Guidelines for Participants

Session Focus

This Orientation session is designed to help you get to know (or review) the basics about online learning in general and this course in particular. You will learn about the benefits of online learning as well as strategies to have a successful experience in an online course; have the opportunity to explore the course environment, including taking a brief orientation survey, and reading about course requirements and expectations; reflect on your own experiences learning fractions; and watch and listen to Investigations authors talk about Investigations and the Common Core State Standards. Finally, you will introduce yourself to your colleagues in the Orientation discussion forum.

Guidelines for Participants

In each session of this course you will:

  • Complete readings and activities posted in each session.
  • Participate in the Discussion Forum
    • Read all conversations in the Discussion Forum (threads).
    • Post a minimum of three substantial messages to weekly discussions. You may join in on existing conversations or begin a new conversation based on a new topic.

Please review the Discussion Board Expectations.

Graduate Credit Information

Graduate credit will be available for this course. Your facilitator will provide you with further details.

Investigations and the Common Core Standards

Throughout this course, you will have a chance to see how the sessions’ content is related to the Common Core State Standards (CCSS).

We begin with some history about the CCSS and some details. The CCSS consist of both the Content Standards and the Standards for Mathematical Practice, which are most often referred to by Mathematical Practices (MP). There are eight MPs, and in this document you can see that we have grouped them in the order that makes most sense for us.

It is important to distinguish between the MPs and the Content…

  • Math Practices describe ways in which students should interact with mathematics.
  • Math Content Standards describe what students should understand and be able to do.

Investigations authors went through the entire program to align it with the CCSS. They developed companion materials (Investigations and the Common Core); one unit for each grade level. Of note:

  • Investigations and the Common Core brings Investigations into 100% alignment with the Common Core.
  • The Mathematical Practices are aligned with the goals and principles of Investigations and deeply embedded in the fabric of Investigations.
  • Investigations, when taught as intended, offers students and teachers the coherence, focus, clarity and specificity in the teaching and learning of mathematics.

Common Core companion materials are outlinedhere.

This document shows you the grade level adaptations that were made for the CCSS. As you can see, for most grades, it was minimal. The most changes occurred in Gr. 5. For details about the content and pacing by grade level, see Content and Pacing (by grade level)

When we look at the CCSS and how that affects Investigations, we believe that the most important part is to teach the program and teach it well.

The companion materials should be thought of as a part of Investigations, and together with the companion materials, Investigations is aligned with the CCSS.

Most importantly, the CCSS are intended to be used with CS (Common Sense)!

Watch and listen to Investigations authors Keith Cochran, Susan Jo Russell and Karen Economopoulos talk about the Common Core and what they did to align Investigations with the CCSS.

Readings

Tips for Online Success, Illinois Online Network
This is a list of ten important tips to ensure your success when taking an online course.

How to be a Good Online Learner, Virginia Adult Learning Resource Center

Explore the Course Environment

Many of the activities that you will be completing during this course, from posting on the discussion board to submitting surveys, will be done using the Moodle course management system. Take some time during the Orientation to get to know Moodle and the tools you will be using to participate in the course. Here are some suggestions for getting started:

  1. On the course homepage, review the overall course outline. Click on a session title to view the session content, which includes the overview, readings, activities, discussion questions and key learnings for the session.
  2. Watch the video tutorial Updating Your User Profile (Transcript) to learn how to modify your Moodle profile, including the addition of a personal picture or icon.
  3. Click on the “Participants” link in the left hand navigation bar to see a list of your colleagues in this course.
  4. Click on the “Discussion Tab” and begin to familiarize yourself with the discussion area.
  5. After the sentence “Attach a photo of yourself” add the following text: “For additional support on how to capture and upload a photo in the Moodle discussion board, please refer to our tutorial page.”

Technology Preparation

Web Browsers

On occasion, you may find that certain applications or websites in this course may work differently in different browsers. We recommend that you become familiar with how to use an alternate web browser, in addition to the one that is included on the computer you primarily use (often Internet Explorer for PCs, and Safari for Macs).

Firefox is a free, open-source web browser with many features that enhance navigation and security, and which is compatible with both PC and Mac computers. You can download Firefox here.

PDF Format

PDF (which stands for "Portable Document Format") is a popular format for distributing documents on the Internet. A number of readings in this course are posted in PDF format. To view and print PDF documents, you need Acrobat Reader software, available free from Adobe's web site. If you do not yet have Acrobat Reader installed, download it from the Adobe site and follow the directions for installation.

Orientation Survey

Please take a few minutes to complete the Orientation Survey. This survey collects some background information about your job role, teaching and administrative experience, and familiarity with online learning. In addition, it invites you to comment on your expectations and any questions you may have about participating in this course. You will receive an email message with a link for the “Orientation Survey”.

Fractions in Your Life

In this final orientation activity you will reflect on your personal experiences learning fractions. You will consider a few statements people say about fractions and have a preliminary look at the development of the work with fractions across the grades. You will review the course goals and expectations.

About the Notebook

You will be using the notebook tool throughout the course. The notebook icon will appear with a link to the location in the notebook where you will respond to the questions. You can also access your notebook by using the Notebook Tab at the top of the session page. In addition, there is a field in each session for you to include personal reflections.

