Getting Ready for AP STATISTICS: LEVELS OF MEASUREMENT

Data can be separated into categories according to what is being measured and what information can be determined from the data.  Different levels of measurement are appropriate for different arithmetic and statistical operations. For example, it makes no sense to find the mean, median, or mode of a list of Social Security numbers.

NOMINAL

The nominal level of measurement is the lowest of the four ways to characterize data because it holds the least potential for instructive analysis. Nominal means "in name only" and nominal data deal with names, categories, or labels -- qualitative groups (see previous post: Getting Ready for AP STATISTICS: VOCABULARY BASICS).

Because data at the nominal level are qualitative, they can't be ordered in a meaningful way, and it makes no sense to calculate things such as the mean or standard deviation.

Examples:
Colors
Yes or no responses to a survey
Favorite class subject
Gender
Makes of cars  

Some number groups can be nominal:  the numbers assigned to marathon runners, for example, are used to identify or name the entrants.

 ORDINAL

The next level is called the ordinal level of measurement. Data at this level CAN be put in some order, but the differences between elements are not meaningful.

Letter grades in your classes are an example of ordinal measurement.  In some schools, a minimum of 94% is required for an A, but another school may count a 90% as an A.  It is not surprising that colleges have difficulty comparing applicants through letter grades alone, or even through class rank.  Both measures tell nothing about the difference between separate elements within a group.

As with the nominal level, data at the ordinal level should not be used in calculations.

Examples:
Movie ratings (G,P-G,PG13,R,NC17)
The Tonight Show’s “TOP 10” of anything
Classroom letter grades
IQ scores

INTERVAL

The third level of measurement is the Interval level.  It deals with data that CAN BE ORDERED, and in which differences between the data DO make sense.  It can be used meaningfully in calculations, but Interval level data DOES NOT HAVE A STARTING POINT.

Temperature for example can be put in increasing or decreasing order and the difference between 20 degrees and 80 degrees makes sense.  Zero degrees, however, does NOT mean a total absence of temperature.  Without a starting point, ratios of element values are meaningless.  An 80 degree day is not four times as hot as a 20 degree day.

Examples:
Temperature
Sea level
A college student's checking account balance (hopefully that's only a joke)

RATIO

The fourth and highest level of measurement is the ratio level where data possess all of the features of the other three levels and also a ZERO VALUE, so it makes sense to compare the ratios of measurements. Phrases such as "four times" and "twice" are meaningful at the ratio level.

Examples:
Monthly precipitation
Any system of measurement (length, weight, distance)




Since organizing data is a constant task in statistics, let's encapsulate characteristics of the four levels of measurement.

Notice that each level of measurement meets the criteria for the previous levels plus one more.

As you get further along in the curriculum, you will be introduced to essential statistical operations.  The level of measurement is an important factor in determining which
computations are viable.  Save the chart below for future reference and check your textbook glossary to reference each of the computations in the left column.

WHAT'S NEXT IN STATISTICS?
Now that we have some background and terminology, we can start developing a statistical survey.  Get a jump start on the classroom by thinking of a study you might want to conduct as a practical application.  Are you in another class (like American Politics during this election year) which would give extra credit for completing the survey?  What is your population?  What sample would be appropriate?  What would you measure?  How would you measure it?  Based on the chart above, what statistical computations would be possible?  Later in the curriculum, we'll investigate the information that can be garnered from the calculations.  For now....have fun!!


                       

PARAMETRIC EQUATIONS: Math Art

Even for those who are not enamored by the intricacies of math, the potential for entering an equation into a grapher and watching an incredible design appear can be appealing.  Parametric equations are the artists of the math world.



Parametric equations appear every now and then on the SATII, in Precalculus classes, and in Calculus as well.  These equations express two variables (usually x and y) each in terms of a third variable called the parameter (often t).

