Session Summary

Welcome! In this Orientation session, you will learn about the goals and guiding principles of Investigations, explore the structure of a lesson and begin to consider issues of equity in the teaching and learning of mathematics. You will also complete an orientation survey and explore the course website. Finally, you will introduce yourself to your fellow participants using the online discussion board.

Guidelines for Participation

In each session of this course you will:

• Complete activities and readings. This will include posting a response to a problem or prompt in an Activity Forum.
• 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.

Graduate Credit Information

Participants in this course are eligible to receive 3 semester graduate credits from Framingham State University. There are weekly extra written assignments and readings, a final paper and additional cost required to receive credit. Please let your facilitator know if you plan to participate in this course for graduate credit, or have questions about the graduate credit program.

Investigations and the Mathematical Practices

Investigations has always integrated mathematical practices that focus on reasoning, communication, and making sense. The math practices are the way that students engage with mathematics. What students learn in elementary school

The eight practices laid out by the Common Core State Standards (CCSS) in the reading below, are important for students, whether or not their classroom is working with the rest of the CCSS.

Throughout this course, you will see icons where you will read essays and notes about how students engage with the Math Practices.

Read Investigations and the Mathematical Practices from the Investigations Implementation Guide.

 

 

This is going to be a busy course with lots of learning – some of it will feel easy, and some might not seem that way. Re-read the welcome letter as a reminder of how we think about the course, including the Guiding Questions.

Many of the activities that you will be completing during this course 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. Each session, like this session, includes tabs at the top of the page: Overview, Activity 1, Discussion, Readings, etc.  Click on each tab above to become more familiar with the structure of a session. Go to the course homepage and become familiar with the structure of the page.  Each week a new session with a description and links to the session and discussion forums will appear below where you now see the Orientation Session.
2. Watch the video tutorial 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 on the course homepage to see a list of your colleagues in this course.
4. Begin to familiarize yourself with the discussion area. You can access the discussion forum for this session in the “Discussion” tab, above, or via the link in the Orientation Session box on the course homepage.
5. Watch the video tutorial about the Discussion Forum and then post a message introducing yourself in the Orientation Forum.

   Include:

   • Your name and the grade level you teach (or your role in your school/district).
   • 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 you primarily use.

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 role and teaching experience. In addition, it invites you to share your expectations and ask any questions you may have about participating in this course.

Consent Form

Please take a few minutes to read the consent form and respond.

In this activity, you will solve a problem mentally (no paper-and-pencil); think about the strategy you used; focus on what you knew that helped you solve the problem; and learn about the goals and guiding principles of Investigations.

Opening Problem

To begin, solve the following problem mentally.

What is 75% of 2000?

Share your solution and the math knowledge you used to helped you solve the problem in the Opening Problem Forum.

Each person brings their own mathematical understandings to solving this problem. Throughout the course, you will be solving many problems yourself, sharing your solutions with other participants, and examining students’ solutions to problems.

Goals and Guiding Principles of Investigations

One of the main goals of Investigations is to support students to make sense of mathematics and learn that they can be mathematical thinkers. Just as you used your mathematical understandings to solve the problem above, in Investigations students learn to apply what they understand to new situations and problems. They learn that they are capable of having mathematical ideas, applying what they know to new situations, and thinking and reasoning about unfamiliar problems.

Watch Investigations authors Megan Murray and Karen Economopoulos talk about the goals of Investigations and Keith Cochran and Susan Jo Russell talk about the guiding principles of Investigations.

Read Goals and Guiding Principles of Investigations. Visit and revisit this page throughout the course as you continue to make connections between your own learning and what the curriculum is about.

This activity will give you a sense of the structure of a session, and orient you to some of the features of an Investigations unit (e.g. Assessment Checklists, Teacher Notes, Dialogue Boxes). It is designed particularly for participants who are new to Investigations. 

If you are new to Investigations, or would like to review the components and features of Investigations 3, the short videos below provide: a tour of a print unit, a tour of an e-text, and a tour of the digital components that are part of the curriculum. Similar information is available in these pages from the Implementing Investigations guide at your grade level.

For this activity, choose a grade. Review the sample session, and any of the additional material/readings that are listed. These are resources that are referenced in that session.  

Use Looking at a Session to find the parts and features of a session. Note that not all sessions have all features, so you might want review more than one grade. (Note: The handout also calls out features of a unit and an investigation, on p. 2. If you have a unit to look at, you might want to look for those as well.) 

The remaining six sessions of this course focus on the pedagogy and content in Investigations and not on the structure of the curriculum. However, many of the components/features will be highlighted as you explore how the content unfolds across the grades.

Because of the history and continued presence of institutionalized racism and inequality in the United States generally, and within math education specifically, and because “deficit-based thinking is historical, cultural, institutional, ideological, and persistent” (Aguirre, 2019), we think it is important to consider what equity in the teaching and learning of mathematics means and looks like. Our staff has been examining issues of equity, identity, and agency and -- as one aspect of this online course -- we are asking you to examine them with us.

