The Marriage of Math and Literacy: Infusing Writing into Your MS/HS Math Classroom

1. The Marriage of Math and Literacy:Infusing Writing into Your MS/HS Math Classroom Jennifer Spong Gina Palermo Cattaraugus Allegany BOCES

2. Why are we here today? This learning opportunity targets NYS Teaching Standards: II - Knowledge of Content and Instruction III – Instructional Practice

3. What are we doing today? • Explore the Standards for Mathematical Practice • Examine what these look like in a classroom and how students interpret them • Discuss the writing standards and different types of writing • Infusing writing in to your math class • Reflection

4. Overview:Standards for Mathematical Practice • Mathematical habits of mind • All math educators should seek to develop these habits in their students • Standards are based on important processes and proficiencies with longstanding importance in math • The Standards for Mathematical Content are a balance between procedure and understanding • Students who lack understanding may rely too heavily on procedures • Need a flexible base to work from • Teaches students to use computational skills in a meaningful context • Content standards that set an expectation for understanding are “points of intersection” with Mathematical Practice Standards. Writing in math is a justification of this understanding.

5. Standards for Mathematical Practice • Table 1: (green) • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively • Table 2: (blue) • Construct viable arguments and critique the reasoning of others • Model with mathematics • Table 3: (purple) • Use appropriate tools strategically • Attend to precision • Table 4: (yellow) • Look for and make use of structure • Look for an express regularity in repeated reasoning

6. Jigsaw with the Standards for Mathematical Practice Read through the Standards for Mathematical Practice; focus on your assigned standard(s) Think about: • How would you explain these standards to the kids or a colleague? • What would it look like in your classroom? Create a chart that explains the most important part of your assigned SMP(s) and how they would look to students/colleagues

7. Check it Out and Share SHARE out the main tenant of your SMP(s) Regroup by grade level and shareways SMPs would look in your classroom

8. Kid Friendly SMPs Looking through the eyes of a child… Takeaways: “Solving problems is not only a goal of learning mathematics but also a major means of doing so.” National Council of Teachers of Mathematics Principles and Standards for School Mathematics • Plan to solve • Use numbers and words to solve • Explain thinking • Recognize math in everyday life • Use math tools • Be clear in explanations • Recognize parts of wholes • See patterns

9. Modeling in Math • Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. • The basic modeling cycle is summarized in the diagram. It involves (1) identifying variables in the situation and selecting those that represent essential features, (2) formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables, (3) analyzing and performing operations on these relationships to draw conclusions, (4) interpreting the results of the mathematics in terms of the original situation, (5) validating the conclusions by comparing them with the situation, and then either improving the model or, if it is acceptable, (6) reporting on the conclusions and the reasoning behind them. Choices, assumptions, and approximations are present throughout this cycle.

10. All You Need to Know About CCSS Writing Anchor Standards in 1 Minute

11. Writing in the Content Areas 3 Types: Narrative, Expository, Argument • Expository writingis writing where the purpose is to inform, describe, explain, or define the author's subject to the reader. Expository text is meant to deposit information and is the most frequently used type of writing by students in elementary schools, middle schools, high schools, colleges and universities. A well-written exposition remains focused on its topic and lists events in chronological order. (also called informational/explanatory writing). • Argument writing is at the core of critical thinking. An argument is not simply a dispute, as when people disagree with one another or yell at each other. Argument is about making a case in support of a claim in everyday affairs—in science, in policy making, in courtrooms, and so forth. Writing an argument is expressing a point of view on a subject and supporting it with evidence. • Narrative writingis writing that tells a story, whether true or fictional.

12. How can we infuse writing into math? Writing the Argument Informational/ Explanatory Writing Open ended problems: These problems have multiple answers. Ask the students to solve the problem in 2 different ways, show their work and defend their solutions in writing. Open middle problems: These problems have one answer but many ways to get there. Students would solve the problem and write an explanation about their process. Narrative Writing Student created problems **Journal writing can be seen throughout each type of writing depending on the prompt

13. Math Argument

14. What is Argumentative Writing? Being a math teacher my first question is, "What is argumentative writing?“ Followed closely by, "How am I suppose to teach my students how to write an argumentative essay?" and "How am I suppose to grade their final product?" Don’t worry…there’s a tutorial!

