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 blogging in the K-8 classroom.
This week you have been exploring the national standards for each of your respective methods courses. For this blog, we want you to do a comparative analysis of the math and science standards. For example, 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?
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.
Next week we will be splitting into your grade band learning communities.
Also, for next week's science methods class, please bring your copy of the National Science Education Standards to class or print out a copy of chapter six and bring it to class. Thank You!
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The NCTM and NSES standards share many similarities. Both sets of standards emphasize content area that students should be able to know and understand, and the processes in which this content should be taught. While the content of the standards are different, both focus on students moving from inquiry to understanding and being able to demonstrate the nature of a specific subject in each subject. The math and science standards emphasize action verbs such as analyze, apply, specify, select and use, and develop to have students actively participating and mentally engaged in developing an understanding for concepts. Both standards deem connections, communication, problem-solving, representation, and reasoning as important processes for students to formulate questions about concepts, use data, explore, and draw conclusions. The standards in both subjects also emphasize that the standards are interrelated, not isolated parts of science or math. All the standards should work toghether and be addressed as a whole and complete way to teach science and math. Finally, both standards contain benchmarks for certain grade levels and concepts to cover the entire k-12 education of students.
The are several differences in the NCTM and NSES standards. The math standards are more specific, in that they address specific material and ideas in each content area (for example, scatter plots in data analysis and probability). Also, the math standards divide their benchmarks into four categories (k-2, 3-5,6-8, and 9-12) instead of three for science, so they are therefore more specific. The NCTM standards are also more specific in that they have seperate standards for the content and processes for math, while those two are imbedded together in the science standards. I also noticed that the math standards do not contain a section for the history and science of math,unlike science, as perhaps this is not such a vital component in mathematics.
The central teaching strategies for teaching math and science are consistent and essentially the same. Both ask teachers to use an inquiry-based approach so students are actively participating and constucting knowledge and understaning from experiences and experiments they perform and often create. Both subjects incorporate the processes of creating connections, communication, representation, problem-solving and reasoning as vital components of how teachers should teach these subjects. Both standards want students to be using "action verbs" to explore concepts in math and science.
The standards for science and math are very similar in that they are fundamentally trying to get teachers to teach in a way that the students are able to learn concepts through many different teaching techniques. Both sets of standards are driven by the idea that all students learn differently, therefore they need to learn in their own ways, creating their own conclusions and tying the information to their own lives and experiences. The standards are inquiry-based, asking students to explore the concepts through experimentation in order for them to be masters of their own knowledge and learning.
I agree with Bryn that the science standards are more general and vague, while the math standards are more specific and focused. It seems that the science standards really beat you over the head with the idea of inquiry-based learning. Almost every standard states that students must learn through inquiry, but doesn't necessarily state what they should learn. The math standards are more specific in that they state certain content that needs to be taught (algebra, geometry, communication, connections, etc.)
All of the standards for all of the content areas are interrelated. Teaching one subject relates to another subject. No content area stands completely alone. Areas of learning should be tied together so that students can recognize the common themes of all learning. Science has to do with math, and math has to do with science. They both relate to language arts, which relates to art in general. And so on and so forth.
Students must explore learning through their own inquiry and experimentation (with the guidance of the teacher) so that they can create their own understandings. It is this process of learning through personal understanding that the standards are trying to emphasize. And although they state this purpose a little differently, the main focus of both the math and science standards is for students to learn through inquiry and personal experience.
The math and science standards are alike in many ways. They both show expectations of what the students must know by building new knowledge through problem solving. Children are expected to gain knowledge from what they already know in both the math and science standards. They also both focus on keeping the children in an engaged classroom where they are making sense of the information and not just learning it. However, the science standards are very general. They still touch on six different areas of science but they leave the option open on what to teach. The math standards are pretty focused on the different topics that are to be taught. ex) algebra, geometry, measurement, etc... Another difference is that the science standards all ask the students to be able to demonstrate different science concepts while the math standards are broken into content standards and process standards. The science standards have already incorporated both the content and processes. These standards are alike in some ways but different in others, but they both use communication, reasoning, and problem solving to gain new knowledge from what is already known.
I think it is very important that Scott pointed out how all content standards are interrelated in the fact that every subject is connected. You can't teach science without at some point refering to math, literature, history, etc... It's so much easier to teach something as an integrated unit instead of trying to teach every subject seperately.
As the previous three bloggers attest, the two subject areas, science and math, overlap in the objectives of their content standards. Bryn does a good job of speciying the overarching goals, and the concepts that drive teachers towards these goals.
The most interesting aspect of the standards, overall, is the inquiry process. This new language opens a new way for teachers to stimulate the energy in the classroom and the input from the students. Without reform language incorporated into the math and science standards, these subjects would still be operating under the old school systems of drilling, rote memorization, worksheets, lecture, and the like. Both subject areas have been expanded to foster real thinking and exploration, with the understanding that when students conprehend on a deeper, more connected level, they retain more, learn more, and are excited about school in a more personal and connected way. Knowledge becomes something they relate to, instead of having to spit out what was pushed into them. These reforms have opened up academics in a new and inspiring way, fostering a true love of learning, as opposed to getting through another grade.
