Math Leadership Network December 3rd, 2015

Learning Goals Attendees will deepen their existing knowledge of one or more of the following: Research-Based Instructional Practices Equity (Instructional Practices for Diverse Student Populations) Professional Collaboration (Sharing with Colleagues)

Welcome Activator Go Around State your name, position and school district Warm-up Activator 30 minutes

Doing the Math… 30 minutes What components of Rigor? Work with someone in another grade band if possible.

The Three Shifts in Mathematics Focus: strongly where the standards focus Coherence: Think across grades and link to major topics within grades Rigor: Require conceptual understanding, fluency, and application

What is Fluency? Engage NY

What is Fluency? 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 such as multiplication tables so that they are more able to understand and manipulate more complex functions. Engage NY

What is Fluency? 3A’s Protocol Skim the reading and select Identify a piece of text that focuses on an Assumption the author makes, a piece of text you Agree with and a piece of text you Aspire to Act upon Use a Go Around for the 3A’s spending 1 minute per person, per A Once finished, discuss as a group what one idea comes to mind when your group thinks of Fluency Group of 3-4

Frequently Asked Questions How can we assess fluency other than giving a timed test? Is it really possible to assess conceptual understanding? What does it look like? Aren’t the Common Core State Standards for Math all about application and meaningful tasks? Here are a few frequently asked questions about the idea of rigor and balance. How can we assess fluency other than giving a timed test? When you talk about assessment items that get at fluency, it is not always only going to be weekly timed tests. That may be an instructional practice that works for certain people, but it is not a mandate that everyone across the country will be doing timed tests. There are lots of different ways to get to this idea of fluency and there are lots of different ways to know if a student is fluent in something. On a side note, it is important to remember that assessing fluency is not necessarily the same as practicing fluency. Often schools will do timed tests 3 days a week and think they are fulfilling the “fluency requirement.” Students need opportunities to practice fluency, as well.   Is it really possible to assess conceptual understanding? What does it look like? So, how do you take the math that we want students to know out of context and how do we ask them something that just by doing the problem will tell us that they have conceptual understanding? We will be doing a set of sample problems in a moment. Spend some time really thinking about the problems under conceptual understanding and see what is different. Asking students to show work and explain can be informative, but it isn’t the only way to assess conceptual understanding and can become tiring for students. Lastly, are the Common Core Standards in Math all about application and meaningful tasks?  It is a common misconception that CCSSM is only about rich application tasks. That is only one piece of the puzzle. You cannot just do these tasks and think that everything else is going to happen. This is not a criticism of the tasks that are out there. The tasks are often good. Performance tasks are great, but where in those performance tasks are you getting at procedural skill and fluency? Where are you getting at conceptual understanding? We cannot just expect those things to happen if we only do those tasks. Remember that rigor in the Standards is a balance of time spent on conceptual understanding, procedural skill and fluency, and application. The Standards themselves will typically guide the reader to what aspect of rigor is expected.

Rigor Pass out the math problems and solve a few Note which component of Rigor is most prevalent: Conceptual understanding Procedural skill and fluency Application Use Go-Around protocol to share your thinking and sort the problems Be prepared to discuss something you observed from one of the problems you looked at

Rigor Conceptual Understanding: Procedural Skill and Fluency: 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Procedural Skill and Fluency: 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Application: 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. Here are some of the key words to look for when determining if a standard should be assessed for conceptual understanding, procedural skill and fluency, or through an application type problem. What are some other words that would highlight a “conceptual understanding” standard? (Interpret, recognize, describe, explain…) Of course, these three aspects of rigor are not always addressed separately from each other, but what is clear is that the wording of each standard can help the teacher determine what the main goal of this standard is.

Rigor: Illustrations of Conceptual Understanding, Fluency, and Application Here rigor does not mean “hard problems” It’s a balance of three fundamental components that result in deep mathematical understanding There must be variety in what students are asked to produce Rigor, as defined here, does not mean hard problems. It doesn’t mean more difficult. Rigor, here, means something very specific. We are talking about the balance of these components of conceptual understanding, fluency, and application. We are going to look at a set of problems; some assess fluency, some require conceptual understanding, and some are examples of application. By working through these problems, we can start seeing what this looks like.

BREAK

Looking At Student Work

Looking At Student Work In Grade Bands: Review student work samples using the Student Task Reflection Protocol This afternoon: Choose new task to try with students Bring back student work samples on March 17th

Handshake Task 6th grade Students Haller Middle School, Arlington School District There are 10 students in the classroom. If each person shakes every hand in the classroom only once, excluding their own, how many handshakes will that be?

Curious Subtraction Task Achieve the Core Decide which component of rigor is most prevalent in the task. http://achievethecore.org/page/907/curious-subtraction-task-detail-pg

Why Do We Do Math Together? “Teaching mathematics required specialized expertise and professional knowledge that includes not only knowing mathematics but knowing it in ways that make it useful for the work of teaching” (Ball & Forzani 2010; Ball, Thames, and Phelps 2008). -Principles to Action NCTM (p.11)

Jo Boaler – Professor Stanford University Begin video at 1:15 and PAUSE once she gives the problem (18 x 5). Give participants an opportunity to solve the problem and model a number talk – don’t take as long as the first one – record 3-4 solutions. Then continue to show video from 1:36 to 7:02. Number Talks Video https://www.youcubed.org/jo-dot-card-number-talk/

Number Talks

Number Talks 8:00-8:30-Jon/Jamie Dot Tasks

Number Talks for High School 3(x + 2) + 5(x +2) - 7 = 20

Number Talks for High School (2006 x 2008) – (2007 x 2007)

Number Talks Jo Boalar Stanford video

Number Talks Jo Boalar Stanford video picture of 3 ten point photo and some problems from HS

Wrap Up AESD Math Professional Development Reflection 6 hours http://www.surveygizmo.com/s3/2302860/AESD-Math-Professional-Development-Reflection-2015-2016 6 hours Goals B,C and E only! Principles to Actions Read pages 48-52; Supporting Productive Struggle Administer Task or Try a Number Talk