Bravo to everyone who blogged for the first time and thank you to all of you who blogged and offered purposeful insights into the use of technology in the classroom and examples from Willlowdale Elementary.Don't feel left out if you were not one of the "cool" kids (as Chris so aptly coined them) from the 306 course taught by Jeff Crews. We will all get plenty of practice this semester. While we are primarily using the blog as a way to build community and further develop ideas discussed in class, the blog also serves as a way to reinforce the use of technologies (Norm, I suppose we could also use it for political commentary). Levels of frustration will vary depending on prior experiences, but it will be important to remember that seat time is still the best way to become proficient. In fact, Professor Cobbs and I initiated the use of this blog just last semester as a way for us to stay current in the use of classroom technologies so it is a relatively new format for us too.
This week the UM campus will be dedicating an entire day to exploring global climate change. Living in an electronic genre can be frustrating, but moving away from a paper-dependent classroom has many environmental benefits. (This said, we acknowledge that computers bring their share of environmental hazards.)
We consider the migration of course components to an electronic course format to be an important part of our effort to engage in campus-wide efforts to address climate change and challenge you to think about how you will structure your classroom in ways that fundamentally address the issue of global climate change.
For example, an interesting class exploration could be to challenge the supposition that an electronic classroom is more environmentally sustainable than a paper-based classroom. Create a list of activities that students could pursue to answer this question.
In class this week we will be exploring the national standards for math and science and ask that your blog entry contribute to a comparative analysis of the standards. (For science, we will focus on chapter six of the NSES only: http://www.nap.edu/readingroom/books/nses/6a.html).
To get us started, consider the main emphasis areas for the two standards. How are they the same? How are they different? What is the central teaching strategy or strategies recommended? Are they consistent or do they conflict? Many of you noticed that the math standards do not talk about the history of math, and yet they comprise a fundamental part of the science standards? Why is this?
For this blog, unless you are the first one to comment, the expectation will be that you have read at least one other student's entry (and preferably three) and incorporated their conclusions in your response as well as end your entry with a question you still have about the math or science standards.
Next week we hope to be splitting you into your grade band learning communities. Until then, we will continue with a group blogging format.
37 comments:
Considering the main emphasis areas for both the math and science standards, there are many differences and similarities. Both the math and science standards are categorized by their sub-disciplines, though they break their expectations for grade levels down differently. The math standards are broken down P/K-2, 3-5, 6-8, 9-12, while the science standards are broken down K-4, 5-8, 9-12. The science standards recommend the use of all of the content standards togather, including the history and nature of science, which allows for an integrated approach to science teaching. The math standards go a bit more in-depth, specifically outlining and suggesting everything from "worthwhile Mathematical Tasks" to "Tools for Enhancing Discourse," but do not necessarily offer a central teaching strategy. The science standards offer guides to the content standards, giving the reader a clearer foundation for the standards themselves. The math standards did not offer such guides. History comprises a fundamental part of the science standards because (to quote the author) "In learning science, students need to understand that science reflects its history and is an ongoing, changing enterprise." Teaching the history and nature of the human aspects of science, and the role that science has played in the development of various cultures is critical components the NSES's comprehensive vision of science education. I am unsure as to why there are no such standards in the field of math. I think that they may be eaqually as important, though may be boring.
Math and science standards are similar in serveral ways. Both sets of standards are interested in the students being able to use processes, reasoning and in essence problem solving to come to conclusions and arrive at answers or theories. Critical thinking is also a part of both sets of standards, although this is more aparent in the science standards. Science standards are really based upon unifying the scientific concepts and bringing them together as a basis of knowedge. Math standards are much more cut and seperated into very specific subject matter (standards are different for geometry, algebra, problem soloving, measurment, etc...). Another way that these standards are different is that in math you build new math knowledge through problem solving and math standards will most likely stay the same.Although this is somewhat the case with science, we must remember that scientific advances may continually change science standards. Thus, we must continue to remember the conceptual organization of science to provide students with the ability to improve scientific literacy in an ever increasing scientific world.
Also, as Kevin already noted, one of the differences in the math and science standards is how they are broken down. Math standards have 4 grade bands while science standards are broken into 3 grade bands. He also points out that math standards don't offer much of a guide to teach the standards while the science standards recommend using all the standards together.
The history of science is very important to students because it is an ever changing field and students need to know where scientific principles came from and understand the changes in scientific thought throughout our world's history. Like Kevin I am unsure why math history isn't included in the standards. My guess would be that because math concepts build upon basic fundamentals the history isn't viewed as essential for students to understand, rather processess and basic fundamentals are thought of as critical for students to understand.
A question that I still have about these standards is how to incorporate both the science standards and the math standards together into a lesson that will work well and not be over zealous in trying to achieve too many standards in a short lesson.
I agree with Sarah that both Math and Science standards promote students using processes, reasoning, and problem solving. This isn't at all shocking as it is quite an efficient way of working through problems and applies nicely to both Science and Mathematics. A key difference, as both Kevin and Sarah mentioned, is that Science has a more specific teaching strategy than does Mathematics. This leaves the door open for applying a variety of teaching strategies for Mathematics which I like.
