach me how to do this. I feel the CPM curriculum is rich, however the discovery learning takes time. The recommendation the the authors state we need 60 minutes of class time per lesson ( and that is without going over any homework!) We have 45 minutes! What do we cut??? We get shorten time but I feel no instructions on what and how we change our instruction when we have less time.What are teachers doing? " Allocating substantial instructional time to making connection among representations? I do not feel we are achieving this. I do feel we have a math staff that is willing to work! We need instruction and examples as to how this works! The reading gives examples at to low a level. WE need examples and instruction for the classes we teach."Selecting tasks that encourage students to use multiple representations in solving problems?" The students and teachers are really struggling with this. Both of us need help in this area. However, if I amgoing to be evaluated on an ACT exam. Why wouldn't I spend more time on ACT type questions? What are the ACT questions going to look like? My goal is for every student to get the concepts and score a 100%! However I do not think that is their goal all the time! For a lot of good reasons and a lot of not so good reasons. This is a very complex problem! this is all I have time for now! More questions than answers!