math and literacy Making a Connection

What does it mean to be mathematically literate? Mathematical literacy is being able to do, understand, and apply mathematics, not only in the classroom, but in everyday lives. Students must develop skills to think, read, communicate and perform in many academic contexts. Therefore, educators must consider how students learn to read, write, think, speak and listen in their discipline. Researchers agree that, like reading, improving students’ writing skills improves their capacity to learn (National Institute for Literacy, 2007). Excerpts from Wisconsin’s approach to Disciplinary Literacy : Common Core State Standards What does literacy look like in the mathematics classroom? Learning to read mathematical text, Communicating using correct mathematical terminology, Reading, discussing and applying the mathematics found in literature, Researching mathematics topics or related problems, Reading appropriated text providing explanations for mathematical concepts, reasoning or procedures, Applying readings as citing mathematical reasoning, Listening and critiquing peer explanations, Justifying orally and in writing mathematical reasoning, Representing and interpreting data Ohio DOE Wisconsin Department of Public Instruction

http://files.eric.ed.gov/fulltext/ED544239.pdf Hyperlink to article. Very applicable to secondary teachers!

“Writing in mathematics gives me a window into my students’ thoughts that I don’t normally get when they just compute problems. It shows me their roadblocks, and it also gives me, as a teacher, a road map.” -Maggie Johnston 9th grade mathematics teacher, Denver, Colorado “Using Writing in Mathematics to Deepen Student Learning” by Vicki Urquhart http://files.eric.ed.gov/fulltext/ED544239.pdf

Why are we writing in math class? David Pugalee (2005), who researches the relationship between language and mathematics learning, asserts that writing supports reasoning and problem solving and helps students internalize the characteristics of effective communication. He suggests that teachers read student writing for evidence of logical conclusions, justification of answers and processes, and the use of facts to explain their thinking. Why are we writing in math class? http://files.eric.ed. gov/fulltext/ED544 239.pdf http://files.eric.ed.gov/fulltext/ED544239.pdf Pg. 6

Benefit #1 Benefit #2 Benefit #3 Benefit #4 “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.” http://files.eric.ed.gov/fulltext/ED544239.pdf “Using Writing in Mathematics to Deepen Student Understanding” www.mcrel.org According to Joan Countryman, author of “Writing to Learn Mathematics: Strategies That Work, K-12 “, she offers the following four benefits of writing in mathematics classes: #1 – While students are writing, they can restate new material in their own words, identify computations that are easy or difficult, or reflect on aspects that confuse them. (They could even do this in writing a letter to their teacher.) #2 – Students can write the facts they need to answer a question beforehand and afterwards, then check their computations against their written facts. This also helps them see different ways to arrive at an answer. #3 – When students write explanations of their work and give examples, teachers can better assess student understanding and progress throughout time. Writing is an ideal vehicle for formative assessment, providing teachers with information they need to adjust their instruction. #4 – Writing about problem solving requires students to monitor and reflect on the strategies and processes they select. This frequently includes metacognitive aspect on the student’s part.

Writing to explain and describe Content prompts deal with mathematical concepts and relationships. Examples : Define parallel in your own words. How would you describe a number line? Write a paragraph about the data displayed in the graph. What properties do triangles have? Tell everything you remember about the key points in today’s lesson. Reflective writing prompts provide students a vehicle for describing their learning processes. Ideas: What about providing students writing prompts at the beginning of a unit that gives them the opportunity to “voice” what they think/know already about a problem that has been posted? Students can describe how they feel about the problem and why.

Section 3 of the article breaks each one of the six “types” of writing that generally would take place in a mathematics classroom. What a neat idea!

Integrating writing into the mathematics classroom Writing can provide valuable insight for teachers into their students’ mastery of math concepts. Writing often reveals gaps in learning and misconceptions which can help inform teachers for instructional planning and intervention strategies. Communicating about mathematics through writing helps strengthen student learning which can build conceptual understanding. Students are able to clarify their thinking about a math topic through writing. Integrating writing into the curriculum can be easy with a little planning. http://www.glencoe.com/sec/teachingtoday/subject/int_writing_math.phtml Teaching Today website

Professional Development Parent & Afterschool Resources http://www.readwritethink.org Classroom Resources Professional Development Parent & Afterschool Resources For Teacher Resources you can sort … by grade refine your search by resource type, theme, learning objective, and professional development type