As for the history of Science being taught I think Sarah explained it perfectly... "The history of science is very important to students because it is an ever changing field and students need to know where scientific principles came from and understand the changes in scientific thought throughout our world's history." It is a great way for students to see and understand the processes, reasoning, and problem solving that science has seen throughout its long history.
I guess a question I am curious about is what the various different teaching strategies for Mathematics are since the standards aren't quite as specific as with Science. I am really tired so I hope my post is coherent.
I have two questions. First, if I wanted to list the math standards that I have used in a math lesson, how would I most efficiently do so? (They are not assigned numbers and can be a little wordy) Second, does the OPI model their standards directly from these organizations? In our lessons, must we note the NCTM standards always, or may we just cite the Montana standards?
I have two questions. First, if I wanted to list the math standards that I have used in a math lesson, how would I most efficiently do so? (They are not assigned numbers and can be a little wordy) Second, does the OPI model their standards directly from these organizations? In our lessons, must we note the NCTM standards always, or may we just cite the Montana standards?
There are differences and similarities with both standards in math and science. This is rather obvious given that the two subjects are different but can easily be integrated. Like Kevin mentioned in his blog, the standards in each subject are broken down into their sub-disciplines. Math contains five and science has five as well, however, physical science, life science, and earth and space science each have their own standards so that makes eight, if we include those as separate disciplines. Further more, both math and science break down grade levels, which is very important because every grade requires different levels of thinking.
The main difference I noticed was the grades levels defined by each standard was different. For example math broke down it's standards into Pre-k- grade 2, grades 3-5, grades 6-8, and 9-12 and then labeled the standards and further more the expectations. Science on the other hand simply has their standards broken down into k-4, 5-8, and 9-12 and that's it. I really like the math standards because they are more precise and developed. However, it seems understandable because math is more cut and dry, where as science is always changing and there is more freedom as to what teachers can do in their classrooms.
Math and science seem to have many similarities with teaching strategies like analyzation, application, prediction, formulas, understanding etc. Both subjects compliment each other wonderfully on teaching strategies and are quite consistent, however, because they are different, materials and the extent at which these similarities will reach are going to be diverse.
Concerning why there is no history standard in math, I would have to agree with Sarah and say that students need to have an understanding of the history of science because it is a subject that has changed the most in terms of not only discovering but realizing that some discoveries in scientific methods and so on are in fact incorrect. Like many of my classmates have commented, I as well, am not sure why there is not a history of mathematics but I am guessing that math consists mostly of discoveries and has not changed much except for providing a deeper understanding of the subject but not much of maths principals have changed.
I do not wish to sound as every other person who has already posted to this blog, unfortunately I agree with most of their observations. The most blatant observation, besides the grade band divisions, is the emphasis (by both disciplines) on the use of reasoning, analyzing, prediction, formulating questions, developing inferences, and selecting the appropriate methods or tools to approach a problem, in all of their standards. Sarah, Ryand, and Ranelle all seemed to come up with this same conclusion. I think this is for a very good reason, the learning strategies are very similar, in that they are/should be largely hands-on. When students perform hands- on work they must observe the reactions of their actions, and in doing so almost automatically began using the afore mentioned skills such as analyzing and prediction.
Like Kevin, I feel the history of math should be included in older students’ curriculum. I had a math teacher in high school who every week would feature a mathematician and give us a little history about the math concepts they discovered and who they were. By studying some of the history of math, I feel that it helps build the schemata of the students and may help them to remember certain concepts, as it did with me.
I disagree somewhat with the reasoning Sarah gave as to why history is not currently incorporated into math. I believe in the higher level mathematics, much higher than I could ever even understand, the history of mathematics is just as vital as it is to science, but the mathematical concepts that are currently evolving or being discovered are not the concepts that we are teaching to our students and the concepts we are teaching are relatively stable. In science however, as Sarah mentioned, the history is vital in our classrooms because some of the topics we discuss with our students are continually changing, for instance Pluto’s “planet hood,” therefore because science that deals with their curriculum is continually changing, it is important that they learn where and how the concepts came about.
As far as a question to end, “Because the standards are so broad, how do you pick and choose which ones to put on the lesson plan, do you just pick one or two to focus on, or is it recommended to put all that apply?”
I'm going to try not and reiterate what has already been said a bunch before, but if I do, sorry!
The math and science standards do have some similarities on the main emphasis points. It seems like all the standards involve doing activities that allow students to discover information themselves. Like Julia extensively listed, these activities could include analyzing, prediction, formulating questions, etc, etc, etc. I really don't have much of a memory for what learning math and science was like in elementary school, but I know that wasn't what it was like in high school. Math was generally just rote memorization, and I'm almost certain that isn't included in any of the standards. Also, like Julia said, I think it would be a good idea to incorporate historical figures into mathematics and I like the idea of introducing a new person every week or maybe with each new unit. I guess that my question to end this is, "Is there a way that administration keeps tabs on you to make sure that you follow the standards? What happens if you don't follow one of the standards?" I'm not saying I'm going to defy the almighty standards, I am just curious how gung ho the administration is at making you implement the standards.
P.S. Sorry if my post doesn't make sense. I'm just real tired
I think the math and science standards are very similar in many ways. First, it seems to me that both are based around the concept of problem-solving. It is also obvious (and probably previously stated by somebody) that the content areas of the two subjects overlap tremendously making it very easy to link the two subjects together.
