When children arrive at school, they have many ideas about numbers. Teachers work with students and build on to those ideas. They also help them develop new relationships. However, many students do not have a full understanding of numbers. As a result, their ideas do not grow and develop into more advanced-related concepts as they progress through school. It is imperative that students understand number sense and mathematical operations because they are the building blocks to all other concepts in mathematics.
According to Principles and Standards, the term number sense is used throughout the Number and Operations standard. It states As students work with numbers, they gradually develop flexibility in thinking about numbers, which is a hallmark of number sense. . . . Number sense develops as students understand the size of numbers, develop multiple ways of thinking about and representing numbers, use numbers as referents, and develop accurate perceptions about the effects of operations on numbers” (p. 80).
Children expand on number sense as they practice using numbers in operations, place value, and understand how to make estimates of larger numbers, fractions, decimals, and even percents. Early number sense is vital because it builds upon other important concepts, such as addition and subtraction. In the lesson Lets Count to Five found on http://illuminations.nctm.org/LessonDetail.aspx?ID=L501, this issue is addressed. The lesson focuses on counting to five.
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The counting concepts are understanding cardinal numbers, rote counting, rational counting, numerals, and benchmark numbers. It is in accordance with NCTM’s Numbers and Operations Standard for Pre-K-2nd grade. According to the site, they are: 1. Connect number words and numerals to the quantities they represent, using various physical models and representations. 2. Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers. 3. Count with understanding and recognize “how many” in sets of objects. As a part of differentiated instruction, counting books are used. To target all students and make sure they understand, I would ask them to count the number of fingers on their friends hand and then their hands. If they understand why the term “Hi Five” is used, then I know they understand the concept.
I would also have them attempt to write the numbers one through five above the fingers they have traced. I could even write on my hands to show that we have five fingers. Manipulatives used were connecting cubes, crayons, paper, bowls, number cards, and an activity sheet. In the second website, the objectives were: 1. The student will learn the value of digits and their special place within each period of large numbers. 2. The student will be able to round large numbers to the thousands, millions and billions. 3. The student will be able to read coordinate grids and create their own map using coordinates. 4. The student will be able to label and identify the different parts of a Medieval Castle/Manor
(http://www.educationfund.org/uploads/docs/Publications/Curriculum_Ideas_Packets/Once_Upon_a_Math_Lesson.pdf).
The lesson correlates the Middle Ages and mathematical concepts, such as place value, coordinates, and grouping. After the lesson, the students are directed to design a castle (Medieval Manor) and assign coordinates for each part of their map. They also have to color/decorate a map key. The lesson is geared towards primary students, although it did not specifically state which grade.
These lessons are important to a student’s understanding of mathematics. These ideas are expanded on as the student progresses through school. Students need to know more than how to count; they need time and many different experiences to develop an understanding of numbers that grow and develop into more advanced mathematical skills as they go from one grade to the other.
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References
Figuero, M. (n.d.) Once upon a math lesson…everyone had fun! Retrieved on September 3, 2012, from http://www.educationfund.org/uploads/docs/Publications/Curriculum_Ideas_Packe
