Writing to TextWeymouth: MathDR. DEBORAH BRADY

DBRADY3702@MSN.COM

RIBAS ASSOCIATES

AgendaI. IntroductionsII. Writing and Talking Can Improve Mathematical

Understanding◦ Informational Text: define, describe, explain the sequence◦ Metacognition: Narrative: describe how you solved the

equation◦ Argument: Critique others’ thinking

Middle Schoolers and Math

“The middle school mind is emotional, social, intelligent, and independent. These adolescents are constantly working to balance school, public activities, and home life in order to develop a strong sense of self.”

Because too many students mistakenly believe that success in mathematics requires remembering countless unrelated facts, they have a tendency to disengage, give up, and assume a fixed mindset in mathematics.

www.literacyinlearningexchange.org/sites/default/files/mathematical-language_and_the_ccss_for_english_ej_may2013.pdf

Reaching the middle school mind means increasing engagement, building

connections, encouraging motivation, and fostering

independence.

Trend Lines Show Progress

Processing Partners (Handout)◦ Find someone with whom you

do not generally work◦ Find a mutually open blank line

in the Processing Partners handout

◦ Put your name on your colleague’s sheet

◦ Put your partner’s name on your sheet

◦ Fill in all of the blanks

◦Purpose: time to assimilate information

◦Opportunity for short-term break and movement

◦Research-based need for learning

Writing to TextReading and Writing and Math

TEXTS

Word problemsVideos, photographs, diagrams,

charts, maps and graphsTextbooks alsoReading accuratelyUnderstanding the readingBeing able to communicate the

understanding

WRITING

◦ Writing in Math◦ Talking before Writing

◦ To define, explain◦ To compare ◦ To see patterns and

relationships◦ To critique the ideas of others

WRITING IN THE Mathematics ClassroomTHE WHY, THE WHAT, THE HOW

“College Readiness Stretch”

Students who can comfortably read and comprehend most high school texts may be able to access only the important ideas in “about one fourth of the reading materials in military, citizenship, and workplace text collections and perhaps as little as five percent of postsecondary texts.” (Gary Williamson. A Text Readability Continuum for Postsecondary Readiness, 2008).

Why this SHIFT?Processing Partners

As a Result

20% of college freshmen are in remedial coursesOnly 30% of these remedial students finish college75% of college dropouts report reading as a primary cause for leaving college

Aspects of Text Complexity Project David Liben www.achieve.org

History, English,Science

9 Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

8 Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text.

7 Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

6 Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

5 Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text

Standard 1 K-12Figure 1.3 Anchor Standard 1: Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

TABLE TALK: “Get the Gist” Count off by 3’s

Get the Gist of the Expectations for one of the following

1. An effective mathematics program builds upon and develops students’ literacy skills and knowledge.

2. Standards of Mathematical Practice: Construct viable arguments and critique the reasoning of others.

3. Standards of Mathematical Practice: Attend to precision.

On your own, read one of the passages listed above.

Then, with your group, summarize what this means BUT use no more than 20 words for each type of writing.Use chart paper to share.

How have the expectations shifted in Math?

Mathematical PracticesArgumentOpen Response

Writing to Text AssignmentContent Area Grade Level Unit or Ongoing Activity

Techniques you might useAccountable Talk/Sentence Frames

Narrative Math Journals Metacognitive awareness of Mathematical Processes

Informational Text: Defining concepts, describing data displays, sequence to solve problems

Math Journals: explain, describe

Miniature Golf Task exampleWrite a proposal

Argument: Make plausible argumentsCompare the effectiveness of two arguments Distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is

My Favorite No (Step 1)

Looking at others’ work

Guided practice—critiquing

Independent critique

Accountable Tal

Scaffolds for Reading Complex Text

• Get the Gist (research based)• Reading and rereading (GtG)• Strategic think aloud (your

thinking)• Chunking • Scaffolding

• Annotation strategies• Cornell notes (Interactive Notebook/2 sides)• Journal work in your text

•Homework Club•My Favorite No •Argument in Math (critiquing the work of others)•PAL

15

Homework Club (5-10 minutes)Students work in teams to check homeworkThe teacher asks which problem gave each group the greatest challenge and why.The first group to have all of the HW correct check the other teams’ homework

Each group puts their problematic problem on the board (corrected) and explains why it was a problemWhy is this an effective practice? (2 ways) (Processing Partner)

Math Journal ScaffoldingStarting Out Gently with Affective, Open-Ended PromptsWriting about thinking is challenging. For this reason, it's best not to start out having students write about unfamiliar mathematical ideas. First get them used to writing in a math class:

Begin with affective, open-ended questions about students' feelings.