Also there are several distinct differences between the math and science standards. For example, the math standards seem to be very precise whereas the science standards are very vague. Also it seems strange that math and science standards are broken down into grade ranges. For example math is k-2, 3-5, 6-8, and 9-12, while science is k-4, 5-8, and 9-12. I think this illustrates the flexibility of science allowing the teacher some freedom in the curriculum. For example, while you could be teaching the concepts of light, heat, magnetism, and electricity to 4th grade, the same concepts could be taught in kindergarten. On the otherhand math curriculum is much more structured; You have guidelines for exactly what should be taught when. For example students in 4th grade would most likely working with numbers and operations like division and multiplication, the kindergarten would be learning how to count and understand the concept of value. (not sure that reads how I want it to but it will work)
I’m not really sure why the math standards don’t cover the history of math. As Sarah has already stated, I would guess that the standards are focused more towards processes, basic fundamentals, and problem-solving. Also, as previously stated, I think that the history of science is an integral part of understanding science as it is today. For example, many concepts and theories first discovered hundreds of years ago still stand today. What better way to allow students to obtain knowledge of scientific concepts and theories than through science?
My main question is: Why do the grade bands for the math and science standards not match up?
I Have to agree with julia in that many of the similarities I have found have already been posted, such as the way both sets of standards are broken down by the sub-disciplines and grade bands. I think the Science Standards are broken down in a way that the disciplines can relate to each other and give a more integrated approach. The math standards on the other hand are more segregated and each discipline is kept separate. I also think the science standards give a more detailed description of what to teach, whereas the math standards are more broad. However, both sets of standards show the importance of problem solving, reasoning, and using different processes in both math and science.
I agree with Kevin about how the history of science is really important to that field. We need to see how far we've come and how things have changed so much over time. This also shows that science is composed of many theories that evolve as new evidence is discovered. As for math, history may be important in the higher levels, but in elementary school, I think the concepts are more important. The history of math doesn't teach us as much about math as the history of science teaches us about science. Math is composed of more facts than theories and many of the things we teach in elementary school aren't changing with time.
I have a similar question as Kevin's about citing Standards... What information about the standards do we need to include in our lesson plans? Do we just list the heading or main title of the standard or do we need more information? Also, since I plan on teaching in Colorado, should I put MT or CO standards into my lesson plans?
When comparing math standards and science standards, it really becomes clear how codependent the subjects really are. Both standards (and all standards) emphasize what students should know, understand, and be able to do. That said, let me try to make sense of what is going on in my head.
Aside from the grade level chunking being different between the two subjects (as noted by Kevin) the main difference I observed was in content standards vs. process standards.
In regards to the content standards, it is fairly easy to see how math is used in science -for example, data analysis as part of science inquiry, or measurement in physical science. However, I wasn’t always able to go the opposite direction and see how science content standards (like life science) matches up in a math lesson. I think this in part has to do with science’s specific teaching strategy (as mentioned be Ryan).
The point I am trying to make is that even though the content standards are not always interchangeable, the process standards of both math and science are woven very tight. I can tie every one of math process standards to an area of science and vice versa. Both subjects consistently rely on questions and answers, on reasoning and problem solving, on exploration and explanation, etc… In this sense, math and science need each other. These process standards (as most of my classmates agree) are essential to both math and science!
And in answer to why math standards don’t talk about the history of math and science does, is perhaps that math is more concrete (as mentioned) and science is constantly evolving. Or perhaps, it has to do with pinpointing? Maybe the real question is “what IS the history of math?” Or… maybe the math standards are using the “less is more” theory? Hmmm , it makes a future teacher wonder, doesn’t it?
My question—How often do math standards change? Do they change as frequently as science standards, or less frequently? Does a teacher get in trouble for not using the most updated list of standards?
The math and science standards have multiple similarities and differences. As Sarah stated above, the standards for both math and science are interested in the processes and reasoning behind the actual end results of the problem/question at hand (aka: the answer or theory). This is an important factor in both subjects because it's not necessarily the answer that matters the most, but how the answer was arrived upon. It is through these processes and critical thinking stages that the students' comprehension and understanding of the subject matter comes into play. Another similarity among the math and science standards is that they are both broken down into grade levels. How they are broken down, however is a different story. The math standards are categorized as follows: P/K-2, 3-5, 6-8, & 9-12 and have a set of expectations for each section. The science standards are categorized as follows: K-4, 5-8, & 9-12 and are far more broad in the expectations required. Also, in regards to the question of why the history of science is mentioned in the science standards while there is no mention of the history of math in the math standards, I would have to go along with Kevin and Sarah. I agree that science is constantly changing, thus making its history that much more vital. The history of math doesn't, on the other hand, play that large of a role & is not as necessary to the students' knowledge and understanding of mathematics. My question is, can a lesson have too many standards? If so, how do you go about picking which standards you keep & which ones you eliminate?
