Sparking Meaningful Mathematics Conversations

Coursework Cover Page Course 5851: Sparking Meaningful Mathematics

Conversations

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*Being admitted into a degree program is not required in order to take for-credit courses through the Office of Continuing Education. If, however, you plan to use the credits earned through this course towards a graduate degree at UW-Platteville, you are advised to apply for admission into that program before taking more than 9 credits of graduate coursework as a Special Student (not seeking a degree). If you intend to use any course in an undergraduate or graduate program at any institution, please obtain advance approval from your advisor.

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Honor Code: By signing below, I confirm that I have read the Learners Edge Collaboration and Plagiarism Policy (located on the back of this page), and attest that all work I submit for this course is of my own creation. I have not plagiarized work from a colleague, fellow course participant, or any other source.

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Collaboration & Plagiarism Policy As an institution committed to professional development, Learners Edge believes each course participant will complete coursework with integrity, and will approach the course and all requirements in an honorable manner. At Learners Edge, we believe some of your best resources are your colleagues. As such, we’ll ask you to connect with them to share ideas and best practices. Collegial brainstorming and idea sharing are always encouraged. Teachers are encouraged to read the text together, share information, discuss concepts, etc. However, when it comes time to actually completing the requirements for the course, the following guidelines must be met.

Read and Respond: For the few text questions that are general in nature, your responses may be similar (not identical), as the material might not be unique to an individual teacher’s classroom. However, each person is still expected to craft his/her own responses to these questions following the group’s brainstorming/idea sharing session. Most questions, though, are very classroom specific—and ask teachers to reflect on their personal experience, their own courses, and their own classroom. These questions do require a very individualized response.

Resources: We ask teachers to explore current resources which enhance and individualize learning experiences. You will cite these resources as you consider how to use information obtained. We expect you to summarize the resources in your own words. While two or more teachers may use the same article, the written responses to that article must be unique to you.

Reflection Requirement: Because we, along with our academic partners, believe that reflection is an essential part of learning, this section is designed with prompts that allow you to deepen your understanding of the course content. Specific prompts are provided for this requirement to focus your writing and reflect on how the coursework has deepened your practice and philosophy. This requirement should be written from the perspective of each educational professional, offering details, opinions, and examples that support contentions. Although we value quality over quantity, the Reflection Requirement should be a minimum of 2 double spaced, 1 inch margined pages.

Application Requirements: The intent is to create usable lessons/activities that each teacher can integrate into his/her classroom. In almost every case, this will require a substantially individual design—since each teacher teaches different curriculum, different students, etc. In a rare case where, for example, two teachers team teach—teaching virtually the same students and same

curriculum and can each truly implement the activity they have designed in their classrooms, we would accept work that is similar. However, these situations must have prior approval from Learners Edge. Of course, any evaluation/reflection on team-taught lessons must be individualized. Failure to uphold the collaboration/plagiarism policy may result in a loss of credit and an inability to register for future courses with Learners Edge. Please contact our office if you have any questions about this policy.

Course Syllabus Course 5851: Sparking Meaningful Mathematics Conversations Continuing Education Graduate Credit: 3 semester credits or Non-credit Course Description: Research continues to reflect the need for education to prepare students to contribute to a workforce that requires problem-solving. One strategy to help students build skills that will meet these demands is to teach them to actively manipulate and refine information. Social interaction provides the opportunity for students to do so and to integrate new knowledge with their prior understanding. This course prepares 5-8 grade teachers to shape mathematics discussions that maximize potential to extend students’ thinking and connect it to important mathematical ideas. Participants will apply five practices (anticipating, monitoring, selecting, sequencing and connecting) to orchestrate and manage discussions that will use student work as the launching point for discussions in which important mathematical ideas are brought to the surface, contradictions are exposed, and understandings are developed or consolidated.

Goals and Objectives: Upon completion of this course, participants will be better prepared to: • Reflect on assumptions and insights of practitioners, researchers and self • Apply the Five Practices Model to plan for mathematics discussions that lead to deeper understanding of mathematical concepts • Predict multiple means for students to approach mathematics problems and/or tasks • Evaluate case studies to identify examples of the Five Practices in action • Analyze potential math problems/tasks for implementing the Five Practices • Reflect on assumptions and insights of practitioners, researchers and self

Required Text/Reading: Text(s): Smith, M. & Stein, M. (2011), 5 Practices for Orchestrating Productive Mathematics Instruction. Reston, VA: National Council of Teachers of Mathematics, INC.

