Course Competency Report by Code Descriptions... · Course Competency Report by Code Code: C784...

Course Competency Report

by Code

Code: C784

Applied Healthcare Statistics (C784)

C784 - Applied Healthcare Statistics

Undergraduate

General Education

Mathematics

AOS Mathematics

Course of Study:

Course Level:

Course Division:

Discipline:

Course Type:

Department:

COMPETENCY # COMPETENCY NAME COMPETENCY TEXT

The graduate applies the operations, processes, and procedures ofbasic arithmetic to solve expressions.

Basic Numeracy &Calculation Skills

1012.1.1

The graduate applies the operations, processes, and procedures offractions, decimals, and percentages to evaluate quantitativeexpressions.

Fractions, Decimals &Percentages

1012.1.2

The graduate applies the operations, processes, and procedures ofbasic algebra to evaluate quantitative expressions, and to solveequations and inequalities.

Basic Algebra1012.1.3

The graduate evaluates categorical and quantitative data pertaining to asingle variable using appropriate graphical displays and numericalmeasures.

Descriptive Statistics fora Single Variable

1012.1.4

The graduate evaluates the relationship between two variables throughinterpretation of visual displays and numerical measures.

Descriptive Statistics forTwo Variables

1012.1.5

The graduate evaluates the relationship between two quantitativevariables through correlation and regression.

Correlation & Regression1012.1.6

The graduate applies principles and methods of probability-basedmathematics to explain and solve problems.

Probability1012.1.7

Course Objective Report

by Code

Code: C784



Undergraduate

General Education

Mathematics

AOS Mathematics

Course of Study:

Course Level:

Course Division:

Discipline:

Course Type:

Department:




1012.1.1

OBJECTIVE # OBJECTIVE COMMENTS COG. LEVEL

LR should show how numbers can be in more than 1category. Keep the set small (no more than 5 numbers).For example 0 is in all 3 categories, while -4 is only aninteger and rational number. A visual representation wouldbe helpful, such as the one to the right. (This course is notincluding natural numbers.) Explain that rational numberscan be written as a ratio of two integers.

1012.1.1-01 1 –Remember/Understand

Identify whole numbers, integers, or rational numbers froma finite set of real numbers.

Keep the set small (no more than 5 numbers). The LRshould likely start with showing the order using the numberline and progress to problems without the number line. Thisarea should also introduce set notation.


Order a finite set of real numbers with or without a numberline.

Operations of add, subtract, multiply and divide. Defineproperties such as commutative associative, identity,inverse, and distribute for multiplication and addition, asapplicable.


Apply the mathematical operations to whole numbers.

Operations of add, subtract, multiply and divide. Refer topreviously defined properties as needed, as well as zero-factor law. Discuss sign rules for multiplication and division.


Apply the mathematical operations to integers.

Operations of add, subtract, multiply and divide.1012.1.1-05 1 –Remember/Understand

Apply the mathematical operations to numbers withexponents.

Operations of add, subtract, multiply, divide, andexponents. Expression should not include fractions,decimals, or square roots. Include the abbreviation ofPEMDAS (please excuse my dear Aunt Sally) to helpstudents learn steps, but stress that multiplication anddivision, as well as addition and subtraction are done fromleft to right. Refer to previously defined properties asneeded.


Apply the order of operations correctly to a given numericalexpression.

Keep the estimation simple, preferably withoutfractions/decimals.

1012.1.1-07 2 – ApplyApproximate a solution to a mathematical problem usingestimation skills.

For whole numbers be less than 100. The tree methodwould be great to show in the LR.


Identify the prime factorization of a given whole number.

Again, for numbers less than 100.1012.1.1-09 1 –Remember/Understand

Identify the Greatest Common Factor of two given wholenumbers.


by Code




1012.1.1


For numbers less than 100. The LR should start withperfect squares first, then move into other squares whilekeeping in mind the prime factorization of the number.Again, tie in the tree method from prime factorization.

1012.1.1-10 2 – ApplyCalculate the square root of a whole number.

Linked to Objectives: 01, 03, 04, 051012.1.1-11 2 – ApplyGiven a set of real numbers, the student performs aselected mathematical operation (i.e., addition, subtraction,multiplication, division or exponentiation) on a specifiedsubset of the set of real numbers.

Linked to Objectives: 061012.1.1-12 2 – ApplyGiven a mathematical expression containing real numbers(i.e., integers and numbers with exponents), the studentapplies the order of operations to solve the givenexpression.

Linked to Objectives: 08, 09, 101012.1.1-13 2 – ApplyGiven a pair of whole numbers, the student identifies thegreatest common factor using prime factorization.




1012.1.2


This should also include how to reduce fractions to thesimplest form. It should start with positive fractions thenmove to negative fractions. The placements of the negativesign should be addressed. It may be good to also discusshow fractions can be built to a higher term (multiply bothtop and bottom by the same number).Vocabulary/concepts may include mixed numbers, rationalnumbers, fraction. Explain Butterfly Method.


Identify equivalent fractions.

Define least common denominator. The concept of leastcommon multiple may also need to be defined andexplained.


Identify the Least Common Denominator of two fractions.

