E-Learning for Educators:

Series of Model Courses

Based on input from state/station representatives, the first four series of courses will target elementary and middle school and will focus on mathematics and English language arts.

The NAEP, state standards, and the national standards (NCTM and NCTE) were reviewed to determine topics for the initial course development.

The proposed content and standards that each of the courses will address are detailed below. It should be noted that courses are independent of one another so that each course can be used separately as well as part of a series. Content will become more defined as outlines and drafts are prepared and specific state standards with which courses align will be identified.

Model Courses for Upper Elementary Mathematics, Grades 3-5

According to the NCTM, U.S. students enter the third grade interested in learning mathematics. By fourth grade, nearly three-quarters of them say they like mathematics, seeing it as practical and important. To keep students engaged, mathematics must continue to be interesting and understandable. The 2005 NAEP mathematics framework focuses on two dimensions: mathematical content and cognitive demand. Their stated goal in developing assessment items is to consider both dimensions, balancing content along with a variety of ways of knowing and doing mathematics.

In the first dimension, the framework describes five broad strands of mathematics content, as does the NCTM content standard:

• number sense, properties, and operations;
• measurement;
• geometry and spatial sense;
• data analysis, statistics, and probability; and
• algebra and functions.

The second dimension, mathematical complexity, focuses on cognitive demands and includes aspects of knowing and doing mathematics, such as reasoning, performing procedures, understanding concepts, or solving problems. 

For these reasons we propose the following three math topics for model elementary courses, integrating both the content and cognitive needs of student learning.

1. Fractions. During grades 3–5, students should build their understanding of fractions as parts of a whole and as division. They need to see and explore a variety of models of fractions, focusing primarily on familiar fractions such as halves, thirds, fourths, fifths, sixths, eighths, and tenths, as well as develop strategies for ordering and comparing fractions. Teaching goals should enable students to

• develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;

• use models, benchmarks, and equivalent forms to judge the size of fractions;

• recognize and generate equivalent forms of commonly used fractions, decimals, and percents;

• use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals;

2. Algebraic Thinking. Research results from the National Center for Improving Student Learning and Achievement in Mathematics and Science (NCISLA), show that young students can learn to make and justify generalizations about the underlying structure and properties of arithmetic — generalizations that form the basis for much of algebra. Consistent with goals outlined in the National Council of Teachers of Mathematics (NCTM) Principles and Standards (2000), this NCISLA study shows that young children can begin building a foundation in algebra much earlier than typical curricula allow and that students should be able to

• describe, extend, and make generalizations about geometric and numeric patterns;

• represent and analyze patterns and functions, using words, tables, and graphs.

• represent the idea of a variable as an unknown quantity using a letter or a symbol;

• express mathematical relationships using equations.

• model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

• investigate how a change in one variable relates to a change in a second variable;

• identify and describe situations with constant or varying rates of change and compare them.

3. Measurement - Measurement helps connect ideas within areas of mathematics and between mathematics and other disciplines. It can serve as a context to help students understand important mathematical concepts such as fractions, geometric shapes, and ways of describing data. We suggest developing two aspects within a measurement course.

1. Geometric measurement – By focusing on quadrilaterals, we will look at teaching about area and perimeter, enabling students to

• explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way.

• develop strategies for estimating the perimeters, areas, and volumes of irregular shapes;

• select and apply appropriate standard units and tools to measure length, area, volume;

• select and use benchmarks to estimate measurements;

• develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms.

2. Systems – By looking at systems of linear measure and capacity, we will include activities that have more real-world ties that elementary students can relate to. Students at this level are expected to

• understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems;

• carry out simple unit conversions, such as from centimeters to meters, within a system of measurement;

• understand that measurements are approximations and how differences in units affect precision;

• select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles;

• select and use benchmarks to estimate measurements.

Model Courses for Upper Elementary English Language Arts, Grades 3-5

Course 1: Reading Comprehension

Participants in this course will develop concrete strategies to help their students better understand what they read. The course will use the same framework as tested by the NAEP:

Two different contexts for reading:

• Reading for literary experience (fiction, literary non-fiction, and beginning in 2009, poetry)
• Reading for information

Four different aspects of reading:

• Forming a general understanding
• Developing interpretation
• Making reader/text connections
• Examining content and structure

Additionally, the course will be aligned, where appropriate, to the NCTE standards that address reading strategies:

1.  Students read a wide range of print and non-print texts to build an understanding of texts, of themselves, and of the cultures of the United States and the world; to acquire new information; to respond to the needs and demands of society and the workplace; and for personal fulfillment. Among these texts are fiction and nonfiction, classic and contemporary works.

2.  Students read a wide range of literature from many periods in many genres to build an understanding of the many dimensions (e.g., philosophical, ethical, aesthetic) of human experience.