THE OBVIOUS SOLUTIONS
Given the parametric equations....

    x = t^2 + 3
    y = 2t

....a graph can be plotted by calculating values of (x,y) in a three column chart.

    t      x     y
    0     3     0
    1     4     2
    2     7     4
    3    12    6
    4    19    8
    5    28    10

USING OUR ALGEBRA SKILLS
Many parametric equations can also be manipulated algebraically to form a single rectangular equation which may be easier to graph.   

    Solving for t in terms of either x or y in the example above and
    substituting into the alternate equation gives the function...

    y = 2 sqrt (x-3)


A SPECIAL CAUTION WHEN ELIMINATING THE PARAMETER
Caution should be taken to preserve the range of the original equations when eliminating a parameter.  In this example, the range of x is all real numbers greater than or equal to 3.  Luckily, this exclusion on x is also accounted for in the rectangular equation because of the square root.

But consider...

    x = t^2
    y = 3t^2 + 4

In this case, x doesn’t fall below 0 and y doesn’t fall below 4.  So the graph of the parametric equations is truncated below (0,4).

PARAMETERS CAN DO WHAT FUNCTIONS NEVER WILL
Many interesting shapes cannot be graphed as functions because they don’t pass the vertical line test.  Parametric Equations can be used to graph geometric figures like conics.

The Cartesian equation for a circle, x^2 + y^2 = r^2, can easily be converted to parametrics as
    x = r cos t
    y = r sin t

RECOGNIZE CHARACTERISTICS OF PARAMETRICS
Here are some “expectations” for parametric equations.

1.  x = sin t, y = cos t  represents a point moving clockwise around the unit circle.

2.  x = cos t, y = sin t describes the point moving counter-clockwise around the unit circle.
   
3.  x = t, y = t^2 signals a parabola

4.  x = t^2, y = t  in function form graphs as a square root

RELEASE THE ARTIST WITHIN
YouTube has a plethora of examples of exciting, artful parametric equations to program into a graphing calculator.  Here’s one that draws a butterfly......

    x = sin(t) (e^(cos(t)) - 2 cos (4t) - (sin (t/12))^5)
    y = cos(t) (e^(cos(t)) - 2 cos (4t) - (sin (t/12))^5)

Have fun!!

Getting Ready for AP STATISTICS: VOCABULARY BASICS

As you start the study of statistics, you will find topics and equations that you have studied in previous classes.  Mean-median-mode, for example, should quickly bring to mind average-middlemost-most frequent.  Other familiar terms have unique definitions for statistics class.  Meanings aren’t as much “different” as they are more “specific” and carry definite implications. 

What follows is not a complete list, but rather a sampling of the vocabulary with explicit meanings in the course.  There are only 10 here to get you started and a suggestion for continuing to prepare for AP Stats on your own.

Population: The complete set of data elements is termed the population.

Sample: A sample is a portion of a population selected for further analysis.

Parameter: A parameter is a characteristic of the whole population.

Statistic: A statistic is a characteristic of the sample.

                 Notice that the P’s are associated with each other and 
                 the S’s are associated with each other:  
                 Parameter is to Population as Statistic is to Sample

Individual refers to the elements in a set

Variable refers to the characteristics describing individual elements of a set.

Qualitative data are non-numeric or categorical data.

Quantitative data are numeric and can be either Discrete or Continuous.

     Discrete: numeric data that have a finite number of possible values.  When opinion surveys evaluate answers like “Strongly disagree, Disagree, Neither disagree or agree, Agree, Strongly agree, each possible answer is given a discrete numeric value so meaningful statistical computations can be made.  The same information could be gathered through options like “on a scale of 1 to 5...”

Data counts are always discrete: for example, the number of students enrolled in your statistics classes.

     Continuous: numeric data that have infinite possibilities: the set of all counting numbers or the set of all real, rational numbers between 1 and 2.



If you already have your textbook, look at the glossary to find other terms that you've run into before.  Read definitions to identify how these words might be similar and/or different from your past encounters with them. 