LR should show strategy for each common denominatorsand unlike denominators. The LR should define reciprocalof a fraction and the rules for dividing with zero (both as anumerator as denominator).

1012.1.2-03 2 – ApplyApply the mathematical operations of addition, subtraction,multiplication, and division to fractions.

Should include place values of ten thousands, thousands,hundreds, tens, ones, tenths, hundredths, thousandths,ten-thousandths, and hundred thousandths. This section ofthe LR could also address how to read and/or write decimalplaces.


Identify place values for a given decimal number.

Vocab may include terminating decimal and infiniterepeating decimal. Use traditional rounding procedures (5or up, rounds down. Otherwise, round down).

1012.1.2-05 2 – ApplyApply a given rounding algorithm for decimal numbers.

The LR should start with addition and move through theother operations. Explain that zeros can be written to helpalign digits.

1012.1.2-06 2 – ApplyApply the mathematical operations of addition, subtraction,multiplication, and division to decimals.


by Code




1012.1.2


Incorporate examples that nurses are likely to encounter.For example, percent solutions. How much of a solutiondoes the nurse need to give the patient for the patient tohave the right amount of the drug if they are giving asolution?

1012.1.2-07 2 – ApplyApply the mathematical operations of addition, subtraction,multiplication, and division to percentage values.

Introduce the term of rate. This will help set students up forthe basic conversion problems.

1012.1.2-08 2 – ApplySolve for an unknown quantity using ratios in the context ofa proportion.

Keep decimals to less than 4 places. As students havelearned place values, the LR can have students round tospecific place values as needed.

1012.1.2-09 2 – ApplyConvert between decimals, fractions, and percentages.

The measures should include: kilogram, gram, milligram,microgram, quart, pint, fluid ounce, cup, tablespoon,teaspoon, ounce, pound, liter, milliliter (cc). Keep theconversions simple and relative to those a nurse mayexperience in home or work life.

1012.1.2-10 2 – ApplyApply basic unit conversions for household and metricmeasures.

Linked to Objectives: 01, 02, 031012.1.2-11 2 – ApplyThe student applies mathematical operations (i.e., addition,subtraction, multiplication, division) to fractions.

Linked to Objectives: 04, 05, 061012.1.2-12 2 – ApplyGiven a set of decimal numbers, the student performs aspecified mathematical operation and applies a givenrounding algorithm to the answer.

Linked to Objectives: 07, 081012.1.2-13 2 – ApplyGiven a healthcare context, the student appliesmathematical operations (i.e., addition, subtraction,multiplication, and division) to percentage values or solvesfor an unknown quantity using ratios and proportions.

Linked to Objectives: 09, 101012.1.2-14 2 – ApplyGiven a numerical expression containing a combination ofdecimals, fractions, or percentages and either householdor metric measures, the student solves the expression byperforming necessary conversions and the specifiedoperations (i.e., addition, subtraction, multiplication, ordivision) on the numbers.





Define "inverse operation" and provide examples1012.1.3-01 1 –Remember/Understand

Identify the inverse operation that corresponds to a givenoperation.

Vocabulary may include: variable, constant, algebraicexpression, term, coefficient (if not previously defined)

1012.1.3-02 2 – ApplyEvaluate a given algebraic expression using the distributiveproperty.


by Code





Vocabulary to include: like terms, unlike terms, degree (inrelation to terms). Terms up to third-degree.


Combine like terms to simplify a given algebraicexpression.

Define and display substitution.1012.1.3-04 2 – ApplyEvaluate a given algebraic expression using substitution.

Simple expression or equation with constant. (terms ofdegree 1)


Identify an algebraic expression or equation that defines agiven pattern of relationships for a given real worldproblem.

Define equation, constant. Equation could have onesolution, no solution, infinite number of solutions. LR shouldinclude Addition Principle of Equality, Multiplication (orDivision) of Equality.

1012.1.3-06 2 – ApplySolve a given linear equation of a specified form.

Simple equation with constant. (terms of degree 1). Shouldbe using real-world problems.


Predict a solution to a given an algebraic equation.

Butterfly Method.1012.1.3-08 2 – ApplySolve a given linear equation with fraction coefficients andconstants of the form (a/b)x = c/d.

Introduce concept of intervals of real numbers. Go overinterval notation both on the number line and withparenthesis (closed, open). Only first-degree inequalities.Be sure to include plenty of examples so studentsremember the sign reverses with division or multiplicationof a negative number.

1012.1.3-09 2 – ApplySolve a given linear inequality.

Students will use a number line again.1012.1.3-10 1 –Remember/Understand

Identify a graphical representation of the solution set for alinear inequality.

Vocabulary to include ordered pairs, quadrants, origin,horizontal x-axis, and vertical y-axis. Use integers. It maybe helpful for the LR to use a table approach with onecolumn for the x values and one column for the y values.


Identify the graph of given coordinates on a coordinateplane.

Go over the slope-intercept form of y = mx + b, where m isthe slope and b is the y-intercept. Slope = rise/run = (y2 -y1)/(x2-x1)


Identify the slope when given a graph of a linear equation.

Vocabulary to include x-intercepts, y-intercepts, slope-intercept form, standard form, horizontal line, vertical line


Identify the correct graph for a given linear equation of theform, y = mx + b.