Knowledge Base: The knowledge base of this course, in part, is affirmed in the writing and research of these references: Kazemi, E., and Hintz, A. (2014). Intentional Talk: How to Structure and Lead Productive Mathematical Discussions. Portland, ME: Stenhouse Publishers. Molina, C. (2012). The Problem with Math is English: A Language-Focused Approach to Helping All Students Develop a Deeper Understanding of Mathematics. San Francisco, CA: Jossey-Bass. Slane, G. (2012). Math is All Around Us: A Collection of Story Problems for Students and Teachers, Grades 5-7. Bloomington, IN: AuthorHouse. Smith, M., Hughes, E., Engle R., and Stein, M. “Orchestrating Discussions,” Mathematics Teaching in the Middle School 14 (May 2009): 548-56. Stein, M., Engle, M., Smith, M., and Hughes, E. “Orchestrating Productive Mathematical Discussions: Helping Teachers Learn to Better Incorporate Student Thinking.” Mathematical Thinking and Learning 10, no. 4 (2008): 313-40. Thomas, E., Burnsting, J., and Warrick, P. (2010). Styles and Strategies for Teaching High School Mathematics: 21 Techniques for Differentiating Instruction and Assessment. Thousand Oaks, CA: Corwin Press. Van de Walle, J., Bay-Williams, J., Levin, L., and Karp, K. (2013). Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 6-8. Lebanon, IN: Pearson Education Inc. Willis, J. (2010) Learning to Love Math: Teaching Strategies that Change Student Attitudes and Get Results. Alexandria, VA: ASCD.

Americans with Disabilities Act – Accommodations will be provided for individuals with documented disabilities or special learning needs. Please let us know at [email protected] how we can help!

Important Dates

Our Commitme nt to You Our Mission: Our mission is to provide professional development opportunities that create remarkable experiences that inspire educators and ultimately improve the quality of teaching and learning. We are confident that our courses will challenge your thinking and that you will find numerous practical strategies and/or insights you can immediately apply.

Coursework The required assignments are designed to help you expand the depth and breadth of your understanding of course topics and to help you apply new skills and behaviors to enhance your teaching practice.

Important note: We work with educators at all professional levels, and recognize that modification may be needed to meet your professional goals. If your role is something other than a classroom teacher (school psychologist, social worker, nurse, para-professional, counselor, etc.), some assignments may be challenging to complete. Please contact us with your great ideas for modifications at [email protected]. We will work with you to ensure the coursework is relevant and beneficial, while still meeting course objectives. Formatting Tips Please submit work using the following formatting guidelines:

• 12 point font • Single or double spaced • Label each section as: Read and Respond, Resources, Reflection, and Application (and “A” Requirement if applicable) and number your responses

Rubric Each component of our Learners Edge courses has been designed by our team to help you learn new concepts/skills, stay up to date in the field, reflect on your professional practice and apply new ideas in your classroom.

SECTION To earn a B, you will need to meet the following criteria:

General Coursework Expectations Responses thoroughly address all questions Writing meets graduate level standards of grammar and mechanics

SECTION Additional Section-Specific Requirements

Read and Respond: Responses reflect thorough understanding of course concepts Elaborates on main points

Resources: Selects resources relevant to course concepts Resources meet Learners Edge copyright and citation criteria including: Title, Author, Copyright or publishing date, URL if applicable

Reflect: Openly examines experiences as they relate to the topic Analyzes and identifies growth opportunities

Application: Responses demonstrate ability to apply course content Responses connect course content to future professional practice

OPTIONAL To earn an A, you will need to meet the following additional criteria:

A Requirement Meets all criteria indicated above Completes Additional “A” Requirement found at the end of the syllabus

If your coursework is a shining example of meeting and exceeding our expectations, we may ask your permission to showcase your work. If your coursework doesn’t meet the requirements, we will connect with you to help ensure your revisions are on track. Course work that does not meet standards as described above will not be awarded credit until appropriate revisions are completed.

Let’s Get Started!

Read and Respond – Each of our courses is designed to expose you to current information related to course concepts. Our goal is to provide a balance of ideas connecting theories and practice.

