| Mathematics
Academic Standards For Mathematics
INTRODUCTION
The Pennsylvania Academic Standards for Mathematics are:
2.1. Numbers, Number Systems and Number Relationships
2.2. Computation and Estimation
2.3. Measurement and Estimation
2.4. Mathematical Reasoning and Connections
2.5. Mathematical Problem Solving and Communication
2.6. Statistics and Data Analysis
2.7. Probability and Predictions
2.8. Algebra and Functions
2.9. Geometry
2.10. Trigonometry
2.11. Concepts of Calculus
This document avoids repetition of learned skills, making an obvious progression across grade levels less explicit. Teachers shall expect that students know and can apply the concepts and skills expressed at the preceding level. Consequently, previous learning is reinforced but not retaught. Students who achieve these mathematical standards will be able to communicate mathematically. Although it is an interesting and enjoyable study for its own sake, mathematics is most appropriately used as a tool to help organize and understand information from other academic disciplines.
Because our capacity to deal with all things mathematical is changing rapidly, students must be able to bring the most modern and effective technology to bear on their learning of mathematical concepts and skills.
According to the Pennsylvania System of School Assessment, the Mathematics Content includes "the use of both multiple-choice items and open-ended tasks." The mathematics assessment assess five major content areas. "These have proven useful because they include a wide range of important content, and each of the areas is an understandable piece of the mathematics picture. These five areas are the same as those which have formed the framework for the National Assessment of Educational Progress (NAEP) since 1990. The five major areas are the following:
* NUMBER SENSE, PROPERTIES AND OPERATIONS items focus on the understanding of numbers (whole numbers, fractions, decimals, integers) and their application in real life situations, as well as on computation estimates. Emphasis is placed on understanding numerical relationships as expressed in ratios, proportions and percents and on students' abilities in estimation, mental computations and generalization of numerical patterns.
* MEASUREMENT items focus on the ability of students to describe real world objects using numbers. Students are asked to identify attributes, select appropriate units and apply measures to communicate ideas so that they are understandable to others. Students may be required to read instruments with emphasis on precision and accuracy using metric and customary units. Items also include estimates, measurements, and applications of measurements of length, time, money, temperature, mass/weight, area, perimeter, distance, rates, volume, capacity and angles.
* GEOMETRY items focus on geometric relationships and skills that are important in school, as well as in the real world. Important concepts include projection, transformation, congruence, similarity, coordinate geometry, spatial relations and trigonometric ratios. Students need to be able to model and visualize geometric figures in one, two and three dimensions, as well as communicate geometric ideas.
* DATA ANALYSIS, STATISTICS AND PROBABILITY items focus on the importance of data analysis and the representation of data across all disciplines, and they reflect the prevalence of these activities in our society. Knowledge of probability, sampling and statistics, and the ability to make inferences from tables and graphs are necessary in today's world.
* ALGEBRA AND FUNCTIONS items emphasize a conceptual understanding of algebra as a means of representing situations that involve variable qualities with expressions, equations, inequalities, patterns and systems of equations or inequalities. Some emphasize algebraic processing as a problem solving tool. Functions are viewed not only in terms of algebraic formulas, but also in terms of verbal descriptions, tables of values and graphs.
The proportion of multiple-choice items devoted to each of the five areas varies by grade level. At the grade 5 level the
Advisory Committee recommended that Number Sense, Properties and Outcomes be weighted highest, with about 32 percent of the items. Measurement received the next highest weighting with 20 percent. Both the area of Geometry and the area of Data Analysis, Statistics and Probability were allotted 18 percent of the items. And finally, the committee recommended that 12 percent of the items be allocated to Algebra and Functions. At both the grade 8 and 11 levels, the Advisory Committees recommended that each of the five areas be weighted equally.
Many of the items being used can be viewed as assessing more than one of the five areas. For example, an item in which monetary values are presented within a table requires both the ability to read tables (Data Analysis, Statistics and Probability) and the ability to perform computations with decimals (Number Sense, Properties and Operations). In instances such as this a decision must be made about the area which is most reflective of the primary focus of the item. The item is then grouped in this area."
The Stanford Achievement Test, Ninth Edition (SAT-9) contains two subtests for Mathematics levels Primary 1 through Advanced 2. At the SESAT and Task levels, only one subtest of Mathematics is included.
Algebraic Concepts
The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties.
Calculus and Pre-Calculus
The Calculus/Pre-Calculus Unit includes Competencies/Objectives which focus on calculus concepts. Students study limits, matrix algebra, functions, vectors, conic sections, mathematical induction, and sequence and series using graphical calculators, computers, and models.
Data Interpretation
The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. Students collect and classify data, organize and display data, use logical reasoning, and problem solving.
Decimals
The Decimals Unit includes Competencies/Objectives which focus on number sense and operations with decimals. Students compare and compute decimals, study money, estimate decimals, problem solve using decimals, and reason using decimals.
Fractions
The Fractions Unit includes Competencies/Objectives which focus on number sense and operations with fractions. Students compare and order fractions, study fraction parts, estimate with fractions, reason using fractions, and problem solve using fractions.
Geometry
The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. Students study properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving.
Measurement
The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. Students study length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns, and problem solving.
Number Theory
The Number Theory Unit includes Competencies/Objectives which focus on manipulating number forms and classifications. Students make connections between number forms and their real world applications.
Numeration
The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships.
Probability/Statistics
The Probability/Statistics Unit includes Competencies/Objectives which focus on data analysis and probability concepts. Students collect, analyze, and make sense of real world data (including overlapping data, inconclusive data, etc.).
Problem Solving
The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems.
Technology
The Technology Unit includes Competencies/Objectives which focus on studying computer hardware and software, uses for calculators, and applications of technology in problem solving.
Whole Numbers
The Whole Numbers Unit includes Competencies/Objectives which focus on whole number concepts. Students perform operations with whole numbers, use manipulatives to demonstrate whole number concepts, and solve problems with whole numbers in real world contexts.
|