The math and science standards seem to be both similar and different. Each have sub-categories that further explain the standard. As Kevin has stated the math and science standards are broken down in different levels. The math standards are: p/k-2, 3-5, 6-8, and 9-12, while the science standards are slightly different. They are: K-4, 5-8, and 9-12. I believe that having a smaller grouping for the math standards give a little more information on what is to be taught. One thing that I really like about the science standards is that they recommend that you use all of the content standards together. Using all of the content standards allows for more freedom with lessons and how you choose to teach a lesson. On the other hand the math standards are more detailed and specific. The math standards though are not very guided on helpful or specific teaching strategies. The math standards seem to overlap quite a bit with each other. There are two main components in the science standards. The teaching of the history of science and how it is ongoing. Then, it seems to me the rest seem to be inquiry based. There does not seem to be a distinction like this within the math standards. One question I do have that Kevin sort of brought up is why in math the history of it and how important it is does not seem to be part of the standards?
Both science and math standards expect the students to not only come to a conclusion, but to also be able to provide reasoning to back it up. Both sets of standards have a balance between allowing students to discover solutions on their own and providing proven methods and data. The math standards are much broader than the science standards. In fact, some of the science standards could fall under the categories in the math process standards. For example, "science in personal and social perspectives" could fall into the "connections" category in the math standards.
It doesn't really surprise me that history is not a part of the math standards. Knowing the history of math does not necessarily make it easier for students to solve problems. On the other hand, science seems to depend on historical data and discoveries when making predictions about the future. A lot of observations in science, such as the layering of sedimentary rock, depend on a process that took place over a period of history.
To try to answer Ashley's question, I would say that a lesson can have too many standards in it if you do not have enough time to cover it all. A lesson that is 40 minutes long might only apply to one or two standards. I would pick ones that seem most applicable and easily measured.
There seem to be so many science standards. My question is, how can teachers possibly cover it all in 3 years, while also covering the standards of all the other subjects?
Having compared the math and science standards is very evident that these two subjects are very similar in many aspects. To reiterate what pretty much everyone has talked about already is that the main emphasis for the science standards as well as math standards are teaching strategies in reasoning, analyzing, prediction, formulating questions, developing inferences, and selecting the appropriate methods or tools to approach a problem. As Kevin, and sage noted earlier, both math and science are broken down into sub disciplines as well as by gradebands. The main difference however, is that math is broken down into grade levels of k-2, 3-5, 6-8, 9-12 while science is broken down k-4, 5-8 and 9-12. I like that Sarah noted that Science standards are based upon unifying the scientific concepts and bringing them together as a basis of knowedge while math standards are much more cut and seperated into very specific subject matter such as geometry and algebra for example. This seems to be one of the most obvious differences between the two.
I am not altogether sure why there isn’t a history of math yet there is one for science. Math seems to be more “factually” based while science seems to always be more based on a theoretical aspect. Science appears to be less concrete than math but I think that teaching about the history of math can be very beneficial to student’s understanding and comprehension as well.
My question is do we have to state the standards in our lesson plans verbatim or is there a shorter way to go about this process? (they seem to be a little long, and I was wondering if there is a way to shorten them while still making it clear what standards we are using.
I agree with Sarah N.'s comment that the history of math is not essential in learning math because it doesn't help develop the concept. The history of mathmeticians could be incoporated in a history unit to tie the two subjects together. History is more relevent in the subjest of science when the nature of science model is followed.
While comparing the math and science standards it's easy to see that the science standards are more specific and provide a clear foudation. The math standards however are open ended. The strong correlation between math and science leads me to believe that the math standards should be more direct allowing for a more specific approach to teaching. Both math and science do focus on reasoning, problem solving, and a strucured process which relates the two subject areas together. I agree with Ashley that most important factor is how the students arrived at their answer. This allows for the development of critical thinking skills and the understanding of the process to reach a conclusion.
To anwser Sarah's question the best way to try and meet the standards is to develop different types of science lesson plans and keep a strong focus on a couple of standards each time. The way the curriculum is setup allows for a teacher to give close attention to one area in science which allows for effective lesson plans.
My question envoloves the No Child Left Behind Act. Math is considered a staple in our educatioin and has been a major concern in the education of society. Due to this I wonder why the math standards have not been further developed.
The main emphasis areas for both math and science are similar because they are both guiding teachers to teach a solid foundation of skills. It is important to incorporate the standards in our teaching not only because we have to, but also because it is in our students best interest to know these skills. (This may be a slight stretch, but I’m trying to bring something new to the table here…) The actual skills discussed are similar and include as Sarah said “processes, reasoning and in essence problem solving to come to conclusions and arrive at answers or theories.” As noted above, a clear difference is the grade breakdown. Another difference I noticed was that the math standards are much more cut and dry compared to Science where the standards seemed to be more intertwined.
The teaching strategies seem to be similar. They include words like “analyzing, application, prediction, formulas, understanding” as Raenelle pointed out. More importantly, none of the standards are asking students to memorize and regurgitate information.
The history of science is included because science is always PROGRESSING. Science is changing and evolving each day, and it is important for students to see how we have gotten where we are today.
It seems tough to cater to every single one of these standards in a complete and creative way. How do we decide what to give priority to?
- I know I already posted once, but I just wanted to comment on Jen's post when she stated: "I also think the science standards give a more detailed description of what to teach, whereas the math standards are more broad." I felt the same way, I was just having trouble phrasing it so nicely.
