Word Problems and Literacy

Suggestions for working with word problems and incorporating literacy:

1. Use word problems as a way to establish mnemonic imagery for a math concept.
2. Present word problems orally or audiovisually.
3. Have students write longer math stories.
4. Write word problem poems or verse.
5. Draw word problems (without text).
6. Sing word problems or write word problem music.

Gerofsky, S. (2004). A man left albuquerque heading east: Word problems as genre in mathematics education. New York, NY: Peter Lang.

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Math and Children’s Books

Suggestions for using children’s literature in your math lessons:

1. Enjoy the story – don’t interrupt with math questions.
2. Read the book aloud.  Repeat.
3. Keep the book experience open-ended to engage multiple interpretations.
4. Encourage students to respond to the stories through various forms of expression: poetry, drama, art, narrative, orally.
5. Integrate the books into current themes of study.
6. Use your students as a guide for deciding what to read.
7. Consider your students’ age and your intended use of a book to decide if oral or silent reading is appropriate.

Whitin, D. J., & Wilde, S. (1992). Read any good math lately? Portsmouth, NH: Heinemann.

Communicate Mathematically

In their article, Watch Your Language! Recommendations to Help Students Communicate Mathematically, Bratina and Lipkin “suggest methods to help students improve their critical reading skills and to become better problem solvers” (p. 3).  Here are a few of their suggestions:

1: Include specific language arts activities in mathematics lessons
Use frequent, regular, and brief word wall activities (Bratina & Lipkin, p. 4).

2. Create instances for students to experience words in different contexts
For example, include true-false items such as, “Some squares are rectangles.” or “All squares are rectangles.” or “Some rectangles are squares.”  Items like these will lead to mathematical conversations and help students to comprehend complex statements (Bratina & Lipkin, p. 5).

3. Provide time for students to practice the language.
“Both comprehension and accuracy are essential for the development of proficiency in mathematics, and should precede attempts to perform operations with speed.  But once the students have grasped the meanings of mathematical words and symbols, they need to become fluent in using this mathematical language” (Bratina & Lipkin, p. 7).
Just as students need to master the basics of reading and then practice reading fluently and for comprehension, similarly students need to master the basics of math and then practice math for automaticity.

Suggestions for practicing the language of math:
Say it out loud
Cloze procedures
Games such as word searches, crossword puzzles, and cryptograms

4. Praise student perseverance
“When students are engaged in problem-solving exercises, have them read the entire problem before trying to analyze and dissect it.  Then have them read it again.  And again!  In other words, let the students know that instantaneous understanding is not the norm” (Bratina & Lipkin, p. 9).
Instead of asking, “Does everyone understand what we just read?”, ask students to restate or rewrite the problem in their own words.

5. Be a role model (Bratina & Lipkin, p. 10)
Set up a bulletin board as a “Wall of Fame” and post pictures of students when you catch them performing well, such as exhibiting strong communication skills.  Share examples of “real” people who are role models and involved in the communication and mathematics world, such as news anchors, and the first female shuttle commander, Air Force Colonel Eileen Collins.

You can find Bratina & Lipkin’s full article here.

Math Vocab

“Proficiency in mathematics has increasingly hinged upon a child’s ability to understand and use two kinds of math vocabulary words: math-specific words and ambiguous, multiple-meaning words with math denotations.  Elementary school teachers can identify these words and design lessons that provide student-friendly definitions and offer opportunities for deep processing of word meanings.  These efforts will help students to use the language of math” (Pierce & Fontaine, p. 242).

Math vocab is a challenge for students, especially when taking “high-stakes” math tests.  Pierce and Fontaine show that there are two kinds of math vocabulary words:
1. Math-specific words, or technical vocabulary, which “have a precise mathematical denotation that must be taught explicitly to students (e.g., parallel, isosceles)” (Pierce & Fontaine, p. 240).
2. Multiple-meaning words, or subtechnical vocabulary, which “have a common meaning that students generally know already; however, they also have a less common, mathematical denotation that may be less familiar to students (e.g., mean, table)” (Pierce & Fontaine, p. 240).

Pierce & Fontaine present a list of the most common technical and subtechnical vocabulary words and make suggestions for vocab instruction in mathematics.

They strongly recommend that teachers should guide students through activities where they can create their own student friendly definition and activities that allow for deep processing of the word meaning, instead of simply repeating the definition.

View their article here.

Calendar Math and Language Arts

Most primary classrooms have a daily calendar time and Melissa Biddle uses her calendar time “as a springboard for introducing, reinforcing, and assessing a wide array of math skills” and as a chance to model language arts.  She suggests many great ideas such as: a math word wall and language arts conversations during calendar time.

Ms. Biddle suggests these great activities to make use of your math word wall:
“Write 5-10 word wall words on the chalkboard one letter at a time.  Encourage the class to predict what the words will be.  After all words have been written and reviewed, have students put their heads down.  Erase one word at a time and ask students to open their eyes and guess what word you have erased.”
“Randomly give two different letters to pairs of students.  Allow time for each partner to review and quiz the other on all the words under his or her letter.”

Here are some examples of the language arts conversations Ms. Biddle suggests you model and use during calendar time:
“Let’s ask a question about something special in February.”
“Tell your neighbor a statement about something you did in March.”
“Today is the fifth of January.  Let’s highlight every fifth word on the list.  Let’s sort these words into nouns or verbs.”
“Today is the twelfth of November.  Let’s use the twelfth word from each list and make a November sentence using these words.”
“Today is March 12, 2007.  Let’s list the number synonyms for 12.”  Number synonyms are just like words that are synonyms: words that have the same meaning.  So, possible number synonyms for 12 are: 4 + 8, 20 – 8, 3 + 3 + 3 + 3, 1 ten + 2 ones, 3 x 4, etc!

What a great way to start the day and work on multiple math and reading standards!  Read Melissa Biddle’s great article here.

Biddle, M. (2007, February). When opportunity knocks: Integrating language arts and the daily calendar. The Reading Teacher, 60(5), 488-491. doi:10.1598/‌RT.60.5.8

Math Journals

Susan Carter integrated math and writing workshop by having her students write in a math journal.  Each journal was divided into three sections: Strategies, Questions, and Reflections.  Students would write in their math journal at the end of each math lesson.  Ms. Carter began by using several sentence frames to model mathematical writing for her students.  Here are a few examples:

“At first I was going to try _____, but then I decided to _____.”
“I thought about what _____ said the other day and decided to try his/her strategy.”
“Once I found where I got stuck, I tried the problem again from the beginning.  This time I decided to try _____.”

Then, Ms. Carter taught her students to write mathematical stories, which they shared in the Author’s Chair.  This sharing time, which integrates math and communication, also led to math conversations among students, helping them to think about their strategies and revise their thinking.

Read all about Ms. Carter’s experience integrating math and writing workshop here.

Carter, S. (2009, April). Connecting mathematics and writing workshop: It’s kinda like ice skating. The Reading Teacher, 62(7), 606-610. doi:10.1598/‌RT.62.7.7