Go Math Through the Lens of Danielson Framework Presenter: Simi Minhas Math Achievement Coach CFN204

Please look at the signs at each table and sit accordingly Please look at the signs at each table and sit accordingly. Each table has been marked with a grade level. If you are a coach, or do not teach a particular grade, please pick a grade level you want to work with. The purpose of sitting with a grade level is to share best practices with our colleagues, and learn from each other.

Key Things to Remember from Previous PD Remember we want to help students become problem solvers, so provide them with the tools and stamina through math instruction. Allow for multiple entry points differentiating the components provided in the Go Math Program. Create a safe and respectful environment in the classroom where mistakes become teaching, and learning moments. Create a learning community, where we all learn from each other For students who are performing at higher levels, think about ways to challenge them, without providing the scaffolding provided by the program.

Remember… Go math is just a program or a resource. You can use the components, or modify the components to meet the needs of your students. Any decision that you make should be supported by data (formative or summative) Have a system of monitoring students performance ad progress. Create systems that are easy to manage and are meaningful to you. Group students in a way where you can maximize instructional time. Both heterogeneous and homogeneous groupings have a place depending on the purpose of the grouping.

The Purpose of Assessment What assessment choices did we make. Why The Purpose of Assessment What assessment choices did we make? Why? How are we using the data from assessments to inform instruction and bridge learning gaps? It is very important that as educators we are able to justify the choices that we make for each assessment, and the purpose why those assessments were administered. It is also important that we don’t choose too many assessments, but instead focus on using the data from the few assessments that we pick to identify, and meet the needs of our students. In the pacing, two days are allotted for assessment for each unit. You can either assess both days, or review one day and assess the other.

Share What assessments is your school using and why? How are you collecting formative data on regular basis? How are you using data from the formative and summative assessments to inform instruction? How are you using different components in the program to differentiate instruction? How are you incorporating other resources?

Why Is “Using Questioning and Discussion Techniques” an Important Component of Effective Teaching? High-quality questions encourage students to make connections among concepts or events previously believed to be unrelated and arrive at new understandings of complex materials. In lessons involving small-group work, the quality of students’ questions and discussion in their small groups may be considered as part of the component.  Higher-level questions from students, either in the full class or in small-group discussions, provide evidence that these skills have been taught. Students’ responses to questions are valued.

Discussion techniques § Some teachers report that “we discussed x” when, what they mean is “I said x.” §  Some teachers confuse discussion with explanation of content. As important as explanation is, it’s not discussion. §  In a true discussion, a teacher … poses a question. invites all students’ views to be heard. enables students to engage in discussion directly with one another. does not always mediate.

In a Highly Effective Discussion… The teacher uses open-ended questions, inviting students to think and/or offer multiple possible answers. The teacher makes effective use of wait time. The teacher builds on and uses student responses to questions effectively. Discussions enable students to talk to one another, without ongoing mediation by the teacher. The teacher calls on most students, even those who don’t initially volunteer. Many students actively engage in the discussion.

Discussion Using the Go Math Program Think about… How can use different components of the lesson to facilitate math discussion? Where in the program can you plan small group discussion? How can you create routines and protocols to engage students in meaningful discussions?

Ways of Eliciting Student Responses and Starting Math Discussion Does anyone have a solution they would like to share? Please explain to the rest of the class how you got your answer. How did you begin working on this problem? Can you point to a part of this problem that was difficult? Why was it difficult? Did anyone approach the problem in a different way? Can you explain your thinking?

Probing students’ answers to…  Figure out what a student means or is thinking, when you don’t understand what they are saying  Check whether right answers are supported by correct understanding  Probe wrong answers to understand student thinking

Questions and prompts to Probe Student Responses Explain what you have done so far? What else is there to do? How do you know? Why did you ____? How did you get ____? Could you use models and manipulatives to show how that works? What led you to that idea? Walk us through your steps. Where did you begin? Please give an example. So is what you’re saying ____? When you say ____, do you mean ___? Could you explain a little more about what you are thinking? Can you explain that in a different way? What do you notice when _____?

How would you model or represent ½ ÷ 1/8? Math Models How would you model or represent ½ ÷ 1/8? How would you model or represent ¼ of 1/3? How would you model or represent 63÷ 7? How would you model or represent __+19= 45?

Ways to Use CCSS Math Talk Cards to Facilitate Math Discussions Introduce the cards one or two at a time and have the students use them in small groups Continue this process until you have introduces all of the eight mathematical practices Students can use these cards as a tool These cards allow for entry points for those students who are not comfortable starting a math conversation

Essential Question How can we make a model to compare numbers? Let’s think about… What does compare mean? What does the word ‘model’ mean in math?

Engage Suppose there is a bucket of 25 crayons on the table and a bucket of 31 crayons in the closet. Where are there more crayons? How did you decide?

What models could you use to compare 31 and 25? How many groups of 10 in 31? How many ones cubes? How many groups of 10 in 25? How many ones cubes?

Unlock the Problem Model using base ten blocks Remember to change the models into pictures Label your pictures to clearly explain your thinking Sara says that the children bought more plain milk cartons because 188 has bigger numbers in the ones and the tens place. Do you agree or disagree with Sara? Why?

Components for Differentiation Reteach sheets Enrichment sheets Animation Unlock the problem without scaffolding Teacher created materials- graphic organizers for problem solving, rubrics, prompts etc. Grouping of students Rigorous word problems Expectations for independent work

Shifts in Mathematics Shift 1 Focus Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards. Shift 2 Coherence Principals and teachers carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. Shift 3 Fluency Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions. Shift 4 Deep Understanding Students deeply understand and can operate easily within a math concept before moving on. They learn more than the trick to get the answer right. They learn the math. Shift 5 Application Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. Shift 6 Dual Intensity Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity.

Questions and Feedback Please fill out the Feedback Form before you leave. Thanks!!!! Please visit the CFN204 page for the power point from this workshop.