Before You Begin

1. Describe your experience orchestrating mathematics discussions with students. What are your goals for discussions? How do you plan for the discussions? How do you determine if the discussions have been successful? Introduction 2. The authors provides some important context in the introduction related to learning experiences which will better prepare students for the demands of the 21st Century. Create your own definition of mathematical literacy and share it with us.

3. What resonated with you most about the analysis of David Crane’s classroom? Why? Chapter 1 4. Today, teachers work to balance effective instructional strategies with the demands of content coverage. One might argue that teacher explanations are an effective way to communicate to students what they need to know. Create a list of pros and cons of using discussions focused on student solutions vs. teacher explanations.

5. Now that you’ve been introduced to the 5 steps. Consider the following: a. Which of the five steps do you feel is most important? b. Which of the five steps do feel will be most challenging to you to integrate into your instructional habits and planning? c. How do you predict students would respond to a transition to this five-step model? How might you make this transition positive for students? Chapter 2: 6. Complete Active Engagement Activity 2.2. Consider a lesson you have recently taught in which the learning goal was NOT explicit. If you haven’t recently taught a lesson, look to the future to create a new lesson goal. a. Rewrite the goal so the mathematical idea that you wanted students to learn is explicit b. How might your more explicit goal statement influence the way in which you plan or teach the lesson?

7. Select a lesson you’ve recently taught. If you haven’t recently taught a lesson, look to the future to consider an upcoming lesson. .Use the Task Analysis Guide (Figure 2.3) to determine what level tasks the lesson requires of students. Suggest one lesson tweak that would promote higher level demands on your students. Chapter 3: 8. Complete Active Engagement 3.1. List line numbers and to identify examples of where each of the five practices is applied by Darcy Dunn.

Chapter 4: 9. Review the Nick Bannister example. Now, select one lesson topic you’ve taught in the past or intend to teach in the future. a. Provide three potential approaches students might take to solve the mathematics task/problem. b. What struggles or challenges might students have as they work to find solutions? c. Provide 2-3 probing questions you would ask students to help them overcome challenges or to help them think more deeply.

Chapter 5: 10. Under what circumstances do you think it makes sense to publically share incorrect approaches with students? How do you ensure students are clear that an incorrect solution is not valid?

11. Respond to the authors’ statement that connecting is the most challenging of the five practices.

12. React to the analyses of Nick Bannister – specify your thoughts on both the analysis of Monitoring in Chapter 5 and the analysis of Connecting in Chapter 6.

Chapter 6:

13. Use the Types of Questions Used by Teachers chart (Fig 6.1) to reflect on your own questioning habits. a. Which type of question do you most commonly use? Why? b. Which type of question would you like to use more frequently? Why? c. Revoicing, restating, and applying individual reasoning to another’s are great strategies which can be incorporated into mathematics discussions. Describe how each promotes accountability.

14. React to the analysis of Regina Quigley’s case.

Chapter 7: 15. The authors call determining the goal of the lesson Practice Zero. Do you agree? Explain.

Chapter 8: 16. React to the analysis of Maria Lancaster’s Case

Resources – Here is your opportunity to explore additional aspects of course concepts and to further customize your learning experience.

1. To meet this requirement, please identify two resources related to the course content that will both enhance your professional practice and deepen your understanding of the course. Resources selected may be blogs, wikis, websites, articles, books journals or a combination thereof. Resources selected should be recent - published within the last three years.

2. Summarize what you learn from each resource in 2-3 paragraphs. Include an explanation about how information presented in the resource will impact your professional practice.

3. For each resource, include: • Title • Author • Copyright or publishing date • URL if applicable

Reflect: We understand the importance of reflection on assumptions, insights and philosophies as a key part of the learning process. To meet required depth of reflection, your response should be a minimum of 2 double-spaced pages.

The purpose of this assignment is to provide you the opportunity to dig deep and think critically about teaching and learning.

• Which of the Five Practices are already part of your lesson planning routine? Which of the Five Practices are new to you? • The authors claim that planning is a “premier teaching skill” – explain in your own words what this means and whether or not you agree. • Who could serve as a critical friend/mentor/support to you as you work to transition to regular use of the Five Practices? • What benefits would you predict would result from such a shift for you and for your students? Application: Apply and evaluate new knowledge and skills. Connect coursework to your professional practice.

