- Use the following resources to gain a greater depth of understanding with the middle school mathematics standards.
- NCTM | Common Core | CMP
- Describe how or if these standards harmoniously blend together. Eg, was it a struggle?
- Be specific. Share your assigned standard and experience.
Standards, Standards everywhere.
Begin by reviewing a simplified overview of the Common Core (CC), NCTM, & District (CMP) standards
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ReplyDeleteWhen looking at the 3 different standards websites it was quite daunting to start because each set of standards had a different language for the same concept. As I was able to familiarize myself with the sites I started to see similarities. I noticed patterns and themes about what they were expecting students to know. My partner and I looked at data analysis and probability. Both sites focus on the concept of students being able to use data from one or two different categories and describing the similarities and differences of the data by graphing. The students were then expected to demonstrate how this data could be shown in different graphing styles. I really like how these standards focus on real world application and future skills needed for employment in many different professions.
ReplyDeleteLooking at the three separate sets of standards, it was interesting understanding how the three blend together. I believe with many of the standards, in order to complete one of the National Standards, you end up teaching many of the other standards seen. All of these standards fall into the big picture of teaching numbers and operations. While the verbage is different, the end result is the same. If the student were to complete the goals of one standard, they would inevitably be accomplishing the goals of another, as much of numbers and operations is intertwined. Using the standards that my partner and I are working on, it would be impossible for “students (to)… work flexibly with fractions, decimals, and percents to solve problems” without being able to apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
ReplyDeleteStandards, Standards, Everywhere
ReplyDeleteOur assigned topic was measurement. The ways of stating standards for learning measurements are all different among NCTM, Common Core and CMP. NCTM sets specific goals for measurements, which is that students should understand units of metric system VS. customary system and relationships among the units. It also refers to converting from one unit to another. On the other hand, Common Core does not have the specific category of measurements. Although conversion of units may not get involved, I think Common Core implies learning of units is included by the statement “Solve real-world problem”. Units would be included if students solve real-world problems that involve measurements of length. CMP has a category of measurements but it does not particularly talk about units. However, I think CMP’s statement “Data around us” also implies learning of units since it relates to real world. The three standards all have goals of learning to find areas by the use of some kind of appropriate units.
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ReplyDeleteThe category I was assigned to focus on was Measurements, and right from the start one major difference is that the Common Core doesn't break down the study of measurements like the NCTM or CMP do. For example the NCTM really lays out a long term plan spanning K-12 whereby a student should come to fully understand the nature of what it means to measure things. This student would have a broad concept of the difference of standards with regards to units, be able to select the correct tool for what is being measured, and be able to covert within a given system as well as between two or more systems. In contrast while the Common Core does mention measurements as a standard and does lay out standards that are in line with the NCTM, it does not provide such a detailed framework for achieving this. The CMP only mentions measurements in relation to surface area, volume and angle measurements, and there is no mention of helping students build a philosophy and thus a deeper understanding of how measurement may be applied.
ReplyDeleteThe following statements are the standards expressed by the NCTM, common core, and CMP websites on the topic of 6th-8th grade math respectively:
ReplyDeleteIn grades 6-8, all students will work flexibly with fractions, decimals, and percents to solve problems.
Compare numbers in a variety of ways, including differences, rates, ratios, and percents and choose when each comparison is appropriate (6, 7, 8)
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
The question at hand is "How, if, or when do these sets of standards harmoniously blend together?". All three of these sets seem to have the focus on the topic be in different places, whether it be working flexibly with these numbers, choosing when to use the numbers appropriately, and then how to apply or recognize them on one of the number lines or diagrams. The point of all three of the standards is for these students to understand how to correctly use and apply fractions, decimals, percents and ratios. I honestly think that they each compliment each other very well, and together make a very comprehensive goal for 6th-8th grade students to reach.
So…the biggest thing that I noticed that divided the three was that the NCTM standards have the middle grades grouped into 6-8 whereas the CCS and the CMP both have them lined out as individual goals for grades 6, 7 and 8. I did notice that the CCS have very focused standards for Geometry in each of the grades. For example, in the 6th grade, students are to be able to, “Solve real-world and mathematical problems involving area, surface area, and volume.” After which there are more focused standards. The CMP also has individualized standards for each grade. For the geometry strand, they outline each individual piece of information that a student should learn. What I liked about the NCTM standards however, was that there were overarching concepts in geometry that were to be applied to all students with individual goals for grade groups. This created a major goal that could be built upon throughout the k-12 education pathway.