Linked to Objectives: 01, 02, 03, 06, 081012.1.3-14 2 – ApplyGiven an algebraic expression or linear equation in thegeneral form of Ax + By + C = 0 or (a/b)x = c/d, the studentapplies the operations, processes, and procedures of basicalgebra to solve the equation.

Linked to Objectives: 09, 101012.1.3-15 2 – ApplyGiven a linear inequality in the form of y >/</= mx + b, thestudent identifies the correct graph for this inequality.


by Code





Linked to Objectives: 11, 12, 131012.1.3-16 2 – ApplyGiven a linear equation in the form of y= mx + b, thestudent identifies the correct graph for this equation.

Assessment Notes: Graph refers to a coordinate plane withthe line of the inequality overlaid.




1012.1.4


LR will introduce normal distribution (bell-curve), standarddeviation, and the Standard Deviation Rule (68%, 95%,99.7%). The students will NOT be required to calculate thestandard deviation. Rather, it will be provided, along withthe mean, for these types of problems. These problemshould stay relatively simple, allowing students to easilyapply the standard deviation rule. The problems can alsouse the fact that the entire curve is 100%, so student cancalculate "less than" or "greater than" problems as well.

1012.1.4-01 2 – ApplyApply the standard deviation rule to a special case ofnormal distributions.

The student will need to know that median and IQR areused for non-symmetric data and know that mean andstandard deviation are used for symmetric (typicallynormally distributed) data. They will not be required tocalculate standard deviation. The LR will need to teach thedifferences between symmetric and non-symmetric (akaskewness), as shown by histograms or stem-and-leaf plots.


Identify the appropriate numerical measures for a given setof data in different contexts.

Students should be able to understand how mean, median,standard deviation, and range describe the data. Anexample with the same mean, but different standarddeviations helps demonstrate why we must have ameasurement for both center and spread.


Relate measures of center and spread to the shape of thedistribution.

The data sets should be small (less than 20 numbers) andsimple as the students will be using a 4-function orscientific calculator. Vocabulary may include: center,spread (variability), quartiles, mean, median, mode,interquartile range, standard deviation. Center includesmean and median. Spread includes range and standarddeviation

Mean: the sum of the observations divided by the numberof observations

Median of odd number (n) of observations: The value at the(n+1) / 2 place when data is listed from least to greatest.

Median of even number (n) of observations: The mean ofthe values at the (n / 2) place and the next place whendata is listed from least to greatest.

Q1: median of the lower 50% of the data

Q3: median of the upper 50% of the data

1012.1.4-04 2 – ApplyCalculate the mean, median, mode, quartiles, range, andinterquartile range for a set of quantitative data.


by Code




1012.1.4


Mode: most frequently occurring observation or value in adistributionInterquartile range (IQR): Q3 - Q1

Standard deviation: no formula necessary!

Define: distribution, graphical display, numericalsummaries, categorical, quantitative, shape, outliers,skewness, symmetry, modality (peakedness), unimodal,bimodal, skewed right, skewed left. Include examples suchas zip codes to show that numbers do not automaticallymean quantitative. All displays will need to be fullyexplained.

1012.1.4-05 2 – ApplyEvaluate data from several different graphical displays of adistribution of a categorical variable (bar chart, pie chart)and of a quantitative variable (histogram, stemplot,boxplot).

We expect students to be able to look at a visual displayand choose a correct short summary of what they see. Thesummary should address any variation between categorypercentages.


Describe the distribution of a categorical variable incontext.

For the overall pattern the students should correctly answerquestions regarding the shape, center, and spread of thedata. They should correctly choose whether or not thereare possible outliers, and identify values of those outliers, ifapplicable, based on the 1.5IQR Criterion.


Describe the distribution of a quantitative variable incontext: a) describe the overall pattern, b) describe strikingdeviations from the pattern.

Based on a description of the study the student should beable to choose an appropriate graphical displays: bar chart,pie chart, histogram, stemplot, boxplot.


Identify the appropriate graphical display for a given set ofdata in different contexts.

This could be caused by the design of the chart (3D chartscan skew it), improper scaling, changes to the axes(truncated graphs), no scale, improper intervals, etc.


Explain how graphical displays can be used tomisrepresent data.

Linked to Objectives: 011012.1.4-10 2 – ApplyGiven a mean and standard deviation for a normaldistribution, the student applies the standard deviation rule.

Linked to Objectives: 02, 03, 041012.1.4-11 2 – ApplyGiven a small single variable dataset, the studentevaluates data and measures of center, spread, and shapeas they relate to the distribution.

Linked to Objectives: 05, 06, 071012.1.4-12 2 – ApplyGiven a description or graphical display of categorical orquantitative data, the student interprets single variable dataand determines characteristics of the data and itsdistribution.

Linked to Objectives: 081012.1.4-13 2 – ApplyGiven raw data or a description of a small single variabledataset, the student selects the type of graph thatappropriately represents the data set.

Linked to Objectives: 091012.1.4-14 2 – ApplyGiven a chart or graph that misrepresents data or a smalldataset, the student selects the correct responseexplaining why it is misleading.


by Code




1012.1.5


Define explanatory and response variables. CoverCategorical --> Categorical, Categorical --> Quantitative,and Quantitative --> Quantitative.


