Warm – up Consider The Pattern! From “Mathematics Teaching in the Middle School,” January, Answer the following questions: 1.What are the elements in the next row? 2.Consider the sum of the elements in the 1 st row, 2 nd row, 3 rd row, etc. What is the sum of the elements in the tenth row? 3.Consider the sum of the first two rows, the first three rows, the first 4 rows, etc. What is the sum of the first ten rows?

Warm – up Consider The Pattern! From “Mathematics Teaching in the Middle School,” January, Describe two more patterns in this triangular set of numbers.

3 The student will learn what recent research shows about writing in the mathematics classroom Writing in the Mathematics Classroom The student will learn what recent research shows about writing in the mathematics classroom and will see several examples of how to implement writing in their classrooms.

4 Should we teach thinking in a mathematics class? Introduction Should we teach writing in a mathematics class?

5 Motivation The writing process can be a medium for learning mathematics and thus should be an integral part of every mathematics class.

6 Research Findings Students who write essays explaining specific mathematical techniques do better on traditional exams that their peers who have been taught traditional by methods. As we write we see new relationships, invent new ideas, and learn to communicate better. Using writing in mathematics will not only make mathematics students better writers but will make them better mathematics students. continued

7 Research Findings the classroom environment is less threatening, and anxiety is less likely to interfere with learning. students are more involved in the learning process. students use higher-level skills because writing tasks require those skills.

8 Students who have the opportunities, encouragement, and support for speaking, writing, reading, and listening in mathematics classes reap dual benefits: NCTM Standard - Communication Pre-kindergarten – Grade 12 - they communicate to learn mathematics, and - they learn to communicate mathematically.

9 Organize and consolidate their mathematical thinking through communication NCTM Standard - Communication Pre-kindergarten – Grade 12 - Writing in mathematics can also help students consolidate their thinking because it requires them to reflect on their work and clarify their thoughts about the ideas developed in the lesson. Later, they may find it helpful to reread the record of their own thoughts.

10 Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. NCTM Standard - Communication Pre-kindergarten – Grade 12 - the process of learning to write mathematically is similar to that of learning to write in any genre. Practice, with guidance, is important. So is attention to the specifics of mathematical argument, including the use and special meanings of mathematical language and the representations and standards of explanation and proof.

11 Communication should be focused on worthwhile mathematical tasks. Teachers should identify tasks that - NCTM Standard - Communication Grades relate to important mathematical ideas; are accessible to multiple methods of solutions; allow multiple representations; afford students opportunities to interpret, justify, and conjecture. continued

12 Teachers can use oral and written communication in mathematics to give students opportunities to - NCTM Standard - Communication Grades think through problems; formulate explanations; try out new vocabulary or notation; experiment with forms of argumentation; justify conjectures; critique justifications; reflect on their own understanding an on the ideas of others.

13 High school students should be - NCTM Standard - Communication Grades good critics and good self-critics; able to generate explanations, formulate questions, and write arguments; able to use spreadsheets, geometric diagrams, natural language and algebraic symbols; able to use mathematical symbols and language correctly: good collaborators who work effectively with others: continued

14 Teachers should have an active role in developing communication in grades 9 through 12 - NCTM Standard - Communication Grades help students become more precise in written mathematics; have students read increasingly more technical text; use problems that require explanations; regularly discuss and compare the adequacy of those explanations;

15 Writing Writing is a valuable way of reflecting on and solidifying what one knows, and several kinds of exercises can serve this purpose.

16 Writing Activities for Math Journals Students keep records of feelings, questions, and descriptions of algorithms or processes they have learned. Students can use stickers (red for stress, yellow for AH’s! or bright spots, and blue for good comfort level) when they read a mathematics assignment. These marks can be cross referenced when writing in their journals.

17 Writing Activities for Math Graphic Organizers Compare/Contrast Venn Diagrams Example using right triangles and equiangular triangles.

18 Writing Activities for Math Graphic Organizers Use of a diamond organizer (The Reading Teacher, Vol. 48. No. 3, November, 1994.) to solve the following problem. Dr. Glandon raises rabbits. He also has rabbit pens in which to place his rabbits. If he tries to place one rabbit in each pen he finds that he has one rabbit left without a pen. If he tries to place two rabbits in each pen he finds that he has one pen without any rabbits. How many rabbits does Dr. Glandon have?

19 Writing Activities for Math Story Problems/Test Items Students write story problems to be solved by other students using the concept currently under study. Students submit items for possible inclusion on a test.

20 Writing Activities for Math Describe Something One student describes a drawing to the class while her classmates try to draw it. Let’s try it.

21 Writing Activities for Math Micro Themes Students write short essays to: summarize a mathematical concept; support a position on an issue by reasoning, empirical evidence or some other authority; draw conclusions from data and discover a thesis or general statement; solve a puzzle related to a mathematical concept; teach a concept to an imaginary learner.

22 Writing Activities for Math Magazine Photos Bring in photographs from magazines (of student interest) and have the students write mathematics problems from the content in the photos. Problems then will be given to other students to solve.

23 Writing Activities for Math Post Cards Students write a post card about the days lesson. Try one!

24 PLACE STAMP HERE Dear Pythag, Used your theorem today. Really cool! Looking forward to more tricks and shortcuts. QED Jim Pythagoras of Thebes 22 Agora Way Old Athens

25 Writing Activities for Math Point of View Students take on the identity of a mathematical symbol, geometric figure, etc. and write a description of some of their experiences or pet peeves.

26 Writing Activities for Math Dear Euclid Students write answers to questions about mathematics submitted by their classmates. Dear Euclid, I’m a square dating a triangle. Is it possible for me to circumscribe her? I need to know immediately as our parents are concerned. Polygons in waiting.

27 Writing Activities for Math Ads/Slogans Students write radio or tv ads about the mathematics topic under discussion. Students write a dictionary entry for a mathematical term or process. Students write a mathematical slogan for a bumper sticker.

28 Explain in your own words the meaning of _____. Writing Prompts Reflect on your participation in class today and then complete the following statement (teacher or student selects one). I learned that I (or we)... I was surprised that I... I discovered that I... I was pleased that I... continued

29 Explain what is most important to understand about _____. Writing Prompts 2 The most important thing I learned in math this week (or today) is _______. Write a letter to a classmate who could not attend class today so that she will understand what we did and learn as much as you did. What I liked most (or least) about math class today was _______.

30 Not all writing needs to be evaluated. Perhaps most of it need not. Almost all of it should be viewed by the teacher and often comments included. Remember the purpose of writing in the mathematics classroom is to improve learning. Evaluation of Writing When writing is to be evaluated consider a rubric. A sample will be distributed for discussion.

31 Summary on Writing Students who write essays explaining specific mathematical techniques do better on traditional exams that their peers who have been taught traditional by methods. As we write we see new relationships, invent new ideas, and learn to communicate better. Using writing in mathematics will not only make mathematics students better writers but will make them better mathematics students.

32 Handouts If not previously done pass out the handouts on: 500 Writing Formats, and Expository Writing.

33 Assignment Prepare questions for Wednesday – “Student Teacher” day. Study for the final.