Presenter: Martha Robertson Hello, and welcome to today’s overview of our new Math Navigator Common Core Edition. I’m excited to share it with you.

Goals Understand the philosophy behind Math Navigator research. Understand how misconceptions affect student learning. Know where to find components of the program. Understand the rituals and routines for Math Navigator. Identify rituals and routines in a modeled lesson. Understand how to print tests, enter test data, and find reports on Assessment Reporting Online (ARO). These are the goals for the program implementation training sessions.

To help these struggling students, we know that we have to try an alternative approach. We’ve seen time and again that basic re-teaching doesn’t generally work for most of these students. We need to change the teaching and change the experience so these students get the support they need to truly understand each math concept.

Expert Authorship Phil Daro Senior Fellow, America’s Choice Some of you know of Phil Daro as one of the three lead Common Core writers. Phil’s focus is and always has always been on tools to help improve math instruction at every level and has studied here and abroad. In addition to his role with the Common Core, he also advises states and school districts on their accountability systems and mathematics programs. And, for the decade prior to working on the Common Core, he guided the instructional design of many of America’s Choice intervention programs, including Math Navigator.

Six Principles for Effective Intervention Focus on prior knowledge and misconceptions. Target the intervention. Support the building blocks of algebra. Promote a language-rich environment. Create a learning classroom. Provide accessible instructional support. What Phil and the team coalesced around were six researched-based principles for effective intervention that are incorporated throughout the program, and within each lesson (Pearson Education, Inc. 2012): Focus on prior knowledge and misconceptions. Target the intervention. Support the building blocks of algebra. Promote a language-rich environment. Create a learning classroom. Provide accessible instructional support. Let me speak briefly about how Math Navigator incorporates each principle. (Pearson Education, Inc. 2012)

1. Focus on prior knowledge and misconceptions. “Division always makes the numbers smaller.” “It’s got more digits in the number, “so the number must be bigger.” “But last time, x equaled 1. Doesn’t x always = 1?” “The bigger the bottom number in a fraction, “the larger the fraction.” Here’s one of the very special things about Math Navigator: it gets to the heart of why so many students struggle with math—the misconceptions that they’ve developed about math. Do any of these sound familiar to you? [Click] “Division always makes a number smaller.” “It’s got more digits in the number, so the number must be bigger.” “But last time, x equaled 1. Doesn’t x always = 1?” “The bigger the bottom number in a fraction, the larger the fraction.” Can you think of any others? [Engage audience.] There are many other misconceptions that students come to math with, and we know the misconceptions—based on the research and our teaching. But what do you do about them?

Use this slide for the product overview. Malcolm Swan discusses common misconceptions. (3:50).

Simply re-teaching does not work Simply re-teaching does not work. Correcting Misconceptions versus Re-teaching Misconception Re-teaching 25 20 15 10 5 Pre-Test Post-Test Delayed-Test 17.8 19.1 10.4 12.7 15.8 7.9 Here’s what intervention shouldn’t do—simply reteach the same material again. I want to share the results of a study by the Shell Centre. The study compared students who received misconception-based intervention (the blue line) to students who received remedial re-teaching intervention (the green line). Look at the gap between the groups when they took a delayed test—well after they learned the material (three to four months later). Those that had their misconceptions corrected saw long-term gains and far outperformed those that had simple re-teaching. So how do you address misconceptions? [Additional notes about the graph: On the vertical axis is the Score. The horizontal axis looks at the results from a Pre-Test, Post-Test, and a Delayed Test. The Shell Centre is based at the University of Nottingham in England and known for its innovative work on mathematics education. The study was performed Alan Bell and Malcolm Swan.] (MARS, University of Nottingham, and Shell Centre for Mathematical Education 2015)

2. Target the intervention (deep, not wide). Attack fewer problems. Estimate and clarify. Use multiple representations/ approaches. Answer in a complete sentence. Estimate Diagram, number line, or other representation Equation Answer When the Common Core was released, the message was clear: we were trying to do too much—our state standards had expanded so much that students were struggling to master any part of the math we were teaching. Well, that same principle is true for Intervention: we need to focus on the key topics—and go deep into each. In Math Navigator, students tackle fewer problems, but go through them deeply. Here’s an example from the student pages. [Click] In Work Time, students will work through a problem, in this case the student is asked to [Click] estimate the answer, [Click] build a visual model, [Click] write out an equation, and [Click] explain his or her reasoning. Working deeply through fewer problems cements learning (and establishes best practices). Of course, what you focus on is just as important of how you focus. [Additional notes: The snapshot page is Using Operations to Solve Problems.]