Classify a data analysis situation according to the Role-type Classification.

Graphical displays include two way tables, side-by-side boxplots, and scatter plots. Students should be able to choosethe correct displays based on a description of the study.Students should know the explanatory variables is alwayson the x-axis


Identify the appropriate graphical display for a givenclassification in different contexts.

Numerical measures include conditional percentages anddescriptive statistics.


Identify the appropriate numerical measures for a givenclassification in different contexts.

Row percents and column percents. Students should lookat how the pattern of conditional percentages differsbetween the values of the explanatory variable.


Compare conditional percentages in a two-way table.

This is where students will "dig into" scatter plots a bit morethan simply knowing what they look like and that they areused for Q-->Q classification. For example, do the 2variables have a strong linear relationship?


Summarize distributions of two variables.

Again the student can understand how words like strong orweak, linear or nonlinear, positive or negative describe thescatter plot and the relationship between the two variables.. (Correlation coefficient not addressed in this section, butrather in next competency.)


Determine the relationship between two quantitativevariables, when given a graph.

Are there data points that deviate from the pattern?(outliers) What happens to the data if the outliers areremoved? Is there a positive or a negative relationship? Isthe relationship linear?


Describe the overall pattern and the striking deviations in agraph of two variables.

Linked to Objectives: 01, 021012.1.5-08 2 – ApplyGiven a description of a two-variable study, the studentidentifies the variable classifications or the appropriategraphical display.

Linked to Objectives: 031012.1.5-09 2 – ApplyGiven a graphical display or description of a two-variablestudy, the student identifies the appropriate numericalmeasures.

Linked to Objectives: 041012.1.5-10 2 – ApplyGiven a two-way table or a description of a study with twocategorical variables, the student interprets and identifiespotential relationships between variables.

Linked to Objectives: 05, 061012.1.5-11 2 – ApplyWhen presented with a scatterplot of two variables, thestudent describes the distribution or potential relationshiprepresented between these two variables.

Linked to Objectives: 071012.1.5-12 2 – ApplyGiven a scatterplot of two quantitative variables, thestudent identifies potential outliers or the effects ofpotential outliers on the relationship.



by Code




Vocabulary: lurking variable, association, causation, causalrelationship, confounded. Association does not implycausation. Stress that an observed association is notenough evidence to state that there is a causal relationship.Be sure that the LR addresses how lurking variables caninteract on the variables and that the presence of a lurkingvariables is why we say association, rather than causation.


Explain the distinction between association and causation.

for explaining an observed relationship; lurking variablecannot be the explanatory or the response variables, butrather is an "outside" variable


Identify potential lurking variables.

Stress on the fact that Simpson's Paradox is the whenlurking variable causes a reconsideration in the direction ofthe relationship between 2 variables. This can be shownthrough scatter plots or through tables.


Explain the phenomenon of Simpson's Paradox as itrelates to interpreting the relationship between twovariables.

Vocabulary: correlation coefficient. Students will NOT needto know how to calculate the value, only how to estimate itbased on a scatter plot and how to interpret a value. Theyshould know it describes both strength and direction of therelationship.

1012.1.6-04 2 – ApplyEstimate the value of the correlation coefficient betweentwo variables from a scatterplot.

Students will NOT need to know how to calculate the value,only how to estimate it based on a scatter plot and how tointerpret a value.


Interpret the value of the correlation coefficient betweentwo variables.

Students should know that correlation does not signifylinearity. They need both the correlation coefficient and thescatterplot.


Recognize the limitations of the correlation coefficient as anumerical measure of the association between twoquantitative variables.

Vocabulary: regression, linear regression, least squares,(slope and intercept as review)


Identify regression analysis applications for purposes ofdescription and prediction.

Students will not be required to calculate the equation, butrather it will be provided and they must interpret it. Theyshould be able to conclude from the equation if there is apositive or negative correlation and, likewise, if the slope ispositive or negative. Students also should understand howthe slope is interpreted (average change in the responsevariable when the explanatory variable increases by 1 unit).


Interpret the simple least squares linear regressionequation for a set of data in regards to the overall pattern.

Vocabulary: extrapolate, interpolate. Students shouldunderstand that they can usually interpolate on a strong,linear relationship with a least squares regression line.


Interpret the simple least squares linear regressionequation to make a prediction.

Vocabulary: p-value. Note that we are not going intohypothesis testing in this course so keep this to a verysimple explanation. I could see us providing a few differentoptions for the equation and the student should choosewhich model best fits the data.


Determine whether a regression model is significant.

Students should be cautious of extrapolation beyond therange of the data. (It is not reliable and should be avoided.)


Identify potential problems if regression analysis is usedincorrectly.

Linked to Objectives: 01, 02, 031012.1.6-12 2 – ApplyGiven the description of a two-variable, healthcare-relatedstudy (quantitative variables), the student identifies thetype of relationship (association or causation) and whethera lurking variable or Simpson’s Paradox phenomenon ispresent.


by Code





Linked to Objectives: 04, 05, 061012.1.6-13 2 – ApplyGiven a scatterplot from a healthcare related study, thestudent identifies an appropriate estimation of thecorrelation coefficient and using the correlation coefficient,interpret the correlation between the two variables.