Getting Ready for AP STATISTICS: MEAN-MEDIAN-MODE

MEAN - MEDIAN - MODE

For those of us preparing to earn a 5 on the AP Statistics exam next spring, calculating mean - median - mode should be as natural as eating ice cream on a hot summer’s day.  The measures of central tendency were introduced in upper elementary math classes, but it isn’t until now that the various uses have important implications.  

CALCULATING MEASURES OF CENTRAL TENDENCY

MEAN is the same as “average”  or “arithmetic mean.”
     Add all of the elements and divide the sum by the number of elements.

MEDIAN is the middlemost.  Think of the middle of the street...that’s the median. 
One very easy way to find the median in a small group is to first put all numbers in ascending order. Then count from the right and left simultaneously until you get to the middle.

If there are an odd number of elements, there will be one in the middle that can’t be matched from both the right and left......the median.

If there are an even number of elements, the median is the AVERAGE of the two in the middle.

MODE is the most frequently appearing element.

USING CENTRAL TENDENCY TO DESCRIBE DATA

In Statistics, these measures are used to describe the “typical” element and the relative usefulness of each is determined by the level of measurement.  (Watch this site for an upcoming blog, "Getting Ready for AP Statistics: Levels of Measurement" and share examples with other followers.)

NOMINAL (entries are categories or qualitative data)......MODE

ORDINAL (qualitative or quantitative data)....................MEDIAN

INTERVAL (quantitative data)
--- Symmetric.............................................................MEAN
--- Skewed.................................................................MEDIAN


RATIO (quantitative data)
--- Symmetric.............................................................MEAN
--- Skewed.................................................................MEDIAN

A MEAN is useful only for interval or ratio data.  It considers all of the elements in the sample and is influenced by outliers.  The mean is pulled toward an extreme.

A MEDIAN is useful for all quantitative data: ordinal, interval, and ratio levels and is not effected by an extreme outlier.

A MODE is the only useful descriptor for nominal measurements.  It can be applied in all levels of measurement but may not exist or be meaningful in all cases.

 MEAN - MEDIAN - MODE ON A FREQUENCY GRAPH

  

 

USING A CALCULATOR FOR RECORDING MEAN - MEDIAN 

If you're using a TI-84 or similar grapher, check out the "LIST" and "STAT" buttons.  There are options for finding mean and median after listing the elements in a set.  While you're at it, find the owner's manual for the calculator you'll be using in class and look over the directions for inputting a list and calculating various statistical values.

Keep watching this site for more "Previews" of AP Stats, AP Calc, and other classroom courses.  Let's be prepared before school resumes!

GETTING READY FOR THE PSAT

Why think about the PSAT?
There is no greater honor for a high school senior than to be nominated, selected, chosen, recognized as a National Merit Scholar.  The only way to win the honor which represents the very pinnacle of student achievement is to get an outstanding score on the PSAT in  October of Junior year of high school.  The path to that accolade begins long before the actual distinction, however, perhaps as early as fourth or fifth grade.

How does the elementary education impact results on the PSAT?
The simple answer is VOCABULARY.  On the PSAT, two separate vocabulary assessments are included in the two Critical Reading sections.  Missing just 4 of these questions could knock a test taker out of the running by lowering the raw score by 5 points.

At Tutoring Resources we encourage high ability students to begin expanding recognized vocabulary even before entering Middle School.  “Recognized” basically means listening vocabulary; the student doesn’t need to use the words in normal speech or even written work, but hearing the word should create a usable meaning which can be described out of context.   

Vocabulary can be improved regardless of the student’s grade.  Potential National Merit scholars should develop a plan to expand word skills.  A few suggestions include “SAT Word-a-Day” available free online, any one of several commercial programs, avid reading (with a dictionary close by), prefix/suffix knowledge, and listening closely to educational tv programs in search of college-level terminology.  Word-a-Day (or -Week or -Month) projects  can be family activities to benefit siblings of all ages and parents as well.  My grandmother, who learned English after the age of 30, continued to explore vocabulary well into her 90s by recording new words as she ran across them and looking them up later.

