Writing in Math: Digging Deeper into Short Constructed Responses Slides 1-6 Setting the stage 9:00-9:10

Today’s Learning Deepen content learning through writing, knowing writing is an integral part of learning content Revisit Process Standards in mathematics Elevate the thinking behind short constructed responses Review instructional strategies needed to support mathematical thinking, reasoning, communicating Identify classroom look fors that support writing in math

Writing to Learn Mathematics “The process of writing requires gathering, organizing, and clarifying thoughts. It demands finding out what you know and don’t know. It calls for thinking clearly. Similarly, doing mathematics depends on gathering, organizing, and clarifying thoughts, finding out what you know and don’t know, and thinking clearly. Although the final representation of a mathematical pursuit looks very different from the final product of a writing effort, the mental journey is, at its base, the same—making sense of an idea and presenting it effectively.” -Marilyn Burns

Guiding Principle B: Writing is a tool for thinking Students recognize the act of writing helps them generate new ideas or discover new knowledge. Students become better readers, thinkers, and learners in a discipline by working with the forms and contexts specific to the discipline.

Writing to Learn Mathematics Writing can assist math instruction in two ways - by helping children make sense of mathematics and by helping teachers understand what children are learning.

Writing in Mathematics Marilyn Burns As you read, notate things you are already doing in your classroom, as well as strategies for incorporating writing into your classroom you want to think about more deeply. (page 33) Share with your small group. Writing in math provides opportunities for students to reflect on their own learning and to explore, extend, and cement their ideas about the mathematics they study. Read-reflect-share 25 minutes 9:10-9:35

You have a penny, a nickel, a dime, and a quarter You have a penny, a nickel, a dime, and a quarter. What amounts can you make if you use 1,2,3, or 4 of the coins? Write to help explain your best thinking using words, numbers, or pictures. 9:35-9:50 Strategies? Make a table, chart, or organized list

2nd Grade A snack you want costs 45 cents. You have a quarter, some nickels, some dimes but no pennies. Write two different ways you could pay for your snack.

Definition In the instructional process it is essential to teach students how to write quality responses, across content areas. A well constructed CR item generates the ability to examine student thinking and often requires higher level thinking. CR items are not designed for memorization or simple restating of information; rather, these items require the application of the students’ knowledge. They are developed to engage students in higher level thinking. (making comparisons, identifying patterns, evaluating points of view, make generalizations, synthesizing information…) Looking at rubrics and CSAP released items 9:50-10:00 Slides 10-18

Colorado Department of Education Rubric Guidelines

2 - Point Rubric for Short Constructed-Response Items This rubric is used to score students' responses to short constructed-response items. These items require the students to use problem-solving skills as they apply to all of the Colorado Model Content Standards for mathematics. An item may ask the student to include and communicate reasoning using words and /or numbers, evaluate an answer, or demonstrate the process used to determine an answer. There are several short constructed-response items in CSAP, each taking approximately 3 to 5 minutes to complete. Each short constructed-response item receives a single score of 0,1,or 2 points. 2 Points The response accomplishes the prompted purpose and effectively communicates the student's mathematical understanding. The student's strategy and execution meet the content (including concepts, technique, representations, and connections), thinking processes, and qualitative demands of the task. Minor omissions may exist, but do not detract from the correctness of the response. 1 Point The response partially accomplishes the prompted purpose. The student's strategy and execution lack adequate evidence of the learning and strategic tools that are needed to accomplish the task. The response may show some effort to accomplish the task, but with little success. It is clear that the student requires additional feedback and/or instruction from the teacher in order to accomplish the task. O Points The response lacks evidence of mathematical knowledge that is appropriate to the intent of the task.