Linked to Objectives: 08, 09, 101012.1.6-14 2 – ApplyWhen presented with a least squares regression lineequation from a health-care related study the studentinterprets the overall pattern and predicts the value of Y.



Probability1012.1.7


Vocabulary: likelihood, probability, theoretical (classical)probability, empirical (observational) probability, randomexperiment, fair (in terms of coin, dice, et). Probabilitynotation will be introduced here, as well as the simpleconcept that probability is between 0 and 1.


Relate the probability of an event to the likelihood of thisevent occurring.

Vocabulary: relative frequency, law of large numbers, trueprobability. Keep this simple with events such as flipping acoin, rolling a die, etc.


Explain how relative frequency can be used to estimate theprobability of an event.

Vocabulary: sample space, random experiment (previouslydefined, but review), event. I like to show students howthey can use the tree method to find the sample space.


Determine the sample space of a given randomexperiment.

Vocabulary: equally likely. Keep these simple (no morethan 8-10 outcomes in each sample space). This shouldstart to introduce basic concepts of probability (between 0and 1, sample space outcomes add up to 1)

1012.1.7-04 2 – ApplyFind the probability of events in the case in which alloutcomes are equally likely.

Vocabulary: disjoint (two events cannot happen at thesame time), sample, population.


Determine if two events are disjoint

Problems could include 2 or 3 disjoint events. Identify keyword of "or"

1012.1.7-06 2 – ApplyApply the addition rule to find the probability of a given setof disjoint events.

Vocabulary: independent, dependent. Students should beable to decide independence based on both a descriptionof 2 events, as well as when given probabilities.


Determine if two events are independent.

Identify the key word of "and."1012.1.7-08 2 – ApplyApply the multiplication rule to find the probability of agiven set of independent events.

Include the Complement Rule (identify key phrase of "atleast one"), as well as Addition Rule for events that are notdisjoint

1012.1.7-09 2 – ApplyApply basic probability concepts to interpret and solvemathematical problems.


by Code



Probability1012.1.7


Vocabulary: Venn Diagram, Probability table. Note thatthese concepts may be explained when the LR goesthrough various rules of probability. For example, I find theVenn Diagram helpful when going over the Addition Rule,but when talking about finding the probability of neitherevent occurring the probability table can be helpful.

1012.1.7-10 2 – ApplyFind probabilities using Venn diagrams or probability tablesas aids.

Vocabulary: conditional probability. Introduce probabilitynotation for conditional events. Students should understandhow one event is conditioned onto another and be able tocorrectly notate that in probability notation. It may be worthstressing that the vertical line is not a division sign, butrather is notation, similar to that of a parenthesis. It iswritten to separate the possible event from the knownevent.


Explain the concept of conditional probability and properlyuse the probability notation for a conditional event.

Students should be able to identify if there is a conditionalprobability from the description and be able to correctlywrite the probability notation for the problem. In otherwords, they should be able to identify which one is thegiven.


Identify an example that represents a case of conditionalprobability.

Bayes' Theorem is not included in this course. However,probability trees can be reviewed (previously used forsample spaces) and used to show conditional problems.However, we recommend that the problem be kept to only2 branch-offs. The rule of General Multiplication should beincluded.


Determine the probability of an event using principles ofconditional probability.

Linked to Objectives: 01, 021012.1.7-14 2 – ApplyGiven a categorical dataset, the student identifies therelative frequency of a specified event and the likelihood ofthe event (e.g., impossible, not likely, just as likely asunlikely, likely, or certain).

Linked to Objectives: 03, 041012.1.7-15 2 – ApplyGiven a random experiment with equally likely outcomesand a specified event, the student identifies the samplespace as a list or selects the probability of the specifiedevent.

Linked to Objectives: 05, 06, 07, 101012.1.7-16 2 – ApplyGiven a written description of the probabilities of twoevents, A and B, the student determines if the events aredisjoint or not, whether they are independent or not, andidentifies the probability of (A or B) or (A and B) occurring.

Linked to Objectives: 08, 091012.1.7-17 2 – ApplyGiven a written description or probability notation of a setof events, the student uses the Complement Rule to solvefor a specified event.

Linked to Objectives: 11, 12, 131012.1.7-18 2 – ApplyGiven a written description of the probabilities of twoevents (event A and event B), and the conditionalprobability of A given B, the student applies principles ofconditional probability to determine conditional probabilitiesor corresponding probability notations.

Course Topic Report

by Code

Code: C784



Undergraduate

General Education

Mathematics

AOS Mathematics

Course of Study:

Course Level:

Course Division:

Discipline:

Course Type:

Department:

Topic

Real Numbers




1012.1.1

OBJECTIVE # OBJECTIVE

1012.1.1-01 Identify whole numbers, integers, or rational numbers from a finite set of real numbers.

1012.1.1-02 Order a finite set of real numbers with or without a number line.

1012.1.1-03 Apply the mathematical operations to whole numbers.

1012.1.1-04 Apply the mathematical operations to integers.

