Literacy in Mathematics Emily Elrod Mathematics Lecturer, Appalachian State University Sheila Brookshire Retired Mathematics Coach, Buncombe County Schools

Why? ”The students know how to do the math, they just don’t understand what the question is asking.” “The thing I don’t like about this new series is the way the problems are stated; they’re hard for the students to get what to do.” “The reading level is too hard for the students.” “I have to simplify, to reword the questions for my students, and then they can do it.”

Learning Intentions Differentiate between what literacy looks like in ELA and in Mathematics Identify the difficulties in learning the language of mathematics Develop strategies to overcome the difficulties Develop strategies to help students interpret problems without reading and interpreting for them

Daily Schedule 8:30 – 10:00 Session 1 10:00 – 10:15 Break 11:45 – 12:45 Lunch 12:45 – 2:15 Session 3 2:15 – 2:30 Break 2:30 – 4:00 Session 4 Each day we will integrate strategies for reading, writing, listening to and speaking mathematics in addition to ”doing math”

Agreements for our Work Be on time Silence cell phones Limit sidebar conversations to activities Be respectful Be actively engaged Have Fun!

Reflect and Connect Reflect on personal learning of mathematics (private think time) What was confusing What were your strengths Quick Write Move to the music to connect When the music starts move to find 2-3 people you do not know When the music stops share your name, school, grade level, and experience After sharing, do a public record of commonalities Compare to learning a second language Math is not a first language, it is learned at school and not spoken at home. Students do not talk about mathematically naturally

Standards for Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure.

Questions We Ask Can students synthesize the information? Can they decide what information is important? Can they make inferences from what they read?

Objects and Actions Schwartz (1996) To a large extent the arithmetic curriculum of the elementary school as well as the algebra curriculum of the middle and high school focus on the manipulation of symbols representing mathematical objects, rather than on using mathematical objects in the building and analyzing of arithmetic or algebraic models… Using the mathematical objects and actions as the basis for modeling one’s surround is a neglected piece of the mathematics education enterprise. Schwartz (1996)

Object or Action? Nouns Verbs Numbers Measurements Shapes Spaces Functions Patterns Data Arrangements Items that comfortably map onto commonly accepted content strands Modeling and formulating-creating appropriate representations and relationships to mathematize the original problem Transforming and manipulating-changing the mathematical form in a problem to equivalent forms that that represent solutions Inferring-applying derived results to the original problem situation, and interpreting and generalizing the results in that light Communicating-reporting what has been learned about a problem to a specific audience Finding the Star Number to distinguish between object and action First look through the task and make two lists, one for objects and one for actions. Next label the actions according to the type GIVE SHEET FOR RESOURCE RING

Finding the Star Number

Break!

What about the Text? Distribute the examples of the 4 content area texts and ask participants to work as a group of 4 to find similarities and differences between the texts. Use a Venn diagram to record ideas. Discuss how the structure of the texts affects students. Model ideas with a public record. Look at structure of own text

Math Other What do you notice? More concepts per sentence and paragraph Compact style-much info without redundancy Words as well as numeric and non-numeric symbols Often not traditional left to right reading Graphics Info added to distract as well as enhance Written above reading grade level Traditional text has topic sentence then supporting details. Math gives the details then main idea is at end in the form of a question to find something

Text Comparison More concepts per sentence and paragraph Written above reading grade level Compact style (information without redundancy) Traditional text has topic sentence then supporting details. Math gives the details then main idea is at end in the form of a question to find something Words as well as numeric and non-numeric symbols Often not traditional left to right reading Graphics Information added to distract as well as enhance

Structure of Math Problems Traditional reading there is a topic sentence at the beginning followed by supporting details. In math the key idea comes at the end in the form of a question or statement. Student must read through to find the main idea and then reread to find which details and numbers relate to the question Symbols, words, notations and formats of numbers can be confusing Same words, different languages – example: What’s the difference? Mathematical statements and questions are understood differently when made in non-mathematical context Small words such as how, many, and how many Let's compare EOG assessment items from older assessments to current ones. What do you notice? What is the same, what is different. GIVE SHEET FOR RESOURCE RING

Let’s do some math… A worker placed white tiles around black tiles in the pattern shown in the three figures below: Based on this pattern, how many white tiles would be needed for 4 black tiles? Based on this pattern, how many white tiles would be needed for 50 black tiles? Make a scatter plot of the first five figures in this pattern showing the relationship between the number of white tiles and the number of black tiles. Label the axes. Based on this pattern, explain how you could find the number of white tiles needed for any number, n, of black tiles. Show and explain your work. Have participants complete the task individually, then look at samples of student work and use NEHI to analyze student work. Have participants create a graphic organizer by dividing a sheet of paper horizontally into 4 areas.

Analysis of Learning Make a foldable for this and analyze partner's work on the Tile task using NEHI. Discuss what they understand and where there are misconceptions. Emphasize the importance of using time as a PLC to analyze samples of student work.

Lunch!

Reflect and Connect Reflect on students’ learning of mathematics (private think time) What was confusing What were their strengths Quick Write Move to the music to connect When the music starts move to find a person you do not know When the music stops share what you wrote Partner with the person for the next activity After sharing, do a public record of commonalities Compare to learning a second language Math is not a first language, it is learned at school and not spoken at home. Students do not talk about mathematically naturally

Your work will be analyzed by your partner More Math . . . The Problem: Four students could not go on a field trip. They had paid $32 in total for their tickets . How much money was returned to each student? Directions to the Student: Read the problem. Write down one possible strategy to solve the problem. Use diagrams or pictures when possible. Write down any questions you might have about the problem? Your work will be analyzed by your partner Complete the task, knowing that your work will be analyzed by a partner.

Analysis of Learning Make a foldable for this GIVE SHEET ON WRITING FOR RESOURCE RING

Break!

“I Have, Who Has….?” As a group, do "I Have, Who has" as an opportunity to move as well as talk

Number Talk What number is represented by the arrow? Support your placement with a mathematically convincing argument. Name a number that is greater than this number. How much greater? Prove it on the number line. Name a number that is less than this number. How much less? Prove it on the number line. GIVE SHEET ON DISCOURSE FOR RESOURCE RING

Let’s Apply What We Learned Each day, we will give time for you to apply ideas from the seminar to your work with your students. If you are here with others from your school, you could work together to create a vertical plan so there are consistent routines across grade levels. If you are here as a singleton, join others with the same or nearly the same grade level to create a plan. Ideas discussed today: Mathematics as a Language – objects vs. actions Becoming familiar with the math text Structure of math problems Analysis of student learning – reading, writing, listening, speaking mathematics Emphasize the importance of Number Talks at all levels. We will do these each day. Reference the resource that will be on the wiki.

Brain Break True or False? 1. 2 4 =2 ·4 2. 3 + 3 + 3 + 3 + 3 = 3 5 3. 5 3 = 5 · 5 · 5 4. 2 · 2· 2 · 3 · 3 · 3 = 6 3

Reflection on Today’s Work To what degree do you agree with the items below? 1. Agree 2. Neutral 3. Disagree Today’s Sessions A. were facilitated at an appropriate pace. B. had a format and structure that facilitated my learning. For A and B, simply place a number then respond to the 2 questions. C. What was most useful? Why?   D. What was least useful? Why?