Journaling in Math:Journaling in Math:Relevant? Useful?Relevant? Useful?Journaling in Math:Journaling in Math:Relevant? Useful?Relevant? Useful?

presented by presented by

Donna McLeishDonna McLeishtoto

Rockville Elementary School TeachersRockville Elementary School Teachers

January 18, 2005January 18, 2005

Reading and Writing in Mathematics

What are your questions?

• What about Kindergarten and Grade 1?

• What about students who can’t read well?

• What about special education students?

»What about …

Reading Mathematics

• Being able to read math, and about math, allows students more independence.

• It allows them to have an opinion other than that of their teacher.

Three main levels of comprehension of math

texts

1. Literal Comprehension

2. Inferential Comprehension

3. Analytical Comprehension

Literal Comprehension

• First task in achieving a literal comprehension of text is decoding

• Decoding is the simple recognition of symbols– for instance, decode this symbol…

√¯¯

A potential obstacle to literal comprehension is the habit of reading

English text from left to right

- adding fractions- adding fractions1 1 + + 22 = =22 33

- reading graphs- reading graphs

How can you help students at this literal decoding level?

Have Patience

• Have students– pronounce equations– describe graphs– name symbols

Once a symbol has been decoded, it must have an

attached meaning

Here is where the potential for misunderstanding is great. Words such as difference, solution, function have distinctly different meanings in a mathematical context.

How do you help students assign meanings to mathematical symbols and words?

1. Make yourself as aware of as many misinterpretations or different interpretations as you can.

2. Understand that the meaning we have for a word is not “the” meaning.

Use journals to encourage accurate literal comprehension

Ask students:• whether a given symbol is the same or different from

one in the text• to rewrite or redraw a given symbol• to define a given symbol• whether alternative forms of a given symbol are

acceptable replacements• to interpret between variations of symbol meaning• to describe characteristics of a symbol• to identify examples or instances of use of a symbol• to make representations of a symbol

Keep in mind…

a student having any trouble understanding words or symbols at this level of comprehension is unlikely to be successful drawing inferences or solving problems using them

Your turn…

Take 5 minutes to work with other teachers of your grade level and decide two questions you can ask of your students next Monday to write in their Math Journal. Each question should address literal comprehension. Write down the questions and be prepared to explain why you chose them.

Inferential Comprehension

A reader has inferential comprehension of text if he understands the “signals” in the text. Signals include:

• catching relational structures (“first…,” “second…,” “third…”

• dealing with premature abstractions of a concept (“The main ideas of this lesson are …”)

• understanding summary statements (“In short, …”)

• awareness of “pointer” words or phrases (“more importantly,” “unfortunately”)

Inferential comprehension is finding meaning in the way that literal symbols and words are connected

Questions for inferential comprehension should focus on relationships.

Use journals to encourage accurate inferential

comprehension

Ask students:• to complete a sentence• to verify relationships of symbols in a sentence• to give their opinion about the meaning of

relationships of symbols• to determine the cause and/or effect of

relationships in and between sentences• to use an algorithm• to order mixed-up steps of algorithms• to fill in missing steps in an algorithm

Your turn…

Take 5 minutes to work with other teachers of your grade level and decide two questions you can ask of your students next Wednesday to write in their Math Journal. Each question should address inferential comprehension of mathematical text. Write down the questions and be prepared to explain why you chose them.

Analytic Comprehension

If a reader of text can be motivated to do something relevant to the subject written about, then he has achieved an analytic comprehension of it.

Two General Types ofAnalytic Comprehension

1. First allows readers to apply their literal and inferential understanding of text

2. Second allows readers to critique what they have read

Applying the reading

Solving written mathematical problems requires literal and inferential comprehension and then the realization that certain mathematical skills and models will help.

There should be concrete, informal experience with mathematical ideas well before the ideas are expressed formally and symbolically.

How can you help students achieve greater analytic comprehension in reading mathematical applications (story problems)?

Have PatienceHave students read material that is • rich in ideas• full of connections (then, but, unless, etc.)• relatively dense (much information is

packed into a small space)– both inside and outside of math class

time

Critical Reading

Critical readers ask themselves good questions

The challenge to the teacher is to help students ask those good questions

Often, unraveling the context of an honest, everyday problem (which must necessarily come before solving it) makes the necessary mathematics comparatively trivial to the reader

How can you help students become more critical

readers?

That’s right…Use JOURNALS>>>>>>>

Use journals to encourage analytic comprehension of mathematical textAsk students to:• make generalizations from specific instances• find exceptions to a rule• complete and make analogies• identify missing information in text• identify irrelevant information in text• tell whether an algorithm is appropriate in a

given problem situation• generate logical consequences from stated facts• simplify details to grasp global meanings• guess and check• make mathematical models

Your turn…

Take 5 minutes to work with other teachers of your grade level and decide two questions you can ask of your students next Friday to write in their Math Journal. Each question should address analytic comprehension of mathematical text. Write down the questions and be prepared to explain why you chose them.

Journaling in Math:Relevant? Useful?

It can be. The rest is up to you.

Donna McLeish