note-taking and other effective habits of successful math students

Note-taking Note-taking

And Other Effective Habits And Other Effective Habits of Successful Math of Successful Math

StudentsStudents

The Seven Steps to Effective Math Note-Taking

As Taken From

Paul D. Nolting’s Math Study Skills Workbook•The key to effective note-taking is to record the fewest

words, while retaining the greatest information.

•As you know, it is very difficult to record notes and at the same time fully understand the instructor.

•The seven steps to math note-taking were developed to decrease the amount of note-taking, while at the same time improving math learning.

1. The first area, steps 1 through 3, focuses on recording your notes.

2. Steps 4 through 6 focus on checking yourself to see how much information is retained.

•This is done by recalling key words and concepts and putting a check mark by misunderstood information.

•Recalling information is one of the best learning techniques.

3. Step 7 focuses on understanding key words and concepts that are frequently used.

The seven steps to math note-taking consists of three major

areas.

Note-Taking Memory Note-Taking Memory CuesCues

• One of the best math note-taking One of the best math note-taking methods is demonstrated in Figure 5 methods is demonstrated in Figure 5 on page 51 of Nolting’s Math Study on page 51 of Nolting’s Math Study Skills Workbook. Skills Workbook.

Figure 5Figure 5

Modified Three-Column Note-Taking Modified Three-Column Note-Taking SampleSample

Key Words Examples Key Words Examples Explanations/RulesExplanations/Rules


• To use this effective note-taking To use this effective note-taking system, you need to record a few system, you need to record a few memory cuesmemory cues as reminders. as reminders. – Label the top space between the Label the top space between the

notebook ring and the notebook ring and the red linered line “ “Key Key WordsWords.”.”

Figure 5Figure 5

Modified Three-Column Note-Taking Memory Modified Three-Column Note-Taking Memory CuesCues

Key WordsKey Words


– Label the other side of the Label the other side of the red linered line ““ExamplesExamples.”.”

Figure 5Figure 5


Key Words ExamplesKey Words Examples


Next, label “Next, label “Explanations/RulesExplanations/Rules” about ” about 4 inches from the 4 inches from the redred line. line.

Figure 5Figure 5


Key Words ExamplesKey Words Examples


Next, label “Next, label “Explanations/RulesExplanations/Rules” about ” about 4 inches from the 4 inches from the redred line. line.

Figure 5Figure 5




– Record these same Note-Taking Memory Cues Record these same Note-Taking Memory Cues in the three-column format as shown here in the three-column format as shown here below on the next ten pages of your notebook. below on the next ten pages of your notebook.

– After using this system for ten pages, you may After using this system for ten pages, you may not need to label each page with the memory not need to label each page with the memory cues.cues.

Figure 5Figure 5



Figure 5Figure 5Modified Three-Column Note-Taking Modified Three-Column Note-Taking

SampleSampleKey Words Examples Explanations/RulesKey Words Examples Explanations/Rules

Natural numbersNatural numbers 1, 2, 3, 4, 5, . . . You can 1, 2, 3, 4, 5, . . . You can count count them.them.

Whole numbersWhole numbers 0, 1, 2, 3, 4, . . . 0, 1, 2, 3, 4, . . . Natural numbers and zero Natural numbers and zero

Integers . . . -2, -1, 0, 1, 2, . . .Integers . . . -2, -1, 0, 1, 2, . . . Whole numbers Whole numbers and their and their opposites opposites

- n- n If n = 10, then - n = -10 - n is read “the If n = 10, then - n = -10 - n is read “the opposite” of n, opposite” of n, If n = -7, then - n= 7 If n = -7, then - n= 7

or the or the oppositeopposite of a number. of a number.

Rational Numbers Fractions: ¼ , ½, ¾ , … A/B, where A and Rational Numbers Fractions: ¼ , ½, ¾ , … A/B, where A and B are B are -¼ , -½, -¾ , … -¼ , -½, -¾ , … integers, (B integers, (B cannot = 0)cannot = 0)

Division by 0 is Division by 0 is undefined.undefined.

Using the Note-Taking Memory CuesUsing the Note-Taking Memory Cues

Step 1 Record Step 1 Record each problem stepeach problem step in the “Examples” section. in the “Examples” section.

Key Words Examples Explanations/RulesKey Words Examples Explanations/Rules

Solve this equation.Solve this equation.