15. Math Argument As I was going to St. Ives I met a man with seven wives. Every wife had seven sacks. Every sack had seven cats. Every cat had seven kits. Kits, cats, sacks, wives. How many were going to St. Ives? Solve this problem in three different ways and write an argument for which of the answers is best.

16. Possible Answers • 0 • 1 • 2 • 7 • 9 • 2752 • 2800 • 2801 • 2802

17. Assessing Writing Quality • First, let’s hear your arguments for your answers. • Tips for creating writing prompts and giving feedback • Using math writing rubrics

18. Math Explanation THE PROOF IS IN THE PUDDING The host at a party turned to a guest and said, “I have three daughters and I will tell you how old they are. The product of their ages is 72. The sum of their ages is my house number. How old is each?” The guest rushed to the door, looked at the house number, and informed the host that he needed more information. The host then added, “The oldest likes strawberry pudding.” The guest then announced the ages of the three girls. What are the ages of the three daughters? (All ages are whole numbers. It is possible that there may be twins.) Explain your answer.

19. Solution First, I found all the combinations of 3 numbers that would give me a product of 72. These would be the ages of the daughters. Then I found the sum of each group of numbers that are possible ages. This would be the house number. Note that every combination of possible ages which has a product of 72 has its own unique sum of ages - except for 2, 6, 6 and 3, 3, 8, both of which share the sum of 14. Since the guest can't figure out the ages after looking at the house number, the house number must be 14, because then the ages could be either 2, 6, 6 or 3, 3, 8. Now, the next clue is that the oldest child likes strawberry pudding. This means that there is one oldest child. There is no oldest child when the ages are 2, 6, 6, so the ages of the children must be 3, 3, and 8 years old. After I know that the ages multiply to 72, here is a complete list of the possibilities: Ages: Sum of ages: 1, 1, 72 74 1, 2, 36 39 1, 3, 24 28 1, 4, 18 23 1, 6, 12 19 1, 8, 9 18 2, 2, 18 22 2, 3, 12 17 2, 4, 9 15 2, 6, 6 14 ** 3, 3, 8 14 ** 3, 4, 6 13

20. Math Narrative Write three word problems about this model: Jack 184 ? Betty 63

21. Solution Some examples: • Jack weighs 184 pounds. Betty weighs 63 pounds less than Jack. How much does Betty weigh? • Betty saved $121. She saved $63 less than Jack. How much did they save together? • Jack and Betty have 305 Facebook friends together. If Jack has 184 Facebook friends, how many less than Jack does Betty have?

22. Real Life Math Explanatory Writing • Prescribing Medicine & Preventing Errors article • Journal Writing in the Mathematics Classroom: A Beginner’s Approach—prompts for writing

23. More Resources… • Smart Balance Assessment Consortium http://sampleitems.smarterbalanced.org/itempreview/sbac/index.htm • MARS – Mathematics Assessment Resource Service – Mathematics Assessment Project http://map.mathshell.org/materials/index.php • Inside Mathematics http://insidemathematics.org/index.php/mathematical-content-standards • Illustrative Mathematics http://www.illustrativemathematics.org/ • Exemplars http://www.exemplars.com/ • Math Forum at Drexel University http://mathforum.org/ • CRCS Curriculum Integrator http://www.crcs.wnyric.org/departments.cfm?subpage=1638473 • Catt-Little Valley Curriculum Coordinator http://www.cattlv.wnyric.org/Page/1809

24. Reflection • What did you learn about the three different styles of writing as they relate to math? • What can you do in your classroom to foster these writing styles? • How can you work with the ELA teachers to help you get your students thinking and writing like mathematicians?

25. We believe that if we want students to understand mathematics, it is more helpful to think of understanding as something that results from solving problems, rather than something we can teach directly. Hiebert et al, Making Sense: Teaching and Learning Mathematics with Understanding.

26. RememberS4: StartSmallStaySane!

27. Please fill out the ISS Workshop Evaluation. Thank you for coming! Have a fantastic summer!