1012.1.1-05 Apply the mathematical operations to numbers with exponents.

1012.1.1-06 Apply the order of operations correctly to a given numerical expression.

1012.1.1-07 Approximate a solution to a mathematical problem using estimation skills.

1012.1.1-08 Identify the prime factorization of a given whole number.

1012.1.1-09 Identify the Greatest Common Factor of two given whole numbers.

Course Topic Report

by Code

Topic

Real Numbers




1012.1.1


1012.1.1-10 Calculate the square root of a whole number.

1012.1.1-11 Given a set of real numbers, the student performs a selected mathematical operation (i.e., addition, subtraction, multiplication, division orexponentiation) on a specified subset of the set of real numbers.

1012.1.1-12 Given a mathematical expression containing real numbers (i.e., integers and numbers with exponents), the student applies the order ofoperations to solve the given expression.

1012.1.1-13 Given a pair of whole numbers, the student identifies the greatest common factor using prime factorization.

Topic

Basic Mathematical Operations I




1012.1.1







Course Topic Report

by Code

Topic

Basic Mathematical Operations I




1012.1.1










Topic

Basic Mathematical Operations II




1012.1.1



Course Topic Report

by Code

Topic

Basic Mathematical Operations II




1012.1.1














Topic

Fractions

Course Topic Report

by Code

Topic

Fractions




1012.1.2


1012.1.2-01 Identify equivalent fractions.

1012.1.2-02 Identify the Least Common Denominator of two fractions.

1012.1.2-03 Apply the mathematical operations of addition, subtraction, multiplication, and division to fractions.

1012.1.2-04 Identify place values for a given decimal number.

1012.1.2-05 Apply a given rounding algorithm for decimal numbers.

1012.1.2-06 Apply the mathematical operations of addition, subtraction, multiplication, and division to decimals.

1012.1.2-07 Apply the mathematical operations of addition, subtraction, multiplication, and division to percentage values.

1012.1.2-08 Solve for an unknown quantity using ratios in the context of a proportion.

1012.1.2-09 Convert between decimals, fractions, and percentages.

1012.1.2-10 Apply basic unit conversions for household and metric measures.

1012.1.2-11 The student applies mathematical operations (i.e., addition, subtraction, multiplication, division) to fractions.

1012.1.2-12 Given a set of decimal numbers, the student performs a specified mathematical operation and applies a given rounding algorithm to theanswer.

1012.1.2-13 Given a healthcare context, the student applies mathematical operations (i.e., addition, subtraction, multiplication, and division) topercentage values or solves for an unknown quantity using ratios and proportions.

Course Topic Report

by Code

Topic

Fractions




1012.1.2


1012.1.2-14 Given a numerical expression containing a combination of decimals, fractions, or percentages and either household or metric measures,the student solves the expression by performing necessary conversions and the specified operations (i.e., addition, subtraction,multiplication, or division) on the numbers.

Topic

Decimals




1012.1.2










Course Topic Report

by Code

Topic

Decimals




1012.1.2








Topic

Ratios, Proportions & Percents




1012.1.2





Course Topic Report

by Code

Topic

Ratios, Proportions & Percents




1012.1.2













Topic

Algebraic Expressions

Course Topic Report

by Code

Topic






1012.1.3-01 Identify the inverse operation that corresponds to a given operation.

1012.1.3-02 Evaluate a given algebraic expression using the distributive property.

1012.1.3-03 Combine like terms to simplify a given algebraic expression.

1012.1.3-04 Evaluate a given algebraic expression using substitution.

1012.1.3-05 Identify an algebraic expression or equation that defines a given pattern of relationships for a given real world problem.

1012.1.3-06 Solve a given linear equation of a specified form.

1012.1.3-07 Predict a solution to a given an algebraic equation.

1012.1.3-08 Solve a given linear equation with fraction coefficients and constants of the form (a/b)x = c/d.

1012.1.3-09 Solve a given linear inequality.

1012.1.3-10 Identify a graphical representation of the solution set for a linear inequality.

1012.1.3-11 Identify the graph of given coordinates on a coordinate plane.

1012.1.3-12 Identify the slope when given a graph of a linear equation.

1012.1.3-13 Identify the correct graph for a given linear equation of the form, y = mx + b.

Course Topic Report

by Code

Topic






1012.1.3-14 Given an algebraic expression or linear equation in the general form of Ax + By + C = 0 or (a/b)x = c/d, the student applies theoperations, processes, and procedures of basic algebra to solve the equation.

1012.1.3-15 Given a linear inequality in the form of y >/</= mx + b, the student identifies the correct graph for this inequality.

1012.1.3-16 Given a linear equation in the form of y= mx + b, the student identifies the correct graph for this equation.

Assessment Notes: Graph refers to a coordinate plane with the line of the inequality overlaid.

Topic

Linear Equations











Course Topic Report

by Code

Topic

Linear Equations
















Topic

Linear Inequalities


Course Topic Report

by Code

Topic

Linear Inequalities


















Course Topic Report

by Code

Topic

Linear Inequalities








Topic

Algebraic Expressions & Linear Equations












Course Topic Report

by Code

Topic

Algebraic Expressions & Linear Equations















Topic

Coordinate Plane





Course Topic Report

by Code

Topic

Coordinate Plane


















Course Topic Report

by Code

Topic

Coordinate Plane









Topic

Numerical Measures




1012.1.4


1012.1.4-01 Apply the standard deviation rule to a special case of normal distributions.

