Writing Portfolio EDRL 427 Joshua Garcia

Ideas  A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.” –G.H. Hardy

Mathematicians sit around making patterns of ideas. Writing can be instrumental in helping students express their frustrations about problems and their excitement about discoveries. Daily Journals, Reflective Write, Carousel Brainstorming, etc… Ideas in Mathematics 1 Reflecting upon Ideas 2

RAFT(s) RAFT  Role  Audience  Format  Topic Background: Geometry Class Unit on Circles Based upon one of mankind’s greatest struggle: measuring curves.

RAFT(s)  Role: Architect  Audience: Archimedes  Format: Friendly Letter  Topic: Circular Area

RAFT Sample Dear Archimedes, You rock man! I don’t know how you did it, we architects have struggled for centuries now trying to make our buildings and structures not so…well... Square and boring! I mean, we had rectangles and triangles that we could measure, but we didn’t know what to do with circles. What truly amazes me Archi. is how you used a triangle and polygon to figure out the area of a circle. On a similar note, I think you need to get out more man. How in the world did you find the time to inscribe a circle with a 360-gon? I know you told me that all you had to do was start by inscribing a square and then continually bisect it; but where do you find the time to do all that! Well I hope your pursuit of finding a more precise estimate of π goes well. Best Regards, Architect

Biocrostic  A rea  R egion bound by parameters  E nclosed  A lways squared

Organization Writing can be a used to take all the jumbled information, steps, and thoughts and structure them in such a way that leads to mathematical proof or fact. Writing about the process and steps required to solve a certain problem can help students understand that there is a certain order to math; and help them develop their deductive reasoning.

Reflection We should give students the time to write about all the math happening in the world around them, and just let them contemplate and 'think about math'. That leads to thinking critically about problems, and to be good deductive reasoners. It provides them the chance to come up with solutions which lead to other ideas. To be honest, not all people will love math; but all people are mathematicians. We all think critically every day, and often have problems we need to solve. This requires us to do things like deductive reasoning, without even knowing. So writing in school should be done in the hopes that students will make the connection that the problem solving going on in the classroom is going to be helpful in problem solving in the real world.

Word Choice Background: Algebra I Unit on Ratios & Proportions

Word Choice  Bring in a scale model.  Students will Rally Robin in groups, coming up with reasons for why scale models are important. What’s useful about them?  Whole class brainstorming; create web brainstorm for important ideas and vocabulary. Warm-Up Key Vocabulary: scale, equivalent, and proportional.

Interdisciplinary Teaching Solar System Focus Reflection Algebra I – Quadratic Equations Focus/Theme: Reflective Writing What was great? Think outside the box. What would you do differently? Expand lesson more into a mini-project.

Voice Voice is all about the writer’s personality showing. Now in a math class that may seem weird and highly improbable to do, but I believe that it’s not impossible. I think that all mathematicians struggle with ideas and also come up with solutions to problems. I think voice is possible in a math class by allowing students to make conjectures and proofs on their own, with their own non-technical words. Then allowing them the chance to defend their ideas, correct if necessary, and then refine their conclusions.

1 st Strategy Teacher: Velvet McReynolds 7 th grade 2 nd Strategy Teacher: Velvet McReynolds 7 th grade Critique of Narratives Can be used in a math class to critique mathematical arguments by students. Presentation (Celebration Circles) Once their work has been evaluated and critiqued, they came back together to show off their revised work; and to celebrate it. This can prove to be instrumental in helping all students feel like they are valid mathematicians.

Book Talk Chapter 6 Pg. 130 Looking at Samples BENEFITS Current Mathematics in our generation. Exposing students to more areas of math, things that might interest students. Gives students examples to model their own mathematical arguments and reasoning. Provides more opportunities for students to think about math which can lead to new interesting ideas.

Toolbox  Biocrostic  RAFT(s)  Cornell Notes

Free Space Math Riddles: 1) Pick a number between 1 and 9 2) Subtract 5 3) Multiply by 3 4) Square the number (2x2, 3x3, etc…) 5) Add the digits of that number together, for example, if you number is 83, you would add 8 and 3 and get 11. 6) If the resulting number is less than 5, add five, otherwise subtract 4 7) Multiply by 2 8) Subtract 6 9) Assign a letter to your number. A=1, B=2, C=3, D=4, E=5, etc 10) Pick a country that begins with your letter 11) Pick an animal that begins with the second letter from your country 12) think of the color of that animal.... Answer A grey elephant from Denmark Mathemagics 3:05-4:20

“One day, I too will make a difference.”   I find myself asking, “How am I going to engage students in real math when I’m going to have standards, curriculum and administrators who all want me to get students ready to pass the tests or be ready for next year’s math. However, at the same time, I find the challenge intriguing and worth-while. I find it worthy of my time, years, and career to show my students what real math is all about; at least giving them the opportunity to entertain their natural curiosity and love of pattern making, and giving them a fighting chance to like math.