When should study for PSAT and National Merit begin in earnest?
The PSAT test serves as a qualifier for National Merit recognition only when taken in October of junior year.  Some students begin preparation in Middle School, others after completing Algebra 2, and a few as they enter eleventh grade.  All 2014 grads should be thinking about this opportunity right now.  Those with the potential to excel should double down on preparation immediately.

How do you know if it is worthwhile to study for the PSAT? 
Take one of the REAL ACT tests out of the study manual of the same name.  Individual section scores over 30 on the English, Math, and Reading portions are good indicators of the necessary foundational knowledge.  Because the structure of the two national tests is noticeably different, the study goal should be to fortify content experience while practicing test taking skills unique to the PSAT/SAT.

A sample SAT score can also serve to motivate a student to strive toward PSAT success.  The scoring protocol parallels the PSAT, and scores of 700 or higher indicate a high probability of sufficient background knowledge to warrant enhanced study toward the October test.

What study goals should be established? 
Students identified at Tutoring Resources as potential National Merit scholars are invited to study for the PSAT.  For Illinois students, to accommodate possible anxiety on test day, we set homework goals that would result in a minimum PSAT score of 220, slightly higher than the 216 cut off established last year .

What if I don’t get picked to continue the National Merit qualification process?
As a certifiable academic, I will never be convinced that learning is not worthwhile.  With that prejudice in mind, I would argue that recognizing a high scholastic aptitude is a reward in itself.  Striving toward the coveted academic award has its own compensation in terms of personal satisfaction and ultimate success on national college entrance exams.  Winning a National Merit Scholarship is the icing on the cake but only a small part of the whole experience.

GOOD LUCK!!!

Getting Ready for AP STATISTICS: COMMON GRAPHS

Statistics is the collection and analysis of data for the purpose of discovering trends, formulating conclusions, and making predictions.  Sometimes "picturing" the data can be useful in explaining relationships.  Several forms of visual display are taught in math classes that come before a formal Statistics class.  

Charts and graphs are used to display specific data, categories, trends, and other visualizations which may make it easier to understand statistical measurements.  The advantages and disadvantages of each display determine the best use for each.

EXAMPLE #1

 

HISTOGRAM 

Individual data points are collected into categories which are represented in adjacent bars.

Advantages:  Visually strong

                      Can compare to normal curve

                      Usually vertical axis is a frequency count of items in a category

Disadvantages:  Cannot read exact values because data is grouped into categories

                           More difficult to compare two data sets

                           Use only with continuous data

EXAMPLE #2

 

 

 

 

 

 

 

BAR CHART

Similar to Histogram but individual data points are represented in each bar, avoiding disadvantage of not being able to distinguish exact values.

EXAMPLE #3

LINE GRAPH

Plots continuous data as points and joins them with a line.  Multiple data sets can be graphed together with separate sets identified in a key.
Advantages:  Can compare multiple
                      continuous data sets
                      Interim data can be inferred
                      from graph line
Disadvantages:  Data must be continuous

EXAMPLE #4

 

FREQUENCY POLYGON 

Made by coloring in the area below a line graph.  From a histogram, construct the polygon by connecting midpoints of each column.
Advantages:  Attractive display
Disadvantages:  Ends may imply zero as
                           data points
                           Use only with continuous
                           data

 

 

EXAMPLE #5

SCATTER PLOT (DOT PLOT)

Displays the relationship between two factors of the experiment.  A line of best fit is used to indicate positive, negative, or lack of correlation.
Advantages:  Trends are easy
                      to see in
                      Shows exact
                      values and entire
                      sample set
                      Shows min, max,
                      and outliers
Disadvantages: Both data sets
                          must be
                          continuous

EXAMPLE #6

 

 

 

 

 

 

 

STEM AND LEAF DISPLAY

Data displayed in rows which can easily be converted to histograms or frequency graphs.  If rows become too long,  left column entries may be repeated.  Strings are most useful if entries are in numeric order.
Advantages:  Precise data list
                      Easily identify min, max, gaps, clusters,
                      and outliers
 Disadvantages:  Central tendencies difficult to visualize

EXAMPLE #7

BOX AND WHISKERS   (BOX PLOT)

Showing the five standard measures: median, upper and lower quartiles, smallest value, and largest value . Multiple boxplots can be drawn side by side to compare more than one data set. 

