Were you able to locate all of the "content" that you are currently teaching? What are your thoughts about their organization? Do you think they cover the "core" secondary mathematics topics?
Now, read the Myths vs. Facts: http://www.corestandards.org/about-the-standards/myths-vs-facts
Write any reactions that you have about the myths and responses.
(If you are also interested, read the Key Points in Mathematics: http://www.corestandards.org/about-the-standards/key-points-in-mathematics)
With an eye towards my own high school experience, it's interesting to see a standard like A-APR.1: "Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials." Are students really being asked to see the underlying ring structure, or is it enough for them simply to demonstrate that addition, etc. of two polynomials will produce another? I'm sure I could have done the latter, but explicit, verbal knowledge of the "system" way of seeing things definitely came later.
ReplyDeleteAs for the content I've seen, most of what I student taught in 9th grade algebra (expressions and graphing, functions vs. relations, etc.) is definitely there, although I'm not sure where I'd put lessons like the day we spent memorizing the formula for percent change and other assorted topics from Chapter 3 of our textbook. Modeling, perhaps?
The "myths," uncited and bland, seem like straw men for the publicity team to beat down with vague assurances that the Standards are, indeed, evidence-based. If such objections were being raised, I would assume they'd have to do with the type of evidence being used rather than the apparent assumption that some government types simply made all of them up-- and questions that specific aren't really suitable for an info page like that one. My only real curiosity is where an assertion as specific as "teaching Grapes of Wrath to second-graders" originated.
It was difficult for me to say that I EASILY found the content that I am teaching now, which is calculus. However, it did seem a little more accessible to me than the state standards. The myth fact section seemed to be very weak. It looks like they selected which myths to address and the defense in the fact portion was very dry.
ReplyDeleteI have to say that I do like the idea of having common standards among the states, however the myths section did not calm my concern for the rigor in the mathematics curriculum. It was mentioned that the aim for algebra 1 in 8th grade was going to be to a select few and not necessarily standard for all students. If tests they are seeing contain that content, I would expect a more firm response to 8th grade students covering algebra 1 across the board. This was a myth that I thought could have been more firmly and clearly addressed.
hmm, well i just typed a really long response that got erased when I tried to submit it. So I will summarize what I was going to say.
ReplyDeleteStandards: I generally agree with them, although Jenny is right when she says that Calculus is missing. I think the organization is good with both paragraph descriptions and bullet point listings. I also like how they emphasize mathematical modeling, although I don't think that current textbooks and curriculum meet these standards - they need to do a better job of giving RELEVANT life examples to students.
Myth - yes, this section is a bit dry. Although I do agree with the section: "Myth: Key math topics are missing or appear in the wrong grade", in that it doesn't matter what grade something is taught in and that in integrating curriculums sometimes a standard must move up or down a grade.
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ReplyDeleteInstead of looking at the high school standards, I decided to look at the 7th grade geometry standards, because I just finished teaching the geometry unit to my 7th graders. I noticed that the NY state curriculum does not mention construction and relationship of geometrical figures at all. 7.G.2 talks about drawing geometry shapes with given conditions, problems that seem more fitting in a current high school geometry course than 7th grade. I’m not sure I would be comfortably teaching this to my 7th graders as I’ve only recently learned they can barely trace and cut shapes out correct.
ReplyDeleteThe other portion of geometry involves solving real-life and mathematics problems involving angle measure, area, surface area, and volume. This is reminiscent of the current geometry state standards. My students are able to determine area, circumference/perimeter, surface area, and volume. However, there is a clear lack of emphasis and focus on solving problems as opposed to learning algorithms and basic skills. 7.G.5 is about supplementary, complementary, vertical, and adjacent angles, which is also not mentioned in the state standards. I do really appreciate the mention of multi-step problems to write and solve simple equations. With the recent geometry unit test I gave and graded, I noticed that most of my students have trouble solving multi-step problems, and I think an emphasis on problem solving beyond basic arithmetic and algorithms is advantageous to all students. Of course, this needs to be integrated into the curriculum early on and strongly aligned within the grades. I am just worried about when the core standards will actually be adopted, because there will be a lot of possible confusion as kids start on the core standards at different levels.
I examined the 8th grade standards because I am currently working in an 8th grade classroom. I think I was able to locate the content that I have been teaching, but I did feel like I had to work for it. There were also many conceptual opportunities and modeling opportunities that I do not feel are capitalized on in my current classroom, but are outline in the common core. I have some concerns about addressing all of these standards well over the course of one year. I do appreciate the focus on concepts and not specific (often algorithmic) skills.
