Mathematics Core Curriculum for Grades Essay

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New York State Education Department Standards for Grades 1-5

Each state has its own educational standards that are meant to guide teachers and establish core curriculum goals for each grade level. The New York State Education Department is no different. The state standards of the curriculum based on grade levels one to five is not only to establish particular learning achievements to prepare students for more complex lessons in the future, but it is also meant to engage them within the curriculum in order to allow them to learn more from the material and use it in an applicable way in real life situations. The Mathematics core curriculum established by the New York State Education Department is no different. In its basest form it established the basic fundamentals and mathematic concepts that each student must aster within their respective grade level. Yet, it goes one step further to introduce new ways to engage the student within the material and force the student to use math in an appropriate way to better describe and understand the world around them using mathematical concepts and conceits.Get full Download Microsoft Word File access
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Essay on Mathematics Core Curriculum for Grades 1-5 Assignment

The analysis her begins with a dissection of the first grade standards set by the New York State Department of Education. There are several major hurdles that first grade students must cross over within their mathematic curriculum. In terms of problem solving, the standards ask first grade students to "Interpret information correctly, identify the problem, and generate solutions," (1 PS. 2). This allows for students to understand what is being asked of them to do and then begin to formulate a plan on how to do it. To further this lesson, the curriculum goes one step further by asking first graders to "Formulate problems and solutions from everyday situations," such as "counting the number of children in the class or using the calendar to teach counting," (1.PS.4). This is the beginning of teaching children to envision math as more than just numbers inside a book within the context of the classroom. It teaches children that math is an applicable part of the external world in which the students all live in. Getting back to more of the fundamentals of math, the first grade curriculum also requires students to begin to understand a use the reasoning of equations as proof of their correct or incorrectness in solving basic problems. Students must leave the first grade understanding that math can either be true or false and that decision must be based on valid evidence. Students should also be able to argue the validity of that evidence while also taking in the reasoning of others, both teachers and classmates. Explanations of mathematical decisions can be based on a number of strategies, including "the manipulation of objects, drawings, pictures, charts, and symbols in both written and verbal explanations," (1.CM.3). This once again forces students to engage themselves with mathematics in an informal way, allowing their young minds to understand mathematical concepts visually and verbally. First grade students must efficiently "Understand meanings of operations and how they relate to one another," (1.CN.4). In order to best figure this out, the standards call for the students to use trial and error as a strategy to work out problems on their own. This allows students to begin to use math as a tool to investigate problems around them. By the first grade, students should be able to count to 100 using increments of 1 and 10, while also understanding the basic principles of calculations such as addition and subtraction in order to prepare for later learning. First grade students must be able to distinguish patterns and recognize and match which can then be categorized -- important for more complex concepts later on. Finally, the curriculum asks that students understand monetary values with dollars and coins and how these coins can be combined to make particular denominations.

Second grade standards take the presented lessons first introduced in the first grade standards and then expand upon them. These standards ask students to take an even more engaging role in learning mathematics by acting out and modeling "with manipulating activities involving mathematical content from literature and/or story telling," (2.PS.3). Such activities set by these standards help prepare students for word problems later on. Second grade standards as set by the New York State Education Department take unique moves to use more informal methods of dealing with simple counting calculations which are unique to the child's specific learning method. Along with presenting an argument, the second grade standards ask students to "understand how to organize their thought processes," (2.CM.1). Once again, this forces children to become much more involved with their calculations rather than simply using a calculator. This involvement helps set foundations for the understanding of the importance of math in the world around us and how it can be harnessed as a tool to make important decisions which may affect that world. A step up from the first grade standards is the requirement to use and handle three-digit numbers. Along with this, students must recognize the importance and placement of zero within both actual calculations and in terms of placement on the number line. Students must also take word problems to another level by presenting sentence-based scenarios. This helps them prepare for much more complex word problems in which they will have to dissect the nature and values of the problem. Second grade standards also begin to plant the seeds for multiplication and allow the use of mathematical symbols such as <, >, +, and -. Second grades geometrical standards ask second graders to experiment with slides, flips, and turns to compare two dimensional shapes," along with naming all geometric shapes and manipulating them to make or break original shapes into new ones, (2.G.1). These students must also make use of the ruler and comparing known objects for their length along with the introduction of mass "as a qualitative measure" by asking questions such as "which is heavier? Which is lighter?" (2.M.1). These set standards help prepare the ground work for the more complex operations encountered in the third grade.

Once again the third grade state standards rely on the foundations first put in place in earlier grade levels. Yet, third grade students are asked to go beyond the surface level problem solving skills and "Understand that some ways of representing a problem are more helpful than others," (3.PS.2). Students must begin to differentiate more applicable problem solving strategies over simpler but more laborious ones. This also includes "identifying relevant vs. irrelevant information," (3.PS.17). Students should be able to recognize irrelevant or invalid strategies to solve problems and then adjust the strategy to better suit the problem. Standards also ask students to begin to implement the process of elimination into the previous established strategy of trial and error. Once this is conducted, students must explain how they arrived at such a conclusion and also to be able to restate or organize particular problems in the student own words. By third grade students must be able to pull out the essential elements of a problem -- i.e. In a word problem. This is the grade level that the students take on the responsibility for organizing and accurately labeling their own work and being responsible for mistakes involving organization or labeling. Also seen is an increase in using mathematical vocabulary in evidence or other verbal situations. Students are required to read, compare, order, & write up to 1000 along with being able to "compose and decompose three-digit numbers," (3.N.5). Students must understand how to multiply elements of & zero and how those differ form other whole number multiplications. With this comes understanding of fractions and decimals as parts of a larger whole and see these within the visual reputations associated. The must also master the understanding numerator and denominator and how to order fractions. Dealing with single digit division and three dimensional shapes with symmetry is also a major piece of third grad curriculum. In terms of measurement, students must be able to assess appropriate measurements needed for specific situations, including measurements of weight and capacity questions.

Fourth grade curriculum offers more complex processes to deal with problem solving. It requires students to understand the proper interpretation of problem material "Interpret information correctly, identify the problem, and generate an "appropriate representation of a problem," (4.PS.8). Students must call upon prior knowledge to generalize ideas and consider different solutions along with defending their own solutions against the claims of others. Fourth graders are required to work with numbers up to 10,000 and understand the "associative property of multiplication" (4.N.6). Multiplication moves to dealing with two digit numbers and adding and subtracting decimals to the hundredth position. This is the beginning stages of seeing algebra as a series of line equations, and students must be able to "Evaluate and express relationships using open sentences with one operation," (4.A.2). Along with this, students must be able to add and subtract fractions with common denominations and identify specific geometric shapes and angles.… [END OF PREVIEW] . . . READ MORE

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