Advantages
    Shows 5-point summary and outliers
    Easily compares two or more data sets
    Handles extremely large data sets easily

Disadvantages
    Exact values are lost

EXAMPLE #8

Here's a graph that shows up frequently in calculus problems...

 OGIVE (CUMULATIVE LINE GRAPH)

Displays the total at any given time. The relative slopes from point to point will indicate greater or lesser increases; for example, a steeper slope means a greater increase than a more gradual slope.



For some of these visualizations, like the box and whiskers display or a line of best fit, it is necessary to calculate trends or measures of central tendency.  Can you find the mean? the median? the mode? the first quartile?  the standard deviation?

Definitions and calculations for these and other important principles in Stats will be covered in upcoming blogs.  A little review before school resumes can help get the new term off on the right foot.  Keep watching this sight for tips for AP Stats and other courses.

DOG DAYS MATH

Boy, is it HOT out there!!!  If the temperature outside is 100 but air conditioning keeps the atmosphere inside at 85 degrees, what is the percent change when you come in from the heat?     (100-85)/100........(the original amount minus the new amount) divided by the original amount).......the amount of change divided by the original amount.....The air inside is 15% cooler than the air outside.

In times of extremes, like in the weather, even the kids are aware of numbers.  What a great opportunity to demonstrate a few math concepts like percent change.

Here's another one.  The days are getting shorter.  Yesterday the sun rose at 5:14 and set at 8:24.....that's 15 hours and 10 minutes......910 minutes (multiplication).......tomorrow the sun will rise at 5:16 and set at 8:21.....that's 15 hours and 5 minutes.  [These are simple arithmetic problems and the times are only samples and not accurate.]  Students can look up sunrise and sunset on the computer and do the math on the calculator.  Now, calculate the percent change.  For what portion of the day is the sun up?  (tomorrow: 905/1440)  Can you use ratios to predict the number of minutes of sunshine the day after tomorrow?  next week?

Interested in health?  Take your temperature orally or in the ear.  One reading when you're outside in the heat and another when you're inside an air conditioned space.  Is there a difference?  What about your temperature when you're sitting in the sun versus sitting in the shade?  Do you have one of those forehead temperature readers?  Is there a difference in your skin temperature inside? outside? in the sun? in the shade? Doe sitting in the pool lower your body temperature?  Will pouring water over your head lower the body temperature?  How could these observations apply if you're an athlete working out on the football field or soccer field in this heat?

You may feel more comfortable sitting in front of a fan, but is there a difference in your body temperature just because of the moving air?  Take your temperature with and without the fan.

Is there a candy thermometer in the kitchen?  How hot will a bowl of water get if you set it in the sun?  Will a smaller container get hotter?  more quickly?  glass versus metal?

Will warm water heat up faster than ice water if identical containers are set out in the sun?  Will boiling water cool off at the same rate that warm water heats up if both are put in the sun?

These are teachable moments because even the youngest students are aware of the extreme heat.  Whatever the student's age, there are math and science questions that can be related to today's extraordinary weather.  What questions can your kids come up with?  And how can an answer be found?.....The Teachable Moment for The Normal Genius in each of our kids!!

PAINLESS SUMMER GEEK

It's three weeks into summer vacation.   ARE YOU BORED YET?


While I'm not so out of touch that I'd EVER suggest a reading program over the summer as a voluntary, go-to, engaging activity for any other than the most stalwart student, there are ways for parents to introduce a little geek into normal leisure activities.