The most important factor about any subject is the understanding of the concept as well as the process. Both math and science emphasize on these aspects as well as: problem solving, reasoning, analyzing, predicting, and developing questions to further the learning experience. Because of this, many of the standards go hand in hand relating the studies of math and science. The differences are that science standards have more direction and develop a stronger focus on the content. I do like how the math standards are seperated into the different disciplines but think they should be more like the science standards in providing guidelines for teaching the subject. When it comes to touching on the history of both subjects, I agree with Ashley. The fact that science is an ever developing area of study. What we know today is constantly changing and further developing from what scientists in the past have theorized. Math however is not constantly developing at an alarming rate. The rules of math do not need to be altered in order for the subject to grow.
I do not have a complete answer to Michelle's NCLB question. It led me to wonder if the emphasis on mathematics is a result of past and present educators not knowing exactly where to direct math instruction because of the loose and broad standards. I wonder how relevant this concern is to the emphasis on math in NCLB.
As Kevin said, both the science and math standards are split into grade bands. The math has smaller divisions than science, which allows for more specific standards for each grade. Many people have also stated that the standards allow for hands-on learning as the central teaching strategy where students are more involved in their learning, instead of a very teacher-directed approach. One of the main differences is that science seems to be more based on theories and developing theories, whereas math is somewhat more structured. The standards go well together which is important since math and science overlap. I think that perhaps the history is touched on because of the controversy surrounding some science topics, whereas math does not seem to have this issue. This leads me to my question about the standards. The standards states, “No standards should be eliminated from a category. For instance, “biological evolution” cannot be eliminated from the life science standards.” So as educators, how do we add “biological evolution” and be respectful to all schools of thought?
Erin Barr
The science and math standards have some similarities, as well as some differences, that need to be considered when exploring them. I agree with Natalie when she stated that both math and science involve the ability to reason, predict, analyze, formulate questions, and be able to develop problem-solving skills. It is obvious that math and science compliment each other very well in this way. They both involve all of those aspects (mentioned above) as a critical part of the learning process.
One difference I noticed is the breakdown of the grades, when defining the standards. Math is focused on a smaller grade band, while the span in science is bigger. In math it seems that the standards are more specific per grade. Each standard outlines what the students are expected to know. In science the standards are a little broader and don't offer the specific expectations.
As I mentioned above, science and math both use a lot of the same teaching strategies. However, both subjects are unique in themselves.
I agree with Sarah when she mentioned that history is a very important part of science because it is an ever changing field. In order for students to truly understand science, they have to know the history of it. Certain historical events were a big deal in science (i.e. discovering penicillin), so knowing the background of that is important for students. Like Sarah and Kevin, I am unsure why history is not included in math. I suppose it is because the exact history of math isn't necessary when teaching certain rules or equations.
Both the science and math standards offer a large amount of information (which I'm still trying to digest), which can be great tools in planning lessons, and guiding our instruction in both areas. The emphasis areas very similar in that they touch on the broader range of the topics, while also getting very specific in what areas to teach. For example, Math has requirements in Algebra, Geometry, Measurement, Problem Solving, etc, while Science focuses on physical, life, earth and space...you get the point. As Erin M. suggests, this helps to guide educators in teaching "a solid foundation of skills." I'm going to sound like I'm beating a dead horse here, but one of the main differences between the two standards are the grade bands, which Kevin, Erin, and others have pointed out. The math standards target a smaller range of kids, K-2 for Math v. K-4 for science, etc. Also as Raenelle pointed out, both teaching strategies seem to focus on areas such as "analyzation, application, prediction, formulas, understanding." All of these are important areas for students to work, and are great guidance points for teachers.
As the for the differences in History, I'm not really sure why that is. When I think about it, history seems to be a very important aspect of Mathematics, and I guess I disagree with Kevin's suggestion that it "may be boring." I think Math history offers a variety of interesting lessons and material for students...What would Math be without people like Tycho Brahe...Research how he died, and tell me that is boring. Or what about M.C. Escher's use of geometry in art? Crazy stuff. In any case, I feel that it is equally important in the science classroom, but I am at a loss as to why it wouldn't be required in Math. Seems like a very necessary component, and something that could give students a break from just banging out equations all day.
After reading the standards, and I thinking about how they might be incorporated, I'm wondering as teachers do we really get a chance to focus on the standards and their importance, or will we be too busy worrying about NCLB all day. Hopefully that's not the case, but it's something I worry about.
The math and science standards have a handful of similiarites and differences. To re-state what eveyone else has already talked about, one similarity between the two is that they both put a great deal of emphasis on teaching strategies like problem solving, reasoning, analyzing, and developing questions. Next, another similarity that these two standards share is that both of them are split into grade bands and (From Kevin). However, the math bands are split to be much smaller and very specific. The science standards are cut into larger sections and are very broad and open to your imagination. Another similarity between the two is that they both put a large emphasis on individual problem solving. Both subjects encourage hands on activities that are geared away from a teacher centered lesson plan.
I'm really not sure why the math standard doesn't mention anything about teaching the history of mathematics. In my opinion I think it would be a great idea to introduce students to this type of history because it will give them a greater appreciation for what they are doing. I also think if a child knows where a question or idea came from they will understand it better. As Sarah stated, the history of science is an ever changing development that can change in a blink of an eye and is incredibly important to incorporate in a classroom. However, the history of mathematics could be used in the same way I feel. During my Math 130 course we learned about the hisory of pie and it really helped me understand it better.
