Montville Township Public Schools Middle and High School Introduction to Common Core State Standards for Mathematics Monday, October 8, 2012 Presenter: Elaine Watson, Ed.D.

Introductions Share What feeds your soul personally? What is your professional role? What feeds your soul professionally?

Volunteers for Breaks I need volunteers to remind me when we need breaks! Every 20 minutes, we need a 2-minute “movement break” to help our blood circulate to our brains. Every hour we need a 5-minute bathroom break.

Formative Assessment How familiar are you with the CCSSM?

Goals for this Workshop You will leave with a deeper understanding of: The Content Standards & Practice Standards The types of tasks that build students’ ability to “practice” the Practice Standards How to navigate rich online CCSSM resources How to practice formative instruction to reach the different learners in your class

What are the standards, anyway? The standards are the end product of what students need to understand and be able to do with the content. They do not attempt to tell teachers how to teach the content. Teaching is an art. There is no one method that fits all teachers or all students.

CCSSM Equally Focuses on… Standards for Mathematical Practice Standards for Mathematical Content Same for All Grade Levels Specific to Grade Level

CCSSM Video The Mathematical Standards: How They Were Developed and Who Was Involved

Modeling is both a K - 12 Practice Standard and a 9 – 12 Content Standard.

Modeling Cycle Problem Formulate Compute Interpret Validate Report

Modeling Cycle Problem Identify variables in the situation Select those that represent essential features Problem Identify variables in the situation Select those that represent essential features

Modeling Cycle Formulate Select or create a geometrical, tabular, algebraic, or statistical representation that describes the relationships between the variables Formulate Select or create a geometrical, tabular, algebraic, or statistical representation that describes the relationships between the variables

Modeling Cycle Compute Analyze and perform operations on these relationships to draw conclusions Compute Analyze and perform operations on these relationships to draw conclusions

Modeling Cycle Interpret Interpret the result of the mathematics in terms of the original situation Interpret Interpret the result of the mathematics in terms of the original situation

Modeling Cycle Validate Validate the conclusions by comparing them with the situation… Validate Validate the conclusions by comparing them with the situation…

Modeling Cycle Validate Re - Formulate Report on conclusions and reasoning behind them

Modeling Cycle Problem Formulate Compute Interpret Validate Report

Modeling Cycle The word “modeling” in this context is used as a verb that describes the process of transforming a real situation into an abstract mathematical model.

CCSSM Video High School Math Courses

Students can: start with a model and interpret what it means in real world terms OR start with a real world problem and create a mathematical model in order to solve it.

Possible or Not? Here is an example of a task where students look at mathematical models (graphs of functions) and determine whether they make sense in a real world situation.

Possible or Not?

Questions: Mr. Hedman is going to show you several graphs. For each graph, please answer the following: A. Is this graph possible or not possible? B.If it is impossible, is there a way to modify it to make it possible? C. All graphs can tell a story, create a story for each graph.

One A. Possible or not? B. How would you modify it? C. Create a story.

Two A. Possible or not? B. How would you modify it? C. Create a story.

Three A. Possible or not? B. How would you modify it? C. Create a story.

Four A. Possible or not? B. How would you modify it? C. Create a story.

Five A. Possible or not? B. How would you modify it? C. Create a story.

Six A. Possible or not? B. How would you modify it? C. Create a story.

Seven A. Possible or not? B. How would you modify it? C. Create a story.

Eight A. Possible or not? B. How would you modify it? C. Create a story.

Nine A. Possible or not? B. How would you modify it? C. Create a story.

Ten A. Possible or not? B. How would you modify it? C. Create a story.

All 10 Graphs What do all of the possible graphs have in common?

And now... For some brief notes on functions!!!! Lesson borrowed and modified from Shodor.Shodor Musical Notes borrowed from Abstract Art Pictures Collection.Abstract Art Pictures Collection.

Pyramid of Pennies Here is an example of a task where students look at a real world problem, create a question, and create a mathematical model that will solve the problem.