Take television watching for example.  There are frequent literary references in shows that the younger generation watches.  The Simpsons, South Park, and Family Guy are fraught with allusions to famous quotes especially from the more intellectual characters.  Does your student know what that phrase means or where it came from.  Lisa Simpson saying "A rose by any other name..." can make Shakespeare relevant.

Video games are another popular diversion which can provide cultural reference resources.  My kids played Civilization in their teens.  Many of the character and location names stem from actual people and places.  Familiarity with the terms can create historical reference points.

Vocabulary building may be the easiest summer activity.  Did you notice that the swimming pool at that high school is called the 'natatorium?"  Why was that car named 'Intrepid?"  What words are used in commercials to make you think the product is superlative?  Parental use of a vivid vocabulary can establish contextual clues to new words: "What a beautiful azure sky!  The blue is so crisp and clear."  "That salesperson was certainly ingratiating.  She went out of her way to please us."  The trick to contextual definition is to explain the word in the following sentence.

A car game that was a favorite in our family involved changing the wording of common street signs by using alternative vocabulary.  "Slow - Children at Play" can become "Proximity of youth in the performance of spontaneous gratification impels immediate deceleration of moving vehicles."  The same game can be played with advertising signs or with compliments (or insults that require no profanity).

If every situation is a learning opportunity, parents can sneak an education adventure into even the most mundane occasion.

PLANNING YOUR COLLEGE VISITS

AHHH! The excitement and family bonding of piling into the car (or the train or the plane) and heading off to explore the many college locations that promise a bright future for our maturing young adults! (insert sound of screeching tires) But wait! This scenario is out of order. There are so many other considerations to make before packing a bag, not the least of which is a plan to implement upon arriving at the destination(s).

Let’s start at the beginning and forestall the fun part until we’re better prepared.

There are big schools and small ones, schools far away from home and those close by; schools offering a 4 year degree and others with graduate programs; schools his or her friends are attending and schools where nobody knows your name; the school mom, dad, brother, or sister went to and schools that mom, dad, brother, or sister wish they had. The choices are virtually limitless, injecting the need for a little preplanning.

STEP ONE: Make a list of potential colleges. Don’t limit yourself yet. At this point, 20 schools is not too many to handle and the list will decrease as you make informed decisions.

STEP TWO: Check online to see the qualifications each school seeks in their admission process. Compare the “wants” with your student’s academic and extracurricular history. Decisions at this step can revolve around either end of the spectrum: low GPA and ACT results will not be impressive to the College of William and Mary, but high scores may indicate that your academically gifted student will not be challenged sufficiently by schools with low standards.

STEP THREE: Visit your high school’s website to check for a link to Naviance. Follow the steps to check out the scattergram of recently admitted graduates from your high school to each college, based on GPA and standardized test scores. This information can be a second decision point academically or for other reasons.

I personally chose a college which no person from my high school had attended in the previous 3 years, but I had to wait until graduation to get the most current information. Your student may want to be “the only one” or part of a large contingent from the neighborhood. It's a question often neglected, yet a viable decision point.

STEP FOUR: Select an itinerary (or two or three). Try to limit the number of schools visited on each trip to a reasonable goal, maybe 3, that will avoid getting them confused. While the plan may be geography based, think about having one large campus on the same trip as a smaller one.

STEP FIVE: Contact the admissions department at each school on the itinerary and schedule a guided visit. This gets your name on the roster and gives you someone to answer questions.

STEP SIX: Have a standard list of questions so you can gather comparative information. Other issues will come up at each campus, but you will be assured of having the same baseline input from each school.

STEP SEVEN: Take notes during and after the visit. Write down your opinions as soon as practical and include comments that will bring the specific school to mind, like “huge oak trees in quad.” Anything you can do to keep the memories organized will be helpful once you’re back home.

STEP EIGHT: Pack your bags. Remember that you’ll be walking around these campuses, so be warm (or cool) and have very comfortable shoes.