Sample Direction #1: Reflect on your participation in class today and complete the following statements:

I learned that I...I was surprised that I...I noticed that I...I discovered that I...I was pleased that I...

Sample Direction #2: Describe how you feel about solving _________ problem.

Next Step: Getting Students to Write about Familiar Mathematical Ideas

1. Once your students have become accustomed to writing about their attitudes and feelings toward mathematics in their journals, they are ready to write about simple, familiar math concepts. It is important not to make the writing too difficult by asking them to write about unfamiliar math ideas. Using writing to review familiar math ideas will increase confidence and skill in writing as well as revisit important math concepts. 2. Use student writing samples to help them refine their writing. (Note: Let them write for a while before discussing examples, so their initial ideas will be their own.)

Sample Directions:Explain in your own words what subtraction means.Explain what is most important to understand about fractions.

Then: Introduce the term metacognition to help students understand the reason and audience for their writing.

Moving On: Writing About More Advanced Math Concepts

When you feel your students are ready, ask them to write about more complex mathematical ideas, including concepts being taught at their current grade level. To help you move your students into this more advanced level of writing about their thinking. Here are some other suggestions to help you:

1. Encourage your students to use drawings and graphs to explain their thinking.

Research shows that using simple visual aids (diagrams, graphs, etc.) improves mathematical problem-solving ability, especially in female students.

2. As student writing progresses, ask students to write about their small group work.

Ask the group to write a summary of how they reached a solution, including any "false starts" or "dead ends."

Ask each individual to write an explanation of the group's work on a problem. Have the small groups discuss the individual explanations

After a small group assignment, have students "explain and illustrate two different approaches to solving a problem."

Developing Metacognitive Awareness

Procedure:

1. Introduce "metacognition" by writing it on the overhead and explaining what it means. Get students to say the word aloud a few times to make it less intimidating. Then you might tell a story about research in how the human brain works.

2. Tell students that the more attention we pay to our thinking, the more we'll come to understand about the process of thinking. Although we're used to just being concerned about the results or the "answers," if we pay more attention to how we think, it would help us to think more clearly, and improve the quality of our results.

3. As a non-threatening exercise to illustrate metacognition, ask students how they decided what to wear that day. Ask three or four students to share their answers out loud. Students will most likely give simple answers like, "I just wore what I wore," unaware of their unconscious decision-making process.

Why is Metacognitive Awareness important in Mathematics?

What Improves Writing/Thinking in Math?

1. Writing!

2. Writing cycle (Immersion, planning, defining what is good, drafting, revising, editing)

3. Writing summaries (very difficult!)

4. Collaborative writing (and note-taking)

5. Setting clear goals (rubric/checklist)

6. Using models of good writing

7. Inquiry

8. Effective feedback

What does not work?

1. Too much feedback

2. Think of feedback as coaching—focused on the next steps

3. Train peers (this will improve their writing, too)

4. Grammar actually works against good writing

TABLE TALK: How can math talk and math writing help students to learn

mathematics?

Evidence on Writing about Reading

Graham & Hebert (2010): Meta-analyses of experimental studies show that writing about text can have a powerful impact on writing and reading achievement

93% of studies in which students wrote about text had a positive impact

(grades 2-12)

Writing about text was more powerful than just reading or reading and rereading/studying /discussing

Writing improves reading comprehension.

Writing to Text Improves Learning

Text questions that require elaborated answers rather than questions that require short, specific answers

Studies show that writing answers to questions has a greater impact on learning than just orally answering the questions

However, extended writing leads to more learning than is stimulated by writing short answers for older students

Writing about text more extensively encourages deeper and more thorough thinking about the text ideas which increases learning (series of questions to scaffold the idea)

Seeing Patterns and Relationships

“Guess My Rule” Grade 6

Can you make (and back up/support) a conjecture about any relationship that you see between these three growing patterns/functions.

Remember that conjectures must hold true for similar patterns beyond the problem set that we are examining.

http://www.insidemathematics.org/classroom-videos/public-lessons/5th-6th-grade-math-multiple-representations-of-numerical-patterning/introduction-part-a

What did the students see by the end of the lesson about patterns and relationships?