3. Students apply a wide range of strategies to comprehend, interpret, evaluate, and appreciate texts. They draw on their prior experience, their interactions with other readers and writers, their knowledge of word meaning and of other texts, their word identification strategies, and their understanding of textual features (e.g., sound-letter correspondence, sentence structure, context, graphics).

11. Students participate as knowledgeable, reflective, creative, and critical members of a variety of literacy communities.

12. Students use spoken, written, and visual language to accomplish their own purposes (e.g., for learning, enjoyment, persuasion, and the exchange of information).

Course 2: Vocabulary

This course examines the best practices and strategies for engaging and motivating students to build content area vocabulary. Research has found that knowledge of vocabulary is the single most important factor in reading comprehension (LaFlamme, 1997, p. 372). Vocabulary knowledge is assessed on the NAEP (in multiple content areas—not just reading), as well as on state standardized tests. The course will be aligned to the NCTE standards, where appropriate, that address vocabulary:

3. Students apply a wide range of strategies to comprehend, interpret, evaluate, and appreciate texts. They draw on their prior experience, their interactions with other readers and writers, their knowledge of word meaning and of other texts, their word identification strategies, and their understanding of textual features (e.g., sound-letter correspondence, sentence structure, context, graphics).

4. Students adjust their use of spoken, written, and visual language (e.g., conventions, style, vocabulary) to communicate effectively with a variety of audiences and for different purposes.

6. Students apply knowledge of language structure, language conventions (e.g., spelling and punctuation), media techniques, figurative language, and genre to create, critique, and discuss print and non-print texts.

11.  Students participate as knowledgeable, reflective, creative, and critical members of a variety of literacy communities.

12.  Students use spoken, written, and visual language to accomplish their own purposes (e.g., for learning, enjoyment, persuasion, and the exchange of information).

Course 3: Writing

Participants in this course will gain strategies to improve classroom instruction for helping students write narratives and informational text. This course will use the same framework as tested by the NAEP, focusing specifically on narrative, informative, and persuasive writing tasks. Additionally, the course will be aligned, where appropriate, to the following NCTE standards that address writing:

5.  Students employ a wide range of strategies as they write and use different writing process elements appropriately to communicate with different audiences for a variety of purposes.

7. Students apply knowledge of language structure, language conventions (e.g., spelling and punctuation), media techniques, figurative language, and genre to create, critique, and discuss print and non-print texts.

7.  Students conduct research on issues and interests by generating ideas and questions, and by posing problems. They gather, evaluate, and synthesize data from a variety of sources (e.g., print and non-print texts, artifacts, people) to communicate their discoveries in ways that suit their purpose and audience.

8.  Students use a variety of technological and information resources (e.g., libraries, databases, computer networks, video) to gather and synthesize information and to create and communicate knowledge.

9.  Students develop an understanding of and respect for diversity in language use, patterns, and dialects across cultures, ethnic groups, geographic regions, and social roles.

11. Students participate as knowledgeable, reflective, creative, and critical members of a variety of literacy communities.

12. Students use spoken, written, and visual language to accomplish their own purposes (e.g., for learning, enjoyment, persuasion, and the exchange of information).

Model Courses for Middle School Mathematics

NCTM content standards for grades 6–8 outline expectations in algebra and geometry that would stretch the middle-grades program beyond a preoccupation with number. In recent years, the possibility and necessity of students' gaining facility in algebraic thinking have been widely recognized. The first series of math courses could address fractions, decimals, and percents; proportional reasoning; patterns and relations; and/or geometric measurement. The initial series of courses is will focus on three areas that appear on state assessments and in the NCTM standards.

Course 1: Proportional Reasoning

Participants in this course will learn how to improve their students’ understanding of proportional reasoning and gain strategies to help students overcome their misconceptions. The course will be aligned to the following NCTM standards that address proportional reasoning:

• understand and use ratios and proportions to represent quantitative relationships; and
• develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Course 2: Patterns and Functions

Participants in this course will learn how to improve their students’ understanding of patterns and functions and gain concrete strategies for addressing student misconceptions in this area. The course will be aligned, where appropriate, to the NCTM standards that address patterns and functions:

• represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;
• relate and compare different forms of representation for a relationship;
• identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations; and
• use graphs to analyze the nature of changes in quantities in linear relationships.