The modernization of the standards is a postive aspect for both math and science, though the science standards could use a bit more fleshing out. The math standards are extensive, draw connections, and cover all the bases without fail. The science standards are more brief and concise. Perhaps this is a good thing, actually, as I find reading and re-reading standards, no matter how enlightened, eventually causes a dull droning in my mind. The repetition of format and the slight variation of goals doesn't inspire lesson plans and activities. It becomes a list of obligations, important, yes, but also redundant, at least to me. So, I guess I am torn between the indulgent quantity of math standards which dot all the i's and cross all the t's, and the simple, but expansive, approach found in the science standards. Maybe this exemplifies the two subject areas. I would point out though that science relies heavily on inquiry, while math demands varied abilities: understanding, computing, representation, analyzing and applying. Science hammers home inquiry and demonstration.
Wow, I am impressed with what my classmates have already posted! I agree with Jennie, it is interesting to me how math has separated the content and process standard (although if you look at Montana state standards they are integrated)and science has combined them.
I think for me, the most striking similarity is the focus on constructivism and relational understanding in order to help students become problem solvers, not just students who can work thru and memorize equations. This student centered approach, instead of a teacher centered approach, allows students to construct their own meaning and leads to "rich understanding".
I agree with Bob (Crash and) Bryn, when he spoke of the difference in science bringing in the history content but noting that math did not. Both subjects have historical content that have lead to new pedagogical ideas, so it is interesting that science specifically focuses on this but math does not.
All three of the previous posts pointed out the vagueness of the science content standards compared to the math content standards. I have two thoughts on this, 1: the math content standards could be considered vague as well because you could ask, well, what is all encompassed in the content standard of algebra? I think, maybe, many of us have already created the necessary relationships in our own minds about math that these concepts are easier for us to wrap our brains around than some of the terms in science? Feel free to help me think thru that thought...
and 2: again back to the MT state standards (realizing not all of us will teach in MT, but I would think most state standards would be similar...) I noticed that the MT state standards have outlined specific grade standards. For example: grade 3 should be able to "Recognizes and describes Earth's features, illustrates changes of
those features. Recognizes and describes changes in weather and
seasons. Identify objects in the sky. (e.g. moon, stars, sun, planets)" To me, this gives a specific idea, without telling you how to teach it, of what the standard is that needs to be met. Which brings me back to what I think is the most striking similar feature of both NCTM & NSES - constructivism. This student centered pedagogical approach is meant to meet the learning needs of the students (allowing each learner to construct their own meaning) as well as allow the teacher to create an environment that will foster this rich understanding as well as stay accountable for their students reaching the standards.
Both the math and science standards emphasize the need for students to learn procedural and conceptual knowledge. This goal sticks out the most to me because I have experienced the lack of procedural knowledge accompanied by conceptual knowledge in my own education. Both subject standards encourage students to be active in his or her learning experiences, and include “reasoning” or an “explanation” of the conclusions students discover and create.
I do agree with most of what Bryn and Scott wrote about the subject standards including problem solving being included in both standards and the content in the standards being interrelated. I would like to add that, overall, the science standards are more general, however the standards do mention a few specifics like evolution (biological, earth etc.) and environment (quality, changes in).
Both subject standards include process and content standards (which Jennie also mentioned). In the science standards there exists a “unifying content and processes” portion. The math standards do not have a category like that. The math standards also include principle standards like assessment and technology. Science has an actual section of “science and technology” standards. I agree that the math and science standards are quite similar with a few differences in specifics like geometry and algebra. Further, the two subjects must be related in several ways, because math is a science as stated in the text definition.
I agree with the evaluations of the NCTM and NSES standards by Bryn, Scott, and Jennie. I believe that they are similarities between the math and science standards. Both establish what students should be able to accomplish at designated bench marks. This assists teachers in knowing how students should handle new and existing material. Although the subjects are different, both sets of standards focus on inquiry based learning. They stress that students need to ask their own questions and find solutions to those questions rather than following a list of procedures to find a predetermined “answer.”
The standards vary as well in that the science standards are much more general. The math standards concentrate on specific material while the science standards concentrate on vague ideas. Furthermore, the math standards are divided into content and process standards. The math standards are broken into four grade brackets while the science standards are only broken into three brackets.
I agree with Scott that the content areas are interrelated. Each subject is related to every other subject. Language arts are in math, science, and social studies. Science utilizes math to analyze data, graph results, and more. I like Jennie’s statement that an integrated unit is much easier to teach than individual lessons in each subject.
The math and science standards have similarities and differences. For example, math has both process and content standards (five of each). In other words, there are standards on what to teach and what methods (processes) to utilize. Science has eight content standards. One of the content standards is "science as inquiry." For me, this is similar to the math process standards because it refers to HOW to teach/ what methods to encourage.
Both the math and science content standards are designed to outline what "students should know, understand, and be able to do" in those areas. They are broad categories so that local desires and individual teachers can still have control over the curriculum. They are geared to providing students with the knowledge they need to understand the world and compete economically internationally. The content standards reflect what math and science is used in today's society.