3 - Point Rubric for Medium Constructed-Response Items This rubric is used to score students' responses to medium constructed-response items. These items require the student to use problem-solving skills that may require the construction of a graph or a model, the extension of a pattern, or the use of geometric relationships and spatial reasoning. These items may also include an explanation of reasoning, evaluation of methods, or application to real-world situations. There are several medium constructed-response items in CSAP, each taking approximately 10 minutes to complete. Each extended constructed-response item receives a single score of 0, 1, 2, or 3 points. 3 Points The response accomplishes the prompted purpose and effectively communicates the student's mathematical understanding. The student's strategy and execution meet the content (including concepts, technique, representations, and connections), thinking processes and qualitative demands of the task. Minor omissions may exist, but do not detract from the correctness of the response. 2 Points The response demonstrates adequate evidence of the learning and strategic tools necessary to complete the prompted purpose. It may contain overlooked issues, misleading assumptions, and/or errors in execution. Evidence in the response demonstrates that the student can revise the work to accomplish the task with the help of written feedback or dialogue. 1 Point The response demonstrates some evidence of mathematical knowledge that is appropriate to the intent of the prompted purpose. An effort was made to accomplish the task, but with little success. Evidence in the response demonstrates that with instruction the student can revise the work to accomplish the task. 0 Points The response lacks any evidence of mathematical knowledge that is appropriate to the intent of the task.

4 - Point Rubric for Extended Constructed-Response Items This rubric is used to score students' responses to extended constructed-response items. These items require the student to use problem-solving skills that may require the construction of a graph or a model, the extension of a pattern, or the use of geometric relationships and spatial reasoning. These items may also include an explanation of reasoning, evaluation of methods, or application to real-world situations. There are several extended constructed-response items in CSAP, each taking approximately 15 minutes to complete. Each extended constructed-response item receives a single score of 0, 1, 2, 3 or 4 points. 4 Points The response accomplishes the prompted purpose and effectively communicates the student's mathematical understanding. The student's strategy and execution meet the content (including concepts, technique, representations, and connections), thinking processes and qualitative demands of the task. Minor omissions may exist, but do not detract from the correctness of the response. 3 Points The response provides adequate evidence of the learning and strategic tools necessary to complete the prompted purpose. It may contain overlooked issues, misleading assumptions, and/or errors in execution. Evidence in the response demonstrates that the student can revise the work to accomplish the task with the help of written feedback. The student does not need a dialogue or additional instructions. 2 Points The response partially completes the task, but lacks adequate evidence of the learning and strategic tools that are needed to accomplish the prompted purpose. It is not clear that the student is ready to revise the work without more instruction. 1 Point The response demonstrates some evidence of mathematical knowledge that is appropriate to the intent of the prompted purpose. An effort was made to accomplish the task, but with little success. Minimal evidence in the response demonstrates that with instruction the student can revise the work to accomplish the task. 0 Points The response lacks any evidence of mathematical knowledge that is appropriate to the intent of the task.

Connect to CAP

Prioritized Benchmark (RED) Process Standards: Problem Solving, reasoning and proof, communications, connections, and representations should be incorporated into lessons throughout the school year. 10:00-10:10

Process Standards

Problem Solving Works at understanding a problem before beginning work Uses drawings, graphs, and physical models to help solve problems Has and uses appropriate strategies for solving problems Assesses the validity of answers

Possible Starters for Constructed Responses I/we think the answer is ________. We think this because . . . . . . . . . . OR Use numbers, words or pictures to explain how you got your answer and why you think your answer makes sense and is correct.

Reasoning Justifies solution methods and results Makes conjectures based on reasoning Observes and uses patterns in mathematics

Communication Explains ideas in writing Communicates ideas clearly in class discussions

We know that the Process Standards are assessed We know that the Process Standards are assessed. This is what makes up a constructed response. So . . . . How explicitly are we teaching and using them in our daily instruction?

Let’s think about a unit of study in Math. Embedding process standards How can the instructional resource be used as mentor text to help to know what to look for What else could be used as mentor text?

Table Talk How are you currently embedding process standards into math in your classroom? How might you more systematically apply the process standards to a lessons and/or assessment in Investigations?

Writing is Part of the Mathematics Curriculum Students write to keep ongoing records about what they’re doing and learning Students write in order to solve math problems Students write to explain mathematical ideas Students write to describe learning processes -Joan Countryman Writing to Learn Mathematics

Additional Writing to Learn Structures and Supports Anchor Charts Word Walls Venn Diagrams, Concept Maps CLOZE Sentences and Paragraphs Sentence Starters Exemplars Rubrics Think about how

Anchor Charts Help Scaffold Math Learning  Anchor Charts Support Number Sense Development Anchor Charts Support Math Fact Fluency Anchor Charts That Focus on Problem Solving Strategies  Anchor Charts as Resources Help Students Build Math Vocabulary

Word Walls

Next Steps How will this learning guide you in planning for upcoming math instruction? What data will be important to collect? How will you progress monitor?