Learning Basic Number Behavior

Needs Assessment for Course

1. Instructional Problem:

Many students enter high school with a poor understanding of basic math concepts and poor problem solving skills. According to an article in Mechanical Engineering, “…the President’s National Mathematics Advisory Panel agrees. It says that the American student achievement in math is “at a mediocre level” compared with peer nations.” The article also states that in order to compete with our global competitors the panel finds that “conceptual understanding, computational and procedural fluency, and problem solving skills are equally important and mutually reinforce each other.” (Brown, p. 9)

Furthermore, many students leave high school without ever acquiring these skills. “High school students continue to struggle in algebra, especially in large inner-city schools with underprivileged students.” (Flores & Roberts, 305) Student who enter high school with out the basic understanding of mathematical principles will continue to struggle unless instruction can be designed to foster understanding and develop the basic skill sets needed for upper level mathematical curricula.

Just like any basic math problem, an instructional need should start with an articulation of the question, or in other words, a statement of the problem. Can mathematical instruction be designed such that the learner will correctly apply mathematical concepts in context, while developing problem solving skills with in the context of the New York State 9th grade Mathematics curriculum?

2. Nature of What is to be Learned:

Basic concepts of the way numbers behave and how these behaviors are used to help define and solve mathematical problems.

3. Target Learners:

Ninth grade high school math students taking the New York State Regent's Integrated Algebra Course.

4. Instructional Context:

Instruction will include online activities that provide definitions of number properties and examples of how the apply in context along with practice activities and assessments that test both procedural and conceptual application and understanding of the properties.

5. Exploration of Solution:

Because of funding constraints many institutions have limited resources for new materials to support building skill sets. Therefore this design is intended to be within the constructs of current available materials including textbooks, free online resources and current available technologies. Providing this extra support in the context of the current Integrated Algebra Curriculum, the instructor & students will use the mini course to explore number properties and reflect on how they apply/translate to Integrated Algebra Concepts.

6. Goal:

For students to be proficient in basic number properties so that they can transfer concepts and procedures to advanced mathematics curricula and mathematical problem solving.

Performance Objectives

Click on basic number properties for complete list of the number properties covered in this unit.

Task Analysis

Purpose of the Course

Students will demonstrate the ability to apply basic number behaviors such as concepts, properties, and procedures, in context. Task Analysis.jpg

Learning Outcomes

At the conclusion of this course students will be able to demonstrate:

  • Recognize that all numbers have consistent behaviors
  • Recognize that these consistent behaviors exist even when the number is represented as an unknown such as a variable or Theta
  • Identify and differentiate between different behaviors.
  • Define and identify the behaviors property name.
  • Decide when it is appropriate to apply a number's property to help simplify an expression to solve a problem, or equation.
  • Recognize that the application these properties can be applied to a variety of mathematical situations. (Transference)

Prerequisites

Essential prerequisites

Verbal Information:

  • Definition of addition
  • Definition of subtraction
  • Definition of multiplication
  • Definition of division
  • Definition of the equal symbol
  • Definition of a variable - Know that a variable is an unknown number, therefore it behaves like a number.
  • Definition of terms (in the context of a mathematical expression)
  • Definition of constants (in the context of a mathematical expression)
  • Definition of coefficient (in the context of a mathematical expression)
  • What it means to represent something mathematically (adding 2 to a number is n + 2)

Intellectual Skills:

  • Application of addition
  • Application of subtraction
  • Application of multiplication
  • Application of division
  • Application of equal symbol

Supportive prerequisites

Students should be able to identify:

  • that all numbers have consistent behaviors.
  • relationship between the definition of subtraction and applying the additive inverse.
  • relationship between the definition of division and applying the multiplicative inverse.
  • relationship between n + 0 and n.
  • relationship between n * 1 and n.

Sequencing

Curriculum Map

CurriculumMapPM.jpg

The Course

Basic Number Properties

References

Brown, A. (2009) President’s panel urges more for math, Mechanical Engineering. May 2008, p. 9

Flores, S & Roberts, W. (2009). Strategies for raising achievement in algebra. NASSP Bulletin, 92(4), 305-315