The math and science standards are different because they do not match up directly. Math has five content and five process standards, whereas science has eight content standards. However, both fields have been reformed to emphasize student directed learning. Kids are supposed to ask questions and solve problems with the 'guide on the side' instead of the traditional 'sage on the stage.’ This is the case for both math (as described in the textbook as the five shifts in classroom environment) and science (with the emphasis on inquiry). The national math and science standards and suggestions are consistent in that they recommend more thought, action, and direction from students. These ideas were created in the belief that this training would make kids better thinkers and problem solvers.
The problem solving/ inquiry approach requires action from the kids, which Bryn R elucidates when she discusses the action verbs used in math and science today (analyze, apply, etc.). She also adds that there are grade benchmarks, although each content standard should be taught in each grade in a different way.
Furthermore, I agree with Tara that the science standards seem much more general. Surprisingly, the science and math content standards do not refer to teaching math in direct relation to science, or vice versa, although they are clearly interrelated.
Melissa reminds us of how science and, especially, math used to be taught. Worksheets, practice math sets, and detailed lab instructions dominated the classroom.
My mother used to make me do math flashcards at the kitchen table, but that was after I understood multiplication. Doing some boring drills AFTER the conceptual understanding takes place may have some use.
The standards for science and math are very similar, yet they both have their own characteristics. In comparison, they both emphasize inquiry-based learning. For the math standards, action verbs are used in the expectations to convey that math should involve exploratory learning. And the science standards, as Scott mentioned, really uses the word inquiry to the point of nausea. Also, both standards put the expectations into grade level categories. Each category provides an organization of concepts that are to provide knowledge and comprehension that will improve a students scientific/mathematical literacy.
The one thing that I noticed that was very different between the two standards was that the math standards don’t include a history standard. I have to wonder if it should since the history of math is important. I think that children should be required to know about the significant people/moments in history (Euler, Einstein, etc.) that helped evolve mathematics and bring us to where we are at today.
I agree with Melissa that that the most interesting aspect of the standards is the inquiry process. Inquiry-based education has changed math and science in such a positive way that, not only is it better for the students, but more interesting and engaging for teachers. Great comments everybody! WOW!
After studying both the NCTM and the NSES standards, it becomes apparent that there are similarites in the two sets of standards. They both focus on moving away from a traditional way of teaching, a teacher-centered approach, and toward a new, student-centered approach. This "shift" emphasizes inquiry as a means to understanding the concepts and procedures of the respecive subjects. As Leslie also mentioned, this stands out, in a good way, to me becuase of the lack of procedure based teaching and learning that took place during my math and science education. The two sets of standards also both account for the fact that each child learns differently, and that they, through this student-centered apporach to teaching, should be able to find their own effective way to learn, and bring thier own experiences to the classroom (as Scott mentioned.) The NCTM and the NSES have both set up benchmarks spanning from grades K-12 for math and science, with different emphasis on certain standards in certain grade levels.
Though there are many similarites between the standards for math and science, there are also some quite obvious differences. The first thing that I noticed, is that the NCTM has separated process and content standards, while the NSES has just content standards. This tells me that the math standards are more specific, as almost all of the previous posts have mentioned. Also, there is not history of math included in the NCTM standards, while the history of science is emphasized greatly in the NSES standards.
The approaches to teaching to both of these standards is very similar, though there may be different objectives in math and science. In math, there almost always is a right answer, and by teaching to the standards a teacher hopes to get students to come to thier own way of finding that one right solution. Teaching to the science standards on the other hand, hopes to get studnets to realize that science is a "different way of knowing" and that there isn't always a right answer. Though there are different outcomes when teaching to the standards, the "way of teaching" that is recommended is very much the same. Both standards aim for students to be active participants in the learning process, and as Bryn mentioned, get teachers to teach students to "use action verbs to explore math and science."
The NCTM and NSES standards are very similar but yet very different. They consensus between the two standards is that as teachers, we need to teach each individual student and their needs to create and environment where they can test, create experiments and evaluate their own work with minimum teacher interaction. They are in a sense, beginning to teach themselves (as well as other students in the classroom) and ask questions that they would normally rely on the teacher to answer.
I agree with Scott when he says that the science standards are all about inquiry and having students build and test their own experiments. This is one way that the two National Standards are different. On the other hand, they are different because the math standards are more specific in what each student will learn and what they should be doing and learning at each grade level. I feel that it is a great way to show a teacher where students need to be at with a direct approach to the standards but it doesn't give us much wiggle room for our own ideas and experience.
For the most part, these two standards go hand in hand and fit well with each other but I am sure with more independent study and use with the standards, I will gain a better understanding and develop my own opinion regarding the Standards and how I decide to teach and incorperate them!
Everyone so far has pointed out that there are similarities and differences in the NCTM and NSES standards. The first thing I noticed when I sat down to compare the two sets of standards was that both mentioned a particular standard that served as a foundation for all the other standards to build upon. As soon as the word foundation popped into my head, all I could think about was the house analogy. The foundation and framework must be laid down before the detail can be added. It's not possible to hang curtains when there is no wall. But, in all seriousness, the standards that seemed to be the foundational components in each were: Numbers and Operations in Math, and Unifying Concepts and Processes in Science. Without knowing the basics provided through these standards it will be difficult, if not impossible, to move forward on to more challenging content.