Dan Meyer’s 3-Act Process Act I Show an image or short video of a real world situation in which a question can be generated that can be solved by creating a mathematical model.

Dan Meyer’s 3-Act Math Task Pyramid of Pennies

Dan Meyer’s 3-Act Process Act I (continued) 1. How many pennies are there? 2. Guess as close as you can. 3. Give an answer you know is too high. 4. Give an answer you know is too low.

Dan Meyer’s 3-Act Process Act 2 Students determine the information they need to solve the problem. The teacher gives only the information students ask for.

Dan Meyer’s 3-Act Process What information do you need to solve this problem?

Dan Meyer’s 3-Act Process Act 2 continued Students collaborate with each other to create a mathematical model and solve the problem. Students may need find text or online resources such as formulas.

Dan Meyer’s 3-Act Process Go to it!

Dan Meyer’s 3-Act Process Act 3 The answer is revealed.

Dan Meyer’s 3-Act Process Act 3

Standards for Mathematical Practice Describe ways in which student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity

Standards for Mathematical Practice Provide a balanced combination of Procedure and Understanding Shift the focus to ensure mathematical understanding over computation skills

Standards for Mathematical Practice Students will be able to: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.

Think back to the Pyramid of Pennies. At what point during the problem did you do the following? 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.

Content Standard Activity Work with a partner and on your own laptop, go to Go to at least one content domain and read through some standards that have illustrations. Check out the illustrations. How does the illustration assess the understanding of the standard? How could you use the illustrations in your class?

Formative Instruction How do we know if our students know what we want them to know?

Formative Instruction Formative instructional practices are not new—this work dates back to Benjamin Bloom and mastery learning. Teachers "do" formative instruction every day in their classrooms, but for many teachers it is not ongoing and intentional. The latest research reveals that formative instructional practices are effective in closing the achievement gap. These practices are proven to raise the achievement of all students—with the greatest gains for low-achieving students.

Formative Instruction According to brain research, we know that growth is not fixed; it is a mindset. We have an innate desire to learn. This intrinsic motivation to learn is supported when the student has a sense of control and choice, gets frequent and specific feedback about where he/she is, encounters learning that is challenging but not threatening, is able to self- assess accurately and encounters real-life learning tasks.

Formative Instruction These “supports” are formative instructional practices. Formative instructional practices provide students with opportunities for penalty-free learning, so when it is time to measure (summative assessment), students feel in control of their success.

Examples of Formative Assessment Anecdotal Notes: These are short notes written during a lesson as students work in groups or individually, or after the lesson is complete. The teacher should reflect on a specific aspect of the learning (sorts geometric shapes correctly) and make notes on the student's progress toward mastery of that learning target. The teacher can create a form to organize these notes so that they can easily be used for adjusting instruction based on student needs.

Examples of Formative Assessment Exit Slips are written responses to questions the teacher poses at the end of a lesson or a class to assess student understanding of key concepts. They should take no more than 5 minutes to complete and are taken up as students leave the classroom. The teacher can quickly determine which students have it, which ones need a little help, and which ones are going to require much more instruction on the concept. By assessing the responses on the Exit Slips the teacher can better adjust the instruction in order to accommodate students' needs for the next class.

Examples of Formative Assessment Asking students questions about their reasoning and promoting rich classroom discourse between students creates an opportunity for student to make sense of problems, construct viable arguments, and critique the reasoning of others. It also provides teachers with significant insight into the degree and depth of student understanding. Questions should go beyond the typical factual questions requiring recall of facts or numbers.

Small Group Activity Discuss ways that you can use at least one of these strategies in a lesson during the next week. Commit to at least one: Keeping Anecdotal Notes Using Exit Slips and following up on what the data tell you Rich questioning and encouraging student to student discourse.

Goals for this Workshop You will leave with a deeper understanding of: The Content Standards & Practice Standards The types of tasks that build students’ ability to “practice” the Practice Standards How to navigate rich online CCSSM resources How to practice formative instruction to reach the different learners in your class

Resources “October 8, 2012 Montville Township Middle and High School” on watsonmath.com.