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Math Vocabulary in the Common Core - Attend to Precision
As educators, English as a second language learners are always a concern. In the world of mathematics we must understand that we have 100% of our students who will have language issues in mathematics. Math is essential a second language for all of our students. Math vocabulary and symbolism is critical in the understanding of mathematical concepts. In order to communicate mathematically precisely students must be able to "use clear definitions in discussion with others and in their own reasoning." -- CCSS (Mathematical Practice #6 - Attend to Precision)
Students writing definitions from the back of the book is ineffective and must be banned from all classrooms. There is a variety of research that indicates that this form of direct instruction to promote vocabulary learning is ineffective. Marzano's research so far has taught us:
"When students copy the teacher's explanations or description of a term instead of generating their own explanation, the results are not as strong. Ideally, student explanations should from their own experiences." - Robert Marzano
In Building Background Knowledge (2004), Marzano identifies Six Steps to Effective Vocabulary Instruction:
1. Teacher or other students provide description, explanation, examples and non-examples. Some ideas to help with this step includes:
a. Provide experiences that provide examples of the word.
b. Tell a story that integrates the word.
c. Use video footage as a stimulus for understanding the word.
d. Ask students to investigate the word and present their word via: poster, skit, pantomime, etc.
e. Find pictures that explain the word.
2. Students restate word and explanation in own words, verbally and in writing. It is important at this time to monitor and correct any misunderstandings and words may be included in a math journal. Ideas for this step include:
b. I have, who has?
3. Students create non-linguistic representations this may be a picture, a graph, or a symbol to represent the word. When beginning this process it may be necessary to provide some rough examples of words to give students an idea of how they might represent their word. If necessary, you might want to allow students to find pictures in magazines or on the Internet.
4. Students do periodic activities to refine knowledge of vocabulary terms (compare, classify, analyze, revise, explain, study roots and suffixes) During this time students should have the opportunity to add to or change their definition of the term in their journal. Some ideas to deepen their knowledge include:
a. Listing related words.
b. Use analogies for students to complete
c. Allow students to create their own analogy
d. Compare similarities and differences.
5. Students describe/discuss terms with each other. This step needs to be done periodically. This step is done best through group discussions. Ideas include:
b. Describe their pictures and definitions to one another.
c. Explain to each other where they have found the word outside of class.
d. Identify differences in each other definitions.
6. Students play games to practice the use of words. Games are wonderful for all learners. Marazono's research on games reveals that they have a powerful effect on student recall of vocabulary terms. Games are not only fun, but also non-threatening. A safe environment where students are engaged will increase the mathematical learning. Games can be played on or off line. Some examples are:
b. Name that Category
d. Aps: Word Wrap, Bookworm, Vocabulary, Word Search, SATSample1
I've attached a complete K-12 vocabulary list that aligns the Common Core Standards in Mathematics. This list might be a good starting point to get us started in helping all learners to improve their mathematical vocabulary so attending to precision in the common core can become a reality.