ReplyDeleteI thought we would find more standards involving linear equations or at least more details on the CC standard. The CC standard was a bit more vague than the NCTM standard. When I read the NCTM standard, I immediately knew how we were going to structure our lesson to meet this standard. The CC standard is so broad that you could miss out on making an important connections between the equations and how changes to their properties transform their corresponding graphs or tables. The CPM was more similar to the NCTM in that it states the specific skills that students will learn in regard to linear equations. I feel like I will look more to the CPM for specific help than the other two. CPM has 7 bullet points regarding linear equations, NCTM has two main references, and CC only has one.
ReplyDeleteI forgot to mention that our assigned topic was algebra and the standard we chose was understanding properties of linear equations and their corresponding graphs and tables. I had to hunt a bit to determine where the three different sets of standards harmoniously blended together. Thankfully there is a "find" tool on these web pages to save time and take me right where I needed.
ReplyDeleteCategory: Grade 7-8 Algebra
ReplyDeleteCMP focuses on "recognizing", "distinguishing" and "identify" relationships and patterns. It focuses on construction, familiarity and description. CMP standards suggest that students should have a deep understanding of mathematical concepts. Students should be able to do more than just compute, they should be able to jusify and explain their answers. Students should be able to connect one mathematical idea to another through observations of relationships and patterns. It focuses more on relating math to real, everyday life than NCTM or Common Core.
NCTM was similar to CMP. It also focuses on identifying relationships as an indicator of understanding. It also focuses on the connection of mathematical concepts. Students should be able to "understand patterns" and "analyze."
Common Core is more specific and focused than the other standards. Students are expected to identify patterns and make connections within the concept of algebra (rather than find connections across the math curriculum). It does not ask students to justify or explain their answer. It simply asks students to understand how to find and compute an answer. It focuses on strategy, accuracy and efficiency.
Summary: Common Core focuses on accurate, efficient, compuation--whatever gets the math done correctly. NCTM focuses on building upon prior knowledge about math, and focuses on making connections within the field of mathematics. CMP focuses on making connections between math and life. CMP conveys the idea that Math should be relevant because it is important and it is everywhere.
We were looking at probability, for which we sort of found a few standards that seemed to match. Initially, I made the mistake of matching the top two standards with the last standard. The following is my comparison:
ReplyDeleteThe three standards converge on probability and its computation. However, they all vary on the breadth of strategies involved. The CMP standard is, by far, the most vague and seems to really only involve the computations themselves, with the added bonus of learning to “compare.” NCTM incorporates the task of reading/interpreting graphs and lists to the task of making those computations of probability. In contrast, 7.SP.8 is focused on data collection, observation, and predicting. Indeed, the computations/approximations for probability seem to be secondary to the other tasks and strategies in this particular standard (7.SP.8). the complexity of the tasks should be greater if they are able to meet that last standard—as it is intended to promote higher-order thinking skills (prediction) and practical skills (those that are applicable to life outside of the math classroom). Students whose teachers focus their curriculum around 7.SP.8 should be engaged in steps that are known as “scientific methods. The said standard, I argue, was written with specificity so that there was less of a chance of students spending all of their math class sitting at their desks, staring at books and copying numbers.
Surprisingly, just as I was about to post my thoughts for this week’s discussion, I noticed that I had failed to notice one standard—one that matches the first two more closely.
• 7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Well, there you have it. The first standard (compute probability for simple compound events using lists, etc) and the above one (7.SP.8) really only differ on the event in question (be it the compound event or be it the oxymoron—a simple compound event?). The second standard (CMP) is a mix of the other two; it suggests computing probability for various outcomes, including two-stage outcomes—otherwise known as that compound event as seen in 7.SP.8—and simple compound events. Of course, this is not to say that they “blend harmoniously.” They just happen to all be the same thing, worded a bit differently every time. The good news? If you do some probability questions in your textbooks, you are bound to have met all three standards.
When I first started browsing through the standards I noticed that they are all pretty wordy. By the time that I had gotten through NCTM, Common Core, and CMP standards I realized that they are all saying similar things and have similar objectives but they are using different language to describe the standards. The three groups of standards work together in regards to the big picture of what needs to be taught and learned but it is the educators job to make them blend together in the classroom at all levels to make them relevant. My group had data analysis and probability; I found that all three of the groups of standards want students to be able to analyze data from multiple categories as well as represent them through the use of different graphs. I think that data analysis and probability is easily comparable to many real world situations and teaching to real world situations should make it more fun for the students.