22((3x - 13x - 1)) = 10 = 10

6x - 2 = 106x - 2 = 10 +2 +2+2 +2 6x = 126x = 12

6x = 126x = 12 6 6 6 6

x = 2x = 2

Follow these 7 steps to improve your note-Follow these 7 steps to improve your note-taking:taking:

Using the Note-Taking Memory CuesUsing the Note-Taking Memory CuesStep 2 Record the Step 2 Record the reasonsreasons for each step in the “Explanations/Rules” for each step in the “Explanations/Rules”

section by using: section by using: – Abbreviations, short phrases, …not sentencesAbbreviations, short phrases, …not sentences– Key words, properties, principles, or formulas.Key words, properties, principles, or formulas.


22((3x - 13x - 1)) = 10 = 10 dis to eliminate dis to eliminate

PP ( )( )

6x - 2 = 10 6x - 2 = 10 AddAddopposite opposite of of Term to eliminate Term to eliminate +2 +2 +2 +2 & & compensatecompensate on other side on other side

6x = 126x = 12

6x = 12 6x = 12 DivideDividefactorfactor to to eliminateeliminate factor factor

6 6 & 6 6 & compensatecompensate on other side on other side

x = 2x = 2 Solution. Solution.

Using the Note-Taking Memory CuesUsing the Note-Taking Memory CuesStep 3 Record Step 3 Record key words and conceptskey words and concepts in the left 2-inch margin in the left 2-inch margin

either during or immediately after lecture by reworking your either during or immediately after lecture by reworking your notes.notes.


DistributiveDistributive 22((3x - 13x - 1)) = 10 = 10 Distribute to clearDistribute to clear ( ). ( ). Property Property

6x - 2 = 10 6x - 2 = 10 Add the oppositeAdd the opposite of the of the term,term, -2, -2,

Add the oppositeAdd the opposite +2 +2 +2 +2 to to eliminateeliminate the the termterm & &

compensatecompensate of Term FIRST. of Term FIRST. 6x 6x == 12 12 on on other side by doing the same.other side by doing the same.

6x = 12 6x = 12 DivideDivide by the by the factorfactor, 6, , 6, to to eliminateeliminate

Divide by factor Divide by factor 6 6 6 6 the the factorfactor & & compensatecompensate by LAST.by LAST. doing the same to the doing the same to the other side.other side.

x = 2x = 2 When x is all alone on one side, When x is all alone on one side, the equation is the equation is solved.solved.

Using the Note-Taking Memory CuesUsing the Note-Taking Memory CuesStep 3 Record Step 3 Record key wordskey words and concepts in the left 2-inch margin and concepts in the left 2-inch margin

either during or immediately after lecture by either during or immediately after lecture by reworkingreworking your your notes.notes.


DistributiveDistributive 22((3x - 13x - 1)) = 10 = 10 Distribute to clearDistribute to clear ( ). ( ). Property Property





Divide by factor Divide by factor 6 6 6 6 the the factorfactor & & compensatecompensate by LAST.by LAST. doing the same to the doing the same to the other side.other side.

x = 2x = 2 When x is all alone on one side, When x is all alone on one side, the equation is the equation is solved.solved.


• Step 4 Step 4 Cover upCover up the the “Examples”“Examples” and and “Explanations/Rules”“Explanations/Rules” sections, and sections, and recite out loudrecite out loud the meaning of the key words the meaning of the key words or concepts.or concepts.


DistributiveDistributive Property Property

Add the oppositeAdd the opposite of Term FIRST.of Term FIRST.

Divide by factor Divide by factor LAST. LAST.


• Step 4 Cover up the “Examples” and “Explanations/Rules” Step 4 Cover up the “Examples” and “Explanations/Rules” sections, and sections, and recite out loudrecite out loud the meaning the meaning of the key words of the key words or concepts.or concepts.





Whenever parentheses are present in an equation, apply the Distributive Property to get rid of them as the 1st step.

Terms are the things that are added and they must be eliminated by adding opposite before eliminating the factor.And we must remember to compensate by doing the same thing to the other side of the equation.

Factors are eliminated LAST from an equation by Dividing by the factor we wish to eliminate. Then compensate by Dividing by that same factor on the other side of the equation, as well.


• Step 5 Place a Step 5 Place a check markcheck mark by the key words and concepts by the key words and concepts that you did not know. [Use a highlighter!]that you did not know. [Use a highlighter!]






Step 6 Review the information that you Step 6 Review the information that you checkedchecked [or highlighted] [or highlighted] until it is understood. until it is understood.