There were other similarities in the standards that I noticed. Inquiry and the ability of students to reason through their conclusions is laced through both sets of standards. Also, both emphasize the importance of the teacher as a "guide on the side" to allow students to explore and reach their own conclusions.
Obviously there are some differences in the standards because science and math are not identical subjects. I found the variance in the benchmark grades to be very interesting. I am not sure exactly why they are different. Is there more logic behind them, or was it an arbitrary decision. I find myself doubting the latter. Quite a few people have mentioned the lack of history in the math standards. Jessica noted that she though it important for history to be included in math. I am sitting on the fence right now with this. On one hand, history seems unimportant to the process of learning math (e.g. Why do we need to know about the time and life of Fibonacci to know and apply his sequence?). BUT when I think about it this way, it seems to demerit the history of everything else. Does anybody else have a thought on this that may help me decide one way or the other?
The similarities of the math and science standards are many. First, the standards are focused on student communication and investigation. Second, the standards are broken into content areas, for math content is broken into numbers and operations, geometry, measurement, and data analysis and probability. Science content includes physical, chemical, environmental, earth, and cultures. Another similarity, as Tootsie pointed out, is the unerlying constructivist view of students using prior knowledge to develop deeper understanding through communication and investigation.
The differences of the math and science standards are less obvious to me. Bryn points out the some excellent differences that I initially did't recognize. Specifically that math doesn't include the history and science of math where science does. I think this is because math has concrete rules or formulas developed and science is more abstract and ever changing with new technology. Another difference is the benchmarks, again as pointed out by Bryn, math has four and science has three.
The central teaching strategies for both math and science are inquiry based with teacher facilitation. The theme to allow students to expand on their previous knowledge through communication and exploration leads to students becoming responsible for their own learning. Learning math and sciece can actually be fun when students can share their thoughts and ideas in a safe environment as established by the teacher. The most impressive thing for me about these standards is this safe, inquiry based environment. Learning is more than regurgitating formulas and facts, it is about listening and respecting other students opinions and developing new ways of solving problems. This in turn develops students into more productive citizens through the use of social skills such as respect, listening, and collaboration.
I agree with Melissa, when talking about standards, they are important but it can sometimes feel like a daunting task. As many people have already said, the Math standards seem to be more detailed using math verbs like; analyze, specify, apply; to describe the abilities and skills students should have. The science standards emphasize inquiry repeatedly as Bryn and Scott mentioned.
In a way many of these standards can be combined because of the processes used in both math and science. It will be easy to create lessons that cover both math and science standards especially in problem solving and using the inquiry process. I do think that inquiry is an important concept to emphasize accross all content areas. I believe we should teach children to ask questions about the way things are, by questioning things they learn instead of just accepting what they are told, they will be stronger more independent thinkers.
The NCTM and NSES standards have many similarities. Both sets of standards focus on the learner, and that each leaner learns differently. As Scott mentioned both standards are trying to get educators to teach a variety of teaching techniques to help students develop and learn concepts. By the standards be based on inquiry, students are allowed to focus on making sense of the information and not just learning it. The NCTM and MSES standards also have benchmarks for certain grade levels (K-12). I also agree with Bryn, Scott, and Jennie that the standards are interrelated and are constantly connecting with other subjects, history, literature, math, science, etc...
There are also many difference between the NCTM and NSES standards. The science standards have a history standard while the math standards does not. Also, as Therese mentioned science does not have a separate set of process standards, just eight content standards. Another difference that I noticed and many of the bloggers have already mentioned, is that the NCTM standards are more specific, by addressing specific ideas for each content and processes in math.
The teaching strategies for math and science are very similar. They both focus on students being actively engaged in the learning process. This allows students to explore and learn in their own creative ways.
also agree with the rest of my classmates, in that both the NCTM and NSES standards are similar. Both sets of standards stress inquiry and questioning to lead to comprehension. By asking questions and researching/experienceing a lesson kids will gain a greater understanding of the information. Both stress the importance of making connections between new material and previous knowledge to create a deeper comprehension and better future application.
The NCTM standards are generally more specific in their titles, but the NSES standards are more specific in their benchmarks. I feel that the NCTM tells a teacher what topics to teach and the NSES standards tell a teacher what a student should be able to demonstrate.The NSES standards also include a history portion, which I think that the NCTM standards should add. We cannot fully understand the process of math if we do not understand how we came to learn these concepts originally; as well as to see how mathematics have evolved over time as new formulas and theories have been sugested.
As teachers we need to let learning be more student lead, having the teacher guide learning and supplement the materials. We need to foster a sense of community within our classrooms for students to be able to ask questions, make mistakes, and learn from their trials. We also need to stress the importance of making connections between previous knoweldge, as well as with other subject areas. Students need to be able to see the similarities in math and science and be able both math and science skills together to solve problems. Both sets of standards apply the action verbs, and thus the subjects work in these actions together.
For me, the national standards for mathematics are a little bit easier to understand than the science standards. However, both standards provide excellent assistance for teachers who plan on teaching math and science K-12. Both standards emphasize that they are not to be confused with a curriculum, but rather as guidance for what is expected of the students. One thing that I think is very important is that both standards place more emphasis on understanding the concepts and developing the ability to use those concepts, and less emphasis on knowing or memorizing the facts. Both focus on students using reasoning, logic, and evidence to prove theories or answers, rather than solely getting answers from the teacher. Jennie Folkerts mentioned how children are expected to gain knowledge from what they already know, and I agree. Students in both math and science, are expected to be able to take what they already know, and build off of that. If teachers understand what students already know and need to learn, then they can respectively challenge the students to grow and develop more knowledge, understanding, and comprehension.
