National Council of Teachers of Mathematics Standards and Math Lessons Essay
National Council of Teachers of Mathematics Standards and Math Lessons
In the following essay there will be four lesson plans discussed from four different websites. All of the lessons concentrate on the National Council for Teachers of Mathematics (NCTM) Standards for Number Sense and Operations. The four lessons will be analyzed using the following criteria; the NCTM Standards, the use of differentiated instruction and the use of manipulative. The four lessons that will be looked into focus on addition, subtraction, fraction and number values.
The NCTM focuses on encouraging instructors to allow students to use their natural insights when discovering number sense and operations. According to the NCTM standards, students would rather explore concepts to figure out each time, instead of just memorizing formulas or using calculators to get the answers. For some students memorization does not always come easy. When students have trouble memorizing information then the students may fall behind in class. Students are using their number sense and operation sense, rather than just learning to add, subtract, multiple or divide.
Standards are not the only thing that needs to be taken into consideration as a teacher. The teachers also need to get to know their students because each student has different strengths, weaknesses, abilities or disabilities. Teachers need to learn what skills work best for the students and how to incorporate them into the lesson plans. This is where the use of differentiated instruction takes place. The use of differentiates instructions means that the teacher needs to capitalize on the strengths and abilities and challenge and conquer the weaknesses and disabilities. Differentiated instruction refers to the alternative methods of instruction used in each lesson as well as the teacher figuring out what skills work best for each student.
As mentioned above manipulative will also be discussed. In a math lesson, manipulative are usually used to illustrate a concept. Instead of a student learning math, the students are doing math. A hands-on approach allows students to understand what ways mathematical principals can be used practically. An example of manipulative in Number Sense and Operations would be building blocks, buttons or dice which students can use to illustrate addition and subtraction. Manipulatives can be both physical and virtual. Website #1- www.teachthechildrenwell.com
The first lesson plan was reviewed from the website called Teach the Children Well. This lesson use technology to help instruct the inverse relationship between addition and subtraction. This lesson plan is directed towards students in first or second grade. At the conclusion of this lesson, the students should be able to identify patterns in numbers and understand how addition and subtraction coincide with one another. The lesson should be delivered to the students in a computer lab, where the students would have access to both a computer and headphones and the teacher would have access to a smart board and speakers. If a teacher can not use a computer lab in order to deliver the lesson, then the teacher should use one computer and a smart board to show all of the students the lesson at once. This is what the students will need in order to help them solve and check their problems. The goal is that the students should be able to write true number sentences, using the symbols +, – and =, with the help of fact families. These are families of information that relates to certain mathematical relationships.
By doing this lesson the students will learn that technology can help them with their mathematics just like calculators have in the past. According to the NCTM, this provides a negative contribution to developing enthusiasm for math. Manipulatives are not too involved in this lesson. There is one part in the lesson that the students wear numbers to form variations of one fact family. Each student is given a number and then another student needs to create a number sentence. Teachers can also use blocks and beads to help write number sentences.
Differentiated instruction can be used in this lesson. When there are different learners, different activities need to take place. The role playing is helpful to kinesthetic learners. Since computers are used sound can be used for auditory learners and the computer helps the visually impaired students. There is also room for special needs students to receive the help they need. Website #2- http://illuminations.nctm.org/Lesson.apx?id=276
The second lesson plan cam from the website Illuminations Resources for Teaching Math. During this lesson the students will learn the game London Bridge. After the students are caught the teacher can then ask the students different questions such as who is fourth in line. After this the students will then create a button train. This lesson will help the students identify the terms before, after and between, as well as name positions using ordinary numbers and counting the elements in a set less than 10 members. This lesson is for students from Pre-K to second grade.
This focuses on the standards that describe objects in the environment using names of shapes and then describes the relative positions of these objects using terms such as above, below, beside, in front of and next to. According to the NCTM, this would represent the use of multiple models to develop initial understandings of place value. Through out the lesson the students will be using buttons this is a manipulative that is used in the lesson.
The buttons also come in handy for students that are kinesthetic because they are physically using the buttons to learn. It is important to include as many different instructions to aide all of the different students. The work sheet the students use to create the button train is a good visual. This is a lesson that will keep the students interested in the activity. Website #3- www.educationfund.org
The lesson plan that was on the Education Fund website is called Once Upon a Math Lesson. This lesson uses different children’s literature to focus on mathematical concepts. This lesson focuses on several NCTM Standards such as to use place values to express, compare and order whole number, estimate sums, differences, products and quotients, record and organize data, draw conclusions by analyzing data and to find the perimeter of a polygon and the circumference of a circle. This lesson would be for grades K through fourth.
During this lesson the teacher would discuss the value of digits and their special place with in a large number. Base ten blocks and a die can be used as a manipulative. The goal is to use the blocks and die to see who can get the closest to 100,000. Students will learn to round during this lesson as well.
Once again this is a lesson that role playing is used which helps students that are kinesthetic learners. Auditory learners can benefit from this lesson as well because they are being read stories to help them learn the math. For some students tying together literature and math can make the lesson fun and interesting.
Website #4 – www.thirteen.org/edonlin/ntti/resources/lesson/m_half/
The fourth lesson is from the website National Teacher Training Institute. The name of the lesson is I’ll Halve S’more Please. This lesson is for grades three to five. The site focuses on identifying the parts of a fraction, reducing fractions and adding fractions with common denominators. The lesson is not only on a website it is also part of the television show Cyberchase where kids attempt to solve riddles using fractions. Students will be able to describe fractions in terms of sharing parts of a whole, understanding what numerator and denominators, add and subtract fractions, use fractions for problem situations and recognizing and using equivalent fractions and represent them geometrically.
The NCTM standards that apply to this lesson are to understand numbers, ways of representing numbers, relationship among numbers and number systems, as well as using computational tools and strategies fluently and estimate appropriately.
In this lesson the students get to make s’mores. This is something that will definitely keep the students interested in the lesson. The s’mores will be used to demonstrate fractions. The s’more itself is the manipulative part of the lesson. This is a fun and enjoyable lesson that can be used for students in third through fifth grade. This lesson consists of visual and kinesthetic learning. In the beginning of the lesson the teacher will take bites of the s’mores to display what fractions look like. Students will then learn to add and subtract the parts of the s’mores to determine the answers to the problems.
These four websites all consists of lesson plans that are fun and interesting. There is room to adjust the lessons if need be to accommodate any special needs that may need to be done. Many times teachers feel that they have to just focus on making sure that the standards are met. This can be stressful on the teachers and students. These lessons mentioned above met the standards while still allowing the teacher to have leeway with the lesson.