Have fun!!

TIPS FOR ELEMENTARY SCHOOL PARENTS: SHOULD WE HIRE A TUTOR?

TIPS FOR PARENTS

My tutoring service does not usually work with elementary school students, but there are others who specialize in this age group. Hearing in a Parent-Teacher Conference that your pride and joy is a whole grade below “standards” can be devastating, especially for the involved parent who is truly committed to education. So the question arises: do we send our child to a tutor.

There is no quick answer to this heart-wrenching question. Whether you choose to use the services of a professional or to tackle the problem yourself is a personal one and only you can make the decision. Here are some thought-provoking questions that will help you feel confident in whatever choice you make.

1. What is the level of the difficulty? If your fifth grader is reading at a 4.5 level, the problem is small and may require only greater exposure to harder reading material. For a fifth grader reading at a 2.0 level, the problem is much greater and remediation is essential, probably from someone with special skills in analyzing the situation and providing an extensive battery of solutions.

A child who has difficulty with just one area, like fractions in math, may overcome the hurdle through a few, fun, at-home activities. Some tips on what you can do within the family are presented later in this article.

2. What is your relationship with the student? Some parent-child connections thrive on an educational component; others are complex enough with daily living and social issues. If you want to “pick your battles,” as some would say, perhaps “teaching” your student about the 19th Century “Scramble for Africa” isn’t the best battleground. Be assured that the parent who takes a student to a tutor is no more and no less honorable than the one who researches Leopold II’s influence at the Berlin Conference. If teaching your student at home is likely to cause strife, then outside help is justifiable. If having your child read Call of the Wild aloud to you and a younger sibling each night and discussing the characters would be enjoyable, then take advantage of the opportunity to strengthen a family bond while improving classroom performance.

3. What are the financial obligations? What are you getting for your money? If a service tells you that they can increase your student’s reading level by a full year in just 9 months, remember that the school year is 9 months long and this kind of improvement is expected without intervention.

4. What is your child’s level of outside activity? A student who is already heavily committed to choir, dance class, Tae Kwon Do, gymnastics, horseback riding, scouts, religious training, and baseball might have to give up an extracurricular to make room for additional study. Make sure that the outside help will not be viewed as a penalty by your student. Learning should be considered a reward, not a punishment, especially at an early age with 10 or so more years of it ahead.

I’ll leave the topic of choosing a tutor for another blog. Let’s consider right now that you’ve decided to address a situation from your own home. Here are some tips to help parents of elementary students design “kitchen table tutorials.”

1. Do Not “over assign” home work. There are too many division problems on a whole page and it wouldn’t be any fun. Instead, ask the student to correctly work just one problem from each section on a page. If the attempt is not successful, you have several other problems to use as demonstration and retesting. Break other work into small parts, say a chapter in a novel or a subsection in history. Use a few minutes after the “assignment” to discuss what was learned and what else the student would like to know about the subject. Verify accuracy of facts and give your student a chance to discuss, no matter how young he or she might be. This will solidify the learning and enhance the student’s ability to integrate information and synthesize knowledge from other subjects.

2. Ask the student to work only as many math problems or answer as many factual questions as you are willing to correct. The feedback must be immediate but math review problems may come with only answers and no solutions manual. You will have to work out every problem the student misses in order to find the point of error.

The same goes for an independent reading assignment. You’ll have to read the same story, chapter, or article and be prepared to show the student where and how to find answers to related questions which you may have to design yourself.

3. Cover a variety of topics each time. A little of this and a little of that each day will help to strengthen each concept in the student’s repertoire. A common problem with many textbooks and curricula is that a subject is covered, tested, and then ignored for the rest of the year. You want to review often and across the curriculum.

4. Provide appropriate rewards. You know your student better than anyone else does, so dream up clever rewards, ask the student for suggestions, and surprise good work with something your extraordinary student will view as special.