Formative AssessmentsHinge Questions and Exit Slips

Hinge Questions Thumbs up Thumbs down Exit Slips

Talking about Tables and EquationsTo get students to use Academic Language Accurately

Jesse Ragent asks the students to do a "matching game." He passes out sets of tables and equations to the students, and challenges the students to "find a triple"-- an equation, a table, and a graph that all make up a "family, triple, or set." He asks students to consider distinctions, characteristics, and attributes as they make their grouping decisions. He reviews group work protocols for turn-taking and talking, asking students to "think out loud, giving mathematical reasons for the selections" they make using language generated by the class.

Pre-Planninghttp://www.insidemathematics.org/classroom-videos/public-lessons/7th-8th-grade-math-graphs-equations-and-tables/pre-lesson

Part 2: http://www.insidemathematics.org/classroom-videos/public-lessons/7th-8th-grade-math-graphs-equations-and-tables/lesson-part-2

What have students learned by sorting

cards and matching to tables?

Peer Assisted Learning Strategy (P.A.L.S)

Metacognition/Procedure1. As a class, develop a step-by-step procedure for a process that you want to make sure

all students follow. (Order of Operations, for example).2. Develop the steps3. Pair up students: One is Coach the Second is the Learner4. The pair is given an example to solve that requires OoO. 5. The Coach reads each step. The learner does ONLY that step. No Skipping.6. Once the process is correct (check with teacher), they switch roles with a new

example.7. At the end of class, discuss the steps. Were there any clarifications needed?

Results: some students who skip steps cannot; each step is provided specific language

Try the PALS process for one

OoO

Debrief

When effective feedback is not given, the learner is unable to clarify errors and misconceptions.

If effective feedback is provided, the student is able to move forward in accessing

complex texts.

6.8

Be mindful with feedback.

Peer Feedback John Hattie, author of Visible Learning for Teachers says “Teachers who do not acknowledge the importance of peer feedback can be most handicapped in their effects on students. Interventions that aim at fostering correct peer feedback are needed”.

As Tammie explains, “Students receive more feedback from their peers than anyone else each day. If they are explicitly taught how to give and receive process-related feedback correctly, this can have a high impact on their learning.” In a study that Tammie conducted together with Trevor Ragan, from Train Ugly, it was revealed that 50% of the feedback respondents received came directly from their peers, further highlighting its necessity within the context of learning.

Looking Closely at Feedback

1. What type(s) of feedback do you provide most often?

2. Why do you think feedback about the process and self-regulation is the most useful to students?

3. Why do you think feedback about the student as a person is limiting?

6.36

Feedback by Peers (a year-long process)

This is as good for peers as for the feedback that they give1.Assume they do not know how to “criticize” or give feedback2.Provide language models for them3.Begin with only positive feedback plus questions. (No

suggestions allowed.)4.Model each new piece of feedback using the priorities for the

class

My Favorite NO: Step 1 Critiquehttps://www.youtube.com/watch?v=Rulmok_9HVs

Step 1—Peer FeedbackCritiquing other’s Thinking

Cecilio Dimas leads a lesson on constructing, communicating, and evaluating student-generated tables while making comparisons between three different financial plans, helping students use multiple representations of mathematical problems: verbal, tabular, graphical, and algebraic generalization. In this clip, Dimas asks his students to examine a table comparing DVD rental plans, and ask themselves, “Does this make mathematical sense? Why or why not?” His goal is for students to make all three representations for a new and different cost analysis situation and discuss the merit of each representation in that particular situation. This clip is also indicative of standard 1 (make sense of problems and persevere in solving them).

http://www.insidemathematics.org/common-core-resources/mathematical-practice-standards/standard-3-construct-viable-arguments-critique-the-reasoning-of-others

Step C: Differing Opinions: http://www.insidemathematics.org/classroom-videos/public-lessons/7th-8th-grade-math-comparing-linear-functions/problem-1-part-c

Next Step: New Solution

Independent Critique

Elevating the language of students’ talk

ACCOUNTABLE TALK

• Modeled in group work

•Sentence frames/Anchor Charts are used

•Use of content area vocabulary is recognized, rewarded

•Use of academic lingo is modeled, supported with sentence frames:• Building on the statements of…., I think• Although his work has many positives, the major

problem is

FEEDBACK THAT IS ACTIONABLE

◦ It provides the next step for this student◦ It is connected to major goals reflected in the

rubric and checklist◦ The student has models of well-written essays

that have been read alouds, modeled by the teacher and that are posted.