ReplyDeleteI chose to evaluate how the NCTM standard of “understanding relationships among units and convert from one unit to another within the same system” compares with a similar standard in the Common Core and CMP standards. For the most part all three standards cover essentially the same thing. However, there are several differences between the three standards. One is that the Connected Math Project standards include conversion between customary and metric systems whereas the Common Core and NCTM standards keep the conversions within the same system. Another difference is the NCTM and CMP consider converting measurements a sixth through eighth grade skill where the Common Core standards place it in the fifth grade classroom. Lastly, the common core standards are the only ones that explicitly state that the skill must be implemented in multi-step, real world problems, which is surprising to me since that seems to be one of the main objectives of the Connected Math Projects standards. While the standards do not match up identically one to one, creating multi-step, real world measurement problems that include converting between customary and metric systems would easily cover all three sets of standards.
ReplyDeleteMy group had numbers and operations and the associated standards. I found the NCTM standards/expectations were pretty general as they covered 6 - 8 in general terms. As I viewed the Common Core and CMP standards, I found they were more difficult to decipher. Standards were more specific, and locating the associated standard to the national standard was more difficult. Overall, I found standards that were similar and shared some of the same wording. Chad Barr
ReplyDeleteOverall our standards blended together pretty well. Our group decided to create a lesson plan around graphing linear equations, creating a table of values, and identifying and explaining x-intercepts, y-intercepts, slopes of an equation. The National Standards are a bit broader compared to the State Common Core Standards and Connected Math goals. All three still touched upon having students construct, compare, predict, and describe the various aspects of linear equations.
ReplyDeleteIt was not that difficult to find the standards from each that were similar. I think that linear equations is a core part of Algebra, and that is why it was quick to find the similar standards in NCTM, CC, and CMP. The wording and description of the middle school math standards under the various categories of standards did differ, but overall were similar when evaluating linear equations with middle school students.
To me it seems that the National standards provide a broad overview of some categories or goals of learning while the common core standards and Salem-Keizer standards (CMP) narrow down what it is that students are learning. My group looked at graphing linear equations and all three sets of standards go over functions and multiple representations of functions and equations. Some of these include tables, charts, and graphs. All of the standards use the words "identify" and "representation." Even though the specific learning goals in all of the individual standards categories may be slightly different in wording or approach, the overall information that students will need to learn (algebra skills) are the same.
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ReplyDeleteThe three sets of standards seem to have certain similarities, but then they also have distinct differences. The NCTM, http://nctm.org/standards/content.aspx?id=7564 is a concise listing of what is expected of students. These statements are very broad, and can be adapted through any teaching method. It seems to be primarily content driven with not as much detail given to the actual teaching process.
ReplyDeleteBy comparison, the common core state standards, http://www.corestandards.org/the-standards/mathematics/grade-7/introduction/ gives a fairly detailed list of suggested content and then concludes with some teaching ideas. For example, the CC asks teachers to attend to precision, look for and insist that students use structure and express regularity in their reasoning. The CC even goes as far as to suggest that teachers model with mathematiccs with the appropriate use of strategic tools. When contrasing this with the NCTM standards for grades 6-8, the distinct difference is clear.
Looking at the CMP, or connected math project http://connectedmath.msu.edu/mathcontent/goals.shtml the information seems to certainly allign more closely with the common core standards than the NCTM ones. However, upon closer analysis, one can see that their number and operation goals are really more of a list of specific content to be taught and not the methods that should be used. They suggest that teachers help students to understand, develop, and use mathematical concepts, but the how component of is really up in the air and open to interpretation.
Blending these three sets of standards would probably result in the best teaching strategy. Although they certainly have their differences, if we can take broad content standards that are identified by the NCTM, and then use some of the suggested methods listed in the common core state standards to help students develop, understand, and use mathematical concepts listed in the CMP we should achieve an acceptable equilibrium with our teaching.
David Brian Dittman
I looked at the standards that dealt primarily with probabilities. After looking at the verbiage of the NCTM, CMP and the common core standard 7.sp.8., I found that in terms of the "big picture there were few differences. The degree of specificity ranged between the standards, however, upon closer look, the NCTM and common core 7.sp.8. were almost identical in language and content. Overall, the CMP goal was the most vague and open to interpretation. I can foresee a teacher reading that goal and feeling able to have a lot of leeway in their curriculum, whereas with the common core and NCTM standards provide more specificity and provides outlines for methods to discover and integrate into the teaching. I feel that a balanced mixture and understanding of these three standards will provide a math instructor with ample direction and space to teach the main ideas of the concept and develop understanding for their students.