ReplyDeleteI would like to agree with both Jennifer and Emily. Yes, it doesn't matter exactly when topics are addressed, so moving topics from one year to another is not necessarily a bad thing. At the same time there are implementation issues, will an 8th grader starting with these standards have to play catch up?
The myths/facts section seemed superficial, and the myths were carefully selected.
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ReplyDeleteI think the most powerful part of the new standards are the Standards for Mathematical practice (similar to the process standards of NCTM). I only wish that they would have broken down these standards as clearly as they did for the content standards. Nonetheless, the language of reasoning, understanding, application, decision, and problem solving are much more clear and coherent throughout the standards. In this sense, I think the new standards do in fact capture much more of the core of mathematics than the past standards. While the content strand progressions do provide a very skill based break down of mathematics, it seems that these are more deeply thought through in terms of what is necessary for students to do well in high school.
ReplyDeleteIn looking through the high school standards, I found it much more useful to look at the standards as they are laid out in Appendix A. This section sorts all of the standards into the course and unit sequence you might use in the actual classes. These sections include descriptions about how the high school standards connect to student learning in middle and elementary school, and this coherence and longitudinal planning seems very strong. I think as a teacher, using these parts of the standards to build from past student experiences could be very useful.
I’m looking forward to seeing the new common core assessments that are being developed (supposedly more task based and conceptual).
Similar to Jenny above...I'm also teaching Calculus so I had a difficult time finding the content I'm currently teaching.
ReplyDeleteI really liked the layout and organization of the site. I felt that it was very easy to navigate and locate standards at each specific grade level. I was surprised at the amount of sections that incorporated real world situations and modeling. This is always something that's important to keep in mind while planning.
I have to agree with the others that the myth and fact section on mathematics was pretty weak.
I looked at the standards for high school Algebra because I am currently teaching 8th grade Algebra. I don't think my cooperating teacher and I covered every bullet point they listed. Specifically, A-APR.1 - "Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials." Since we are preparing the students for the regents, we cover limited materials that lied out side of the regents exam.
ReplyDeleteAs for Myths vs. Facts, it's obviously carefully organized to make their standards look valid (I am not saying they are not). So that article is more like an advertisement instead of unbiased facts.
I agree that the "Myths vs Facts" resembles an advertisement.
ReplyDeleteAdding on to what Jennifer said, I feel that the textbook which I have used to teach Integrated Algebra (Holt) does not adequately provide students with relatable, real-world problems. Instead of integrating problems into the objectives of the lessons, the textbook treats problem solving as a supplement to the math.
Like Jenni and Nathan, I'm teaching Calculus right now, and there isn't anything explicitly about Calculus in the Common Core. I wonder why they don't have anything about Calculus, especially because one of the main pushes of the Common Core is that all students will be prepared to take Algebra in 8th grade. As this is a year earlier than the current State Standards have Algebra, I wonder that the CCSS doesn't talk about Calculus as content that could be added to the curriculum with the extra time made by pushing Algebra earlier.
ReplyDeleteWhere did these myths come from???
I prefer the organization of the New York State Standards, at least for high school, because it has specific standards for each class, and then breaks them down into each strand. The CCSS doesn't specify which of the standards should be taught in each class. Although I do think they cover the "core" secondary math topics, I am concerned that many of the standards will be skipped over because teachers may assume that particular standards will be covered in classes other than the ones they are teaching.
ReplyDeleteI agree with what everyone said about the myths vs. facts. They do seem carefully chosen to make the CCSS sound like the best thing ever.
As I looked over the Geometry CCSS, one of the things I struggled to find was standards for the unit on quadrilaterals I recently finished teaching. I was able to find a standard for proving properties of parallelograms, but could not find any for properties of rhombi, rectangles, squares, and trapezoids. This was a unit I enjoyed teaching, and found that it provided students the opportunity to discuss the relationships between the different figures with each other.
ReplyDeleteAs far as the myths verses facts section, the "Myth: Key math topics are missing or appear in the wrong grade" touches on what I was mentioning above with me believing that a section of Geometry is missing, so I went back to look at different grades for this standard, and well... I am still looking. Also just to tag onto what Pat said, I am also very curious where the Grapes of Wrath myth came from!