Standards of Mathematical Practice

        The Common Core Standard of Mathematical Practice that I researched was Standard 2: Reason Abstractly and Quantitatively. My partner and I learned that standard 2 involves students decontextualizing and contextualizing problems to help make sense of them to solve them. Decontextualizing involves taking a complex problem and representing it with symbols that are easier to understand. An example of this would be a student drawing a picture of a word problem and then being able to make a number sentence or equation that they are able to solve. Contextualizing involves taking a problem that is numbers or symbols and putting them into a real-world situation (often a word problem) to help students understand how to solve the problem. To help young students develop this skill, teachers need to help students learn the relationships between numbers (greater than, less than, or equal to) and also teach students how to do basic addition, subtraction, multiplication, and division skills. Teachers should also encourage discussions among students about how they got their answers and why their methods work.

        As for the other Common Core State Standards of Mathematical Practice, they were designed to create a foundation for teachers to be able to design their lessons and curriculum to teach students in the best way so they will be able to understand the context of each lesson and how it applies to the real world. The first CCSSM standard is to Make Sense of Problems and Persevere in solving them, which means a problem can be viewed as a situation that students can overcome to solve. This standard suggests that memorizing may not be the most effective way to learn and understand mathematics and encourages teachers to differentiate instruction to best help each student. The second standard is Reason Abstractly and Quantitatively. This is the standard my partner and I researched and made our poster on and i discussed above. Standard 3 is Construct Viable Arguments and Critique Others Reasoning, which is when students learn how to explain and communicate their mathematical work to themselves, the teacher, and their classmates. Talking through the problem and how they found the solution shows their proficiency and understanding and can help other students understand the problem and how to get the solution. Standard 4 is Model with mathematics which is when students are able to solve everyday problems using mathematics and when students reflect on if their answer makes sense and is in the same context of the problem. An example of this is when students are telling time. If the teacher asks "It is 9:45 now, what time will it be in 30 minutes?", students will be able to understand that it will be 10:15 and not 9:75. Standard 5 is Using Appropriate Tools Strategically, which is when students are able to look at the tools and manipulatives provided to them and can distinguish which will help them solve the problem at hand. For example, base 10 blocks will not be a good choice of manipulative for students learning to tell time or count money.  Standard 6 is Attend to Precision which is where students and teachers communicate to effectively teach and understand the content. This can include using mathematical vocabulary accurately, using symbols correctly, using correct units, and explaining clearly and concisely. The seventh standard is Look for and Make Sense of Structure which is when students use routines and patterns until they expect what to do and can find the solution using prior knowledge. The final and eighth standard is Look for and Express Regularity in Repeated Reasoning, which is when students recognize patterns and make connections between previously learned concepts and lessons. This standard also emphasizes that students need full understanding before introducing shortcuts and little tips and tricks.

        The 5 NCTM Process Standards go hand in hand with the CCSSMPs. The first NCTM Process standard is problem solving which includes students solving complex mathematical problems that require them to think and connect multiple lessons together and then reflect on their processes and stragagies. The second NCTM Process Standard is Reasoning and Proof, which involves students thinking analytically about the math problems and then being able to justify their answers and solutions. The next NCTM Process Standard is communication to have students explain their solutions and reasoning to other students as well as teachers verbally or by showing work or writing. The fourth Process Standars is making connections between different mathematical topics and among math in different subject areas. The last Process Standard is Representations which involves using manipulatives or other symbols to help solve and explain the mathematical problem or situation. 

        The CCSSMP and NCTM Process Standards can be used in classrooms of any grade or mathematical subject. Teachers should incorporate these standards into their lessons instead of teachers just standing at the front of the room giving a lecture. Teachers need to give students a variety of real world problems that expand student's knowledge of the lesson, give students a chance to share and communicate their work and reasoning with other students and the teacher, and teachers also need to provide the students with different manipulatives and ways to solve the problems.