As you read earlier, one of Investigations' guiding principles is:

Students have mathematical ideas. Students come to school with ideas about numbers, shapes, measurements, patterns, and data. If given the opportunity to learn in an environment that stresses making sense of mathematics, students build on the ideas they already have and learn about new mathematics they have never encountered. They learn mathematical content and develop fluency and skill that is well grounded in meaning. Students learn that they are capable of having mathematical ideas, applying what they know to new situations, and thinking and reasoning about unfamiliar problems.

This and the other two guiding principles for Investigations have implications for equity in the teaching and learning of mathematics. But, as our staff has become more cognizant of current work about equity and identity, we recognize the importance of talking about these ideas more explicitly. What does equity mean in the realm of mathematics learning? And what does it look like in the classroom?

Equity

In order to talk about equitable practices in the math classroom, it is important to consider what we mean by equity. Here is one definition of equity in math teaching and learning that we have found useful: “All students, in light of their humanity—their personal experiences, backgrounds, histories, languages, and physical and emotional well-being—must have the opportunity and support to learn rich mathematics that fosters meaning making, empowers decision making, and critiques, challenges, and transforms inequities and injustices. Equity does not mean that every student should receive identical instruction. Instead, equity demands that responsive accommodations be made as needed to promote equitable access, attainment, and advancement in mathematics education for each student. This perspective on equity challenges common notions that students need to learn math “in spite of ” or “regardless of ” who they are. We argue that students need to learn mathematics in light of who they are and the diverse gifts that they bring to their experiences every day.” (Aguirre, Mayfield-Ingram & Martin, 2013, p. 9)

What strikes you in this description of equity? Are there other aspects of equity in a math classroom that you think are important to include in a definition?

Mathematics Identity and Agency

In the learning of mathematics, students’ mathematics identities and sense of agency play significant roles in their success with mathematics. Mathematics identity can be defined as: “The dispositions and deeply held beliefs that students develop about their ability to participate and perform effectively in mathematical contexts and to use mathematics in powerful ways across the contexts of their lives.” (Aguirre, Mayfield-Ingram & Martin, 2013, p. 14)

Students who have a strong sense of mathematical agency are: “active participants in, rather than passive recipients of, their mathematics education experiences… They can exercise these forms of agency in productive ways – resisting negative identities that are imposed on them, developing mathematical strategies within the context of small-group work, or using mathematics as a tool to understand their life circumstances or events in the world.” (Aguirre, Mayfield-Ingram & Martin, 2013, p.15)

Educators have a significant impact on students’ mathematical identities and their sense of agency. What can we as educators do to support and nurture students’ mathematical identities and their sense of agency and not undermine them?

Equity-Oriented Teaching Practices

Giving all students access to rich mathematics, giving them opportunities to solve problems in ways that make sense to them, and giving them opportunities to share their mathematical ideas are important elements of equity-oriented teaching practices. However, there is more to think about beyond these elements because “many of these students attend schools and sit in classrooms each day where their cultures are not reflected in the curriculum, where their ideas are not taken up in the public space of class discussions, and where they are seen not as individuals with unique identities and cultural perspectives but instead as data points on a measure of underachievement.” (Goffney, 2018, p. 159). How do we go beyond simply saying that all students’ ideas are valued? How do we make sure we are mindful of our personal biases? How do we work consciously against inequities?

Lens on Equity in this Course

Throughout this course we will take time to consider the teaching and learning of mathematics with Investigations through a lens focused on issues of equity. We hope to offer a space for thinking about these important issues along with our focus on the pedagogy and content of the Investigations curriculum.

In all subsequent sessions you will find a “Lens on Equity” section, highlighted in blue.

Additional Resources and References

Below are references for the quotes above, as well as additional readings for those interested in learning more about issues of equity in mathematics teaching and learning.

Aguirre, J., Mayfield-Ingram, K. & Martin, D. B. (2013). The Impact of Identity in K-8 Mathematics: Rethinking Equity-Based Practices. Reston, VA: The National Council of Teachers of Mathematics, Inc.

Aguirre, J. (April, 2019). Math Strong: Cultivating Equity and Social Justice in Mathematics Education. Presentation at National Council of Supervisors of Mathematics Annual Conference, San Diego, CA.

Ball, D. L. (April, 2018). Just Dreams and Imperatives: The Power of Teaching in the Struggle for Public Education. AERA 2018 Presidential Address, New York, NY. (Ball’s talk starts at about 53:30.)

Gutiérrez, R. & Goffney, I. (Eds). (2018). Annual Perspectives in Mathematics Education, 2018: Rehumanizing Mathematics for Students Who Are Black, Indigenous and Latinx. Reston, VA: National Council of Teachers of Mathematics.

Moschkovich, J. (2013). Principles and Guidelines for Equitable Mathematics Teaching Practices and Materials for English Language Learners. Journal of Urban Mathematics Education, 6, (1), 45–57.

Nasir, N. S. (2016). Why Should Mathematics Educators Care About Race and Culture? Journal of Urban Mathematics Education, 9 (1), 7–18.

NCSM & TODOS (2016). Mathematics Education Through the Lens of Social Justice: Acknowledgment, Actions, and Accountability [position paper].

Once you have completed the work in this session, go to the Orientation Discussion Forum.

On the forum post a message introducing yourself. Please include the following:

• Your name and the grade level you teach (or your role in your school/district).
• 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.

Follow the instructions in this tutorial tutorial to upload pictures or images.