Congruency to Math Standards How do we successfully monitor and support our teachers when we can’t be an expert in every content area?

Math Packet Page 1

DOK? Verbs/Bloom’s Comprehension Application Fluency Standard(s)? Target(s)? Standard consistent vocabulary? Artifact(s) Artifact(s): assessment, lesson plan, activity, etc. Artifact(s)

The Rabbit Fencing Task: Domain 1 Planning & Preparation- What evidence from the lesson plan? What questions might you ask the teacher to gain insight to other components where you may be lacking evidence? Math Packet Page 2

Artifact(s) Standard(s)? Target(s)? Standard consistent vocabulary? Artifact(s) Artifact(s): assessment, lesson plan, activity, etc. Artifact(s) DOK? Verbs/Bloom’s Comprehension Application Fluency Products Performance Task

Take your recording sheet to each poster. Take your recording sheet to each poster. You will have a couple minutes at each station to review and record information about the student work. You will have a couple minutes at each station to review and record information about the student work. Student Work Recording Sheet Math Packet Page 3 Student Work Samples Math Packet Page 4-7

Artifact(s) Standard(s)? Target(s)? Standard consistent vocabulary ? Artifact(s) Students engage in content at appropriate level Artifact(s): assessment, lesson plan, activity, etc. Observation Artifact(s) Products Performance Task DOK? Verbs/Bloom’s Comprehension Application Fluency

Working at your table review each of the vignettes that correspond to the student work. Working at your table review each of the vignettes that correspond to the student work. Record your insights on your recording sheet. Record your insights on your recording sheet. Teaching Scenarios Recording Sheet Math Packet Page 11 Student Work Samples Math Packet Page 12-15

My brain hurts! Simplest definition of rigor ~what we should be looking for in the classroom~ Debriefing the scenarios

Questions to ask about the math classroom: Who is doing most of the talking? Who is working the problems? What kinds of questions are being asked? What are the problems like? What happens when a student gets stuck? Where is the teacher during practice? How does s/he answer students when they ask a question? It depends! They require students to apply what they know about mathematics They talk with a partner to try to figure it out. The teacher may ask a question to help them figure out what they already know that can help them. They try out different ideas. Usually with another question such as, “What have you already tried?” “What do you already know that can help you?” “Does it matter that …?” Moving around the classroom asking questions and taking notes about the conversations, strategies, etc. s/he observes. Higher order questions that require higher level cognitive engagement. Always the students!!!

How are Martha’s Carpeting Task and the Rabbit Fencing Task the same and how are they different? 13 Don’t confuse problems with exercises….

Martha’s Carpeting Task: Martha was recarpeting her bedroom, which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase? 14

Martha’s Carpeting Task Solution Strategies: Using the Area Formula A = l x w A = 15 x 10 A = 150 square feet Drawing a Picture

The Rabbit Fencing Task:. Ms. Brown’s class will raise rabbits for Their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits. –If Ms. Brown’s students want their rabbits to have as much room as possible, how long would each of the sides of the pen be? –How long would each of the sides of the pen be if they had only 16 feet of fencing? –How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it. 16

The Rabbit Fencing Task Solution Strategies: 17 Diagrams on Grid Paper

The Rabbit Fencing Task Solution Strategies: Using a Table LengthWidthPerimeterArea

The Rabbit Fencing Task Solution Strategies: Graph of Length vs Area 19 Max

Similarities and Differences Similarities Both are “area” problems Both require prior knowledge of area Differences The amount of thinking and reasoning required The number of ways the problem can be solved Way in which the area formula is used The need to generalize The range of ways to enter the problem Requires enduring understandings in math How are Martha’s Carpeting Task and the Rabbit Fencing Task the same and how are they different?

If the Rabbit Task is high level how did it go so wrong? TASKS GONE WRONG

Factors Associated with the Maintenance and Decline of High-Level Cognitive Demands Decline Routinizing problematic aspects of the task Shifting the emphasis from meaning, concepts, or understanding to the correctness or completeness of the answer Providing insufficient time to wrestle with the demanding aspects of the task or so much time that students drift into off-task behavior Engaging in high-level cognitive activities is prevented due to classroom management problems Selecting a task that is inappropriate for a given group of students Failing to hold students accountable for high-level products or processes Maintenance Scaffolding of student thinking and reasoning Providing a means by which students can monitor their own progress Modeling of high-level performance by teacher or capable students Pressing for justifications, explanations, and/or meaning through questioning, comments, and/or feedback Selecting tasks that build on students’ prior knowledge Drawing frequent conceptual connections Providing sufficient time to explore

Post Observation Conference Keeping Domain 4 in mind, what questions would you ask and topics would be discussed during the post observation conference? How should the math PLC be utilized to help teachers plan rigorous math lessons and evaluate student work? Math Packet Page 8

Artifact(s) Observation Standard(s)? Target(s)? Standard consistent vocabulary? Artifact(s) Students engage in content at appropriate level Artifact(s): assessment, lesson plan, activity, etc. Artifact(s) The work of PLCs… Products Performance Task DOK? Verbs/Bloom’s Comprehension Application Fluency

Math Packet Pages 9-10

Math Packet Pages 16-17

Standard(s)? Target(s)? Standard consistent vocabulary? Students engage in content at appropriate level Which of these is the most likely culprit impeding congruency in your school? DOK? Verbs/Bloom’s Comprehension Application Fluency ProductsPerformance Task