My question is... Because the science and math standards seem to be quite long how are teachers suppose to cover all of these without doing injustice to other subjects? Throughout college we have taken ART, DANCE, DRAMA, PHYSICAL EDUCATION, MUSIC and every teacher keeps saying that we have to incorporate these into the classroom or else the kids are getting the shaft. It just seems that there are not enough hours in the day
Like many have already blogged, science is forever changing, for this reason, the science standards have to be very broad and almost general to apply to these changes This is also important given the history of science, it is essential to have knowledge of this to gain a sense of what we know now and will learn in the future. I think it is important to know the history of math as well to be able to grasp what it is that we are trying to figure. Math concepts are more set in stone and like Raenelle mentioned, the standards are more precise and developed. Math standards have been broken down into 4 grade bands while science standards are broken into 3 grade bands most likely because each grade level is taught a different form of math such as, algebra, geometry and statistics.
I think that Erin made a good point suggesting how hard it is to cater to all standards in a creative, educational way but, also deciphering which to give the most focus and attention to. There is just so much content and so much that is critical to teach.
Science and math parallel each other in a lot of ways as too, both require analyzing, predicting, and formulating.
I guess the question that comes o mind after trying to type big words for the last hour is, How important are the standards and is it fair to make them? It just seems like every child learns in his/her own unique way and is it fair to limit or hinder that because we are to follow are strict book of rules?
After looking at both the science and math standards, it seems to me that both have one underlying standard that would fit into most lessons or activities. For science this would be the unifying concepts and processes standard, and for math this would be the problem solving process standard each of these standards appear to have a connection to one another. I also agree with Kevin and most of everyone else that one main difference between the math and science standards is that they break the expectations down into different grade bands. The math breakdown is a little more clear and specific, which is what Erin Barr also stated. Atleast the math expectations are much more developed. I think this specification would make it much easier on a teacher, I know that the math standards are much easier for me to follow. (That may just be me.)
I think it is fairly clear why the science standards incorporate history into one of the standards, in science it is always changing and new discoveries are being made. Students need to understand how we have made it to where we are and why science is important. With math sadly, new discoveries aren’t really being made and concepts aren’t changing so much.
My question which also goes along with Erin McGrath’s is, with so many standards how do we cover them all in such a short amount of time, while also covering all the other subject areas? Since this seems near impossible how do we know which ones to give precedence to? (I guess that was two questions).
The math and science standards encourage students to use problem solving, order, explanation, and measurement to find answers and conclusions. Technology is also emphasized in both of these standards. The math standards have divided the grades up into four different groups, P/K-2, 3-5, 6-8, and 9-12, while science has divided the grades into only three groups, K-4, 5-8, and 9-12. Like Sarah mentioned above the math standards are more concreate than the science standards because math is built from fundamental concepts and science is constantly changing and developing. I think that the history of math is interesting, but not important for students to know in order to learn math skills. But since science is constantly changing it is important for students to understand where the ideas and theories they are learning are coming from. My question is why are the math and science standards divided into different grade bands?
After reviewing our readings, I would have to say that math and science have many similarities within standards as well as content areas.
I noticed, as well as kevin, how the standards are broken down differently by grade levels. I believe this is because although math and science are similar, it takes different cognitive processes to compute this information , so certain ages need more emphasis on these two subjects.
The math standards are a lot more refined. As where our science standards do not have specific instruction or goals. I think that this is a proper way to handle the science standards, because this allows the teacher and class a lot more room to experiment and be flexible with the curriculum.
I looked through peoples posts and I found that I agree with Jen when history was brought up within the syllabus. I also was confused earlier but I feel Jen worded it perfectly by saying that science is always changing. Ever day we are making new history, and children need to see these factors in order to make their own comprehension choices. Math is more fact based and concept formed subject. Students need to concentrate on math to grasp concepts to lead to more understanding.
As for some similarities, some that struck me were how a lot strategies are complementary. They both use formula's, understanding, predication, some application techniques, and so on. I really feel that science and math have a lot of similarties within the actual content of the course. I have always struggled with math, and because of this I have also found myself struggling in science. If these two subjects could work together in a certain school, with similar strategies, I feel children could learn to master these two subjects faster.
All in all I have to say I enjoyed reading these blogs. People asked questions that i already had in my head, and then others answered before I could even agree on the question. I think I will learn a lot from this blog!
Standards for science emphasize the desired outcomes for students, but do not prescribe a curriculum. For math, the emphasis of particular standards varies across the grade bands. Like Sarah and Ryan mentioned, both Math and Science standards are similar in that they focus on students’ use of processes, reasoning, and problem solving. Science and Math standards are different in many ways however. The Science standard for unifying concepts and processes is presented for grades K-12, because the understanding associated with major concepts and procedural schemes need to be developed over a students’ entire education. The next seven standards are separated for grades K-4, 5-8, and 9-12. Each of the math Standards consists of two to four specific goals that apply across all the grades. The history of science is an important science standard, because it’s great for kids to see the role humans have played in helping us understand the world in which we live. I think it also shows them the importance of conducting good explorations, and coming up with their own conclusions, because there’s much to still be discovered. Like Kevin mentioned, the author stated, “Science reflects its history and is an ongoing, changing enterprise.” Science has played an enormous role in the development of various cultures, has greatly affected the world in which we live, and has much potential to change in the future. Although the history of math is no doubt equally as important and fascinating, I think the standards are more focused on the improvement of math in the future, rather than looking back to the past. As far as my question goes, I have to borrow Chris’ which was asking how strictly we will be expected to use the standards in each of our future lessons. Maybe by becoming more and more familiar with them over the years it will become easier to plan lessons with them as the focus. For now however, it seems quite overwhelming.