3. Support the building blocks of algebra. 13 + 5 As the National Panel reported a few years ago (Pearson Education, Inc. 2012), algebra is really the gateway to higher-order math. We know this is a transition point that trips up most of our students. Navigator addresses this problem early—even in our Grade 1 modules. If you remember, I mentioned one of the six principles of the program is to focus on the building blocks of algebra. Here’s an example: [Click] Instead of teaching our students to “line the numbers up on the right,” to add double digit numbers, like I did here, …. [Click.] … Navigator depicts such problems in a horizontal format. These “equations” utilize a variety of ways to depict the missing part—such as question marks, boxes, and circles. You can see how this helps not only explain equivalence, the topic in this particular lesson, but also begins to set the important algebraic foundation of using letters to represent those missing values. These, simple, but thoughtful adjustments in the early presentation of arithmetic can create a fundamental cognitive shift for students. In Math Navigator, you’ll see we infuse such techniques throughout the program that will lead to a firmer grasp of algebra later on.

4. Promote a language-rich environment. Learn the words. Use the words. Internalize the concepts. The research suggests (Pearson Education, Inc. 2012) that using mathematical language when working through math can lead to a stronger understanding of the math itself. This program has an explicit goal of introducing the math vocabulary early on—and making it a part of the classroom discussion. Students must routinely articulate their understanding of mathematical situations; in this way, academic language is introduced and explicitly defined. It is then used over and over again in the context of the mathematics. In Math Navigator, the Teacher Edition provides necessary vocabulary supports—including Spanish cognates—to guide the teacher in incorporating vocabulary throughout each class. [Additional notes: The snapshot is taken from Positive Rational Numbers.]

5. Create a learning classroom. SHOW ME REFLECTION SETTING THE DIRECTION The lesson elements are 1: Show Me Cards; 2: Setting the Stage; 3: Work Time; 4: Reflection. Navigator accommodates alternate class time arrangements, but all lessons should include these elements. In the Secondary module titles, the Show Me comes at the end of the lesson. WORK TIME

6. Provide accessible instructional support. Strategies for scaffolding and English language learners (ELLs) Explicit reference to the misconception Embedded tips Alignment to standards and math practices Diagnostic and progress assessment In Math Navigator, students tackle fewer problems, but go through them deeply. For students to go deeper into math concepts, teachers need support, strategies and suggested question prompts. The materials will help the teacher to expose misconceptions, but it must be the student who realizes that his or her thinking needs to be corrected. The Teacher Materials help teachers uncover student misconceptions. [Additional notes: The snapshot page is from Using Operations to Solve Problems.]

Common Core State Standards Common Core State Standards (listed in every Teacher Edition of every module) Common Core State Standards Only in the Teacher Edition will you find the grade-level Common Core State Standards to which this module is tailored. The student materials do not list a grade level; they just list the topic. This is intentional, because the authors did not want students to see a below-grade-level reference, but did want students to be engaged in materials where their misconceptions could be exposed. [Additional notes: The snapshot page is from Using Operations to Solve Problems.]