“Going on a Shape Hunt: Integrating Math and Literacy” http://www.readwritethink.org Grade Levels: K-2 “Going on a Shape Hunt: Integrating Math and Literacy” Students are introduced to the idea of shapes through a read-aloud session with an appropriate book. They then use models to learn the names of shapes, work together and individually to locate shapes in their real-world environment, practice spelling out the names of shapes they locate, and reflect in writing on the process. This lesson provides opportunities to engage students using many different learning modalities. Grade Levels: 1-2 “Draw a Math Story: From the Concrete to the Symbolic” Readwritethink is a website that has… Classroom Resources Professional Development Videos Parent Resources identify and use key mathematical terms in discussion and in writing. draw a series of pictures telling a sequential story which depicts objects being added or taken away. tell and write a sequential story which corresponds to their drawings. state or write equations that correspond to their stories.

http://www.readwritethink.org Grades Levels 3-5 “Talking, Writing, and Reasoning: Making Thinking Visible with Math Journals” Getting Started with Math Journals Sharing a good math-related children’s book or exploring puzzles – such as the Magic Triangle are good ways to begin working with Math Journals. At the beginning stages of working with Math Journals, it helps students if they are presented with an open-ended prompt instead of having to develop an idea on their own. This kind of prompt is best for revealing students’ thinking, too. Teachers should collect and view journal entries and make written comments to encourage the written dialogue between the student. Teachers can ask specific questions. Intermediate Grades 3-5 Lesson Plan: “Talking, Writing, and Reasoning: Making Thinking Visible with Math Journals” http://www.readwritethink.org/classroom-resources/lesson-plans/talking-writing-reasoning-making-820.html?tab=4#tabs (The Magic Triangle Puzzle) http://www.readwritethink.org/files/resources/lesson_images/lesson820/TrianglePuzzle.pdf Math Journal Writing about Problem-Solving (From activity on Magic Triangle Puzzle) http://www.readwritethink.org/files/resources/lesson_images/lesson820/JournalPrompts.pdf

Ideas for mathematics activities Math Journals Explain a formula. Write about a time you were confused in math and tell about what you did. Write everything you know about __________. (Can do this at the beginning of new material or as a recap of what’s been taught.) Present a graph from the newspaper, magazine, online resource and have students write everything they can understand from the data in the graph. Write/Draw as many examples of a ratio (or something else) that you can think of in 5 min. Use all of the vocabulary words from a unit and write a paragraph/story using them correctly.

More… Ideas for mathematics activities Poetry – Writing and sharing poems is a popular way for many secondary students to share ideas about math concepts, ideas, and experiences. (Example: Haiku – 3 lines – 5 syllable, 7 syllable, 5 syllable format is simple and appropriate for math.) Triangular Prism Five faces, all flat Your straight edges count to nine Triangles — a must! Advice Columns – Students write fictitious advice columns as you might find in a news column, but specific to mathematics. Use math re-lated names, like “Dear Algy (algebra or algorithm) and “Dear Dr. Pi”.

http://www. readwritethink http://www.readwritethink.org/files/resources/printouts/Diamante%20Poem.pdf Diamante Poem Diamond-shaped poems that use nouns, adjectives, and gerunds to describe either one central topic or two opposing topics. Line 1: one-word topic (a noun) (Beginning topic) Line 2: two adjectives (about beginning topic) Line 3: three verbs (about beginning topic) Line 4: a four-word phrase (about both beginning and ending topics) Line 5: three verbs (about ending topic) Line 6: two adjectives (about ending topic) Line 7: a renaming noun for the topic (Ending topic)

Why Literature in MATH? Generates interest in a math concept Motivates students to think and reason mathematically Helps students make connections between math concepts and their personal lives Accommodates different learning modalities Promotes critical thinking Engages learners in problem solving experiences Illustrates interdisciplinary connections to mathematics

Current Theory Literature provides a framework to help students learn math in a way that is non - threatening and familiar. Picture Books Math Reduced Anxiety Even though middle school students haven’t studied algebra yet, our society has caused many of them to experience anxiety over the mention of it. Because of this it is hard for them to believe that they are able to explore algebraic relationships. By using literature as a way to explore patterns and express algebraic thinking, we can expose our students to a fun and interesting way to look at algebraic relationships. When students recognize and write about patterns they are developing their algebraic thinking. By using these stories, our students will find it easier to express relationships symbolically in algebra class. These activities will help them to better understand a more abstract approach to using symbols to represents real-world situations. Patterns in Literature Rosemary G. Schmitt Pittsburgh South Brook

Marilyn Burns suggests… “Students for whom math is their first love learn to look at books in a new way; students who love to read – but for whom math is not “their thing” – are helped to experience the wonder of mathematics in the same way they already enjoy the wonder of books.”