The math standards seemed a lot more specific to me, with five content standards and five process standards. I think math can afford to have such clear cut standards because a considerable amount of time is, and should be, spent on math. Science, on the other hand, doesn’t usually have as much time afforded to it in traditional curriculum. I felt the science standards are set up very nicely to help teacher integrate science with other disciplines, such as math. The math process standard of connections also helps connect math to other curriculum. I feel like the Unifying Concepts and Processes standard in science ties in perfectly with math process standards—within math, the reasoning and proof standard seems to mirror the evidence, models and explanations component of the science concepts and processes standard. Like Tara said, math and science have much in common and the standards reflect that. I think in both the math and science standards a child-centered approach seems to be favored. Problem-based learning seems to be a common theme.
The point about History of Science standard was brought up often. Although math doesn’t have a specific history standard, the math process standard of Connections would give the teacher an opportunity to discuss math history while fulfilling this standard. Science, which sometimes can be overlooked with current emphasis on reading and math, has the specific history standard to “provide many opportunities for integrated approaches to science teaching” (as the article states). Imagine studying vaccines—you could research and read about life during/before the Polio vaccine was discovered; you could learn about Jonas Salk. If you look at the history of a society and recognize possible problems or important issues they faced, such as epidemics, it often directly correlates to what scientists were developing. For some reason the inclusion of history into the science standards excited me, probably because science and history are my two favorite subjects.
After reading many of the blogs, I agree with Sarah in the fact that both sets of standards have students using problem solving and other skills to come to their conclusions of whatever problem they are looking at. Using this way of thinking works well for both science and math. Students learn more through problem solving than any other tool in math and science. I also agree with Kevin that the math standards leave more room for different types of teaching, not just the average cookie cutter way of doing things. Science standards are layed out for teachers in full detail. Also the history of science is so important to teach to the students, with science changing every second of every day children need to know where what they are learning about came from. This will give them a better understanding of how science works and how it is everywhere in our world. My questions are very much like Chris's. What will happen if as a teacher you refuse to follow these standards or only use them once in a while in your lessons? Who enforces that these standards are to be used in your everyday teaching and how do they evalutate or assess this?
After reading and comparing both the math and science standards it is clear to me that the two have both similarities as well as differences. I agree with Erin M. in the fact that the main emphasis of both is to guide teachers to teach and offer a comprehensive base of skills to their students. I also believe that both math and science standards really emphasize the underlying concept of problem solving. Another similarity that Julia, Ranelle, and many others also noticed was both the math and science standards central teaching strategies incorporate the use of analyzing, formulating questions, reasoning, predicting, and finding different methods or approaches to finding solutions. I agree with Ashley when she says both standards seem to emphasize the importance of how students are arrive at answers and less on the actual answer. One more quite obvious similarity is that both standards are divided into grade bands. On the other hand a distinction between the two is that the grade bands are broken up differently. In case not enough people have already mentioned this I will show you one more time just how the grade bands are broken up, since it was the first difference I noticed. In Math the standards are divided by P/K-2, 3-5, 6-8, and 9-12. The science standards are divided K-4, 5-8, 9-12. The division of the Math standards seems more logical to me, however the division of grade bands for the science standards seems to offer teachers a little more freedom. Also the math standards seem to be a little more clear cut, where the science standards seem to be a little harder to follow. It is great that the two standards overlap with similarities because it offers teachers the opportunity to easily intertwine the two subject areas. Although the similarities are beneficial, the differences between the two standards give each discipline a sense of uniqueness and importance.
I do believe like many others understanding the history of Science is of great importance. I know that the history is incorporated into the standard because the nature of science is forever changing an ongoing, and to truly understand anything in science students must have and understanding of how it came to be. Science continues to progress and change everyday so it is important for students to know how it has developed and brought us to where we re today. I do however agree with many others in saying that I think the history of Math should be included in the standards. I think it would be very beneficial for students to see how mathematics has developed and changed the world we live in today.
My question after reading the standards is, when writing or creating a new lesson should you always choose which standards you want to address first before writing the lesson, or is it okay to begin creating your lesson and then see which standards the lesson meets?