1012.1.4-02 Identify the appropriate numerical measures for a given set of data in different contexts.

1012.1.4-03 Relate measures of center and spread to the shape of the distribution.

1012.1.4-04 Calculate the mean, median, mode, quartiles, range, and interquartile range for a set of quantitative data.

1012.1.4-05 Evaluate data from several different graphical displays of a distribution of a categorical variable (bar chart, pie chart) and of a quantitativevariable (histogram, stemplot, boxplot).

1012.1.4-06 Describe the distribution of a categorical variable in context.

Course Topic Report

by Code

Topic

Numerical Measures




1012.1.4


1012.1.4-07 Describe the distribution of a quantitative variable in context: a) describe the overall pattern, b) describe striking deviations from thepattern.

1012.1.4-08 Identify the appropriate graphical display for a given set of data in different contexts.

1012.1.4-09 Explain how graphical displays can be used to misrepresent data.

1012.1.4-10 Given a mean and standard deviation for a normal distribution, the student applies the standard deviation rule.

1012.1.4-11 Given a small single variable dataset, the student evaluates data and measures of center, spread, and shape as they relate to thedistribution.

1012.1.4-12 Given a description or graphical display of categorical or quantitative data, the student interprets single variable data and determinescharacteristics of the data and its distribution.

1012.1.4-13 Given raw data or a description of a small single variable dataset, the student selects the type of graph that appropriately represents thedata set.

1012.1.4-14 Given a chart or graph that misrepresents data or a small dataset, the student selects the correct response explaining why it ismisleading.

Topic

Graphical Displays




1012.1.4


1012.1.4-01 Apply the standard deviation rule to a special case of normal distributions.

Course Topic Report

by Code

Topic

Graphical Displays




1012.1.4


1012.1.4-02 Identify the appropriate numerical measures for a given set of data in different contexts.

1012.1.4-03 Relate measures of center and spread to the shape of the distribution.

1012.1.4-04 Calculate the mean, median, mode, quartiles, range, and interquartile range for a set of quantitative data.

1012.1.4-05 Evaluate data from several different graphical displays of a distribution of a categorical variable (bar chart, pie chart) and of a quantitativevariable (histogram, stemplot, boxplot).

1012.1.4-06 Describe the distribution of a categorical variable in context.

1012.1.4-07 Describe the distribution of a quantitative variable in context: a) describe the overall pattern, b) describe striking deviations from thepattern.

1012.1.4-08 Identify the appropriate graphical display for a given set of data in different contexts.

1012.1.4-09 Explain how graphical displays can be used to misrepresent data.

1012.1.4-10 Given a mean and standard deviation for a normal distribution, the student applies the standard deviation rule.

1012.1.4-11 Given a small single variable dataset, the student evaluates data and measures of center, spread, and shape as they relate to thedistribution.

1012.1.4-12 Given a description or graphical display of categorical or quantitative data, the student interprets single variable data and determinescharacteristics of the data and its distribution.

1012.1.4-13 Given raw data or a description of a small single variable dataset, the student selects the type of graph that appropriately represents thedata set.

1012.1.4-14 Given a chart or graph that misrepresents data or a small dataset, the student selects the correct response explaining why it ismisleading.

Course Topic Report

by Code

Topic

Role-type Classification of Two Variables




1012.1.5


1012.1.5-01 Classify a data analysis situation according to the Role-type Classification.

1012.1.5-02 Identify the appropriate graphical display for a given classification in different contexts.

1012.1.5-03 Identify the appropriate numerical measures for a given classification in different contexts.

1012.1.5-04 Compare conditional percentages in a two-way table.

1012.1.5-05 Summarize distributions of two variables.

1012.1.5-06 Determine the relationship between two quantitative variables, when given a graph.

1012.1.5-07 Describe the overall pattern and the striking deviations in a graph of two variables.

1012.1.5-08 Given a description of a two-variable study, the student identifies the variable classifications or the appropriate graphical display.

1012.1.5-09 Given a graphical display or description of a two-variable study, the student identifies the appropriate numerical measures.

1012.1.5-10 Given a two-way table or a description of a study with two categorical variables, the student interprets and identifies potentialrelationships between variables.

1012.1.5-11 When presented with a scatterplot of two variables, the student describes the distribution or potential relationship represented betweenthese two variables.

1012.1.5-12 Given a scatterplot of two quantitative variables, the student identifies potential outliers or the effects of potential outliers on therelationship.

Topic

Two Quantitative Variables

Course Topic Report

by Code

Topic

Two Quantitative Variables




1012.1.5


1012.1.5-01 Classify a data analysis situation according to the Role-type Classification.

1012.1.5-02 Identify the appropriate graphical display for a given classification in different contexts.

1012.1.5-03 Identify the appropriate numerical measures for a given classification in different contexts.

1012.1.5-04 Compare conditional percentages in a two-way table.

1012.1.5-05 Summarize distributions of two variables.