One difference I noticed between the two was that the math standards focused more on the classroom being used as a community and less of a collection of individuals. The science standards didn’t seem to mention such things. Bryn described the standards for science to be broader than the math standards, and I do have to agree. Math standard appear to be more specific and detailed.
After reading Scott’s blog, I realized that all of the standards for every subject are interconnected. I like the fact that all areas of learning can be tied together. A teacher can create and teach a science lesson using math content standards also. That’s great!
Wow! It is going to be hard to say what I have to say without saying what everyone else already has. Everyone so far has done such a great job comparing the NCTM and NSES standards.
After looking at the NCTM and NSES standards, it is obvious that they have many similarities. Both sets of standards show action within the classroom. They show this by developing, applying, specifying, and analyzing. Both sets of standards also stressed the importance of inquiry and the ability of students to reason through their conclusions. Also, both emphasize the importance of the teacher as a "guide on the side" to allow students to explore and reach their own conclusions.
I also noticed, as did Bryn along with many others, that both sets of standards showed connections, communication, problem-solving, representation, and reasoning to be extremely important for students to use when trying to come up with an end result. I think it makes sense that these two sets of standards are so similar. We have read in the text and also heard in class that math is a science. It is also very obvious already through experience this semester alone that science and math are similar. For example, we have already used problem solving in both classes!
Though these two sets of standards are similar, there are also a few differences. I agree with Bryn, Scott, and Leslie that the science standards are a bit more general than the math standards.
I also found that the math standards do not include history like science does. When I look at math compared to science, it seems to me that history would be integrated with math before science. History of math has been recorded without as much debate, where as SOME of the history of science is extremely debatable. I understand that science is not right and wrong, it is based on conclusions supported by data and research. My personal opinion is that history should be in both science and math standards.
The bench marks are also a difference in the math and science standards. As pointed out by Bryn and Bob, math has 4 and science has 3.
As has been mentioned by several other postings, the Math and Science standards have strong correlations in how material is presented to students. The content in each varies, of course, but the idea that the students are in a place of self-discovery and are no longer "blank slates" carries on as a theme throughout both standards. Bryn's post clarified this well when she pointed out how each set of standards utilizes "action verbs". The students are participants in their learning and no longer bored regurgitators of disconnected facts fed to them by a teacher.
The differences between the standards have more to do with organization and content covered than they do with approach. Math covers math, science covers science. As was mentioned in other postings, the math makes a point of being more specific in how it divides and specifies its content. The science, however, makes a point of addressing the history of science.
In my opinion, the standards continue to provide a strong guiding focus for what we need to achieve as teachers. Their real strength is that they imply a new, involving method of approach to their teaching strategies. I feel that both the standards are consistent in how they want teachers to approach the material (and also, in my opinion, more effective in their methodology than when I was taught in school).
I have to start by saying, I think I learned more from reading the peer comments about the math and science standards than I did from examining them myself! The idea of blogging is starting to grow on me. There were several items mentioned that I would have missed if not for reading what other people had to say.
The standars of both math and science are very similar in teaching approach. Having students active and responsible for their learning is an idea that I love. (How many times did I pack information into my brain just to forget it after taking a test?) Students need to be able to problem solve and reason out what they learn so they are able to retain the information we provide.
Several people addressed math missing a history standard. (Kim, Bob, and Bryn) Personally this does not bother me,but as a teacher I think my students could benefit from some form of math history. The history could even provide students a better understanding of why math is so important in our daily lives.
I did find that the math standards were more specific and direct. This gives a more strict approach to what a teacher should teach, however I don't think it limits creativity in lesson planning.
The standards conflict in some areas but they are consitant in their approach and they both relate to one another. The standards make it easy to integrate subject matter.(As Scott and Jennie pointed out.)
One last thought to throw out; even though the science standards lacked a seperate set of process standards the math process standards can easily fill in for science and other subjects.
It is very clear that the content standards for NCTM and NSES are very similar. Both standards really stress for the Constructivism approach to be used and allow children to design, communicate, connect, reason, etc., in order to learn. This form of learning is perfect for science and math because it gives children a chance to really explore topics they are interested in and lets them dive in and not worry about making a mistake.
I agree with Tootsie about how the student centered approach is providing great experiences for children. I remember sitting in the classroom trying to learn things without ever getting a chance to have a go at things myself. Melissa reflects upon this and it really shows how quickly teaching has changed over the past couple decades. I remember he experiences that stick out the most in my mind are the ones where I was actively involved and having a hands on experience. Through many of the things we have read studies show that the student centered approach has been more successful and the standards do a good job of trying to get teachers to teach this way.
I think Scott hits the nail on the head when he says, "All of the standards for all of the content areas are interrelated. Teaching one subject relates to another subject." We are teaching our children so they can be functional, responsible adults int he world and every day we are faced with many things that are interrelated therefore it is best that we let kids make the connections to the real world so they can see the connections clearly.