Well I certainly hope I'm not the last to be posting at this point because now I'm really "that guy" who gets to say things like I just said. Anyways after reading the standards and then perusing everyone's posts I have to say for the most part, ditto. Both sets have emphasis on problem solving, reason, and analysis. Math and Science have many overlaps; I think that for the most part it would be hard if not impossible to have one subject without the other so this makes perfect sense. The fact that they are broken down into different grade bands does not suprise me though (I hope by now everyone knows the break down). The science standards are a little broader while math standards get a bit more specific going into algebra, geometry, and so on. I think Jeff asks an interesting question in how do we incorporate all these other subjects we've been told and use them in math and science. I find that having science standards be more broad that it does leave a bit more leeway for incorporation while math is a bit harder, at least at first glance. Science's history is ever changing so having its history included isn't suprising to me at all. While I'm not all that suprised that the math standards having nothing about teaching math history I don't agree that it is not needed or unimportant. I like that Norm talked about M.C. Escher and his use of geometry in art. I do think that math is overlooked in many ways for being boring and showing students his art may be a way to spark excitment in math.
I agree with Erin M in pointing out that, "none of the standards are asking students to memorize and regurgitate information." Math has been plagued by memorize and test forever in my life and that has put a taint over the subject for me. I don't think that I am probably alone in this, so having the standards keep open teaching options will, hopefully, ensure that students get a more positive outlook on math,in particularly. Because while science could be hard at least you got to experiment with stuff that was potentially dangerous. I don't remember being all that frightened that a word problem might kill me. Well... I take that back but for totally different reasons. Anyways, I do have the same concerns about NCLB and the math and science standards. What kind of effect do the standards have on the emphasis in math and science in our schools? Hopefully at some point this question will be answered for us.
While the math and science standards seem similar in their structure (both organized into subcategories and grade bands), I feel that they differ quite a bit in their focuses. This is somewhat related to what some (Jen, Julia)had said about the math standards being more broad while the science standards give a more detailed description of what to teach. It seems that the science standards focus on the information that will be taught, while the math standards focus on what the outcome of the edducation will be. Although both subjects claim to have a purpose of teaching kids to analyze and problem solve, I don't think that the science standards reflect that as much as the math standards. While the math standards cover concepts and ideas that students should be able to understand in order to problem solve and analyze information, the science standards cover much more specific information, pointing out single science concepts such as population growth or transfer of energy. However, (as noted at the bottom of the science standards page) the NSES is moving toward a change of emphasis, moving from teaching "scientific facts and information" to a broader understanding and integrating of "concepts and developing abilities of inquiry."
I definitely agree with what Sarah and Ryan said about the history of science. Science has been developing and evolving throughout history. Knowing where science concepts and theories originated from is all part of the process of science investigation. I feel that the history of various mathematical concepts could also be a great support system when teaching them in the classroom. So many students struggle with the "whys" on math, and I think that sharing where many of the mathematical concepts came from would help explain some of the reasoning behind the systems.
There are so many different sets of standards out there, how do you decide which set of standards to follow? Is it up to your school administrators? Who monitors your curriculum as far as the standards you cover?
Sorry so late, but I have been having problems accessing my account. Either way it has been nice getting to see EVERYONES blog before creating my own. The similarities I noticed were the same as most of my peers. The main one I saw was the idea that students can create their own knowledge base, rather than a techer centered approach. Like Chris said, this allows students to discover information on their own. Like we discussed in class today it is very important for kids to not only understand the concepts, but the process as well. Becasue there are so many advancements in science, the history asspect of it becomes very important. I believe it is important for students to compare and contrast the beliefs and ideas that we had in the past with the ones we have today. Not to say that the history of math is not important as well, but at the moment I am kind of drawing a blank as to what that might be. The question I had was why are the science grade groupings so much different for the math?
This is the second time I’ve posted for this blog: apparently my originals have been lost somewhere in space….
The National Science Education Standards (NSES) groups its curriculum standards according to eight different branches of science. As Kevin has pointed out, the NSES breaks down the expectations of the content standards by grade bands, which include K-4, 3-5, 5-8, and 9-12. The National Council of Teachers of Mathematics (NCTM), on the other hand, builds their expectations of the curriculum around ten standards: 5 of which are content standards, and the other 5 are process standards. Like the science standards, the math standards correlate with specific grade bands, which include P/K-2, 3-5, 6-8, and 9-12.
Although the math and science standards share the same educational approach of problem-solving, one of the main differences I’ve noticed between the standards of the two disciplines is how and when material is taught to students. As many of my classmates have pointed out, the science content standards appear to be more broad and flexible regarding age and grade level. The math standards, however, cover specific times when certain material is appropriate to teach in the classroom. As Dustin noted, a science teacher could teach students about magnetism, whether they were in kindergarten or 8th grade. On the contrary, mathematical concepts are not so easily adaptable to the range of grade levels. Students wouldn’t be able to understand probability or data analysis without first knowing their numbers and operations. Mathematical understanding builds on a foundational knowledge of math concepts, thus chunking math education in a sort of sequential order (easy to difficult, basic to complex).
Perhaps the reason the NCTM doesn’t include the history of math like the NSES includes the history of science is because science is forever changing, making prior scientific beliefs, hypotheses, theories, etc., important elements on which to base further scientific exploration. Therefore, it may be of higher importance that the NSES include historical scientific content/knowledge within students’ education. Take, for instance, Julia’s reference to Pluto as the 9th planet in our solar system. As far as science is concerned, poor little Pluto is not considered a planet anymore, but rather a “dwarf planet,” whereas, in mathematics, 2+2 will always = 4. (The Pluto change makes me sad because I know this great School House Rock song about the order of the planets.)
My question is: How do you incorporate Indian Education for All into the science and math standards?
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