DistributiveDistributive 2(3x - 1) = 10 2(3x - 1) = 10 Distribute to clear ( ). Distribute to clear ( ). Property Property





Divide by factor Divide by factor 6 6 6 6 the the factorfactor & & compensatecompensate by LAST. by LAST. doing the doing the same to the other side.same to the other side.

x = 2x = 2 When x is all alone on When x is all alone on one side, one side, the equation is the equation is solved.solved.

Step 7 Develop a math glossary for difficult-to-Step 7 Develop a math glossary for difficult-to-remember key words and concepts.remember key words and concepts.

• Your personal math glossary is created to define a math Your personal math glossary is created to define a math vocabulary in vocabulary in your ownyour own words. words.

• Since math is considered a Since math is considered a foreign languageforeign language, , understanding the math vocabularyunderstanding the math vocabulary becomes the becomes the key to key to comprehending math.comprehending math.

• Creating Creating your ownyour own math glossary for each chapter of your math glossary for each chapter of your textbook will textbook will help you understandhelp you understand math. math.– Many math textbooks come with glossaries or Many math textbooks come with glossaries or

summaries of summaries of key termskey terms used in the chapter written in used in the chapter written in the back of each chapter.the back of each chapter.

– Show the Show the transparencytransparency of one such summary from a of one such summary from a math textbook used at this college.math textbook used at this college.

Your Math GlossaryYour Math Glossary

• Your glossary should include all words printed in Your glossary should include all words printed in bold face in the text and any words you do not bold face in the text and any words you do not understand.understand.

• If you cannot explain the math vocabulary in your If you cannot explain the math vocabulary in your own words, ask your instructor or tutor for help.own words, ask your instructor or tutor for help.

• You may want to use the last pages of your You may want to use the last pages of your notebook to develop a math glossary for each notebook to develop a math glossary for each chapter in your textbook. chapter in your textbook.

• Review your math glossary before each test.Review your math glossary before each test.

Other Helpful Habits of Successful Math Other Helpful Habits of Successful Math StudentsStudents

1.1. Use the Use the computerized coursewarecomputerized courseware that that accompanies the textbook accompanies the textbook effectivelyeffectively..– Take a test to discover math weaknesses.Take a test to discover math weaknesses.– Do the study plan set as result of that test.Do the study plan set as result of that test.

• Use the videos that accompany your textbook when Use the videos that accompany your textbook when you are having difficulty understanding the concepts.you are having difficulty understanding the concepts.

• See a tutor, if necessary.See a tutor, if necessary.

– Do bookwork for those sections as well.Do bookwork for those sections as well.– Retake the same test in the computer to see if Retake the same test in the computer to see if

you acquired the missing math skills.you acquired the missing math skills.– Continue in this manner until mastery of all Continue in this manner until mastery of all

concepts is reached.concepts is reached.


2. Use your 2. Use your textbooktextbook effectively. effectively.– Use the Cover-Sheet strategy to help see the step-Use the Cover-Sheet strategy to help see the step-

by- step process displayed in your textbook.by- step process displayed in your textbook.– Show the Show the transparencytransparency of a page of the textbook of a page of the textbook

and block off portions of the page to show and block off portions of the page to show effectiveness of the Cover-Sheet strategy.effectiveness of the Cover-Sheet strategy.

– Look at the end of each chapter for Look at the end of each chapter for study helpsstudy helps::

•Study the Summary of Key Terms and Formulas.Study the Summary of Key Terms and Formulas.•Study the Quick Review (including key concepts Study the Quick Review (including key concepts

and examples) using techniques learned in and examples) using techniques learned in Nolting’s note-taking section.Nolting’s note-taking section.

•Show the Show the transparencytransparency of a of a Quick ReviewQuick Review found found at the end of a chapter in one of our textbooks.at the end of a chapter in one of our textbooks.


3. Use your 3. Use your pencil and brainpencil and brain effectively. effectively.– Do Do bookworkbookwork for those sections that need your for those sections that need your

attention as per the study plan given from your attention as per the study plan given from your computerized courseware.computerized courseware.

– Use your textbook’s chapter test as a Use your textbook’s chapter test as a practice practice testtest, using the Smart-sheet and Cover-sheet , using the Smart-sheet and Cover-sheet strategies.strategies.

– Use your Use your highlighterhighlighter to mark those items in your to mark those items in your textbook or notes when you have difficulty textbook or notes when you have difficulty grasping the concepts or when your teacher grasping the concepts or when your teacher comes right out and warns you that you will ‘see comes right out and warns you that you will ‘see this type problem on the test.’this type problem on the test.’

You have to You have to think think like a successful math student like a successful math student

if you are to become one!!if you are to become one!!

note-taking and other effective habits of successful math students

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