As the previous blogs have mentioned, the NCTM and NSES standards have quite a few similarities.
First of all, both standards are guidelines as to what students should know and be able to do by a specific developmental age. Both sets of standards also emphasize that the separate domains within the subject should be connected and interrelated, so students view the subject as a whole instead of a bunch of separate ideas that don’t relate. This idea goes along with the statement Jennie mentioned about how children gain knowledge from what they already know. I concur with the majority of the other blogs, that both the NCTM and NSES standards suggest having students learn through an inquiry process where students come to understandings and discoveries on their own, with the guidance of a teacher.
Even though the two sets of standards are quite similar, they also have some differences. As others mentioned, they are different in that the NCTM standards have standards for both the content and process, while for NSES there are only standards for the content. Because of this, the NCTM standards are more specific with more detailed ideas at to what needs to be taught at each grade level. They are also different in that the NSES seem to focus more on the inquiry process, whereas for the NCTM standards don’t mention it as often even though I believe it is the main focus and goal for how math should be learned.
Well, just as everyone else has stated, I also agree that the NCTM and NSES standards have both their similarities and differences. They both focus on what students need to learn, understand, and do. Both give specific content areas that need to be met. For example, algebra, geometry, measurement, ect. (for math) and physical science, earth and space science, life science, ect. (for science). Within each of these content standards are brief goals or expectations for specific grade areas. Also, both the NCTM and NSES standards incoporate an emphasis, like Leslie said,on conceptual as well as procedural knowledge. I feel this is very important because it recognizes the fact that students need to understand why or how something works the way it does before being told or shown without having to think about the how and why.
Though there are these obvious similatities, which I feel are good because as Scott mentioned, science and math are connected, I feel that some of the differences are more apparent to me than anything. One of these differences is that as Helena said, only the math standards have processes that are separate and not incoporated in like that of the science. The science standardas simply state students need to have the ability to do something, but do not mention what the ability is like the processes of math. Also as almost all of my classmates pointed out, the math standards are more specific.
However, I feel that both do allow for interprutation as to what should actually be taught in terms of the very specifics, but math is the most specific by far. Math is also broken down into 4 different areas of grade levels while science has 3.
Overall, I feel it is important to be aware of both the differences and similarities because it is important to find ways to link the two subjects. It is also important to pay attention to the fact that both focus on an inquiry method and there is obviously a good reason for doing so. Using inquiry teaches students to think for themselves and that they can figure problems out on their own, which in turn leads to better learners.
Once again :) The NCTM and NSES standards are both similiar and different. They are different in the number of standards and benchmarks included in each subject. They are similiar in their focus on constructivism and relational understanding.
Like Melissa, I find myself drifting off after reading the standards and benchmarks for more than 10 minutes. They are very important and should be taken seriously, I just have a hard time concentrating after too many, "students, through the inquiry process" or "students will demonstrate understanding". (Just a personal problem of mine, not neccessarily a critique of the standards!)
I believe, like Helena, that the both the NCTM and NSES standards are written as specifically as they can be so as to remain broad enough to still give local districts some choice in their curriculum.
Leslie and Therese mentioned that their schooling lacked procedure based knowledge. My experience, as I remember it, was different. I feel that I was too often taught procedural knowledge rather than conceptual. During school, as a result, I strugged with solving problems that did not fit the "formula" perfectly.
I think it is fantastic that students are now being encouraged to discover their own way of solving problems and answering questions that makes sense to them.
The NCTM and NSES standards are similar in that they emphasize the content areas that students should know and understand. The math standards are more detailed and build on a foundation of knowledge students learn as they progress through school. The science standards are inquiry based on procedural and conceptual learning that are unified throughout the educational experience. These are obtained by learning skills that include observation, inference and experimentation.
I agree with Destinie that the standards focus on the learner and that each student learns differently. I also agree with Scott that we must use a variety of techniques in both math and science to help students learn the concepts that are needed to build on future understanding.
The math standards are much more specific about what should be taught at each grade level and are also divided into different process standards. The science standards are not as specific but include a category about the history and science of nature. Many of my math teachers added short history lessons to help to understand how important math is and the different ways it has been used throughout time. I will try to incorporate this idea with my classes.
I agree with my classmates that the content standards are connected and that science can't be taught without integrating math, history, literacy, etc.
I agree that both NCTM and NSES sets of standards are very similar, and have to agree as well that they have differences as well. I like the fact that they both promote inquiry, that they unify concepts and processes, and that proof is required (or a way to measure), for both. The standards set a guideline for the important processes students need to have to base their inquiry upon, and processes that they need to give proof of their hypothesis. With math and science alike, there is system, order, and organization.
Math standards are more specific, while science seems vaguer; however, I found more similarities than I found differences. I liked what Melissa A. said about the most interesting part was the inquiry process because it leads to discovery. Using verbs such as explore, investigate, predict, describe, formulate, justify, and explain are all good terms to build excitement for learning in these areas. Bryn also gave a good umbrella overview of both sets of standards, and bravo to everyone for their excellent input.
I don’t know about anybody else, but I really liked the clip we watched in Math yesterday with Kay Toliver teaching and her doll Samantha. What a great way to engage these kids in a subject area that is mostly ‘dreaded’ by some kids. I saw that the children were engaged in everything she was doing with them, and she covered the content standards for math in her class.