◦ For ELA—5-minute models of “great sentences”

Miniature Golf Problem http://www.achieve.org/ccss-cte-classroom-tasks

The local miniature golf course would like to increase their profits by increasing the difficulty and number of holes in the course. The owners believe players will like being able to play more holes for their money and then may spend more at the concession stand. In order to find designs for three new holes, they have decided to hold a design contest. Each design will be judged on the most creative use of materials, the least likelihood that someone will score a hole-in-one, and the best use of the available space. The contest requires documentation of your design, including a scale drawing of the design with dimensions, all of your calculations, and a report to the owners that explains your design.

Tasks:

1. Sketch a miniature golf hole design including any obstacles or general items required. The designed hole must fit within a rectangle of no more than 128 square feet of area. Draw your design to scale, using appropriate tools, and include all measurements. Make sure your dimensions will allow for a player to comfortably approach the ball within the golf hole area. Identify the cup, the tee box, obstacles, and all angles of approach. For purposes of computing area, your design should be composed of two-dimensional shapes for which you can find the area.

2. Show that your design will fit within a rectangle of dimensions that meet the 128 sq ft specification. Be sure to use as much of the area as possible, while still maintaining a creative design.

3. Calculate the total area of your golf hole design and the percentage of this total area you have used. Show all your work. (Remember: You will be judged partially on the best use of space.)

4. Research and describe the regulation size for a golf cup for consideration and placement in your design.

5. Identify and sketch two possible paths from tee to cup, with at least one path being a bank shot. Explain the possible approaches and show and calculate all angles associated with your bank shot(s).

How could you scaffold this proposal?

Write a report to submit with your design to explain why yours should be selected. Include information regarding the creativity of your design, the level of difficulty, and the best use of available space.

Your Writing to Text AssignmentContent Area Grade Level Unit or Ongoing Activity

Techniques you might useAccountable Talk/Sentence Frames

Narrative: Math Journals Metacognitive awareness of Mathematical Processes

Informational Text: Defining concepts, describing data displays, sequence to solve problems

Journal: Define Concepts, Describe Data Displays, describe sequenceMiniature Golf Task exampleWrite a proposal

Argument Make plausible argumentsCompare the effectiveness of two plausible arguments Distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.

My Favorite No (Step 1)Two more steps to scaffold independent critique

Accountable Talk/Sentence Frames

“Juried” Resources for Math Massachusetts Model Curriculum Hundreds of Units K-12 ELA, Math, SS, Sci. (http://www.doe.mass.edu Ask to see them and provide email.) ENGAGE New York https://www.engageny.org/common-core-curriculum

A Case for Using Reading and Writing in a Mathematics Classroom Speaking from her own experiences as a math teacher, Sarah Kasten tells how -- and why -- she introduced reading and writing in her classroom. She shares how she directed her classes to do 5-minute, impromptu writing assignments, explain their problem-solving process, or even explain a new concept and create their own example problems.

Using Writing in Mathematics This article includes specific suggestions for managing journals, developing prompts for writing, and providing students with feedback on their writing. In addition, the site includes two sample lessons for introducing writing activities in a math classroom.

Writing in Mathematics A brief teacher-to-teacher article on getting started with writing in math class — moving from think-pair-share to a less-known model: think-write-pair-share. Bias Sampling The purpose of this activity, designing a survey, is “to demonstrate how the results of a poll or other scientific study can be biased by selecting special types of people

to respond or by asking only certain questions.” In this well-constructed lesson, students gather opinions on how much homework time is appropriate. Who should they interview? What questions should they ask? The task culminates in a persuasive, hopefully unbiased, report to the school principal.

Math Out Loud! In this one-pager, Robyn Silbey, a school-based math specialist, contends that “speaking and writing in math offer students an opportunity to synthesize their thinking and articulate it for others.” Moreover, she offers practical ideas for carrying out the classroom process.

59 Writing Prompts for Math Teachers Teachers will find these prompts useful for students who are writing in math journals, learning logs, and classroom reflections. Math and Communication You’ll find solid tips on encouraging and supporting math talk in this brief piece by well-known math teacher Kay Toliver. Adapting Literacy Strategies to Improve Student Performance on Constructed-Response Items This article discusses ways of adapting various reading strategies to help students

improve their answers to extended-response questions on the mathematics portion of high-stakes tests. A practical article directed to teachers. More MATH RESOURCES

Assessment Tasks for grades 6 - 12http://map.mathshell.org/materials/tasks.phpAchieve.Org math tasks for gr 6 - 12http://www.achieve.org/ccss-cte-classroom-tasksResource for understanding Math Practice Standards:http://insidemathematics.org/index.php/mathematical-practice-standards

http://writingtotextbrady.wikispaces.com/Weymouth+Middle+School