Math Solutions Publications series Hyperlink to Document Kg – 8th Grade Literature Books with Title, Author, Grade Level, and the Math Concept/Topic Math Solutions Publications series www.mathsolutions.com

Guidelines for Choosing Literature Select books that… Use the mathematics correctly, are set in reasonable contexts, and are expressed in an easily understandable manner. Are visually pleasing as well as functional; they unleash the imagination and curiosity of the reader through stories and rich illustrations. Appeal to multiple grade levels and provoke thinking and learning for a wide range of ages. Look at operations and copy document with literature for grades K-5

From Subject Received Size Categories Harrell, Iris Grds K thru 5 Math Concepts With Literature.docx Tue 1:32 PM 1 MB

Students gather similar research from their own classroom Use the computer to graph data Create a “class book” full of meaningful statistics

Model Eliciting Activities MEAs are a collection of realistic problem-solving activities aligned to multiple subject-area standards. meas Model Eliciting Activities SAY: Have you heard about MEAs? These activities are accessible on Cpalms.

Model Eliciting Activities MEAs are open-ended, interdisciplinary problem- solving activities that are meant to reveal students’ thinking about the concepts embedded in these realistic activities. MEAs resemble engineering problems because students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs and clearly documenting their thought process. MEA components on CPALMS include lesson plans with learning objectives, wide range of lesson resources, assessments and differentiation pieces. SAY: The collection of MEAs was written by educators across the state of Florida who participated in the ongoing Model Eliciting Activities Initiative.  All MEAs are aligned to standards in at least two subject areas, including Common Core Mathematics, Common Core English/Language Arts and/or Literacy in the Content Areas, and NGSSS Science. The MEAs in this collection range from grade levels K to 12.

Integrated STEM Lessons as Model Eliciting Activities http://www.cpalms.org/cpalms/MEA.aspx DIRECT WEB LINKS are also on the slide. Hyperlink to Introduction video (11:00 min. appox) NOTE*** Show the introduction video first. It is an overview of MEAs. Example is specific to high school; however, it’s of value to middle school teachers as well, especially if they are not familiar at all with MEA lessons! Hyperlink is also under the 2nd video graphic (7:00 min. approx.) This video is of value to extend on how to use MEAs in any grade level classrooms. Teachers are being interviewed as well as in-class video with students engaged in collaborative groups working on MEA lessons. stemlesson.org mea.cpalms.org

Click on Resources to access “MEAs”. http://www.cpalms.org/Public/ Click once for arrow identifier to appear for accessing resources on CPALMS. Then, click on the word to link to website and navigate to MEAs. http://www.cpalms.org/Public/search/Resource COMMENTS: http://www.cpalms.org/Public/

MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. MEAs have been used successfully as teaching tools in a range of subject areas and grade levels. Students gain a deeper understanding of the content as specified in the aligned standards and increase their ability to effectively apply their knowledge of the content to solve an open-ended problem. Besides gaining content knowledge, MEAs foster the development of 21st century skills like communication, teamwork, technical analysis, and problem solving. Individual MEAs typically align to standards in multiple subject areas. Read each bulleted point on the slide for a recap of the benefits for students being able to participate in Model-Elicited Activities in classes.

Primary Grades MEA LESSON TITLES mea.cpalms.org Kg – We Love Pets! MAFS.K.CC.2.4 1st Grade – Flower Power Flower Company MAFS.1.OA.1.1 MAFS.1.OA.3.5 MAFS.1.NBT.1.1 MAFS.1.MD.3.4 2nd Grade – Carnival MAFS.2.NBT.1.4 MAFS.2.NBT.2.5 MEA LESSON TITLES http://www.cpalms.org/Public/PreviewResourceLesson/Preview/32331#/#standards-toggle mea.cpalms.org

Intermediate Grades MEA LESSON TITLES mea.cpalms.org 3rd Grade - Spin Beyblades MAFS.3.OA.2.6 MAFS.3.OA.3.7 4th Grade - Donuts and Decimals MAFS.4.NF.3.6 5th Grade - X-treme Roller Coasters MAFS.5.NBT.1.2 MAFS.5.NBT.1.3 MAFS.5.MD.1.1 MEA LESSON TITLES mea.cpalms.org

In Summary Introducing a math concept or practicing a math skill by using fun, interactive Children’s Picture books can help reduce math anxiety and make the “math experience” more enjoyable for your students!

Resources http://mathsolutions.com/qa-effective-math-instruction-using-childrens-literature/ http://www.carolhurst.com/subjects/math/math.html http://www.mathcats.com/grownupcats/ideabankmathandliterature.html http://www.davidson.k12.nc.us/education/components/scrapbook/default.php?sectiondetailid=47899 http://www.nctm.org/resources/content.aspx?id=2880 http://www.livingmath.net/ReaderLists/tabid/268/language/en-US/Default.aspx http://www.chatham.edu/pti/curriculum/units/2009/Schmitt.pdf http://ohiorc.org/for/math/bookshelf/ http://files.eric.ed.gov/fulltext/ED544239.pdf http://www.readwritethink.org