Alright, so I just spent the last half hour writing my blog only to have my computer crash. Not very excited that I have to redo this. Anyhow, I just want to tell all of my classmates that you have all done an awesome job with your comments. I have learned so much from reading everyone's posts, moreso than I would have learned if I was just to examine the math and science standards myself. I have to agree with Nichole that this blog thing is starting to grow on me.
To begin my discussion on the math and science standards, Therese makes a very good point when she states that both subject area standards are written in a way that shifts the learning process away from a traditional teacher centered approach to more constructivist student centered approach. In my opinion, this is due to the fact that in our rapidly advancing society the skills required to keep up, such as logical reasoning, abstract thinking, and problem solving, are just not taught well enough via a teacher centered approach to schooling. It just not enough to have teachers spoon feed their students information. If students want to find out something, the internet and other informational sources are available at their fingers 24/7. Rather, as teachers we need to teach our students how to decipher and evaluate the information that they have access to and this requires reasoning skills. Hence, in my opinion, this is why in my opinion the math and science standards are so focused in on conceptual knowledge and inquiry based learning. Through these processes students are taught to reason and think, and in our society today these are the skills one needs to succeed.
When it comes to differences between the math and science standards, many people wrote about how the science standards are more vague than the math standards. The major difference that I am most concerned about is why the math standards do not contain a historical or cultural subset (I can't remember who talked about this first, but good observation). Perhaps, this is covered under the process standard of connections? Whatever be the case, in my opinion there is huge historical and cultural connection involved in mathematics that should be taught in schools.
I agree with everyone else that the math and science standards share many important similarities. Both are student centered and stress the importance of knowing and understanding the subject matter. I agree with Sam that the standards are great in that they place more emphasis on the understanding and ability to use what they know rather than just memorizing facts. The more that students are involved, the more they will learn.
I also agree with Scott that both standards use different techniques so that each student is able to learn in their own way due to the inquiry based standards, where students use their reasoning and thinking skills.
It is agreed that the Science standards seem more inquiry based and vague, focusing mainly on how one should learn, while the math standards focus on how as well as what students should learn.
Although there are some differences, the main goal of both standards seems to be that students learn through inquiry and experience. The students should be leading more than just sitting back and watching.
Wow, I don't know if I can add much to what has already been stated. I have been pleasantly surprized with the joining of the procedural and conceptual knowledge within our schooling. (As was stated by Leslie) As a non-tradional student I have not been able to experience the type of classroom that promotes individual thinking and knowledge building--rather I was taught in the "traditional" behaviorist scenario. I am so excited that I am not required to teach that way as I would have to break some rules. I like Tootsie's observation about the Montana State Standards being directed to the grade levels and that looks to be a useful tool for the aspiring teacher, such as myself. With the standards being so specific teachers can focus on the particular one needed. As for the comparision between the Science and Math standards, I found the comment about the absence of history of Math made by Jessica B. to be a great discovery. I had never thought about that before. Great observation! :) The standards are more alike than different in my opinion, they both state the common goal of assisting the student to achieve understanding of the subject matter through inquiry-based learning. I am so excited about the integrated lessons as I think they do make it easier for kids to make connections between one subject matter and another as was stated by several others. (Scott, Lynnsey, and Jennie Folkerts).
Once again, the NCTM and NSES standards contain many similar components. In my mind the most profound and helpful for teachers being the emphasis on redirecting student outcomes from the rote memorization of facts and processes to a more conceptual understanding, in other words a trasfer from a teacher-centered to student-centered aproach. The development of both a scientific and mathematical way of thinking as a goal seems much more productive in terms of student achievement and is more in line with constructivist educational theory. I also appreciate the incorporation and acknowledgement of communication in both sets of standards as a necessary and vital component of each field. The emphasis on communication provides opportunities for integration with other fields as well as provides students with a necessary life skill.
I did not realize, and appreciate that Bryn did, that the math standards are broken into 4 benchmarks while science contains only three, making the math standards more grade specific. In addition, as Samantha and others pointed out, the math standards focus on creating a "classroom community" that is a safe environment for students to be problem solvers and take learning risks, while the science standards focus strictly on concent.
In an attempt to respond to Tootsie's comments as well as tie them into my own, I agree that the math standards could be considered vague in addition to the science standards, but I think that the NCTM and NSES had a specific goal in mind. The standards are not a curriculum, and are written in broad terms so that it becomes the teacher's responsibility to use a constructivist approach throughout their curriculum to reach those goals. What works in one classroom may not work for another. It is the conceptual understanding of algebra and inquiry processes that is important, not necessarily the specific topics covered or activities used in the classroom. If students are given opportunities to explore science and math in an environment where they are safe and supported their learning experiences will be much more meaningful and their conceptual understanding of both will be more profound.
The NCTM and NSES have set the benchmark of what is expected of students. The standards can be used as a good reference for teachers to check if students are up to par. Agreeing with Jessica B the science standards have been collaborated using inquiry learning as the main focus. The standards are promoting a new and exciting way for teachers to teach. Teachers are now encouraged to have students think about what their learning about, rather then the traditional methods. The math standards are more direct in what content knowledge should be known, however, the same philosophy of having kids think about their thinking is emphasized.