Course 3: Geometric Measurement

This course would include developing reasoning, visualizations, and looking at two and three dimensions. Participants in this course would study how to improve their students’ understanding of geometric measurement and develop concrete strategies that they can use in their own classrooms. The course will be aligned to the following NCTM standards that address geometric measurement:

• precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties;
• understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;
• create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship;
• use coordinate geometry to represent and examine the properties of geometric shapes;
• use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides;
• describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling;
• examine the congruence, similarity, and line or rotational symmetry of objects using transformations;
• draw geometric objects with specified properties, such as side lengths or angle measures;
• use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume;
• use visual tools such as networks to represent and solve problems;
• use geometric models to represent and explain numerical and algebraic relationships; and
• recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

Model Courses for Middle School English Language Arts

The first series of ELA courses will address three core areas in middle school English Language Arts: reading comprehension, writing, and vocabulary. While reading, writing, and vocabulary span all subjects and all grade levels, English language arts teachers are frequently in a position to take the lead in teaching students these necessary skills.

Course 1: Reading Strategies

Participants in this course will develop concrete strategies to help their students better understand what they read in all content areas. The course will use the same framework as tested by the NAEP:

Three different contexts for reading:

• Reading for literary experience
• Reading for information
• Reading to perform a task

Four different aspects of reading:

• Forming a general understanding
• Developing interpretation
• Making reader/text connections
• Examining content and structure

Additionally, the course will be aligned to the following NCTE standards that address reading strategies:

1.  Students read a wide range of print and non-print texts to build an understanding of texts, of themselves, and of the cultures of the United States and the world; to acquire new information; to respond to the needs and demands of society and the workplace; and for personal fulfillment. Among these texts are fiction and nonfiction, classic and contemporary works.

2.  Students read a wide range of literature from many periods in many genres to build an understanding of the many dimensions (e.g., philosophical, ethical, aesthetic) of human experience.

4. Students apply a wide range of strategies to comprehend, interpret, evaluate, and appreciate texts. They draw on their prior experience, their interactions with other readers and writers, their knowledge of word meaning and of other texts, their word identification strategies, and their understanding of textual features (e.g., sound-letter correspondence, sentence structure, context, graphics).

11. Students participate as knowledgeable, reflective, creative, and critical members of a variety of literacy communities.

12. Students use spoken, written, and visual language to accomplish their own purposes (e.g., for learning, enjoyment, persuasion, and the exchange of information).

Course 2: Vocabulary

Vocabulary knowledge is important for success in all subjects, and all teachers have responsibilities for vocabulary development in their content areas. English language arts teachers, however, have an additional and significant responsibility to teach decoding strategies and context skills that serve as the foundation for learning vocabulary across all content areas. This course examines the best practices and strategies for engaging and motivating students to build content area vocabulary. Research has found that knowledge of vocabulary is the single most important factor in reading comprehension (LaFlamme, 1997, p. 372). Vocabulary knowledge is assessed on the NAEP in multiple content areas, as well as on state standardized tests. The course will be aligned to the NCTE standards that address vocabulary:

5. Students apply a wide range of strategies to comprehend, interpret, evaluate, and appreciate texts. They draw on their prior experience, their interactions with other readers and writers, their knowledge of word meaning and of other texts, their word identification strategies, and their understanding of textual features (e.g., sound-letter correspondence, sentence structure, context, graphics).

6. Students adjust their use of spoken, written, and visual language (e.g., conventions, style, vocabulary) to communicate effectively with a variety of audiences and for different purposes.

8. Students apply knowledge of language structure, language conventions (e.g., spelling and punctuation), media techniques, figurative language, and genre to create, critique, and discuss print and non-print texts.

11.  Students participate as knowledgeable, reflective, creative, and critical members of a variety of literacy communities.

12.  Students use spoken, written, and visual language to accomplish their own purposes (e.g., for learning, enjoyment, persuasion, and the exchange of information).

Course 3: Writing Essays

Participants in this course will gain strategies to improve classroom instruction for essay writing. This course will use the same framework as tested by the NAEP, focusing specifically on narrative writing, informative writing, and persuasive writing. Additionally, the course will be aligned, where appropriate, to the following NCTE standards that address writing:

5.  Students employ a wide range of strategies as they write and use different writing process elements appropriately to communicate with different audiences for a variety of purposes.

6. Students apply knowledge of language structure, language conventions (e.g.,

spelling and punctuation), media techniques, figurative language, and genre to create, critique, and discuss print and non-print texts.

7.  Students conduct research on issues and interests by generating ideas and questions, and by posing problems. They gather, evaluate, and synthesize data from a variety of sources (e.g., print and non-print texts, artifacts, people) to communicate their discoveries in ways that suit their purpose and audience.

8.  Students use a variety of technological and information resources (e.g., libraries, databases, computer networks, video) to gather and synthesize information and to create and communicate knowledge.

9.  Students develop an understanding of and respect for diversity in language use, patterns, and dialects across cultures, ethnic groups, geographic regions, and social roles.

11. Students participate as knowledgeable, reflective, creative, and critical members of a variety of literacy communities.

12. Students use spoken, written, and visual language to accomplish their own purposes (e.g., for learning, enjoyment, persuasion, and the exchange of information).