ReplyDeleteAs I looked through the 3 different sets of standards online, I got a sense of each one trying to create an individual name for itself, and therefore did not get a sense of unity or having a common goal. As I looked further into each resource, I found that each site was saying practically the same thing but just used a different way of communicating it with the verbage.
ReplyDeleteThe subject area that I researched was in middle school math in the topic of geometry and measurement. In the Common Core standards site, they broke down the topics very clearly and used less formal language to communicate what the students should be able to do at the end of each unit. It didn't necessarily tell the teacher how to present the information which is great I think because it gives teachers flexibility to use whatever activities they want to use. In the NCTM site, the language they used was a little more formal compared to the Common Core resource, but was still understandable for me to interpret. Lastly, in the Connected Math standards, they presented the topics by grade level and associated them with specific workbooks (ones you find at teacher supply stores) that have catchy titles in an attempt to grab students' interest. Overall, each of the standards' sites presented similar topics, but just had their own language to convey their message, and because of the competition aspect of these three resources, I didn't get the feeling of unity that I'd like to see in the education realm; especially when it comes to teaching to standards.
Illumination response:
ReplyDeleteThe illumination that I selected to talk about is called Turtle Pond. This activity is directed to a K-8 audience and works on basic computer skills along with directional and measurement skills. Basically, the purpose of the illumination is to direct the turtle to the pond filled with nice lilly pads are at nice and safely. On the left hand side of the screen, are some directional arrows that the user can command the turtle to move in any direction. It gets more challenging as you play; where you can add boulders and trees that get in the way of the turtle's path, and you must avoid them to get to the pond.
This game reinforces distance, measurement, and directional skills. It is a very simple game and I do believe that it does a great job of showing kids how to manipulate the directions. However, I would just use it very minimally and in supplement to real manipulatives that are hands-on. The use of this technology does has some advantages over hands-on materials in that it takes up less room and doesn't involve a big mess like blocks or big shapes may have. Another advantage of using the computer as a medium for honing these skills is that many of them will enter possible professions that will require them to have certain computer skills and therefore we are helping to foster some of these basic skills early on in the classroom. Does it take away from the "old school" of learning though? That is an issue that I see more and more today; like we are getting out of touch with fundamentals and relying on technology more and doing less thinking because we entrust a machine to do virtually everything for us. Like stated before, I am not super opposed to using technology in the classroom, but I would just use it as a supplement and not make it a main focus. If I were in charge of this particular lesson, I would use tangible items such as meter sticks, tape measures, and use outdoor objects and have the students go outside to conduct these measurements. It will help them to see actual real life distances and then scaling them down on a screen.
I feel that the National Standards, though very thorough, are quite difficult to wade through in order to make decisions about what you are actually supposed to teach your students. The Oregon state standards and the CMP standards are much easier to understand, and as a future teacher, I would probably just stick with going through one or the other (if I were in Salem-Kaiser, I would do CMP of course), and trust that everything I need to teach will be included in them. I’m a little hesitant about the grade level designations on the CMP standards. I know that at the middle school I am currently at, there are several 8th grade students that are going over to the high school to take Algebra II. Would you wait to teach these standards until they are in the right grade level, or would you group the standards according to the course that the students have proven they are ready for.
ReplyDeleteCommon Core: (grade 5) M5.MD.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
ReplyDeleteNCTM: (grades 6-8) Understand both metric and customary systems of measurement; Understand relationships among units and convert from one unit to another within the same system; Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.
CMP: (grades 6-7) Relate units within and between the customary and metric systems.
There doesn't appear to be a specific Common Core for measurements in the middle grades (6-8). The closest one I found was the Measurement and Data listing under grade 5 of the Common Core standards. But it closely reflects the same standards expressed by NCTM and CMP. All three of these seek to relate units of measurement to each other, though the CMP also include converting measurement units between both metric and customary systems, whereas Common Core and NCTM specifically state within the same system of measurement. It also appears the Common Core and the CMP standards already expect a background knowledge and understanding of the differences between the two measurement systems. The NCTM standards also include a few other expectations (measure angles, perimeter, area, surface area and volume) that the other two standard categories have listed as expectations separately (i didn't include them here). The application to "real world problems," as expressed by the Common Core standards, seems to me to be understood in the general presentation of information in the classroom, but I like how it is explicitly spelled out. In short, the curriculum standards of all three are very closely aligned in regards to this specific topic, measurement.
I think that at a very general level the standards are very capable of working together. The state standards are very articulate in my opinion. I don't want them telling me everything to do, but I would say that they offer good guidance, especially when connected with to the Salem Keizer standards. I like quotes such as "Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers." They tell me what to do, and leave it up to me to figure it out.
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