Guidelines for Participants
Session Summary
Welcome! In this Orientation, you will learn more about the TERC Investigations curriculum, review tips for success in online learning, take an orientation survey and explore the course website. You will also introduce yourself to your fellow participants using the online discussion board.
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).
- Engage in at least three conversations (threads) each week – by either starting a conversation or joining existing conversations.
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.
Self-Evaluation for Potential Online Students, Illinois Online Network
This short, twelve-question tutorial helps you determine how ready you are for an online course.
Counting Readings
Counting is More Than 1, 2, 3 from Counting and Comparing (Grade K)
Counting and the Number System (K-2)
Building a Multiple Tower from Multiple Towers and Division Stories (Grade 4)
The readings above are all published in Russell, S.J.; Economopoulos, K.; Wittenberg, L.; et al. Investigations in Number, Data, and Space®, Second Edition. Glenview: Pearson, 2012.
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:
- 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.
- 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.
- Click on the “Participants” link in the left hand navigation bar to see a list of your colleagues in this course.
- Click on the "Orientation Discussion" link within the Orientation session outline on the main course page, and begin to familiarize yourself with the discussion area.
- Watch the video tutorial Posting and Replying to Messages in the Moodle Discussion Board (Transcript) and then post a message introducing yourself in the Orientation forum. Include:
- Your name and the grade level/discipline you teach (or your role in your organization).
- Explain what motivated you to enroll in this course, what you hope to learn, and how you hope to apply what you learn to your professional life.
- Attach a photo of yourself or of something that represents your interests.
- Make sure to read and respond to some of your colleagues' introductions.
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.
Mobile Devices
If you use an iPhone or an iPad and plan to access this course regularly with your mobile device, you may want to download and make use of MoodleTouch. MTouch is a native app for iPhone and iPod Touch only and is available in the Apple App Store for $3.
VoiceThreads
If you use an iPad to access this course, you will need to download the free VoiceThread app and then click on the link “View in VoiceThread mobile” wherever the VoiceThreads appear in the course.
Orientation Survey
You will receive an email message from your course facilitator with a link to access the Orientation Survey titled CF - Multiplication and Division Orientation Survey. Your course number will also be included in the description.
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. Please take your time responding to it.
Computational Fluency and Course Goals
In this final orientation activity, you will have an opportunity to think about:
- what you understand computational fluency to be
- what you feel good about in regard to your math teaching (celebrations)
- what challenges you are facing
You will also go over the goals and expectations for the course.
Notebook
Take a few moments to think about “computational fluency.” What does it mean to you? Write your thoughts in your notebook. You will be using this tool throughout the course.
Course Goals
1. Develop a deeper understanding of computation with whole numbers.
As you solve problems in this course, you will hear different strategies and reflect on what needs to be in place for children to successfully and efficiently solve whole number computation problems. The focus will be on strategies based on place value, properties of operations and/or the relationships between operations.
2. Examine students’ thinking and the activities that support their development of computational fluency.
You will have the opportunity to watch and listen to children’s thinking as they solve multi-digit arithmetic problems. That, and seeing their written work, will give you a better idea of how to support their development of computational fluency.
3. Understand how computational fluency builds across the grades.
While we are each interested in helping students in our own classrooms, one of the advantages of this course is that you will expand your view to grades below and above your own. You will look across grade levels to examine how computational fluency builds.
Course Expectations
This will be an intense and busy course with lots of learning – some of it will feel familiar, and some will feel new.
You can expect…
- To be engaged as a mathematics learner in each session
- To look at how computational fluency develops across the grades in Investigations, focusing on:
- - Counting
- - Decomposing Numbers
- - Multiplication and division
- To examine activities that support students in developing increasingly efficient problem-solving strategies
- To read and reflect each week
We expect that you…
- Will actively engage in the activities, think about, question, and contribute ideas each week
- Will reflect on the work we do in this course and how it will impact what you do in your classroom
Celebrations and Challenges
Consider the following questions.
- What parts of your instruction related to computational fluency do you consider as successes?
- What parts of your instruction related to computational fluency do you find challenging?
Post one or two challenges and celebrations in the Celebrations/Challenges Discussion Forum.
Read what others have shared.
When you read through others’ comments, what stands out for you as a pattern in the responses?
Getting Started - Building Multiplication and Division Understanding
Multiple Towers
In this activity you will use a multiple tower to solve multiplication problems and relate it to how students build their understanding of multiplication and division.
Students use adding machine tape to create the towers. They begin by marking off the strip. Then they start at the bottom of the strip and record multiples of a given number. In the example below the students are make a multiple tower of 16.
Look at the multiple tower of 21. Without counting from the bottom, figure out how many numbers are in this multiple tower; that is, how many 21’s are in are in 1,029
- What is the 10th step of the multiple tower of 21?
- How might knowing how many 21’s are in 420 or 630 or 830 help you figure this out?
Solve the following problems:
Watch this fifth grade class as they find multiples of 10 on the multiple tower and solve multiplication and division problems using the multiple tower.
As you watch the video, think about how students are:
- using multiples of 10
- making connections between the multiplication and division
- developing understanding of multiplication and division
- use multiples of 10 to reason about other multiples
Read
Building a Multiple Tower from Multiple Towers and Division Stories (Grade 4)
Developing Computational Fluency
Computational fluency is at the core of the work in the elementary grades. Students develop meaning of the operations, structure of the base-ten number system, and a repertoire of number strategies. Computational fluency has a different meaning at each grade.
Listen to Investigations authors Keith Cochran and Megan Murray as they describe some aspects of computational fluency.
Three Facets Aspects of Computational Fluency
Watch and listen to Investigations author Susan Jo Russell as she describes the three facets aspects of computational fluency – accuracy, efficiency and flexibility.
Practice and Review
Listen to Investigations authors Megan Murray and Arusha Hollister talk about practice and review opportunities.
Notebook
In your notebook, record the connections you made as you listened to TERC authors talk about aspects of computational fluency and the importance of practice and review.
Final Thoughts: Understanding Mathematics
– from the National Research Council’s Helping Children Learn Mathematics (2002), edited by Jeremy Kilpatrick and Jane Swafford.
In this course we will work on figuring out just how to help students have a greater understanding of mathematics so that they can have that view and be successful.
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 and respond to some of your colleagues’ introductions, be sure to check back often to continue the conversations.
Common Core Alignment
Counting and Cardinality
Known number names and the count sequence.
- CSS.Math Content.K.CC.A.1 Count to 100 by ones and by tens.
- CCSS.Math.Content.K.CC.A.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
- CCSS.Math.Content.K.CC.A.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
Count to tell the number of objects.
- CCSS.Math.Content.K.CC.B.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
- CCSS.Math.Content.K.CC.B.4a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
- CCSS.Math.Content.K.CC.B.4b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
- CCSS.Math.Content.K.CC.B.4c Understand that each successive number name refers to a quantity that is one larger.
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.