A short afterthought for those willing to try home work. Home schooling is not easy, but working at home can be tremendously rewarding for both student and parent. Use the grocery store (or, even better, a toy store or electronics center) to explore fractions, percents, and social interactions. Play “car games” to improve vocabulary, visual discrimination ability, and deductive reasoning. Use cartoons to discuss “beginning, middle, end” writing strategies, identify themes, and watch for new vocabulary words.

Even if you choose to employ a tutor for specialized learning, the first, best, and perpetual teachers are our parents.

PAYING FOR COLLEGE: SAVING MONEY ON TEXTBOOKS

Hearing the phrase “paying for college” usually makes us think of tuition, scholarships, and maybe housing. It makes our kids think about clothes, computers, and decorations for the dorm room. Many of us have been flabbergasted by one of the major expenses of college -- TEXTBOOKS.

In 2008, the federal government revised the Higher Education Act in more ways than just adding “Opportunity” to the name. Colleges now must provide information about a majority of classroom textbooks at the time of registration. Students will know the title, ISBN, and retail price of the textbook in all acceptable formats.

When I was in school, we just went to the college bookstore the day before classes started, found the shelf labeled with the course number, and grabbed the books stacked there. The price at the register might have been as much as $100. To save a few bucks, we might have looked for the texts that had that yellow tape, “used.” That’s still an option for your college students, but it might be a costly one. A single text could cost nearly $200!!

Textbook expenses may be minimized by one of these alternatives.

BUY ONLINE
Many websites are available for searching out a used version of the textbook. You might try Amazon.com or one of these:

http://usedtextbook.blogspot.com/2011_07_12_archive.html

www.cheaptextbooksblog.com

It’s preferable to have the ISBN to be sure you have the right edition and the page references from the syllabus match the page numbers in the textbook. I’ve had the challenge of matching an old version with a newer one several times and it is not fun!! Sans the ISBN, be sure you have the proper title, author, and publication date in order to have a usable text.

Look for books that are “like new” or similar terminology, but don’t immediately dismiss the really cheap ones that might be described with “binding torn,” especially if the course isn’t one that your student is particularly passionate about. Do try to avoid those which are “majorly highlighted” or have “many marginal notes.” The student should be able to make his or her own notes for reference and study.

Since shipping might take a week or longer, start the search for the best price as early as possible. Having the book early may have a hidden benefit. Your student may be inspired to actually look at the content before classes start!

RENT TEXTBOOKS
Some of the same websites offer the option to rent books for 30 days or longer. A semester is longer! Watch for the cost of extending the rental period.

You might check out these websites:

www.ecampus.com/textbook-rental.asp

www.cheapbookrenter.com

One benefit to rental may be that most sites will exchange a book that arrives in really bad condition. And you don’t have to worry about reselling a rental.

E-TEXTBOOKS
Some publishers even offer texts in electronic format which may be appealing for our technically literate offspring. This alternative wouldn’t work well, however, for the student who makes marginal notes or highlights in context. Even if pages can be downloaded and printed, the cost of duplication could be excessively expensive and inconvenient.

STUDENT EXCHANGE
If your students (or you) are members of a fraternity or sorority, older students may be willing to pass down their books, particularly in the Gen Ed courses that almost everyone is required to take.

ESPECIALLY FOR MATH
As a math teacher, I always suggest that my students look for a COMPLETE SOLUTIONS MANUAL rather than just the Student Version. I also look for solutions, not just answers. I’ve discovered many professors who use the unassigned problems as test questions, and having worked the problem previously can take some of the challenge out of a test.

WHAT ABOUT HIGH SCHOOL TEXTBOOKS?
Although these suggestions are geared toward college students, I always try to have the high school textbooks available in my tutoring service. If your school requires students to purchase their textbooks or if your student doesn’t want to lug the huge history book back and forth between home and school, it can be expedient to have a copy at home. Also, if your student wants to be a doctor and is taking an advanced biology course, having the high school text available for reference in college can serve as a refresher to previous knowledge.