The notebook is a place for you to solidify your thinking and understanding, make connections and think about questions you may be pondering. It helps to do this as you work through the session and before you engage in conversations with your colleagues in the Discussion Forum.

Notebook

Take a few moments to think back about your experiences learning fractions. What memories do you have? …in school? …at home? Write your thoughts in the notebook.

Fractions

You may have heard some of the following:

  • “A fraction is a small piece of a whole.”
  • “You cannot have a fraction that’s bigger than one.”
  • “Five is less than six, so 1/5 is less than 1/6.”
  • “If you multiply the same number to the top and bottom of a fraction, the fraction gets bigger in value.”
  • “Yours in not to reason why, just invert and multiply.”
  • “When you multiply the product is always bigger. When you divide, the quotient is always smaller.”

The Dangerous Rush to Rules

“Premature attention to rules for fraction computation has a number of serious drawbacks. None of the rules helps students think about the operations and what they mean. Armed only with rules, students have no means of assessing their results to see if they make sense. Surface mastery of rules in the short term is quickly lost. When mixed together, the myriad rules of fractions computation soon becomes a meaningless jumble.” (Van de Walle, p. 161)

When students are provided opportunities to make meaning of fractions through representations and contexts, they learn to reason, justify and make generalizations about fraction concepts, comparisons and operations.

Enacting the Common Core Fraction Standards

Listen to Investigations author Keith Cochran talking about essential ideas about fractions and how they connect to the Common Core Content Standards and Standards for Mathematical Practice.

Video

How would you create a classroom environment in which all students have an opportunity to learn about fractions in a productive way?

Fractions Through the Grades

Most students enter Kindergarten with informal experiences that build their understanding of fractions through situations in which they share. These early experiences are embedded in other content strands, such as filling pattern block puzzles and measuring lengths that involve partial units. The Common Core formally lists standards for fractions beginning in first grade. By the end of fifth grade, students will multiply one fraction by another and divide a whole number by a unit fraction.

Course Goals

Through participation in this course, you will:

  1. Gain a better understanding of fractions.
    Throughout this course you will work through many math activities to deepen your own understanding of the content.
  2. Recognize the importance of conceptual work with fractions in the elementary grades.
    The work that students do with fractions focuses on developing a conceptual understanding. Students that have this strong foundation will be much better prepared to learn procedures for operating with fractions.
  3. Focus on the teaching of fractions.
    Many of us were taught fractions with an emphasis on learning and memorizing procedures. For students to develop a deep understanding of fractions and fraction operations we must shift the way we teach fractions. The focus is on students using models, visual representations and story contexts to make meaning of fractions and their operations.

Expectations

This is going to be an intense and busy course with lots of learning – some of it will feel familiar, and some will feel new.

You can expect:

  • Engage as a math learner.
    Even though you know fractions you will think about them more to uncover the many layers of ideas, approaches and understanding that comprise them
  • Focus on how children make sense of, use, represent, and solve problems involving fractions.
    Engage in activities with an eye toward thinking, “How can this activity help, support and extend the thinking of my students?”
  • Do, think and reflect.
    After you complete each activity, take time to reflect about teaching and learning fractions.

We expect that you:

  • Engage in the activities, ask questions, and contribute ideas each week.
    Draw upon your experience working with children as you solve problems, discuss strategies, and communicate with others
  • Bring your own experiences and ideas to the conversation and be open to others’ ideas.
    We have different ways to approach, make sense of, and solve problems – the same is true of our students
  • Reflect on your own learning and how it will impact the work in your classroom.
    When you find out what helps you learn, understand, solve and make sense of problems, make a note of it; some of your students will share these ways, and others will learn differently
  • Participate in the Discussion Forum by posting and responding to others’ posts.
  • Seek help when you need it: ask your facilitator or the group.

Notebook

In the final field of your notebook, reflect on the key take-aways from this session for your own learning and record ideas that you want to remember and/or try with students.

In Closing…

In this course you will work on figuring out how to help students gain an understanding of fractions so they can be flexible and fluent when solving problems. The following quote from the Investigations Teacher Note, Visualizing Fractions and Percents, sums up the students’ work on fractions in the elementary grades.

“When students first encounter fractions in the elementary grades, they have to sort out what these numbers are and how they are different from the whole numbers they have been using. By using a variety of representations of fractions, decimals and percents, students learn to visualize the meaning of these numbers, their equivalents, and relationships to landmarks such as ½ and 1. The more familiar students are with different representations and the more fluent they are in moving between them, the better able they will be to choose a representation that helps them think through a particular problem.”

Discussion

Watch the tutorial Posting and Replying to Messages in the Moodle Discussion Board (Transcript). Then introduce yourself to your online colleagues by creating a new thread in the discussion board. Give your thread a descriptive title and include the following:

  • Your name, your role in your school, and your motivation for taking this course;
  • Two or three facts about yourself so that we can get to know you better; and
  • A photo of yourself (optional).

After you post, read and respond to some of your colleagues' introductions. Be sure to check back often to continue the discussion!

Go to the Forum

Notebook

Fill out the Session 1 Notebook Page to reflect on your own learning and record ideas that you want to remember and/or try with students.

Select the link to go to the Notebook.