I agree with Deanna that we should use the standards as a guideline. Taking that one step further, I feel that standards are important for teachers to know what is “expected” of the students. Though, I believe teachers should focus more on the main ideas of the standards. After talking to teachers out in the field, it can become overwhelming if every lesson you are freaking out about meeting every little standard.
So teachers should have the main concepts of the standards known and show that in their teachings.
The math and science standards are similar in that they both connect to the real world and exsisting knowledge. However, I agree with Adrienne that the standards for math are much more specific then the standards for science. I think it is great that they are specific because their is so much about math that should be taught and understood. The science standards however speak to the historical aspects of science which math does not do. I think both sets of standards work because they expect the teachers to incorporate the real world aspect of specifics to each area.
Wow! I'm not sure what's left to say... What I believe is the most important feature of the standards for both subjects is their constructivist or student directed learning approach (as mentioned by many others, including Helena, Melissa, Jamie, etc.) The standards are filled with words such as inquiry, demonstrate, solve, engage. Teaching kids to find the problems and discover the answers for themselves is the best gift we can give them as teachers. I'm glad to see the standards reflect this approach.
Of course, they both also go through the concepts students need to understand to master the subject at the different grade levels. As a future teacher, I really appreciate these guidelines, as well as the fact that I get to choose exactly how to fulfill them.
As for differences, many things have been mentioned, such as the lack of a historical element with science (by Jessica and others.) Considering how "uninformed" some past science beliefs were (ie. the article on women's brains) it's probably best that that aspect is not required in science!
Well, as it seems I might be the last person to post a blog today, I have read through many very thoughtful and thorough thoughts about the NCTM and NSES standards. Both sets of standards are very well articulated as to what is expected in the specific content standard. Like Patti stated, they both take on a construtivist and student-centered learning approach with many "active" verbs like demonstrate and communicate which is necessary for understanding to take place. The difference between the standards is the simplicity of the science standards. Like Melissa said, they are brief and concise and could use a little more explanation or development. In both standards, they seem to be consistent with the ideas of the inquiry-based approach of teaching and like Bryn commented, they both incorporate the processes of connecting, communicating, and problem-solving (to name a few) as essential elements to include when teaching these subject areas.
I forgot to post my comments before 5:00pm. I am still going to post my thoughts after reading several blogs on the subject.
I agree with Patti that there is not much left to say, but I find it interesting that some of the comments conflict with one another. Someone mentions that history of the subject is left out of the standards for science but I believe that the national standards mention this with nature of science (if my memory serves me correctly).
I find it interesting that the standards promote an inquiry based environment. By using the standards, we are encouraging our students to respect one another and their ideas. Thinking back to the days of people believing that the world was flat did not allow for such freedom of thinking that we promote within our classrooms. I think that it would be interesting to explore this idea within the classroom to further the idea of inquiry and not judging others based on their incorrect comments.
Kim mentions that history in math may not be important because we do not need to know the time in which Fibonacci lived and discovered his sequence. But knowing that someone had taken a chance to prove a theory that may or may not have worked and the process that the individual when through is what students are learning about. Because in their own way, they are discovering the world of math and science with valid reasoning for the first time.
I wish that I had gone to school with reformed and inquiry based math and science. Students are able to learn and understand the material presented at each level as long as the teacher expects that of them. And we witnessed that in the math video.
So I think I'm going to be the last poster because I am so tardy today. Everyone has a lot of great things to say and I appreciate the detail and thoughtfulness of everyone's comments. I especially like what Tootsie and Jennie that the standards are similar in a lot of ways.
I appreciate the movement away from rote memorization and the constant and consistent encouragement for students to become thinkers capable of processing information and coming up with their own unique solutions to the problems they face not only in the classroom but also in the world around them.
In class this week watching the math videos and the science video featuring Wilson Science and Technology school in Bozeman really demonstrated the importance of encouraging children to think independently and I think the current standards can be a useful tool in helping teachers to assist their students in becoming creative, constructive, and capable members of their communities.
It seems like all of the differences and similarities of the standards have been covered quite well. It was helpful reading all of the posts and seeing others' perspectives.
Many have posted about the student-centered and constructivist goals of the standards. I think this is the most important feature. It will be our job to help students construct knowledge building off of what they already know. Standards that reflect this are important.
Also as others have pointed out, the math standards have separated content and process standards, which I think is helpful.
Wow!! I think I missed the memo that we were to write either a book or thesis in this blogging. I am thrilled with the level of analysis and thought given to the comparison and similarities of the two sets of standards. I also agree that both have student centered learning and inquiry as an integral core for learning in the classroom. Bryn, I saw that you noticed the lack of history base in the math standards. I feel that we can do better by integrating the history of math as we teach it. This summer I took Math 131 with Professor Seth Braver. It was a great class! (This from someone who did not do well in high school math.) Seth told many stories of math theorists and history that I've never been exposed to. It is a shame that I'm only now hearing about who and what, rather than just how. Problem solving and inquiry based learning are most certainly key to keeping students focused, on task, excited, and involved. As the magazine quote states..."Inquiring minds want to know!"
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