Math Navigator Materials

Components Student Edition Study Cards Show Me Cards Teacher Edition Go through the print components. Teacher Edition: Walk through the Roman Numeral pages for the following: Purpose, Common Core Standards, Overview Goals for the module, and materials for the entire module; then move to the three Appendices in the Elementary modules—there are only two in the Secondary titles. Finally, show a buff-colored page at the beginning of a daily lesson to show the features on that page. Secondary Modules do not contain the appendix for Rituals and Routines, but these pages are included in the Secondary Participant’s workbook for reference/use. Show Me Cards: Have teachers look through the cards (quickly for now), and ask what they notice. Student Edition: This is a consumable book. Look for different types of lessons. Ask teachers to find three things that they notice, share with a partner, and then ask for four things they noticed (via the whole group). Student Study Cards: Have teachers look through the stack and ask again if they can find two front pages, and two back pages. Mention the proper use of the rings and alternative methods to store the Study Cards if the rings are not appropriate for some students. These are also consumable.

Rituals and Routines Using the Show Me Cards Using the Study Cards Using the Student Book Presenting the Task Solo Work Partner Work Probing for Understanding Conferencing with Students Using a Workspace Setting the Direction Work Time Reflection Class Profile Mathematical Goals Misconceptions Rituals and Routines are in regular bold font. Teacher/program components are in italic font. Give teachers a topic assignment from the chart, and have them locate the information in the Teacher Edition and Student Edition where appropriate. This activity should take approximately ten minutes for the teachers to read and prepare their assigned topics. The best way to do this is for teachers to make a poster for the routine. Have teachers answer the following questions as they prepare to share out with the whole group. Questions that lead thinking for rituals and routines: What is expected from the student in this routine? What is expected from the teacher in this routine? How much time should this take? How often does it occur? Questions for program components: Where can I find these, and when will I use it? How do the program components interface with the rituals and routines?

Rituals and Routines Material Routines Using a Workspace Using the Show Me Cards Using the Student Book Using the Study Cards This is a good way to go through the Material Routines. Call on the teacher(s) who were assigned each of these routines, and allow them to share out to the whole group. Make sure that they answer all of the questions from the previous slide. If teachers made posters, have them hang the posters as they present. If the posters display student behaviors and time for the routine, these would be great posters for their classrooms. Teachers may want to take pictures of each poster if they want to replicate them for their own classrooms.

Rituals and Routines Lesson Routines Setting the Direction Presenting the Task Work Time Solo Work Partner Work Probing for Understanding Reflection Here is an example of a Solo Work poster that another group prepared. Here is the list of the Lesson Routines: The Cycle of Learning for Work Time includes the following: Presenting the Task, Solo Work, Partner Work, and Probing for Understanding. The components of the Cycle of Learning should always be presented together to students. Each problem in the Student Edition usually has this cycle and should be kept together in a lesson before going to another part or ending of the lesson.

Rituals and Routines Teacher Support Routines Mathematical Goals Class Profiles Misconceptions Focus on the Language Scaffolding for Success/ELL Module Purpose my Pearson Training Teacher Resources Teacher Support Routines Most of these are found in the buff-colored teacher pages or via the my Pearson Training website. Teach the lesson at this point in the training. You could show slide 17 which lists all of the Rituals and Routines to help remind you of the routines to emphasize and for the teachers to identify them in use.

Assessments ARO Demo Site http://aro.pearsoncmg.com Username: arodemo Password: acsd Go live to show ARO, and use the other PPT for NYC on ARO (NYC_MathNavARO_WalkThrough_5.11.16.ppt). This Demo site contains student data. Be sure to use School Year 2014-2015 and use Ferguesen ES or Grisham MS when sharing data with teachers. Use the Roster Report and view Pre and Post test data. Use this site to train teacher on how to print tests (in Participants Workbook) and… Associate Students to test (Manage Tab) Enter student data for Pre and Post tests Enter data for Checkpoints View Roster Report – see pre and post test data

Teacher Resources Here is the web address for my Pearson Training. http://mytrainingconnection.com/products/math-navigator-2012-cc/tutorials

References Mathematics Assessment Resource Service (MARS), University of Nottingham, and Shell Centre for Mathematical Education. 2015. “Mathematics Assessment Project.” Accessed May 20, 2016. http://map.mathshell.org/. Pearson Education, Inc. 2012. Mathematics Navigator: Research Basis. Accessed May 20, 2016. http://assets.pearsonschool.com/asset_mgr/current/201215 /math_nav_research_basis.pdf.

Martha Robertson