Application 1: Lesson Protocol

A. Use the Thinking Through a Lesson Protocol (TTLP shown in Fig 7.5) to design a mathematics lesson that demonstrates incorporation of the Five Steps. B. The Monitoring Chart strategy is introduced in Chapter 1 (Fig 1.1). Create a monitoring chart which could be used during the lesson you described in Application 1. Explain how you would use the chart. C. Review the questions not addressed by the Five Practices (Fig 7.6). Select one question and describe how you would integrate it into the lesson. D. What are the benefits and drawbacks of investing this level of detail and preparation for mathematics lessons? E. How might use of the TTLP promote rich conversations with students and/or parents about students’ progress?

Application 2: Step Zero The authors state that “Practice Zero” is determining the goal of the lesson. Find three lesson/topic ideas that you believe would be a good match for applying the Five Practices Model. For each, share the goal of the lesson. Application 2: Select One of the Following Options Option 1: Pay it Forward Develop an outline for an in-service (30 minutes) you would use to train your math peers on the Five Practices. Your in- service should include a minimum of one interactive activity. Which of the tools presented in the text (monitoring chart, TLLP, etc.) would you include and why? Option 2: Try it Use the lesson you crafted for Application 1 or any other lesson and implement the 5 Practices with students. Share the success of each of the following steps of the process.

• Evaluate student responses during work time to help frame large group discussions • Sequence discussions strategically to ensure learning goals are met • Analyze student work samples to create teachable moments in large group discussions  What would you do differently if given the chance to re-do this lesson and why?

The Finish Line

If your goal was to complete coursework for a B grade, congratulations! You’re done  Please review the instructions for submitting coursework found on the next page.

If your goal is to complete coursework for an A grade, you’ll need to complete this additional assignment. Select one of the options below and clearly label it as “A Requirement” on your submission. Include this additional assignment with the submission of your other coursework. Option 1: Top Three Take-aways. Please summarize the top three things you will “take-away” (or have learned) from this course. For each takeaway- explain why this concept was especially relevant to you and how it will impact your professional practice. Your response should include a minimum of at least one paragraph per take-away. Option 2: -Share Your Great Ideas with Your Colleagues! You will contribute to the Online Discussion Forum by completing all three of the following: • Describe a lesson/activity • Share an idea, post a question, or respond to an existing post • “Steal” one great idea from a peer’s post and explain how you would utilize it in your practice.

Directions to post your comments in the Forum: • Go to www.LearnersEdgeInc.com • click on Access my Online Course • Enter your log-in information provided in your Learners Edge Online Course Information email. • Click on the link to the Discussion Forums located on the left navigation menu:

• Click on the “Class Discussions” link • Click on the link to each of the three topics. Once inside the discussion forum, click post reply

The Choice is Yours!

TWO options for submitting coursework to Learners Edge: Option 1: Submit via our Online Platform

Go to www.learnersedgeinc.com and click on Access my Online Course.

• Login using your Learners Edge credentials • Click on the Assignment Link on the left hand navigation menu

• Review all instructions carefully • Save your work as a pdf • Upload the document • Click “submit” • It is not necessary to include the cover page with your coursework • If you choose to complete the Additional “A” Requirement, please clearly label it on your submission • Comments will be provided in the online environment upon evaluation of your coursework, please check back in the online environment to ensure all requirements are satisfactory

ONLINE SUBMISSION CHECKLIST  I have completed all requirements for each part of the course Read and Respond Resources Reflect Application “A” Requirement (optional)  I have saved a copy of all coursework

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MAIL SUBMISSION CHECKLIST  I have completed all requirements for each part of the course . Read and Respond . Resources . Reflect . Application . “A” Requirement (optional)  I have saved a copy of all coursework  I have attached the cover page to the front of my coursework  I have signed the Collaboration and Plagiarism policy

Grades – If your coursework meets all criteria, you will receive a completion email and your grade will be posted within 5-7 business days of work being received or submitted. Transcript Information: Learners Edge does not process transcripts. To request a transcript:  Wait until you receive completion emails for each of your courses.  Contact your chosen academic partner

 For questions related to transcripts, please visit our website:

o www.learnersedgeinc.com, o Hover on the Partners tab, o Click Academic o Select your academic partner and follow the transcript instructions provided

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