1012.1.5-06 Determine the relationship between two quantitative variables, when given a graph.

1012.1.5-07 Describe the overall pattern and the striking deviations in a graph of two variables.

1012.1.5-08 Given a description of a two-variable study, the student identifies the variable classifications or the appropriate graphical display.

1012.1.5-09 Given a graphical display or description of a two-variable study, the student identifies the appropriate numerical measures.

1012.1.5-10 Given a two-way table or a description of a study with two categorical variables, the student interprets and identifies potentialrelationships between variables.

1012.1.5-11 When presented with a scatterplot of two variables, the student describes the distribution or potential relationship represented betweenthese two variables.

1012.1.5-12 Given a scatterplot of two quantitative variables, the student identifies potential outliers or the effects of potential outliers on therelationship.

Topic

Causation

Course Topic Report

by Code

Topic

Causation





1012.1.6-01 Explain the distinction between association and causation.

1012.1.6-02 Identify potential lurking variables.

1012.1.6-03 Explain the phenomenon of Simpson's Paradox as it relates to interpreting the relationship between two variables.

1012.1.6-04 Estimate the value of the correlation coefficient between two variables from a scatterplot.

1012.1.6-05 Interpret the value of the correlation coefficient between two variables.

1012.1.6-06 Recognize the limitations of the correlation coefficient as a numerical measure of the association between two quantitative variables.

1012.1.6-07 Identify regression analysis applications for purposes of description and prediction.

1012.1.6-08 Interpret the simple least squares linear regression equation for a set of data in regards to the overall pattern.

1012.1.6-09 Interpret the simple least squares linear regression equation to make a prediction.

1012.1.6-10 Determine whether a regression model is significant.

1012.1.6-11 Identify potential problems if regression analysis is used incorrectly.

1012.1.6-12 Given the description of a two-variable, healthcare-related study (quantitative variables), the student identifies the type of relationship(association or causation) and whether a lurking variable or Simpson’s Paradox phenomenon is present.

1012.1.6-13 Given a scatterplot from a healthcare related study, the student identifies an appropriate estimation of the correlation coefficient andusing the correlation coefficient, interpret the correlation between the two variables.

Course Topic Report

by Code

Topic

Causation





1012.1.6-14 When presented with a least squares regression line equation from a health-care related study the student interprets the overall patternand predicts the value of Y.

Topic

Correlation













Course Topic Report

by Code

Topic

Correlation











Topic

Regression








Course Topic Report

by Code

Topic

Regression
















Topic

Theoretical and Empirical Probability

Course Topic Report

by Code

Topic




Probability1012.1.7


1012.1.7-01 Relate the probability of an event to the likelihood of this event occurring.

1012.1.7-02 Explain how relative frequency can be used to estimate the probability of an event.

1012.1.7-03 Determine the sample space of a given random experiment.

1012.1.7-04 Find the probability of events in the case in which all outcomes are equally likely.

1012.1.7-05 Determine if two events are disjoint

1012.1.7-06 Apply the addition rule to find the probability of a given set of disjoint events.

1012.1.7-07 Determine if two events are independent.

1012.1.7-08 Apply the multiplication rule to find the probability of a given set of independent events.

1012.1.7-09 Apply basic probability concepts to interpret and solve mathematical problems.

1012.1.7-10 Find probabilities using Venn diagrams or probability tables as aids.

1012.1.7-11 Explain the concept of conditional probability and properly use the probability notation for a conditional event.

1012.1.7-12 Identify an example that represents a case of conditional probability.

1012.1.7-13 Determine the probability of an event using principles of conditional probability.

Course Topic Report

by Code

Topic




Probability1012.1.7


1012.1.7-14 Given a categorical dataset, the student identifies the relative frequency of a specified event and the likelihood of the event (e.g.,impossible, not likely, just as likely as unlikely, likely, or certain).

1012.1.7-15 Given a random experiment with equally likely outcomes and a specified event, the student identifies the sample space as a list orselects the probability of the specified event.

1012.1.7-16 Given a written description of the probabilities of two events, A and B, the student determines if the events are disjoint or not, whetherthey are independent or not, and identifies the probability of (A or B) or (A and B) occurring.

1012.1.7-17 Given a written description or probability notation of a set of events, the student uses the Complement Rule to solve for a specified event.

1012.1.7-18 Given a written description of the probabilities of two events (event A and event B), and the conditional probability of A given B, thestudent applies principles of conditional probability to determine conditional probabilities or corresponding probability notations.

Topic

Sample Spaces and Events



Probability1012.1.7






Course Topic Report

by Code

Topic




Probability1012.1.7















Course Topic Report

by Code

Topic




Probability1012.1.7



Topic

Finding Probability of Events



Probability1012.1.7










Course Topic Report

by Code

Topic

Finding Probability of Events



Probability1012.1.7












Topic

Independence and Dependence


Course Topic Report

by Code

Topic



Probability1012.1.7
















Course Topic Report

by Code

Topic




Probability1012.1.7






Course Competency Report by Code Descriptions... · Course Competency Report by Code Code: C784...

Documents

Transcript of Course Competency Report by Code Descriptions... · Course Competency Report by Code Code: C784...